Wikiversity talk:Main Page

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{{attention}} To request an edit to the [[Wikiversity:Page protection|protected]] Main Page, add {{tl|editprotected}} to your request. Such requests should either be obvious or uncontroversial, or be discussed to show consensus, so please do not make vague requests here. If possible, describe exactly what changes should be made so that any custodian can quickly satisfy the request.&lt;br&gt;
{{attention}} To raise general topics about [[Wikiversity]], make general suggestions about Wikiversity, to ask questions, or to talk about anything else of a general nature, use the [[Wikiversity:Colloquium|Colloquium]].&lt;br&gt;
{{attention}} To discuss the structure, appearance, etc. of the [[Wikiversity:Main Page|Main Page]], go to the [[Wikiversity:Main page learning project]] and the [[Wikiversity talk:Main page learning project|talk page for the main page learning project]].
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'''''If you wish to post something below, go ahead. It's a talk page. But you are more likely to get a response by going to the [[Wikiversity:Colloquium|Colloquium]], which is where the main talking at Wikiversity goes on! See you there.'''''

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== The Wikiversity:Main page learning project ==

The [[Wikiversity:Main page learning project]] was launched after the redesign of the main page in December 2007. The [[Wikiversity:Main page learning project]] has as its goal &quot;the promotion of responsible involvement of the Wikiversity community in an efficient, productive, open and inclusive maintenance of the Wikiversity main page as a flagship of the activity and values of the Wikiversity community&quot;. If you would like to get involved in the design of the main page, this is where to go. 

If you have general comments about the main page, but you don't especially want to get involved in the main page project, then you can also leave comments on the [[Wikiversity_talk:Main page learning project|talk page for the main page learning project]].

:I've suggested that it might be time to retire the &quot;quote of the day&quot; project and remove the quotes from the Main Page. See: [[Wikiversity talk:Main page learning project/QOTD]]. It might also be appropriate to deprecate the inactive [[Wikiversity:Main page learning project]] and archive it. Thoughts? --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:37, 29 November 2019 (UTC)

== add new language university ==
Now that Chinese Wikiversity is created, please add a cross-wiki link to it. --[[User:WQL|WQL]] ([[User talk:WQL|discuss]] • [[Special:Contributions/WQL|contribs]]) 12:52, 12 August 2018 (UTC)

:{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:29, 12 August 2018 (UTC)
::What about zulu language [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 05:57, 30 April 2025 (UTC)

== Edit request from 204.234.101.112, 14 February 2019 ==

&lt;nowiki&gt;{{editprotected}}&lt;/nowiki&gt;
&lt;!-- Begin request --&gt;


&lt;!-- End request --&gt;
[[Special:Contributions/204.234.101.112|204.234.101.112]] ([[User talk:204.234.101.112|discuss]]) 21:17, 14 February 2019 (UTC)

:{{Not done}} Empty request -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 01:11, 15 February 2019 (UTC)

== Georgian (ka) wikiversity ==
PLEASE 

Help me to make Georgian (ka) wikiversity--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 17:23, 1 March 2019 (UTC)

:{{at|ჯეო}} See https://beta.wikiversity.org/wiki/Main_Page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:00, 1 March 2019 (UTC)

დიდი მადლობა (Didi Madloba-Thank You)!--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 08:44, 2 March 2019 (UTC)

::Please see [[betawikiversity:Category:KA]]. That is the appropriate place to create learning pages in this language. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 14:11, 10 March 2019 (UTC)

== new langueages ==

we should admit crosing of languajes to have a better understanding--[[Special:Contributions/201.208.239.198|201.208.239.198]] ([[User talk:201.208.239.198|discuss]]) 19:34, 25 July 2019 (UTC)

:This is the English Wikiversity. See [[:es:Portada|Wikiversidad]] for Wikiversity in Spanish. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 22:39, 25 July 2019 (UTC)

== How to change an username? ==

How to change an username? --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:27, 28 August 2019 (UTC)
*{{ping|Josephina Phoebe White}} You can request at [[Special:GlobalRenameRequest]] --[[User:94rain|94rain]] ([[User talk:94rain|discuss]] • [[Special:Contributions/94rain|contribs]]) 07:29, 28 August 2019 (UTC)
Thanks. --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:45, 28 August 2019 (UTC)

==Religious user names allowed in Wikiversity?==

https://en.m.wikiversity.org/wiki/Wikiversity:Username

Names of religious figures such as &quot;God&quot;, &quot;Jehovah&quot;,&quot;Buddha&quot;,&quot;Jainism&quot;,&quot;Bonadea&quot;,Hinduism or &quot;Allah&quot;, which user names prohibited

Please answer for my question. This Wikiversity user name policy still alive? Religious user names are prohibited? 

:It isn't a policy, but it's a guideline for people who are wanting to register an account are recommended to follow (as per the page, which could be changed with community consensus). I see no reason for this statement to be &quot;dead&quot;. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 00:15, 2 September 2019 (UTC)
::: Yes: Religious user names are under hedding &quot;Inflammatory usernames&quot;, will be blocked and not allowed.

== LinkedIn ==

I insist that a Wikiversity page should be added on LinkedIn. Wikimedia has its LinkedIn page; Wikipedia, too. But not Wikiversity. I tried to show my Swedish studies but could not choose Wikiversity as the Institution. Why not? Even when it is not a &quot;granting degree&quot; Institution, is is still an Institution, right? When I contacted LinkedIn about this, they sent me the link so that I can create myself the Wikiversity page. But then there is box I must tick: &quot; I confirm I am an approved authority of this Institution to create this page&quot;, which is not the case. But I think there are many Wikiversity experts on here that woud qualify as Wikiversity Linkedin page creators. I can create the page if someone here approves, but I would need some info: # of employees, etc. --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 23:34, 18 January 2020 (UTC)

:The information would go here [https://www.linkedin.com/company/setup/new/ Wikiversity institution] but it probably should have a bureaucrat or someone from the WMF tick &quot;I verify that I am an authorized representative of this organization and have the right to act on its behalf in the creation and management of this page. The organization and I agree to the additional terms for Pages.&quot; The number of employees (volunteers is not an option but we are unpaid) for our Wikiversity I guess could be the number of active users 201-500. The current logo is File:Wikiversity logo 2017.svg. The website can be https://en.wikiversity.org/wiki/Wikiversity:Main_Page.--[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 00:16, 19 January 2020 (UTC)

{{At|Leonardo T. Cardillo}} Wikiversity is a community. None of us gets to insist that anything happen on behalf of the community unless there is consensus to do so. This requires a discussion in the [[Wikiversity:Colloquium]] and a vote for support or lack thereof. Because this request involves an outside organization, it may also require support from the WMF.

I have some concerns at this point that your passion regarding this issue far exceeds your demonstrated commitment to either Wikiversity or the wider Wikimedia community. It might be better to let this rest for a bit and learn more about how Wikiversity functions before insisting that this be discussed. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:29, 19 January 2020 (UTC)

:{{At|Dave Braunschweig}}: I apologize for the use of the word &quot;insist&quot;, I have taken note to not use it anymore here to avoid distractions from the main topic of conversation. Also, I do not like you judge how much my passions should go against my level of contributions. With that being said, and for my personal learning on this environment, can someone please guide me on the very first step I should take to have a Wikiversity page created on LinkedIn? I think you mentioned something like a &quot;poll&quot;, how do I do that? --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 04:38, 19 January 2020 (UTC)

::{{At|Leonardo T. Cardillo}} I have already guided you on the next step to take. Please read my response carefully. Then slow down and learn more about Wikiversity. We often have people come in with high passions and quick fixes that Wikiversity must make in order to improve. They're typically gone within a month and we're left having to clean up after them. That's not to suggest that this is or isn't a good idea. It is simply to point out that this is a community. You must first learn to work with the community before you try to change it. We look forward to working with you as you figure this out. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:31, 19 January 2020 (UTC)

:::{{At|Dave Braunschweig}} Thanks so much for your inputs. I have created this: https://en.wikiversity.org/wiki/Wikiversity:Colloquium#LinkedIn. Please indicate if that is the next step that was intended to be created. Also, please guide on the following ones. Best regards, --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 16:27, 19 January 2020 (UTC)

== Add New Language ==

Why not bn.wikiversity?  But there is Hindi!  Make it, please.  I am ready to cooperate if needed. [[User:Hirok Raja|Hirok Raja]] ([[User talk:Hirok Raja|discuss]] • [[Special:Contributions/Hirok Raja|contribs]]) 03:07, 1 August 2020 (UTC)

:[[User:Hirok Raja|Hirok Raja]]: please see [[:betawikiversity:|Wikiversity Beta]]. &amp;mdash;Hasley&amp;nbsp;[[user talk:Hasley|&lt;span style=&quot;color: #0645AD; vertical-align: super; font-size: smaller;&quot;&gt;talk&lt;/span&gt;]] 13:04, 1 August 2020 (UTC)

:{{At|Hirok Raja}} Also see [[meta:Wikiversity]]. We are the English Wikiversity. We have no role in setting up new Wikiversity languages. When bn.wikiversity is added, please let us know, and we will add it to our main page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 1 August 2020 (UTC)

== I'm learning Turkish🤩 ==

Hi(to the person reading this)! I'm learning Turkish and I would like someone(native Turkish speaker) to teach how to pronounce Turkish. I do know some words,alphabets and number☺️ and I'm still learning and I hope someone is willing to help me🥺.

@JinahJady! [[User:JanehJody|JanehJody]] ([[User talk:JanehJody|discuss]] • [[Special:Contributions/JanehJody|contribs]]) 18:14, 4 February 2021 (UTC)

:Hi. Welcome to Wikiversity! Please see our [[Turkish|resources relating to the study of the Turkish language]]. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:41, 4 February 2021 (UTC)
::Hi,@[[User:JanehJody|JanehJody]] can i help you ::) [[User:MexmetW|MexmetW]] ([[User talk:MexmetW|discuss]] • [[Special:Contributions/MexmetW|contribs]]) 07:47, 28 September 2022 (UTC)
:Hi,@[[User:JanehJody|JanehJody]] I would love to help you to learning turkish :) [[Special:Contributions/85.105.185.109|85.105.185.109]] ([[User talk:85.105.185.109|discuss]]) 07:31, 28 September 2022 (UTC)

== Is it Wikipedia remodeled or a copy of wikipedia? ==

I am confused--[[User:Noukden|Noukden]] ([[User talk:Noukden|discuss]] • [[Special:Contributions/Noukden|contribs]]) 20:45, 24 May 2021 (UTC)

:{{At|Noukden}} None of the above. See [[What is Wikiversity?]] and [[What Wikiversity is not]]. Wikiversity is learning projects. Link to Wikipedia rather than duplicating it and then add hands-on activities so users can learn by doing. See [[IT Fundamentals]] for one approach. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:15, 25 May 2021 (UTC)

== Action in the earliest? ==

I want to know much more of all action that happend in the earliest centuries. [[User:Dilbkhay|Dilbkhay]] ([[User talk:Dilbkhay|discuss]] • [[Special:Contributions/Dilbkhay|contribs]]) 14:57, 21 August 2021 (UTC)

:Depending upon what you mean by &quot;earliest&quot;, have a look at [[Paleanthropology]] or [[Philosophy/Sciences]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:07, 20 September 2021 (UTC)

== Biology ==

What are the basic principles of ecology [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 18:25, 25 January 2022 (UTC)

:{{At|Aludriyo Dominic}} Welcome! See [[Wikipedia:Ecology]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:17, 26 January 2022 (UTC)
:{{ping|Aludriyo Dominic}} I invite you to read [[User:Atcovi/Science/Ecology]] if you're interested in learning about the basics of Ecology. Also check out the wikipedia link above and [[:Category:Ecology|this category]]. Thanks and weclome! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 03:44, 26 January 2022 (UTC)

I will try to study [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 05:41, 28 January 2022 (UTC)

== Physics ==

Physics Can Be defined as A Pure Science Subject That deals with the Measurement Of Matter In relation to energy. --{{Unsigned|Oyeyemi Abdul-warith|29 January 2022}}

: Welcome to Wikiversity! Here is a landing page that may be helpful: [[Physics]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 16:42, 29 January 2022 (UTC)

== Popularize ==

Can someone popularize California or the State of Washington on the Main Page? [[Special:Contributions/2604:3D08:6286:7500:B441:2710:77A4:1304|2604:3D08:6286:7500:B441:2710:77A4:1304]] ([[User talk:2604:3D08:6286:7500:B441:2710:77A4:1304|discuss]]) 03:33, 26 June 2022 (UTC)

:No, sorry, promotion isn't part of the [[Wikiversity:Mission]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 12:06, 26 June 2022 (UTC)

== [[w:Armistice of WWI|Armistice of WWI]], [[w:Paris Peace Conference|Paris Peace Conference]] and Aftermath ==

The best time to feature this on the main page was last week or yesterday;  the second best time is today.

* [[w:Template:First_World_War_treaties]]  (this template should get transcluded or copied to wikiversity, since this doesn't work: {{w:First_World_War_treaties}} although I wish it would)
* [[Wikiversity:Colloquium#Proclaiming_Armistice_of_WWI_Remembrance_and_Veterans_Day_for_11th_Nov]] our course on WWI is woefully inadequate, but this is a good time to start improving it!
[[User:Jaredscribe|Jaredscribe]] ([[User talk:Jaredscribe|discuss]] • [[Special:Contributions/Jaredscribe|contribs]]) 10:22, 12 November 2023 (UTC)

== Can you please add isiZulu plz ==

Because all othere languages her so i can umderstand batter  [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 06:06, 30 April 2025 (UTC)

:Add it how? Add more resources to learn the language? I think that would be fantastic, but it's very labor-intensive and I doubt anyone here has the competence to add that kind of material. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:40, 30 April 2025 (UTC)

== banner ==

says set learning free, propare grammer would be Start learning for free [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 20:21, 3 February 2026 (UTC)

:I'm a native American English speaker and this banner is grammatical. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:52, 4 February 2026 (UTC)
::That’s not the problem. I’m wondering if we should more clearly emphasize what Wikiversity is on this banner. Idk maybe it’s fine as it is I would just like it to be clearer[[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:15, 4 February 2026 (UTC)
:::nevermind i just got the banner thought it was supposed to say start learning free, but its actually set learning free(like release learning) [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:12, 6 February 2026 (UTC)

== EcoRide Delivery (Unbreakable Business Plan) ==


'''Business Name''': EcoRide Delivery

'''Type''': Delivery &amp; Courier Service

'''Products/Services''':

Parcel delivery

Food delivery

Document courier service

Same-day delivery

'''&lt;big&gt;Business Start-Up&lt;/big&gt;'''

'''1. Services Offered'''

Fast and affordable delivery service

Safe handling of packages and documents

'''2. Materials Needed'''

Motorcycle or bicycle

Delivery bags and helmets

Mobile phone with internet

'''3. Ordering System'''

Orders through Facebook/text/call

Delivery booking form

'''4. Payment Method'''

Cash on delivery

GCash payment

'''5. Testing'''

Test delivery routes

Check communication system

Ensure package safety

'''6. Launch'''

Free delivery promo

Social media advertisements

Referral discounts

&lt;big&gt;'''Business Manual (SOP)'''&lt;/big&gt;

'''1. Backup Plan'''

Extra delivery rider

Backup vehicle

Spare fuel budget

Why: Prevents delayed deliveries

'''2. Security'''

Verify customer information

Track parcels carefully

Monitor rider safety

Why: Ensures safe transactions

'''3. Emergency Contacts'''

Delivery riders

Vehicle mechanic

Customers

Why: Fast response during emergencies

'''4. Monitoring'''

Track delivery status daily

Check customer feedback

Monitor fuel and expenses

Why: Maintains efficient operations

'''5. Redundancy Plan (Plan B)'''

Alternative rider available

Manual booking system

Partner courier service

Why: Deliveries continue even during problems

'''Audit Trail (Change Log)'''

Added backup delivery rider

Improved tracking system

Updated booking process

Enhanced package safety procedures [[Special:Contributions/&amp;#126;2026-30030-49|&amp;#126;2026-30030-49]] ([[User talk:&amp;#126;2026-30030-49|talk]]) 07:20, 19 May 2026 (UTC)</text>
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{{attention}} To request an edit to the [[Wikiversity:Page protection|protected]] Main Page, add {{tl|editprotected}} to your request. Such requests should either be obvious or uncontroversial, or be discussed to show consensus, so please do not make vague requests here. If possible, describe exactly what changes should be made so that any custodian can quickly satisfy the request.&lt;br&gt;
{{attention}} To raise general topics about [[Wikiversity]], make general suggestions about Wikiversity, to ask questions, or to talk about anything else of a general nature, use the [[Wikiversity:Colloquium|Colloquium]].&lt;br&gt;
{{attention}} To discuss the structure, appearance, etc. of the [[Wikiversity:Main Page|Main Page]], go to the [[Wikiversity:Main page learning project]] and the [[Wikiversity talk:Main page learning project|talk page for the main page learning project]].
&lt;/div&gt;

----
'''''If you wish to post something below, go ahead. It's a talk page. But you are more likely to get a response by going to the [[Wikiversity:Colloquium|Colloquium]], which is where the main talking at Wikiversity goes on! See you there.'''''

{{archive box|
{{center top}}'''List of talk archives'''{{center bottom}}
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== The Wikiversity:Main page learning project ==

The [[Wikiversity:Main page learning project]] was launched after the redesign of the main page in December 2007. The [[Wikiversity:Main page learning project]] has as its goal &quot;the promotion of responsible involvement of the Wikiversity community in an efficient, productive, open and inclusive maintenance of the Wikiversity main page as a flagship of the activity and values of the Wikiversity community&quot;. If you would like to get involved in the design of the main page, this is where to go. 

If you have general comments about the main page, but you don't especially want to get involved in the main page project, then you can also leave comments on the [[Wikiversity_talk:Main page learning project|talk page for the main page learning project]].

:I've suggested that it might be time to retire the &quot;quote of the day&quot; project and remove the quotes from the Main Page. See: [[Wikiversity talk:Main page learning project/QOTD]]. It might also be appropriate to deprecate the inactive [[Wikiversity:Main page learning project]] and archive it. Thoughts? --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:37, 29 November 2019 (UTC)

== add new language university ==
Now that Chinese Wikiversity is created, please add a cross-wiki link to it. --[[User:WQL|WQL]] ([[User talk:WQL|discuss]] • [[Special:Contributions/WQL|contribs]]) 12:52, 12 August 2018 (UTC)

:{{Done}} -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 14:29, 12 August 2018 (UTC)
::What about zulu language [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 05:57, 30 April 2025 (UTC)

== Edit request from 204.234.101.112, 14 February 2019 ==

&lt;nowiki&gt;{{editprotected}}&lt;/nowiki&gt;
&lt;!-- Begin request --&gt;


&lt;!-- End request --&gt;
[[Special:Contributions/204.234.101.112|204.234.101.112]] ([[User talk:204.234.101.112|discuss]]) 21:17, 14 February 2019 (UTC)

:{{Not done}} Empty request -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 01:11, 15 February 2019 (UTC)

== Georgian (ka) wikiversity ==
PLEASE 

Help me to make Georgian (ka) wikiversity--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 17:23, 1 March 2019 (UTC)

:{{at|ჯეო}} See https://beta.wikiversity.org/wiki/Main_Page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:00, 1 March 2019 (UTC)

დიდი მადლობა (Didi Madloba-Thank You)!--[[User:ჯეო|ჯეო]] ([[User talk:ჯეო|discuss]] • [[Special:Contributions/ჯეო|contribs]]) 08:44, 2 March 2019 (UTC)

::Please see [[betawikiversity:Category:KA]]. That is the appropriate place to create learning pages in this language. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 14:11, 10 March 2019 (UTC)

== new langueages ==

we should admit crosing of languajes to have a better understanding--[[Special:Contributions/201.208.239.198|201.208.239.198]] ([[User talk:201.208.239.198|discuss]]) 19:34, 25 July 2019 (UTC)

:This is the English Wikiversity. See [[:es:Portada|Wikiversidad]] for Wikiversity in Spanish. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 22:39, 25 July 2019 (UTC)

== How to change an username? ==

How to change an username? --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:27, 28 August 2019 (UTC)
*{{ping|Josephina Phoebe White}} You can request at [[Special:GlobalRenameRequest]] --[[User:94rain|94rain]] ([[User talk:94rain|discuss]] • [[Special:Contributions/94rain|contribs]]) 07:29, 28 August 2019 (UTC)
Thanks. --[[User:Josephina Phoebe White|Josephina Phoebe White]] ([[User talk:Josephina Phoebe White|discuss]] • [[Special:Contributions/Josephina Phoebe White|contribs]]) 07:45, 28 August 2019 (UTC)

==Religious user names allowed in Wikiversity?==

https://en.m.wikiversity.org/wiki/Wikiversity:Username

Names of religious figures such as &quot;God&quot;, &quot;Jehovah&quot;,&quot;Buddha&quot;,&quot;Jainism&quot;,&quot;Bonadea&quot;,Hinduism or &quot;Allah&quot;, which user names prohibited

Please answer for my question. This Wikiversity user name policy still alive? Religious user names are prohibited? 

:It isn't a policy, but it's a guideline for people who are wanting to register an account are recommended to follow (as per the page, which could be changed with community consensus). I see no reason for this statement to be &quot;dead&quot;. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 00:15, 2 September 2019 (UTC)
::: Yes: Religious user names are under hedding &quot;Inflammatory usernames&quot;, will be blocked and not allowed.

== LinkedIn ==

I insist that a Wikiversity page should be added on LinkedIn. Wikimedia has its LinkedIn page; Wikipedia, too. But not Wikiversity. I tried to show my Swedish studies but could not choose Wikiversity as the Institution. Why not? Even when it is not a &quot;granting degree&quot; Institution, is is still an Institution, right? When I contacted LinkedIn about this, they sent me the link so that I can create myself the Wikiversity page. But then there is box I must tick: &quot; I confirm I am an approved authority of this Institution to create this page&quot;, which is not the case. But I think there are many Wikiversity experts on here that woud qualify as Wikiversity Linkedin page creators. I can create the page if someone here approves, but I would need some info: # of employees, etc. --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 23:34, 18 January 2020 (UTC)

:The information would go here [https://www.linkedin.com/company/setup/new/ Wikiversity institution] but it probably should have a bureaucrat or someone from the WMF tick &quot;I verify that I am an authorized representative of this organization and have the right to act on its behalf in the creation and management of this page. The organization and I agree to the additional terms for Pages.&quot; The number of employees (volunteers is not an option but we are unpaid) for our Wikiversity I guess could be the number of active users 201-500. The current logo is File:Wikiversity logo 2017.svg. The website can be https://en.wikiversity.org/wiki/Wikiversity:Main_Page.--[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 00:16, 19 January 2020 (UTC)

{{At|Leonardo T. Cardillo}} Wikiversity is a community. None of us gets to insist that anything happen on behalf of the community unless there is consensus to do so. This requires a discussion in the [[Wikiversity:Colloquium]] and a vote for support or lack thereof. Because this request involves an outside organization, it may also require support from the WMF.

I have some concerns at this point that your passion regarding this issue far exceeds your demonstrated commitment to either Wikiversity or the wider Wikimedia community. It might be better to let this rest for a bit and learn more about how Wikiversity functions before insisting that this be discussed. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:29, 19 January 2020 (UTC)

:{{At|Dave Braunschweig}}: I apologize for the use of the word &quot;insist&quot;, I have taken note to not use it anymore here to avoid distractions from the main topic of conversation. Also, I do not like you judge how much my passions should go against my level of contributions. With that being said, and for my personal learning on this environment, can someone please guide me on the very first step I should take to have a Wikiversity page created on LinkedIn? I think you mentioned something like a &quot;poll&quot;, how do I do that? --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 04:38, 19 January 2020 (UTC)

::{{At|Leonardo T. Cardillo}} I have already guided you on the next step to take. Please read my response carefully. Then slow down and learn more about Wikiversity. We often have people come in with high passions and quick fixes that Wikiversity must make in order to improve. They're typically gone within a month and we're left having to clean up after them. That's not to suggest that this is or isn't a good idea. It is simply to point out that this is a community. You must first learn to work with the community before you try to change it. We look forward to working with you as you figure this out. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 15:31, 19 January 2020 (UTC)

:::{{At|Dave Braunschweig}} Thanks so much for your inputs. I have created this: https://en.wikiversity.org/wiki/Wikiversity:Colloquium#LinkedIn. Please indicate if that is the next step that was intended to be created. Also, please guide on the following ones. Best regards, --[[User:Leonardo T. Cardillo|Leonardo T. Cardillo]] ([[User talk:Leonardo T. Cardillo|discuss]] • [[Special:Contributions/Leonardo T. Cardillo|contribs]]) 16:27, 19 January 2020 (UTC)

== Add New Language ==

Why not bn.wikiversity?  But there is Hindi!  Make it, please.  I am ready to cooperate if needed. [[User:Hirok Raja|Hirok Raja]] ([[User talk:Hirok Raja|discuss]] • [[Special:Contributions/Hirok Raja|contribs]]) 03:07, 1 August 2020 (UTC)

:[[User:Hirok Raja|Hirok Raja]]: please see [[:betawikiversity:|Wikiversity Beta]]. &amp;mdash;Hasley&amp;nbsp;[[user talk:Hasley|&lt;span style=&quot;color: #0645AD; vertical-align: super; font-size: smaller;&quot;&gt;talk&lt;/span&gt;]] 13:04, 1 August 2020 (UTC)

:{{At|Hirok Raja}} Also see [[meta:Wikiversity]]. We are the English Wikiversity. We have no role in setting up new Wikiversity languages. When bn.wikiversity is added, please let us know, and we will add it to our main page. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:59, 1 August 2020 (UTC)

== I'm learning Turkish🤩 ==

Hi(to the person reading this)! I'm learning Turkish and I would like someone(native Turkish speaker) to teach how to pronounce Turkish. I do know some words,alphabets and number☺️ and I'm still learning and I hope someone is willing to help me🥺.

@JinahJady! [[User:JanehJody|JanehJody]] ([[User talk:JanehJody|discuss]] • [[Special:Contributions/JanehJody|contribs]]) 18:14, 4 February 2021 (UTC)

:Hi. Welcome to Wikiversity! Please see our [[Turkish|resources relating to the study of the Turkish language]]. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:41, 4 February 2021 (UTC)
::Hi,@[[User:JanehJody|JanehJody]] can i help you ::) [[User:MexmetW|MexmetW]] ([[User talk:MexmetW|discuss]] • [[Special:Contributions/MexmetW|contribs]]) 07:47, 28 September 2022 (UTC)
:Hi,@[[User:JanehJody|JanehJody]] I would love to help you to learning turkish :) [[Special:Contributions/85.105.185.109|85.105.185.109]] ([[User talk:85.105.185.109|discuss]]) 07:31, 28 September 2022 (UTC)

== Is it Wikipedia remodeled or a copy of wikipedia? ==

I am confused--[[User:Noukden|Noukden]] ([[User talk:Noukden|discuss]] • [[Special:Contributions/Noukden|contribs]]) 20:45, 24 May 2021 (UTC)

:{{At|Noukden}} None of the above. See [[What is Wikiversity?]] and [[What Wikiversity is not]]. Wikiversity is learning projects. Link to Wikipedia rather than duplicating it and then add hands-on activities so users can learn by doing. See [[IT Fundamentals]] for one approach. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:15, 25 May 2021 (UTC)

== Action in the earliest? ==

I want to know much more of all action that happend in the earliest centuries. [[User:Dilbkhay|Dilbkhay]] ([[User talk:Dilbkhay|discuss]] • [[Special:Contributions/Dilbkhay|contribs]]) 14:57, 21 August 2021 (UTC)

:Depending upon what you mean by &quot;earliest&quot;, have a look at [[Paleanthropology]] or [[Philosophy/Sciences]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:07, 20 September 2021 (UTC)

== Biology ==

What are the basic principles of ecology [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 18:25, 25 January 2022 (UTC)

:{{At|Aludriyo Dominic}} Welcome! See [[Wikipedia:Ecology]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:17, 26 January 2022 (UTC)
:{{ping|Aludriyo Dominic}} I invite you to read [[User:Atcovi/Science/Ecology]] if you're interested in learning about the basics of Ecology. Also check out the wikipedia link above and [[:Category:Ecology|this category]]. Thanks and weclome! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 03:44, 26 January 2022 (UTC)

I will try to study [[User:Aludriyo Dominic|Aludriyo Dominic]] ([[User talk:Aludriyo Dominic|discuss]] • [[Special:Contributions/Aludriyo Dominic|contribs]]) 05:41, 28 January 2022 (UTC)

== Physics ==

Physics Can Be defined as A Pure Science Subject That deals with the Measurement Of Matter In relation to energy. --{{Unsigned|Oyeyemi Abdul-warith|29 January 2022}}

: Welcome to Wikiversity! Here is a landing page that may be helpful: [[Physics]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 16:42, 29 January 2022 (UTC)

== Popularize ==

Can someone popularize California or the State of Washington on the Main Page? [[Special:Contributions/2604:3D08:6286:7500:B441:2710:77A4:1304|2604:3D08:6286:7500:B441:2710:77A4:1304]] ([[User talk:2604:3D08:6286:7500:B441:2710:77A4:1304|discuss]]) 03:33, 26 June 2022 (UTC)

:No, sorry, promotion isn't part of the [[Wikiversity:Mission]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 12:06, 26 June 2022 (UTC)

== [[w:Armistice of WWI|Armistice of WWI]], [[w:Paris Peace Conference|Paris Peace Conference]] and Aftermath ==

The best time to feature this on the main page was last week or yesterday;  the second best time is today.

* [[w:Template:First_World_War_treaties]]  (this template should get transcluded or copied to wikiversity, since this doesn't work: {{w:First_World_War_treaties}} although I wish it would)
* [[Wikiversity:Colloquium#Proclaiming_Armistice_of_WWI_Remembrance_and_Veterans_Day_for_11th_Nov]] our course on WWI is woefully inadequate, but this is a good time to start improving it!
[[User:Jaredscribe|Jaredscribe]] ([[User talk:Jaredscribe|discuss]] • [[Special:Contributions/Jaredscribe|contribs]]) 10:22, 12 November 2023 (UTC)

== Can you please add isiZulu plz ==

Because all othere languages her so i can umderstand batter  [[User:Lucky Shabalala|Lucky Shabalala]] ([[User talk:Lucky Shabalala|discuss]] • [[Special:Contributions/Lucky Shabalala|contribs]]) 06:06, 30 April 2025 (UTC)

:Add it how? Add more resources to learn the language? I think that would be fantastic, but it's very labor-intensive and I doubt anyone here has the competence to add that kind of material. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:40, 30 April 2025 (UTC)

== banner ==

says set learning free, propare grammer would be Start learning for free [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 20:21, 3 February 2026 (UTC)

:I'm a native American English speaker and this banner is grammatical. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 08:52, 4 February 2026 (UTC)
::That’s not the problem. I’m wondering if we should more clearly emphasize what Wikiversity is on this banner. Idk maybe it’s fine as it is I would just like it to be clearer[[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:15, 4 February 2026 (UTC)
:::nevermind i just got the banner thought it was supposed to say start learning free, but its actually set learning free(like release learning) [[User:Ducklan|Ducklan]] ([[User talk:Ducklan|discuss]] • [[Special:Contributions/Ducklan|contribs]]) 16:12, 6 February 2026 (UTC)</text>
      <sha1>p9vnqdyeawhkhw1jz0zp7l65lh9pdcq</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Colloquium</title>
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        <username>Atcovi</username>
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      <text bytes="83898" sha1="0qv4d57zrklogg05aoyke9z9wo27k29" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
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== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. However, can curators add and remove pseudo-bot from their own accounts (and not others)?
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

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== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. However, can curators add and remove pseudo-bot from their own accounts (and not others)?
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <text bytes="84607" sha1="0q05wq5j5rtjh9eaw6j7p37edxn2drd" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. However, can curators add and remove pseudo-bot from their own accounts (and not others)?
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <id>2810338</id>
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        <username>Codename Noreste</username>
        <id>2969951</id>
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      <comment>/* Create a pseudo-bot user group? */ reply to Jtneill ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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&lt;!-- MESSAGES GO BELOW --&gt;
== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <id>2810343</id>
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        <username>Codename Noreste</username>
        <id>2969951</id>
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      <comment>/* New titles for user right nominations */ archive to [[Wikiversity:Colloquium/archives/March 2026#New titles for user right nominations]] ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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&lt;!-- MESSAGES GO BELOW --&gt;
== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <id>2810351</id>
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      <comment>/* Create a pseudo-bot user group? */ reply to Codename Noreste: Yes, that sounds good. (-) ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <id>2810353</id>
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        <id>10242</id>
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      <comment>/* Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) */ archive to [[Wikiversity:Colloquium/archives/April 2026#Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226)]] ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
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== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
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== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)
: This was completed on 30 April.
: Perhaps we could benefit from some documentation (e.g., [[Wikiversity:Patrol]] or [[Wikiversity:Patrolling]]?) and updates to the curator, custodian, bureaucrat pages? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:49, 19 May 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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      <id>2810368</id>
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      <comment>/* Add some user rights to the curator user group? */ reply to Jtneill ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
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== Technical Request:  Courtesy link.. ==

[[Template_talk:Information#Background_must_have_color_defined_as_well]] [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
: I can't edit the template directly as it need an sysop/interface admin to do it. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)
:: Also if the Template field of - https://en.wikiversity.org/wiki/Special:LintErrors/night-mode-unaware-background-color is examined, there is poential for an admin to clear a substantial proportion of these by implmenting a simmilar fix to the indciated templates (and underlying stylesheets). It would be nice to clear things like Project box and others, as many other templates (and thus pages depend on them.) :)
[[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 11:43, 20 March 2026 (UTC)

:I think it would be best to grant you interface admin rights for a short period of time to make these changes. However, I still have doubts about the suitability of this solution, which may cause other problems and no one has explained to me why dark mode has to be implemented this way @[[User:ShakespeareFan00|ShakespeareFan00]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:43, 20 March 2026 (UTC)

: I would have reservations about holding such rights, which is why I was trying to do what I could without needing them. However if it is the only way to get the required changes made, I would suggest asking on Wikipedia to find technical editors, willing to undertake the changes needed. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 09:32, 21 March 2026 (UTC)

== WikiEducator has closed ==

Some of you may know of a similar project to Wikiversity, called [https://wikieducator.org/Main_Page WikiEducator], championed by [https://oerfoundation.org/about/staff/wayne-mackintosh/ Wayne Mackintosh][https://www.linkedin.com/posts/waynemackintosh_important-notice-about-the-oer-foundation-activity-7405113051688931329-Nhm9/][https://openeducation.nz/killed-not-starved/].

It seems [https://openeducation.nz/terminating-oer-foundation their foundation has closed] and they are no longer operating.

They had done quite a bit of outreach (e.g., in the Pacific and Africa) to get educators using wiki.

The WikiEducator content is still available in MediaWiki - and potentially could be imported to Wikiversity ([https://wikieducator.org/WikiEducator:Copyrights CC-BY-SA] is the default license).

The closing of WikiEducator arguably makes the nurturing of Wikiversity even more important.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:09, 1 April 2026 (UTC)

:I was never active there. If anyone has an account or is otherwise in contact, we may want to copy relevant information here or even at [[:outreach:]]. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:46, 1 April 2026 (UTC)

:: I reached out to [[User:Mackiwg~enwikiversity|Wayne]] in January, and he responded briefly but positively (while travelling).  I wrote to the low-traffic wikieducator mailing list today and got a nice [https://groups.google.com/g/wikieducator/c/r_yIyUw6ZIA reply] from [[user:SteveFoerster|Steve Foerster]] who's interested in helping. If we can figure out a migration path it would be great to adopt at least the main namespace pages here.  
:: A few questions that come to mind: 
:: - would people want to create matching user accounts
:: - are there any namespaces (user/talk?) that should not be moved over
:: We could look at how this was done for the [[m:Wikivoyage/Migration]] wikivoyage migration. &lt;span style=&quot;padding:0 2px 0 2px;background-color:white;color:#bbb;&quot;&gt;&amp;ndash;[[User:Sj|SJ]][[User Talk:Sj|&lt;span style=&quot;color:#ff9900;&quot;&gt;+&lt;/span&gt;]]&lt;/span&gt; 04:27, 1 May 2026 (UTC)
:::That's fantastic, SJ, that you've reached out and that Wayne, Steve, and Jim are receptive—and that you can help! -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:52, 1 May 2026 (UTC)
::::A matching accound makes sense to give credits to the original authors and keep a clean chain of versions. The initial commit into wikiversity could have a &quot;marker with timestamp&quot; similar to signature with a reference where the content's source or a Web archive. This would allow authors to continue there work on wikiversity if they wish. [[User:Bert Niehaus|Bert Niehaus]] ([[User talk:Bert Niehaus|discuss]] • [[Special:Contributions/Bert Niehaus|contribs]]) 06:30, 15 May 2026 (UTC)

== Wikinews is ending ==

Apparently mainly due to low editorial activity, low public interest, but also failure to achieve the goals from the proposal for the creation of the project, the Wikinews project is ending after years of discussions ([[Meta:Proposal for Closing Wikinews|some reading]]).

And I would be interested to see how Wikiversity is doing in the monitored metrics. We probably have more editors than Wikinews had, but what about consumers and achieving the goals? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 19:14, 1 April 2026 (UTC)

:Wikiversity's biggest issue in recent times was the hosting of low-quality, trash content. Thankfully we've done a great job in removing pseudoscience and other embarrassingly trash content (Wikidebates, for example), but the biggest concern moving forward is proper maintenance IMO. I've caught several pseudoscience pages being created within the last few months that could easily have flown under the radar (ex, [[The Kelemen Dilemma: Causal Collapse and Axiomatic Instability]]), so I'd urge our custodians/curators to be on the lookout for this type of content. Usually an AI-overview can point this type of content out relatively well.
:In terms of visibility, I believe Wikiversity is a high-traffic project. I remember my [[Mathematical Properties]] showing up on the first page of Google when searching up &quot;math properties&quot; for the longest time (and is still showing up in the first page 'till this day!). Besides, Wikinews hosted a lot of short-term content (the nature of news articles), while Wikiversity hosts content that can still be useful a decade later (ex, [[A Reader's Guide to Annotation]]). 
:I think we are on a better path than we were a few months ago, and I do want to thank everyone here who has been helping out with maintaining our website! —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:48, 1 April 2026 (UTC)
:For what it's worth, the group that did that study has since disbanded, so no one is monitoring the other sister projects in the same way. Additionally, Wikinews had some catastrophic server issues due to the maintenance of [[:m:Extension:DynamicPageList]] which don't apply here. Your questions are still worth addressing, but I just wanted to cut off any concern at the pass about Wikiversity being in the same precarious situation. Wikiversity is definitely the biggest &quot;lagging behind&quot; or &quot;failure&quot; project now that Wikinews is being shuttered, but I don't see any near- or medium-term pathway to closing Wikiversity. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:46, 2 April 2026 (UTC)

:[[w:en:Wikipedia:Wikipedia Signpost/2026-03-31/News and notes|Entirety of Wikinews to be shut down]] (Wikipedia Signpost) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:03, 11 April 2026 (UTC)

== Add some user rights to the curator user group? ==

By default, only custodians have the ability to mark new pages as patrolled (&lt;code&gt;patrol&lt;/code&gt;) and have their own page creations automatically marked as patrolled (&lt;code&gt;autopatrol&lt;/code&gt;). I am proposing both of the following:
* Curators can mark new pages as patrolled, helping on reducing the backlog of new, unpatrolled pages.
* New pages made by curators will be automatically marked as patrolled by the MediaWiki software.
Before we implement this, I would suggest implementing a proposed guideline for marking new pages as patrolled for curators and custodians.

Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:32, 17 April 2026 (UTC)

:Agree, &lt;s&gt;also can we also allow curators to undelete pages since they already have the rights to delete them?&lt;/s&gt; [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 02:54, 18 April 2026 (UTC)
::I think the requirement that undelete NOT be included came from above (meta / stewards / central office). Having access to the undelete page gives access to information that is restricted by their policies to admins (custodians and bureaucrats). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:12, 18 April 2026 (UTC)
::: [[User:PieWriter|PieWriter]], unless if requests for curator and custodian should be RfA-like processes (that is, including voting and comments), then I have to agree with Dave above. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:03, 18 April 2026 (UTC)
::::Oh, I didn’t realise that. Withdrawing my comment.. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:08, 19 April 2026 (UTC)
:{{support}} Seems reasonable and would reduce overhead. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 14:35, 18 April 2026 (UTC)
:'''Agree''', implement it also to [[Wikiversity:Curators]] proposal please. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:11, 18 April 2026 (UTC)
: I went ahead and filed [[phab:T424445]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:39, 26 April 2026 (UTC)
: This was completed on 30 April.
: Perhaps we could benefit from some documentation (e.g., [[Wikiversity:Patrol]] or [[Wikiversity:Patrolling]]?) and updates to the curator, custodian, bureaucrat pages? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:49, 19 May 2026 (UTC)
:: Yes, but I would recommend [[Wikiversity:Patrolling]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 02:26, 19 May 2026 (UTC)

== [[Wikiversity:Curators|Curators and curators policy]] ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:15, 9 May 2026 (UTC)}}
How does it come, that Wikiversity has curators, but Curators policy is still being proposed? How do the curators exists and act if the policy about them havent been approved yet? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:33, 16 October 2025 (UTC)

:It looks as if it is not just curators. The policy on Bureaucratship is still being proposed as well. See [[Wikiversity:Bureaucratship]]. —[[User:RailwayEnthusiast2025|&lt;span style=&quot;font-family:Verdana; color:#008000; text-shadow:gray 0.2em 0.2em 0.4em;&quot;&gt;RailwayEnthusiast2025&lt;/span&gt;]] &lt;sup&gt;[[User talk:RailwayEnthusiast2025|&lt;span style=&quot;color:#59a53f&quot;&gt;''talk with me!''&lt;/span&gt;]]&lt;/sup&gt; 18:33, 27 October 2025 (UTC)

:I think its just the nature of a small WMF sister project in that there are lots of drafts, gaps, and potential improvements. In this case, these community would need to vote on those proposed Wikiversity staff policies if we think they're ready. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:08, 3 December 2025 (UTC)
:What? I thought you were getting it approved, Juandev... :) [[User:I&amp;#39;m Mr. Chris|I&amp;#39;m Mr. Chris]] ([[User talk:I&amp;#39;m Mr. Chris|discuss]] • [[Special:Contributions/I&amp;#39;m Mr. Chris|contribs]]) 14:20, 12 February 2026 (UTC)
::Yeah I think this one is important too and we need to aprove it too @[[User:I'm Mr. Chris|I'm Mr. Chris]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:56, 12 February 2026 (UTC)
:::I thinks its ready to made into a policy, it seems to be complete and informative about what the rights does and how to get it. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:08, 15 February 2026 (UTC)
::::Agree -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:00, 27 March 2026 (UTC)

Let's make this the official discussion about adopting the [[Wikiversity:Curators|curators policy]] policy. Your comments are invited and welcome. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:40, 24 April 2026 (UTC)
: There were two similar Colloquium threads in separate places about the proposed curators policy. So I've moved them to be adjacent. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
{{archive bottom}}

== Wikiversity:Curators to become a policy ==
{{archive top|There is strong consensus, so [[Wikiversity:Curators]] is now a policy. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:16, 9 May 2026 (UTC)}}
I've looked at the discussions about the Curators policy, I've looked at the practices, and it seems to me that there is no dispute about the wording of the policy, and what's more, the community has been using this proposal as if it were an offical policy for several years. Therefore, I propose that [[Wikiversity:Curators]] become a policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 18 April 2026 (UTC)

:{{support}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 18 April 2026 (UTC)
:{{support}} —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 20:21, 18 April 2026 (UTC)
: {{support|Yes, please}}. Especially after when I and PieWriter proposed above, I agree. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:27, 24 April 2026 (UTC)
:: @[[User:Juandev|Juandev]]; as of now, curators now have the user rights &lt;code&gt;autopatrol&lt;/code&gt; and &lt;code&gt;patrol&lt;/code&gt;. Perhaps we should also include that in [[Wikiversity:Custodianship]]? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 12:07, 30 April 2026 (UTC)
:::You meant [[Wikiversity:Curators]] @[[User:Codename Noreste|Codename Noreste]]? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:15, 5 May 2026 (UTC)
:::: I agree that we must develop what rules curators should follow when marking new pages as patrolled; the same can be added for custodians since they can also mark new pages as patrolled. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:37, 5 May 2026 (UTC)
:::::I see, well I think you can just add this to the policy. It is not major change and it probably reflects actual practice or actual technical possibilities for those flags. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:20, 7 May 2026 (UTC)
:{{support}} -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:42, 1 May 2026 (UTC)
:{{Support}} per nom. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 13:32, 1 May 2026 (UTC)
{{Archive bottom}}

== Is anyone interested in Neurodiversity? ==

Is anyone interested in Neurodiversity? Is there anyone here who is interested for Neurodiversity to be &quot;something more&quot; than it already is? Does anyone here consider Neurodiversity one of the &quot;harder topics&quot; to work on or discuss? Does anyone here have an opinion about the [[Neurodiversity Movement]]? So these questions don't appear like &quot;out of a vacuum&quot; I can tell you a bit about my background:

Many years ago I got a psychiatric diagnosis &quot;Asperger's&quot;. After I stepped out of the office and my Äsperger's was 'concluded', I stepped out into the street and thought my first negative thought(but the positive thought followed after). The thought was about concentration camps in the second world war and that the world seemed to be going into the direction of &quot;labeling others&quot;. I was unsure whether this was &quot;real science&quot; and sort of &quot;challenged myself&quot; to make up my own mind after meeting people that had been given this diagnosis. The more adults with this diagnosis I met the more I started seeing &quot;patterns&quot;.

Was it a coincidence that the first person with Asperger's I met reminded me about my father later after I had plenty of times of experience with interacting with him? None of the people I interacted with online through IRC text chat...I felt I got any clue about how &quot;their brains work&quot;. Only when I met one person from the Asperger's chat community in person we both realized that whatever we experienced was akin to the &quot;chaos theory&quot;. He told me about &quot;chaos theory&quot; while I didn't know even what that term meant but I guess I 'read between the lines'. My question that I linger on still today is &quot;did he understand about me what I think I understood about him?&quot;? That our brains had the same configuration? Most autistic adults who meet other autistic adults usually get disappointed. They think the diagnosis will help them meet somebody like themselves and then they realize the great diversity in the autistic spectrum created by Psychiatry.

I later stopped interacting with autistic communities that much, I felt that it did not benefit me. Also Neurodiversity's &quot;neurotypes&quot; interested me for a while until I realized I had &quot;misunderstood everything&quot; about them and how they are used in the Neurodiversity Movement or &quot;Neurodiversity community&quot; if that even can precisely be defined? I doubt it but if you want to contribute to the [[Neurodiversity Movement]]. My previous attempts failed as I got more and more confused. I think a community project needs a community. With a lack of that I don't think it is worth my time. If any of you would like to work on that project let me know on my talk page.

So I was kinda lost and was talking to my friend and psychologist and I realized if I never talk about my idea to anyone in a &quot;comprehensive way&quot; or show that it matters to me nothing is going to ever happen. So I started talking about my &quot;idea&quot; more. Nobody could understand the &quot;idea&quot; because I had not developed my skills regarding where to start...although the process had already started &quot;automatically&quot; and that's why I often think of &quot;well my brain sort of activated me&quot;. I don't feel like I did have a plan and this idea happened. It happened &quot;by itself&quot;. My brain reacted to what I was seeing in a video or stream.

I value interaction highly in this idea. I think it would be helpful to make a community of people who are not paranoid about stuff that can express itself like &quot;don't analyze me!&quot;, &quot;don't compare me to anyone!&quot;. 

On the contrary, more often than not those adults who were diagnosed were actually openly comparing themselves with each other and I think that is healthy in a &quot;science&quot; way if done the &quot;right way&quot; which probably means &quot;Do no harm&quot;.

I found video material is important but I'm very unsure if uploading own video material to Wikimedia Commons would constitute a &quot;reasonable&quot; use of the resources there. Maybe somebody here needs to ask more questions to me that I should answer before that happens. I also know the '''be bold''' so I could just do what I think might be ok. Though I work better in a group as long as I know what &quot;group configurations&quot; help me. This is in a non-profit way. Since the state supported me this might be a way I am trying to &quot;give back&quot; to the state and &quot;the world&quot;. May seem overly ambitious and crazy but this thing gives me energy. It gives me hope when trying to develop this idea. [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:47, 23 April 2026 (UTC)

:Thanks for sharing. There is plenty of room for neurodiversity community learning. However, the challenge I think is that the intersection of those interested in (a) ND, and (b) English Wikiversity might be very small (e.g., 1!) at this point in time.
:But don't give up hope. For example, Wikipedia has many more ND-interested editors; maybe consider reaching out to see who might be interested:
:[[w:Category:Wikipedians interested in neurodiversity]]
:You could also start an equivalent category here:
:[[:Category:Wikiversitarians interested in neurodiversity]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:46, 6 May 2026 (UTC)

== Request for comment (global AI policy) ==

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;A [[:m:Requests for comment/Artificial intelligence policy|request for comment]] is currently being held to decide on a global AI policy. {{int:Feedback-thanks-title}} [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 00:58, 26 April 2026 (UTC)&lt;/bdi&gt;
&lt;!-- Message sent by User:Codename Noreste@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&amp;oldid=30424282 --&gt;

== Language learning  ==

toki! I am trying to add or see what the toki pona language learning stuff on here is but I don't see anything that is language learning for anything. [[User:Jan Imon|Jan Imon]] ([[User talk:Jan Imon|discuss]] • [[Special:Contributions/Jan Imon|contribs]]) 23:13, 2 May 2026 (UTC) —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:29, 3 May 2026 (UTC)

:We have language materials ([[:Category:Languages]], [[World Languages]], [[Portal:Foreign Language Learning]], [[Portal:Multilingual Studies]]). They are not as developed as I think we would all like and there's not any coverage of Toki Pona, but in principle, we could and would like that. You can also see [[:b:Subject:Languages]] at our sister project Wikibooks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:33, 3 May 2026 (UTC)

== Timeline format? ==

I’ve been working on the World War II articles, including the [[World War II/Timeline|timeline]], and is there a specific timeline format that should be used? Right now it’s just a table, and there’s no separation between different periods/phases of the war.

I don’t want to use [[mw:Extension:EasyTimeline]] because this will be displaying dates and not time periods. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 01:35, 4 May 2026 (UTC)

:I dont think we have a policy or guideline, how to format a timeline. But you may try to browes wikiversity by Google if someone was dealing with this in the past somewhow @[[User:PhilDaBirdMan|PhilDaBirdMan]]. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:23, 5 May 2026 (UTC)
::+1 - there's no specific guideline on how to format a timeline, it's really up to you. In my opinion I think the timeline is good. I'd personally bold the dates just to make it easier to separate it from the event description, but that's my personal 2 cents. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:18, 5 May 2026 (UTC)
:::I’ll probably remove links to the dates/years, they’re just Wikipedia pages that shouldn’t be over linked to. [[User:PhilDaBirdMan|PhilDaBirdMan]] ([[User talk:PhilDaBirdMan|discuss]] • [[Special:Contributions/PhilDaBirdMan|contribs]]) 00:39, 6 May 2026 (UTC)

== Interface administrator for Codename Noreste ==
{{Archive top|After running for a week, there is clear consensus for [[User:Codename Noreste]] to have Interface admin rights for 120 days; implemented until 10 September, 2026 -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 12 May 2026 (UTC)}}

Hello, everyone. I am requesting interface administrator access on this wiki.

The main reasoning is that I would benefit from having the user right &lt;code&gt;editinterface&lt;/code&gt;, which would allow me to make dark mode changes to pages in the MediaWiki namespace, add &lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-parser-output&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt; to some interface pages using templates, handle interface-protected edit requests, and similar stuff. Additionally, I have some knowledge of CSS, and I would like to assist with modifying CSS pages whenever necessary, such as moving MediaWiki common.css code to TemplateStyles CSS pages.

I am requesting the maximum time that is allowed per the [[Wikiversity:Interface administrators|policy]], and I have 2FA enabled on my account. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:55, 6 May 2026 (UTC)

*{{support}} Globally trusted user. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:07, 6 May 2026 (UTC)
*{{support}} Trusted and knowledgeable. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:35, 6 May 2026 (UTC)
*{{support}} WV would benefit from this. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 08:32, 6 May 2026 (UTC)
*{{support}} --[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:13, 7 May 2026 (UTC)

:{{Comment}} Could @[[User:Codename Noreste|Codename Noreste]] delete [[MediaWiki:Gadget-WikiSign.js]], which was requested to be deleted @[[User:Koavf|Justin]], @[[User:Jtneill|Jtneill]], @[[User:Atcovi|Atcovi]]? I dont think we need it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:40, 9 May 2026 (UTC)
::Yes - clearly no longer used -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:18, 9 May 2026 (UTC)
::: I can't delete it because I don't have the required permissions to do so.
::: On a side note, if this project has a need for permanent interface administrators, I would suggest that we have a minimum of two IAs, similar to how there must be two CUs and/or suppressors (or none). Maybe Koavf can be a good candidate if I am elected for permanent interface adminship, and I believe that permission shouldn't be removed from someone's own account. Instead, a bureaucrat should do it. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:20, 9 May 2026 (UTC)
::::I am willing and happy to do it, unfortunately, we do not have an appetite for indef IAs and just had a discussion that resulted in a [https://en.wikiversity.org/w/index.php?title=Wikiversity:Interface_administrators&amp;diff=prev&amp;oldid=2807543 consensus that we can have IAs that have the user rights for 14 to 120 days]. So once you have the rights, please make sure to gopher it. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:54, 9 May 2026 (UTC)
:::::@[[User:Koavf|Koavf]] give it time. Look at me, I was in favor of shorter time, now I am looking back to times, when custodians could do it without the need of extra flag. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:31, 9 May 2026 (UTC)
::::::Here's hoping. I think it would reduce administrative overhead, but that's just me and I'm not a bureaucrat here. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:33, 9 May 2026 (UTC)
::::Complicated. Where are the times, admins could do everything! [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:27, 9 May 2026 (UTC)
{{archive bottom}}

== [[Wikiversity:Bureaucratship]] to become a policy ==
{{archive top|'''Approved - now a policy'''. 5 supports + 1 nominator. No objections.}}
Following the recent approval of [[Wikiversity:Curators]] as a policy, I think [[Wikiversity:Bureaucratship]] may also be ready for policy status.

Please share your views about whether bureaucratship is ready to become a policy, or whether further revisions are needed.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 13:58, 9 May 2026 (UTC)
: I added a logo about that user group, but other than that, it looks good to me. {{support}}. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:38, 9 May 2026 (UTC)
:I think that the consensus on this policy is proven by years of using it without further changes. But I I have to say weather I agree with this to become a policy, than of course {{support}}. It works and there were no major issues with it. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:45, 9 May 2026 (UTC)
:{{support}} no issues. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:51, 10 May 2026 (UTC)
:{{support}} [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 12:37, 11 May 2026 (UTC)
:{{support}} ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:51, 12 May 2026 (UTC)
{{archive bottom}}

== Reminder about custodian-related pages ==

I would like to remind the community about what the following custodian pages are:
* [[Wikiversity:Request custodian action]] is for requesting actions to be done by custodians, and
* [[Wikiversity:Notices for custodians]] is for notices of interest to custodians, like an administrator's noticeboard
Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:12, 12 May 2026 (UTC)

:Thanks - I needed this reminder :) -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:21, 12 May 2026 (UTC)

== [[MediaWiki:Protectedpagetext#Protected edit request on 11 December 2025]] ==

I posted an edit request there 5 months ago, so I’ll be taking it to this page. [[Special:Contributions/&amp;#126;2026-28640-56|&amp;#126;2026-28640-56]] ([[User talk:&amp;#126;2026-28640-56|talk]]) 23:33, 12 May 2026 (UTC)

:What exactly is the problem? I don't understand what needs to change and why. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:35, 12 May 2026 (UTC)
: Pinging @[[User:Atcovi|Atcovi]], @[[User:Jtneill|Jtneill]] and @[[User:Juandev|Juandev]] for further input. Someone is requesting a modification to [[MediaWiki:Protectedpagetext]] to use {{tlx|Protected page text}}, but we might need to discuss whether to use the template. In the meantime, I'll start a sandbox version of the protected page text template. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:19, 14 May 2026 (UTC)
::Sounds good -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:13, 15 May 2026 (UTC)

== Create a pseudo-bot user group? ==

I would like to propose adding a new user group to Wikiversity: Pseudo-bot (&lt;code&gt;flood&lt;/code&gt;). This will allow users to perform repetitive actions without flushing the recent changes feed (with only the &lt;code&gt;bot&lt;/code&gt; user right). However, I would suggest that for the pseudo-bot user group:
* It can be granted and revoked by custodians. &lt;s&gt;However, can curators add and remove pseudo-bot from their own accounts (and not others)?&lt;/s&gt;
* Users can remove themselves from it.
* A guideline might be necessary about the information and usage of it.
Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:31, 14 May 2026 (UTC)

:This sounds good. Which other wiki could we model this user group on? e.g., [[b:Wikibooks:Pseudo-bots]]? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:19, 15 May 2026 (UTC)
::@[[User:Jtneill|Jtneill]] Wikiquote has a similar group: [[:wikiquote:Special:ListGroupRights]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 04:25, 15 May 2026 (UTC)
: Should we allow curators to add and remove themselves from the pseudobot user group (from their own account) as well? I see no objections to creating the user group. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 18 May 2026 (UTC)
::My thinking is perhaps not curators by default because there should be clear visibility about their actions until they are well trusted. Let's draft a guideline or proposed policy ([[Wikiversity:Pseudo-bots]]) for the proposed user group. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:39, 18 May 2026 (UTC)
::: A solution is that they can ask any custodian to grant that group, and to remove themselves when done. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:17, 19 May 2026 (UTC)
:::: Yes, that sounds good. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:12, 19 May 2026 (UTC)

== Coming over From wikinews ==
Any chance someone could help me if you are allowed to write news articles here since wikinews is going read only mode soon, thank you! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:43, 1 May 2026 (UTC)

:The scope of Wikiversity is very broad and is basically about more-or-less any learning material. We have made it a point to not have duplicative content of other WMF projects, but since Wikinews is being shuttered, I personally am fine with writing news articles here. One thing that is not controversial at all is a learning resource &lt;em&gt;about&lt;/em&gt; how to write news: that could be hugely useful here and could involve the process of writing news stories to learn and to share back and forth with an editor or fact-checker. In fact, I'd support an entire namespace dedicated to keeping the notion of Wikinews alive here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:38, 1 May 2026 (UTC)
::Thank you so much! How do I start? Cheers! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:07, 2 May 2026 (UTC)
:::I think it's premature to start just making news articles en masse, but if you want to start discussing the topic of citizen journalism, you can do that now. [[:Category:Journalism]] already has some material, so you can start by seeing what we already have, how you can refine that, etc. You can definitely have learning resources with collaborators who want to learn about journalism ASAP. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 01:24, 2 May 2026 (UTC)
::::thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:38, 2 May 2026 (UTC)
::::If I could try and start one News Article could you please tell me how to go about it? Like what style of writing like Wikinews or something else? Thank you Justin! @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:48, 2 May 2026 (UTC)
:::::Honestly, there are very few policies and guidelines here. I think the best way to write a news story would be in a manner that is obvious and instructive. So, for instance, it's common to use the &quot;pyramid style&quot; when you're writing news, so if you were to write a story that makes it very clear that you are using that approach, that would be helpful. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:08, 2 May 2026 (UTC)
::::::cool thanks. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 02:13, 2 May 2026 (UTC)
::::::im ready to write @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 21:30, 13 May 2026 (UTC)
:::::::I think we should get more local consensus for a big project like including the entirety of the scope of Wikinews here. Again, I support it personally. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:55, 13 May 2026 (UTC)
::::::::ok lets begin. [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:15, 13 May 2026 (UTC)

== Proposal to rehost Wikinews here ==

As many of you know, and mentioned here at the Colloquium, our sister project Wikinews recently closed, with all 31 active editions made read-only. [[User:BigKrow]] has asked about the prospect of writing news stories here and I suggested that since we already have [[School:Journalism]] and some resources related to the [[:Category:Journalism|broader topic of journalism]]. I would like to propose that we have continued and indefinite space for {{w|citizen journalism}} by essentially repurposing Wikinews into a sub-project here. The only special infrastructure that Wikinews required was [[:mw:Extension:DynamicPageList]], which was deactivated and caused issues due to a lack of maintenance.

I will add this proposal to the site banner, but I recognize that that may be a conflict of interest, so if anyone requests that I remove it, I will. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:30, 14 May 2026 (UTC)
:I would like to see this conversation go for at least 30 days to establish a consensus. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)

===Votes===
*{{support}} as proposer (with BK's inspiration). I think that an ongoing experiment in citizen journalism is a fit and appropriate use of this site. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:35, 14 May 2026 (UTC)
*{{support}}, hope to seeing ideas about this, and thank you @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 11:08, 14 May 2026 (UTC)
*{{support}} Other than perhaps inflating the total number of pages reported, I see the idea of &quot;practicing journalism&quot; a worthy and relevant activity within the domain of Wikiversity. [[User:IanVG|IanVG]] ([[User talk:IanVG|discuss]] • [[Special:Contributions/IanVG|contribs]]) 21:41, 14 May 2026 (UTC)
*{{support}} Conditional on development of (a) community guidelines that ensure alignment with Wikiversity's purpose, and (b) clear, nested page-naming structures for projects. More detail below. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:48, 15 May 2026 (UTC)
*{{contra}} This proposal doesn't seem interested in expanding educational materials in journalism, but rather in providing space and protection for Wikinews contributors. But this is contrary to the goals of Wikiversity, and I'm not sure it's a good idea, even with regard to WMF. If WMF decides to close a project and another community lets it run on its domain, that's a bit of an undermining of WMF's and the community's decisions. Given that Wikiversity has had several conflicts with other communities and WMF in its history, I'm against it.--[[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:59, 15 May 2026 (UTC)

===Comments and questions===
:Definitely worthy of discussion, so I have no problem with the proposal in the sitenotice.
:Initial questions:
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
:* What are &quot;active editions&quot;?
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
:* Are any changes to the scope of Wikinews proposed?
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[User:BigKrow/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
:-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 05:52, 14 May 2026 (UTC)
:* Does this proposal include importing English Wikinews content e.g., to [[Wikinews]] subpages?
::*No, not at this time.
:* What are &quot;active editions&quot;?
::*There were 30 other active editions of Wikinews in addition to English (e.g. [[:n:es:]]) at the time of universal closure (2026-05-04).
:* How can Wikiversity navigate the concerns that lead to the closure of Wikinews?
::*One of the biggest issues was the problems with DPL, which is now irrelevant. Another was the lack of activity, which can be ameliorated by having it be part of an existing project instead of its own domain (e.g. some editions of Wikipedia host their own Wikinews already and those projects were not impacted by the closure).
:* Are any changes to the scope of Wikinews proposed?
::*Not at this juncture. I would also propose as far as implemention goes that we would request a new namespace and that the material be more-or-less sequestered into its own ongoing project, like Wikijournal is or like the Cookbook and Wikijunior are at our sister [[:b:]].
:* How does [[Wikinews]] fit with the [[Wikiversity:Mission]]? What aligns well? Where might there be tension?
:** e.g., I'm not sure that a page like [[Story/Manchester City moves two points behind Arsenal]] in and of itself will serve as an educational resource.
::*The process of citizen journalists practicing their craft in real-time and collaborating with others to do so is itself an education activity. We would essentially be hosting a real-time experiment in citizen journalism, online communities, and collaborative learning in addition to the prospect of spreading educational information from someone actually reading the news. I would propose that we could also make a more deliberate attempt to engage with learning &lt;em&gt;about&lt;/em&gt; what does and doesn't work with collaborative news writing by experimentation (e.g. audio news, syndicating to other sites, incorporating freely-licensed news from other sources, writing hyper-local news, writing briefs versus longer-term reportage) and also seeing if the problems noted in the Task Force report that recommended closure can be overcome. Note that we have already done some local investigation about and learning about wiki-based journalism on Wikinews here at [[Journalism studies and Wikinews]]. We could continue that learning and refine the process, including incorporating journalism students from universities. As for tensions, Wikinews is the only sister project that must be done with a quick turn-around: if you take a long time to [[:s:|transcribe a book]], that's just how long it takes, but if you take a long time to write news, it ceases to be news entirely. Wikiversity has been a very slow-growing project that has definitely had some successes but has generally come together over a long period with most learning resources being individual passion projects (or sometimes, frankly, crankery) which would not work with collaborative news that requires more than just a single editor writing whatever he feels like.
::Please let me know any other questions/concerns and any other editors feel free to give your own perspective. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:13, 14 May 2026 (UTC)
:::Thanks, Justin — it is food for thought.
:::In attempting to understand how we've arrived here, I've summarised some of the background on this page: [[Wikinews]].
:::Perhaps it could be helpful to flesh out more of the vision / ideas / possibilities / challenges on that page? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:49, 14 May 2026 (UTC)

:::*Having given it some thought, in principle, I support hosting [[citizen journalism]] on Wikiversity where it is clearly connected to a learning project and/or constitutes original research, both of which align strongly with [[Wikiversity:Mission|Wikiversity’s educational mission]].
:::*My chief concern is the potential for news content that is not clearly linked to the purpose of Wikiversity. To avoid this, some community-agreed guidelines would be prudent. These need not be overly restrictive; they should support boldness and experimentation while helping ensure alignment with Wikiversity's purpose.
:::*Given the reported low and declining activity on Wikinews, it seems unlikely that English Wikiversity would be overwhelmed by an influx of news-related editing. My impression is that English Wikinews was the most active edition, but even so, many contributors are likely to disperse to other projects or cease editing altogether. A modest migration of interested editors to Wikiversity seems manageable.
:::*At this stage, I do not think a dedicated namespace is necessary. Subpages under [[Wikinews]] or nested pages under relevant learning or research projects, or user-space draft pages should be suitable. I agree that [[Wikijournal]] offers a useful model, as do several existing course structures on Wikiversity.
:::*I support [[User:Koavf]]’s suggestions about framing Wikinews activity explicitly around learning. This would create a distinctive space for experimenting with collaborative news production in ways that are pedagogically meaningful. I agree that the [[journalism studies and Wikinews]] project developed by David and Leigh Blackall through the University of Wollongong is an excellent example of the intersection between Wikiversity and Wikinews. The [[Wikinews]] page could evolve into a hub for such projects.
:::*I've tidied the [[:Category:Wikinews|Wikinews category]] and merged some content into the [[Wikinews]] page. As part of a reinvigoration effort, please review these and related resources such as [[:Category:Journalism]] and [[School:Journalism]].
:::*A further argument in favour of this initiative is that Wikipedia explicitly excludes both news reporting and original research. So, there is value in maintaining spaces within the Wikimedia ecosystem where these forms of knowledge production can be openly developed and curated. Such work can, in turn, generate valuable evidence and source material that may later inform Wikipedia articles.
:::*The closure of WMF-hosted Wikinews does not imply that open wiki-based news curation lacks value. Indeed, the closure documentation appears supportive of experimentation with alternative news models across Wikimedia projects, including through Wikipedia and Wikidata. In that context, Wikiversity seems a natural home for a Wikinews experiment, provided it is clearly grounded in learning and/or research.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 15 May 2026 (UTC)
My understanding towards Wikinews' failure is that everything takes too long to be approved for the publish status, which means that any breaking news would have already become days-old stale news. Wikinews has a brand recognition (for right or wrong reasons) than Wikiversity and I wonder how effective Wikiversity can attract the &quot;Wikinews refugees&quot; to edit here. And just a quick note on the governance. Since each Wikiversity language operates independently, each language has to vote &amp; adopt this proposal independently. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 13:47, 15 May 2026 (UTC)

:Your assessment about Wikinews is partially correct. I referenced it earlier, but to be explicit, there is a [[:m:Proposal for Closing Wikinews|report by a task force on sister projects]] that outlines their concerns. There are a few, one of which was the nature of the staleness of news. Thanks also for clarifying that this proposal is only relevant to en.wv and is not binding or even proposed for other editions of Wikiversity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:54, 15 May 2026 (UTC)

== Inactivity policy for Curators ==

I was wondering if there is a specific inactivity polity for curators (semi-admins) as I am pretty sure the global policy does not apply to them as they are not ''fully'' sysops. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 03:20, 15 February 2026 (UTC)

:Unfortunately, I don't see an inactivity policy, but if we were to create such a new policy for curators, it should be the same for custodians (administrators). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 18:45, 15 February 2026 (UTC)
::@[[User:Codename Noreste|Codename Noreste]] There is currently none, that I could find, for custodians either. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:47, 17 February 2026 (UTC)
:::I think we should propose a local inactivity policy for custodians (and by extension, curators), which should be at least one year without any edits ''and'' logged actions. However, I don't know which page should it be when the inactivity removal procedure starts. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:53, 17 February 2026 (UTC)
::::@[[User:Codename Noreste|Codename Noreste]] In theory, there should be a section added at [[WV:Candidates for custodianship]] [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 00:55, 17 February 2026 (UTC)
::::: To be consistent with the [[meta:Admin activity review|global period of 2 years inactivity]] for en.wv  [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship#How are bureaucrats removed?|Bureaucrats]] we could add something like this to [[Wikiversity:Curators]]:
::::::The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for curators is two years (consistent with  the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]] which applies for [[Wikiversity:Custodianship#Notes|Custodians]] and [[Wikiversity:Bureaucratship|Bureaucrats]]). After that time a custodian will remove the rights.
::::: -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:51, 27 March 2026 (UTC)
:::::Yup, I agree with Jtneill, there is a policy proposal for Wikiversity:Curators, where it should be logically deployed. The question is if we are ready to aprove the policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:43, 17 April 2026 (UTC)
:::::: I agree, but we should notify the colloquium about inactive curators, just like a steward would do for inactive custodians and bureaucrats per [[:m:Admin activity review|AAR]]. What is the minimum timeframe an inactive curator should receive so they can respond they would keep their rights? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:49, 17 April 2026 (UTC)
:I incorporated these suggestions into the proposed curators policy. Please review/comment/improve. Summary: 2 years, notify curator's user page, then remove rights after 1 month: [[Wikiversity:Curators#Inactivity]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:59, 24 April 2026 (UTC)
:: @[[User:Jtneill|Jtneill]] I created [[Template:Inactive curator]] for this. Feel free to make any changes or improvements. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 14:29, 24 April 2026 (UTC)
:::Wondering, should we also have:
:::* {{tl|Inactive custodian}}
:::* {{tl|Inactive bureaucrat}}
:::or perhaps just a single template with a parameter(s) for the user right(s)/role(s)? e.g., 
:::* if a custodian is inactive for 2 years, then custodian and curator rights are to be removed and 
:::* if a bureaucrat is inactive for 2 years, then bureaucrat, custodian, and curator rights are to to be removed.
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 09:58, 13 May 2026 (UTC)
:::: I would probably modify that template when we actually develop our own inactivity policy, because we're currently under the AAR (a steward notifies the colloquium with [[m:Admin activity review/Notice to communities]], and inactive advanced right holders with [[m:Admin activity review/Notice to inactive right holders]]). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:16, 13 May 2026 (UTC)
:::::Ah, I see. Yes, that makes sense. Thankyou. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:21, 15 May 2026 (UTC)
: In that case, should we develop our own inactivity policy (e.g. on [[Wikiversity:Inactivity policy]] or [[Wikiversity:Support staff/Inactivity]])? I would list the general inactivity part, the process, etc. Once it's approved as a policy, I will [[m:Stewards' noticeboard|notify the stewards]]. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:30, 16 May 2026 (UTC)
::Originally, I would have thought that, for a small wiki like en.wv, it made sense to leave inactivity monitoring to the stewards. However, with the creation of the curator user group, we have already taken on local responsibility for monitoring inactivity in at least one advanced-rights group. Extending this to custodians and bureaucrats would not add much additional overhead and would provide a more consistent and transparent local administrative process.
::One option would be to develop a single, centralised policy covering all advanced-rights groups.
::An alternative would be to include an ==Inactivity== section on each relevant policy page (e.g., we already have [[Wikiversity:Curatorship#Inactivity]], but not yet in the custodianship, and bureaucratship policy pages). This approach would allow some flexibility because different user groups may warrant different criteria (such as inactivity thresholds, qualifying activity, or review procedures).
::A hybrid approach may be best: maintain separate inactivity sections within each user-group policy page, while transcluding these into a central overview page such as Codename Noreste suggests. This would preserve clarity at the local policy level while also providing a single reference point for consistency and oversight. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:09, 16 May 2026 (UTC)
::: I would suggest we develop a centralized inactivity policy page, and include a short summarized section of that page, on the support staff user group pages. We must also include a link to that policy page if we were to add &lt;nowiki&gt;== Inactivity ==&lt;/nowiki&gt; to each of those user group pages. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:48, 17 May 2026 (UTC)

== Inactive curators ==

Hello, even though [[Wikiversity:Curators]] is not a policy yet, there are curators listed here that have been inactive for two years or more:
* {{user|Cody naccarato}} (last edit on 13 Dec 2022, last logged action on 10 Dec 2022)
* {{user|Praxidicae}} (last edit on 10 Sep 2022, last logged action on 12 Sep 2022)
[[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 21:14, 19 April 2026 (UTC)

:Yup, I would remove the rights. To get the rights back if theyll come back should not be a big deal. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:08, 24 April 2026 (UTC)
:: When they don't reply by May 19, feel free (or any custodian) to do so. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:28, 25 April 2026 (UTC)

==Curator inactivity review==
These curators haven't been active for &gt; 2 years. As per the [[Wikiversity:Curatorship|curatorship policy]]:
* [[Special:Log/Cody naccarato]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Praxidicae]] was notified on their talk page by [[User:Codename Noreste|Codename Noreste]] on 24 Apr 2026
* [[Special:Log/Tegel]] was notified on their talk page by [[User:Jtneill|Jtneill]] notified their talk page on 16 May 2026

The policy allows a month to hear from these users. If no response, a custodian will remove their curator rights.

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:14, 16 May 2026 (UTC)
: For Cody naccarato and Praxidicae, their rights are to be removed by the 19th of May if they don't respond either here or on their talk page. For Tegel, the removal will happen on the 16th of June, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:13, 16 May 2026 (UTC)
::Should be 24 May for Cody naccarato and Praxidicae? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:11, 16 May 2026 (UTC)
::: I made [[#Inactive curators]] on the 19th of April. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 03:18, 17 May 2026 (UTC)
::::OK, I see (had missed that thread, sorry - I've now moved the the 3 inactivity topics to be adjacent).
::::I'm thinking the curator policy indicates one month from user talk page notification? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:44, 17 May 2026 (UTC)
::::: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 16:49, 17 May 2026 (UTC)

== [[Wikiversity:Deletion policy]] proposed as policy ==

[[Wikiversity:Deletions]] has been operating as a [[Wikiversity:Guidelines|guideline]]. It has been revised and moved to [[Wikiversity:Deletion policy]], consistent with naming conventions used across sister projects such as Wikipedia, Wikibooks, and Wikiquote. The speedy deletion criteria have also been updated for consistency with [[MediaWiki:Deletereason-dropdown]].

This proposal is for the page to be formally adopted as [[Wikiversity:Policies|Wikiversity policy]].

Community feedback is invited, including suggestions for further improvements that may strengthen the proposed policy.

=== Voting ===
*{{support}} Seems reasonable. If there's somehow something missed here, we can just amend it later. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:33, 18 May 2026 (UTC)
*{{support}} I don't see any issues with the policy. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 16:07, 18 May 2026 (UTC)

=== Comments ===</text>
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    <title>Wikiversity:Custodianship</title>
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      <comment>/* How does one become a custodian? */ Remove &quot;it takes&quot; (redundant)</comment>
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{{Policy|WV:CUST}}
[[File:Wikiversity Administrator.svg|right|130px|link=]]

'''Custodians''' are part of [[Wikiversity]]'s [[Wikiversity:Support staff|support staff]]. They are experienced and trusted users who can [[#Edit and move protection of pages|protect]] and unprotect pages, [[#Deletion and restoration of pages|delete]] and restore pages, and [[#User blocks|block]] or unblock users from editing. Custodians are the Wikiversity equivalent of administrators (also known as sysops, bibliotecarios (librarians), and moderators).

The English Wikiversity currently has {{#expr:{{NUMBEROFADMINS}} -1}} custodians ([[Special:ListUsers/sysop|full list]]).

{{center top}}'''[[Wikiversity:Request custodian action|Request assistance]]''' - '''[[Wikiversity:Support staff#Support staff directory|List of custodians]]''' - '''[[Wikiversity:Candidates for Custodianship|Requests for custodianship]]'''{{center bottom}}

== How does one become a custodian? ==
{{shortcut|WV:CUST/HOW}}
Any [[Wikiversity:Who are Wikiversity participants?|Wikiversity participant]] willing to do a lot of [[#What can custodians do?|dull and boring work]] for the community can become a custodian. If you have a good editing record then you are likely to be trusted and granted the privileges and responsibilities of custodianship. If you are still interested in custodianship, here is the process:

{| style=&quot;border-collapse: collapse&quot; border=&quot;1&quot; cellpadding=&quot;4&quot;
 | style=&quot;padding: 10px; text-align: center&quot; | I
 |
&lt;div id=&quot;Request&quot;&gt;
;Request
&lt;/div&gt;
You must request or be nominated for custodianship at [[Wikiversity:Candidates for Custodianship|Candidates for Custodianship]]. State your reasons for seeking this position and in what areas you are or would like to be active. You may also refer to your contributions and indicate whether you have similar responsibilities at other projects.
 |-
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&lt;div id=&quot;Mentorship&quot;&gt;
;Mentorship
&lt;/div&gt;
[[Wikiversity:List of custodian mentors|Custodian mentors]] are expected to guide and advise you on the appropriate use of custodian privileges in accordance with established policy and [[Wikiversity:Consensus|community consensus]]. If an experienced custodian agrees to mentor you and you agree to their mentorship, then you will be approved as a [[w:Probation (workplace)|probationary]] custodian for a period of at least '''four weeks'''. You will have all the privileges described below. If you have any questions or concerns, you should contact your mentor(s) for guidance and advice. If you or your mentor terminate the mentorship agreement before the probationary period is complete, you will have 48 hours to find a new mentor. Otherwise your mentor may [[Meta:SRP|request removal of custodian privileges]] after 48 hours, without any further notice or community discussion.
 |-
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 |
&lt;div id=&quot;Evaluation&quot;&gt;
;Evaluation
&lt;/div&gt;
Your mentor will submit a request for comments at [[Wikiversity:Candidates for Custodianship|Candidates for Custodianship]] for a period of at least '''seven days''' when you are ready. During that period Wikiversity participants can evaluate how well the custodian privileges are used and how you conducted yourself at Wikiversity.
 |-
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 |
&lt;div id=&quot;Custodianship&quot;&gt;
;Custodianship
&lt;/div&gt;
After one week of evaluation, a bureaucrat will make the final decision based on the arguments provided in the discussion. If you are approved, you will be a [[#Notes|permanent custodian]]. If you are not approved, your probationary period may either be extended or you may request another mentorship later.
 |}

== What can custodians do? ==
{{shortcut|WV:CUST/WHAT}}
=== Deletion and undeletion of pages ===
{{shortcut|WV:CUST/D}}
[[File:Delete and Protect buttons.png|200px|right]]
Custodians can delete pages including images, categories, templates, etc. Deletion is subject to [[Wikiversity:Policies|policy]]. Deletion requests may be submitted by any user at [[Wikiversity:Requests for Deletion]].

Deleting a page does not actually remove it from the database. It is merely invisible to non-custodians and can be restored at request, which may be submitted at [[Wikiversity:Requests for Deletion]]. Page deletions and undeletions can be monitored by viewing the [[Special:Log/delete|deletion log]].

Custodians can also delete individual versions with the [[Wikiversity:Revision deletion|RevisionDelete]] feature. This is particularly useful to remove materials that violate [[Wikiversity:Copyrights|copyrights]] or other applicable law.

Before you delete a page, read: [[Wikiversity:Welcome templates]]. See also: [[Wikiversity:Deletion policy]].

=== Edit and move protection of pages ===
Custodians can [[Wikiversity:Page protection|protect pages]] to prevent editing. There are two types of page protection: semi-protection, which prevents anonymous and new users from editing, and full protection, which prevents all non-custodians from editing. A page can also be protected to prevent moving. Page protection can be lifted by any custodian upon request, which may be submitted at [[Wikiversity:Request custodian action]]. Page protections and unprotections can be monitored by viewing the [[Special:Log/protect|protection log]].

=== Rollback ===
[[Image:Rollback button.png|thumb|300px|Rollback button]]
Custodians have a ''[[Wikiversity:Rollback|rollback tool]]'' to revert the last change or group of changes made to a page by the same user. There is no option to provide an edit summary when using this tool. Instead, a summary such as &quot;Reverted edits by [[Special:Contributions/$2|$2]] ([[User_talk:$2|talk]]) to last version by [[User:$1|$1]] using [[Wikiversity:Rollback|rollback]]&quot; will be used automatically. This tool is primarily used to respond to obvious vandalism. For other edit reversions, the rollback button should not be used and a good edit summary should be provided.

=== User blocks ===
{{shortcut|WV:CUST/B}}
Custodians can block users from editing by specifying a username, an IP address or range of addresses. Blocks can be temporary or permanent. Most frequently, blocking occurs in response to obvious and repeated vandalism. When blocking a user, a reason for blocking must be provided which is displayed in the [[Special:Log/block|block log]]. It is also possible to block IP addresses from creating new user accounts. See [[Wikiversity:Blocking policy]].

=== Editing MediaWiki [[Wikiversity:Namespaces|namespace]] ===
{{shortcut|WV:CUST/MW}}
Custodians are able to edit system messages (the standard texts that are used by the MediaWiki software).

=== Import ===
Custodians have access to the [[Special:Import|Import tool]], to bring materials from Wikipedia, Wikibooks, Beta.Wikiversity, Wikiquote, and Wikisource.

=== User rights ===
Custodians can determine [[Wikiversity:Consensus|consensus]] and grant or revoke the following user permissions:
* [[Wikiversity:Curatorship|Curator]]
* [[Wikiversity:Event organizers|Event organizer]]
* [[Wikiversity:IP block exemption|IP block exemption]]
* [[Wikiversity:Temporary account IP viewer|Temporary account IP viewer]]
However, custodians cannot grant or revoke custodian, bureaucrat, bot, or interface administrator permissions. These actions require [[Wikiversity:Bureaucratship|bureaucrat]] and/or [[m:Steward|steward]] permissions.

== How are custodians expected to act? ==
{{shortcut|WV:CUST/E}}
Custodians are supposed to follow the same principles as every other user, including [[Wikiversity:Civility|being civil]], [[Wikiversity:Assume Good Faith|assuming good faith]], and understanding [[Wikiversity:What is Wikiversity?|what Wikiversity is]]. They are expected to act professionally, and to respect policy and [[Wikiversity:Consensus|community consensus]]. 

For a discussion of possible failure to act professionally, see a proposed recusal policy at [[Wikiversity:Recusal]].

==Problems with custodians==
{{shortcut|WV:CUST/P}}
If you have a question about an action (page deletion, page protection, user block, editing MediaWiki namespace pages, violation of Wikiversity policy or some other action that does serious damage to the project) by a Wikiversity custodian, the first thing to do is leave a message on that custodian's user discussion page. Custodians should always be able to explain how their actions support Wikiversity. If you cannot get satisfaction from discussion with the custodian, you can place comments, suggestions, complaints or questions at [[Wikiversity:Custodian feedback|Custodian feedback]]. Try to resolve all custodian problems by discussion.

Custodians can lose their status for [[wikt:egregious|egregious]] violations of policies. Loss of custodianship involves a process that establishes community consensus. If a specific complaint is not resolved at [[Wikiversity:Custodian feedback|Custodian feedback]] then a [[Wikiversity:Community Review|Community Review]] can be initiated to establish if there is community consensus in support for the custodianship of the custodian who is the subject of the unresolved complaint. At the end of the review, Wikiversity bureaucrats will review the discussion. If a bureaucrat decides that there is good reason for removal of a custodianship, that bureaucrat will go to the meta-wiki and [[m:Requests for permissions|request]] that stewards review the community discussion. If a steward agrees that the Wikiversity community has reached consensus about a problem custodian, then that steward can terminate the custodianship of the custodian.

If you have a question about an action of a probationary custodian, you should consult their mentor(s). Actions of a probationary custodian are the responsibility of their mentor(s) during their probationary period. Partially depending on agreements made in the probationary candidacy, and with respect for the 48 hour period to find a new mentor, a request to remove custodianship for a probationary custodian may often be made at Meta by any mentor or bureaucrat without need for community consensus. The local process to remove custodianship should only need to be used as a last resort, because of this alternative option.

== Notes ==
{{shortcut|WV:CUST/N}}
* Custodianship is a responsibility, not a right. While everyone is encouraged to apply for custodianship, the position is not suited for everyone. Please also note that in all instances not listed above, custodians have no more power or weight than other users.
* Custodians should set their &quot;user preferences&quot; so as to provide for email contacts from other Wikiversity participants. If you do not use email, then you must make yourself easily available by some other means such as [[Wikiversity:Chat|IRC chat]].
* The maximum time period of inactivity &lt;u&gt;without community review&lt;/u&gt; for holders of advanced administrative rights is two years per the [[:meta:Category:Global policies|global policy]] described at [[meta:Admin activity review|Admin activity review]]. After that time, a [[meta:Steward requests/Permissions|steward will be asked to remove the rights]].&lt;ref&gt;See also a decision made in [[Wikiversity:Request custodian action/Archive/24#Reviews for Inactivity]].&lt;/ref&gt;

== Useful reads for custodians ==
{{Wikiversity organization}}
===Wikiversity===
* [[Wikiversity:Blocking policy]]
* [[Wikiversity:No shrines for vandals]]
* [[Wikiversity:Policies]]
* [[Wikiversity:Revision deletion]]
* [[How to be a Wikimedia sysop/Wikiversity]]

===MediaWiki/Wikimedia===
* [[How to be a Wikimedia sysop]]
* [[b:MediaWiki Administrator's Handbook|MediaWiki Administrator's Handbook]]

==See also==
* [[Special:ListUsers/sysop|List of current Wikiversity custodians and bureaucrats]]
* [[Wikiversity:Bureaucratship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:CheckUser policy]]
* [[Wikiversity:Curatorship]]
* [[Wikiversity:History of Wikiversity/Custodianship]]
* [[Wikiversity:Support staff|Wikiversity:Staff]]
* [[Special:ListGroupRights]]

== Reference ==
{{Reflist}}

{{Official policies}}
[[Category:Wikiversity custodianship| ]]</text>
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    <title>Wikiversity:Featured</title>
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This page coordinates and informs about '''featured content''' on Wikiversity. 

== About featured content ==
=== What is featured content? ===

Featured content is considered, for a variety of reasons, to present Wikiversity at its best to the general public. Featured content may show exemplary course design, a novel, usable and fully functioning approach to wiki-based education, or educational resources that have simply reached a high state of completion or had very large amounts of work done on them.

''See also: [[Educational Media Awareness Campaign|the Picture of the Day system]]''

=== How is featured content displayed to the public? ===

There are a number of ways featured content is used.

# Featured content on [[Wikiversity]] is regularly rotated in the &quot;today's featured project&quot; on the main page. 
# A wider range of material from this page, including content which is proposed-for but not-yet featured, is included in a special pseudo-random-page system accessed from the left-hand navigation panel on every page of Wikiversity - see [[Wikiversity:Random|Random project]].
# Many portals also have featured content. This page can be used for finding resources which are suitable for featuring on specific portals. Portals tend to set the bar for featured content somewhat lower, so portals may also feature content not listed here.

An important difference between featured content on Wikiversity and featured content on much larger projects is that on Wikiversity, featured content is '''rotated'''. On very large projects, featured content is selected by special interest groups several weeks or months in advance, and is always new. On Wikiversity, to save time, and as a result of the lower level of content production, featured content is rotated on a daily basis. Featured content therefore reappears on the main page at regular intervals.

=== Who selects featured content? ===

Selecting and maintaining a featured content system requires a time-consuming long-term commitment and a wide knowledge of Wikiversity content. Few people have ever been prepared to invest time in this. On larger projects, featured content is usually selected by democratic vote. However democratic systems only work when there is a large enough body of well-informed participants in a featured content project. The Wikiversity system is unfortunately rather autocratic at the current time, but any user can propose content (just add it below) and comment on other suggestions. Please ''inform'' yourself widely about featured content before commenting if you can.

There is no formal system of criteria at the current time, but you can discuss proposals for criteria on the talk page. On the whole, it would be desirable if featured content could represent as many different subjects and educational levels as possible.

=== Other ways of drawing attention to educational resources ===

The following ideas have been suggested at some time or other:
* '''Events'''
** Add an &quot;events&quot; entry to the left-hand navigation panel, which links to an events page, which in turn lists upcoming events (e.g. meetings, synchronous discussions). This would require someone prepared to regularly maintain the page.
** Notify events on [[Mediawiki:sitenotice]] (requires custodian) or in the main page news box (registered users).
* '''Projects and resources in need of development'''
** These are &quot;development drives&quot;. A development drives page could be created and maintained, which randomly rotates project links in the &quot;development&quot; box on the main page. This would require someone prepared to regularly maintain the page.
* '''Projects and resources in need of participants'''
** This idea relates to educational resources which are &quot;ready&quot; for the public, but which may have very little content because the content is supposed to come from active community participation. These projects might be candidates for featured status once a community has created a substantial body of content, but at the current time these resources are more sketches or skeletons of ideas for participatory learning. The idea of drawing attention to these is to attract participants who will &quot;develop&quot; the resource, but &quot;development&quot; here is not meant in the usual sense of &quot;development&quot; (as in &quot;development drive&quot;) because development (production) and use (consumption) merge. A &quot;needs-participants&quot; page could be created and maintained, which randomly rotates project links in the &quot;community&quot; box on the main page. This would require someone prepared to regularly maintain the page.
** One could also classify a participation drive as an &quot;event&quot;

== Current featured content ==
[[:Category:Featured resources]]
{{/table}}

:''Reference: [[/Archive|Archive of discussions of successful featured content]]''
:''Tour: [[Featured content]]''
:''Admin: [[Template:Featured Content/Nav]], [[Template:FOTD]], [[Template:FOTD/CALC]], [[Template:cool]], [[Template:hot]]''
: ''Number of pages in featured resources: c. 1500-1600 (about 17%-18% of Wikiversity content)''
: ''Number of featured resources: 18''
: ''Average size of featured resources: 83-88 pages''

== Shortlisted   ==

''This is an administrative section. It contains content which will shortly be added to featured content. The content listed here is currently being cleaned up and checked prior to featuring. Please feel welcome to help with the polishing process. When material here has been processed, it is archived at [[/Archive|Archive of discussions of successful featured content]].''

== New proposals for featured content ==

# If you propose something, please give a very brief reason/description (max 1 line) and '''sign your name'''. Thanks!
# Others: please add your comments below the proposal and '''sign your name too'''. Thanks!

Please help identify well developed or complete science resources to feature during [[Wikiversity:Year of Science 2016]]. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 20:20, 18 January 2016 (UTC)

=== IT Fundamentals ===
[[IT Fundamentals]] is an excellent resource and very useful. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:11, 10 February 2016 (UTC)

Review of IT Fundamentals:

The course is aimed at the IT Fundamentals certification. At the outset IT is not a specialty. My initial impression from looking at the course materials starting at Wikiversity is that they are smart, smooth, and well-presented. There are 15 lessons. If there are any weaknesses with the course, I would expect them to be with a dependency on Wikipedia. Sampling, I looked at

1. [[IT Fundamentals/Hardware|Hardware]] and chose something I haven't heard of or read before: from Wikipedia &quot;In computing, a computer bus operating with double data rate (DDR) transfers data on both the rising and falling edges of the clock signal.[1][page needed] This is also known as double pumped, dual-pumped, and double transition.&quot; From Google scholar I found using &quot;double date rate&quot; and &quot;the rising and falling edges of the clock signal&quot;: &quot;For example, a double date rate (DDR) technique may be used, in which both the rising and falling edges of the clock signal are used to latch data.&quot;&lt;ref name=Qawami&gt;{{ cite journal
|author=S Qawami, S Eilert
|title=Writing to non-volatile memory during a volatile memory refresh cycle
|journal=US Patent
|month=
|year=2011
|volume=
|issue=7,944,764
|pages=
|url=https://www.google.com/patents/US7944764
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2016-04-20 }}&lt;/ref&gt; This informs me that on the certification exam something analogous, similar, or exactly phrased would be accepted as the correct answer to &quot;What is DDR?&quot;

4. [[IT Fundamentals/Virtualization|Virtualization]]: from Wikipedia on Cloud computing &quot;SureCloud computing, also on-demand computing, is a kind of Internet-based computing that provides shared processing resources and data to computers and other devices on demand.&quot; From Google scholar I found using &quot;cloud computing&quot; and &quot;shared processing resources and data&quot;: &quot;Cloud computing, also on-demand computing, is a kind of Internet-based computing that provides shared
processing resources and data to computers and other devices on demand.&quot;&lt;ref name=Sharma&gt;{{ cite journal
|author=MP Sharma, A Hirwe
|title=Implementation in Vehicular Communication with Various Approaches &amp; Techniques
|journal=International Journal of Scientific Engineering and Applied Science (IJSEAS)
|month=March
|volume=2
|issue=3
|publisher=ijseas.com
|location=
|year=2016
|url=http://ijseas.com/volume2/v2i3/ijseas20160350.pdf
|accessdate=2016-04-20 }}&lt;/ref&gt; The statement is referenced [25][24] to [R. Meireles, M. Boban, P. Steenkiste, O. Tonguz, and J. Barros, “Experimental study on the impact of vehicular obstructions in vanets,” in Vehicular Networking Conference (VNC), 2010 IEEE, pp. 338–345, IEEE, 2010.] and [Md Whaiduzzaman, Mehdi Sookhak , Abdullah Gani, Rajkumar Buyya, “A survey on vehicular cloud computing” , Journal of Network and Computer Applications.] respectively. Again, I would expect this answer would be successful on the certification exam.

9. [[IT Fundamentals/Commands and Scripting|Commands and Scripting]]: from Wikipedia &quot;Path (computing)&quot;: &quot;A path, the general form of the name of a file or directory, specifies a unique location in a file system.&quot; I found on Google Scholar using &quot;specifies a unique location in a file system&quot; and &quot;path&quot;: &quot;A “file path” specifies a unique location in a file system. A path points to a file system location by following the directory tree hierarchy expressed in a string of characters in which path components, separated by a delimiting character, represent each directory.&quot;&lt;ref name= Namir&gt;{{ cite journal
|author=Yoav Shalom Namir
|title=Method and system for archiving a document
|journal=US Patent Application
|month=7 August
|year=2014, priority date 27 November 2012
|volume=14
|issue=090,416
|pages=
|url=https://www.google.com/patents/US20140222763
|arxiv=
|bibcode=
|doi=
|pmid=
|accessdate=2016-04-20 }}&lt;/ref&gt;

12. [[IT Fundamentals/Security|Security]]: from Wikipedia &quot;Hardening (computing)&quot;: &quot;In computing, hardening is usually the process of securing a system by reducing its surface of vulnerability, which is larger when a system performs more functions; in principle a single-function system is more secure than a multipurpose one.&quot; Using &quot;reducing its surface of vulnerability&quot; and &quot;hardening&quot; on Google Scholar I found &quot;Operating system hardening is the process of securing an operating system by reducing its surface of vulnerability.&quot;&lt;ref name=Arnaud&gt;{{ cite book
|author=Jérôme Arnaud and Jean-Michel Rey
|title=How can cybersecurity be enhanced in existing substations minimizing impact on the automation and control system, In: ''Electricity Distribution''
|publisher=IET
|date=10 June 2013
|pages=1-4
|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6683456
|arxiv=
|bibcode=
|doi=10.1049/cp.2013.0853
|isbn=978-1-84919-732-8
|pmid=
|accessdate=2016-04-20 }}&lt;/ref&gt;

While this is by no means a thorough examination of the merits of the course and its potential to students, it does demonstrate that the creator has double checked on Wikipedia to make sure the correct and necessary information is being conveyed to students through perhaps the weakest link. Although the course is relatively new to Wikiversity, I endorse its being rated as a Featured resource. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 02:16, 21 April 2016 (UTC)

====References====
{{reflist}}

=== Motivation and emotion ===
[[Motivation and emotion]] is one of the longest run and most developed projects on wikiversity. Very high quality. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 23:07, 10 February 2016 (UTC)
:I've gone ahead and added [[Motivation and emotion]] as a featured course: [[Featured_content/20]] and bumped the FOTD counter: [[Template:FOTD/CALC]]. I've tried adding it the featured content tour, but isn't showing: [[Template:Featured Content/Nav]]. Seems to be something to with being at the end? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:54, 13 September 2022 (UTC)

=== Effective defense and ISIL ===
[[Effective defense and ISIL]] is a quality resource that thoroughly cites the sources used to present a neutral point of view on a topic currently in the news. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 20:26, 18 January 2016 (UTC)

=== The Crafting Freedom Project ===
[[The Crafting Freedom Project]] is an excellent resource in the public humanities. It tells the stories of how historic events have an impact on the everyday lives of people who are caught up in events beyond their control. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 21:10, 24 January 2016 (UTC)

=== Egyptian Verbal System (and its Vocalization) ===
[[Egyptian Verbal System (and its Vocalization)]] is one of the more fascinating projects that I've stumbled upon. It is surely a topic of rather idiosyncratic interest, but it is very well done. Resources on this subject would be difficult to find elsewhere. --[[User:Mu301|mikeu]] &lt;sup&gt;[[User talk:Mu301|talk]]&lt;/sup&gt; 22:15, 30 January 2016 (UTC)

== Places to go hunting for featured content ==
* [[:Category:Completed resources]]
* [[Completed courses list]]
* [http://www.google.com/search?hl=en&amp;q=+site:wikiversity.org+wikiversity&amp;ct=more-results Google search of wikiversity.org]
* [[Special:MostRevisions]] (NB: this only has data up to September 2007, so of limited current use).
* [http://stats.wikimedia.org/wikiversity/EN/TablesWikipediaArticleEditsEN.htm Most edited pages] (possibly far more out of date even than the above).
* [[Wikiversity:Participants]] - some of the most active participants are engaged in content development, so keep an eye on what they are producing.

== Most desired content ==

This section lists content which is most strongly desired by Wikiversity participants, but which falls far short of featured status. If you wish to create content which quickly becomes featured, then this is a good place to look for projects to work on.

=== French stream ===
[[French stream]]

* '''French'''. Compare [[French stream]] (people who have explicitly stated a desire to learn French) and [[:Category:French]]. This is a case where demand clearly outstrips supply. Just by providing a coherent set of French learning language resources, we would cater for visitors far better. --[[User:McCormack|McCormack]] 09:51, 18 May 2008 (UTC)

=== Spanish ===
[[Spanish]]

* '''Spanish'''. Ditto. Compare [[Spanish/Registration]] with [[Spanish]]. --[[User:McCormack|McCormack]] 09:56, 18 May 2008 (UTC)
**&lt;small&gt;Its my dream to find a wiki way to help in the area:(--[[User:Juan|Juan]] 09:11, 1 June 2008 (UTC)&lt;/small&gt;

== Content which was proposed and rejected ==

''Items placed here are periodically archived at [[/Archive/Delisted]].''

== See also ==
* [[Wikiversity:School and university projects]]
* [[:Category:Learning projects]]
* [[Wikiversity:Examples]] - started in 2006, this page lists examples of Wikiversity content, divided by type
* [[User:JWSchmidt/Blog/21 January 2007|Another list of portals]] with featured content
* [[Wikiversity:Top100|Top100]] 
* [[Wikiversity:Schools|Complete list of schools]] (?)
* [[/Archive/Delisted]]

== Related resources ==
* [[Educational Media Awareness Campaign]] - includes the Picture of The Day system.

[[Category:Wikiversity]]
[[Category:Wikiversity development]]
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    <title>Convolution</title>
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A '''convolution''' between two signals, &lt;math&gt;x(t)&lt;/math&gt; and &lt;math&gt;y(t)&lt;/math&gt;, is an operation defined as follows:

:&lt;math&gt;x(t)*y(t)=\int_{-\infty}^{+\infty} x(\tau)y(t-\tau)d\tau&lt;/math&gt;

The process of convolution is very useful in the time domain analysis of systems, because we can fully describe a system by its [[w:Impulse_response|impulse response]]. Let's consider the following system which operates on an input as &lt;math&gt;O\{\}&lt;/math&gt;, having characterized its impulse response by &lt;math&gt;o(t)&lt;/math&gt;:

:&lt;math&gt;x(t) \longrightarrow \begin{array}{ |c| }\hline O \{ \} \\ \hline\end{array} \longrightarrow y(t)&lt;/math&gt;

:&lt;math&gt;y(t)=O[x(t)]&lt;/math&gt;

:&lt;math&gt;y(t)=x(t)*o(t)&lt;/math&gt;


Put into other words, the output of a system in an instant &lt;math&gt;t&lt;/math&gt; can be written as a linear combination of past and future instants of the input and its impulse response:

:&lt;math&gt;y(t)=\int_{-\infty}^{+\infty} x(\tau)o(t-\tau)d\tau&lt;/math&gt;

==Discrete Convolution==
In discrete time there is no continuous time &lt;math&gt;x(t)&lt;/math&gt; but finite samples &lt;math&gt;x[n]&lt;/math&gt;. 

So the integral can be rewritten as a sum:

:&lt;math&gt;(x*y)[m]=\sum_{n=-\infty}^\infty x[m-n]*y[n]&lt;/math&gt;

To understand the convolution of finite length signals better, let's look at an example with the signals &lt;math&gt;x=[1, 2, 3]&lt;/math&gt; and &lt;math&gt;y=[6, 9]&lt;/math&gt;. 
&lt;pre&gt;
[ 1] * [6 9] = ?

[ 6 12 18  0]    // [1 2 3] * 6
[ 0  9 18 27]    // [1 2 3] * 9
-------------
[ 6 21 36 27]    // sum of the above
&lt;/pre&gt;

Note that the length of the output signal has the length &lt;math&gt;N + M - 1&lt;/math&gt; where &lt;math&gt;M&lt;/math&gt; is the length of &lt;math&gt;x&lt;/math&gt; and &lt;math&gt;N&lt;/math&gt; the length of &lt;math&gt;y&lt;/math&gt;.

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    <title>Economic Classroom Experiments</title>
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{{featured}}This page refers to information on economic classroom experiments and related material.

Numbers insist that an economic model of giving, can produce an economy of abundance in that, if all were to give consistently, a substantial amount, into, let's picture it as a river of abundance. What you do not need for right now goes to the river. And what you need when you need it comes from the river, for the most part. 
We see something similar to this in paying taxes to support the public welfare system. The problem is that these welfare systems that are in place, are terribly inefficient. And more money goes to paying employees of the system to manage the lesser amount of money actually going to public welfare.

I challenge anyone to run the numbers and prove the giving river wrong. Also, a challenge to anyone to say the public welfare system is not riddled with inefficiency...

==Why use experiments in teaching economics? ==
# They help students to understand an otherwise abstract model. In the [[w:Double auction|double auction]] experiment they experience, for example, how demand and supply drive the market towards equilibrium. It's learning by doing.
# To show that economic theory can work (for instance, in a [[w:Bertrand game|Bertrand game]]). This is important because students or the general public are often sceptical about the use of mathematical analysis in economics.
# To show that economic theory might not work (for instance, in an [[w:Ultimatum game|ultimatum game]]). This quickly leads to questions on the current frontier of our science. 
# An experiment can make it easier for students to grasp a threshold concept like [[w:Nash equilibrium|Nash equilibrium]].

==List of Experiments==
#[[Economic Classroom Experiments/The Twenty-Pound Auction|The Twenty pound auction]]
#[[Economic_Classroom_Experiments/The_Wallet_Game|The Wallet Game]]
#[[Economic_Classroom_Experiments/Ultimatum_Bargaining|The Ultimatum and the Dictator Bargaining Games]]
#[[Economic_Classroom_Experiments/Public_Goods|The Public Good Game]]
#[[Economic_Classroom_Experiments/Private_Value_Auctions|Private Value Auctions]]
#[[Economic_Classroom_Experiments/Insurance|The Insurance Game]]
#[[Economic_Classroom_Experiments/Currency_Attack|Currency Attack]]
#[[Economic Classroom Experiments/Bertrand Competition|Bertrand Competition]]
#[[Economic Classroom Experiments/American Call Option|American Call Option]]
#[[Economic Classroom Experiments/Diamond Dybvig Experiment|Diamond Dybvig Experiment]]
#[[Economic Classroom Experiments/Hold-Up Problem|Hold-Up Problem]]
#[[Economic Classroom Experiments/Kiyotaki Wright Hazlett Experiment|Kiyotaki Wright Hazlett Experiment]]
#[[Economic Classroom Experiments/Lemon Game|Lemon Game]]
#[[Economic Classroom Experiments/Miniconomy|Miniconomy]]
#[[Economic Classroom Experiments/Monty Hall Paradox|Monty Hall Paradox]]
#[[Economic Classroom Experiments/Network Externalities|Network Externalities]]
#[[Economic Classroom Experiments/Price Discrimination|Price Discrimination]]
#[[Economic Classroom Experiments/Team Draft|Team Draft]]
#[[Economic Classroom Experiments/Warren Buffett|Warren Buffett]]
#[[Economic_Classroom_Experiments/Guessing_Game|The Guessing Game]]
#[[Economic_Classroom_Experiments/Search|Search]]
#[[Economic_Classroom_Experiments/Pit_Market|Pit Market]]
# [http://socr.ucla.edu/htmls/SOCR_Experiments.html Complete List of Interactive Experiments]

==Useful Links and Related Literature==

{| class=&quot;prettytable&quot;
!resource
!description
|-
|[http://people.virginia.edu/%7Ecah2k/ Charlie Holt's Homepage] and [http://veconlab.econ.virginia.edu/admin.htm veconlab]
|Charlie Holt’s website has a variety computerized experiments. Students log in to an experiment via [http://veconlab.econ.virginia.edu/login.htm].&lt;br&gt;Simply type &quot;veconlab&quot; into google. The first link shown will be for the instructor to start an experiment. The second is for participating students to log in. You will need a log-in name. 
|-
|[http://www.aw-bc.com/catalog/academic/product/0,1144,0321419316,00.html Charlie Holt's book “Markets, Games, &amp; Strategic Behavior”]
|has many hand-run versions of his computerized experiments on veconlab.
|-
|[http://www.econport.org/econport/request?page=web_home Econport]
|has a beautifully written version of the double auction (Vernon Smith's basic demand- and supply curve experiment).&lt;br&gt;Important information on how to alter the parameters of the experiment is at [http://www.econport.org/econport/request?page=web_experiments_software_marketlink_config_customized]&lt;br&gt;The site also offers a very useful on-line handbook for micro economics.
|-
|[http://www.projects.ex.ac.uk/feele/LecturerStart.shtml FEELE]
|provides access to a set of computerized experiments.  You can quickly log in as a subject to try out various experimennts, both group-participation (playing against recorded data from a real-life session) and individual-progress (playing against the computer).  If you want to set up and run your own experiments, you need to register your email address to obtain a username and password. The site is very similar in purpose to Charlie's site and intended to complement it. 
|-
|[http://www.economicsnetwork.ac.uk/ The Economics Network, UK]
|Loads of useful information from Dr Wong on all aspects of teaching economics, including [http://www.economicsnetwork.ac.uk/themes/games.htm Classroom Experiments and Games].
|-
|[http://marcus.whitman.edu/%7Ehazlett/econ/ Denise Hazlett's Classroom Experiments]
|provides information for 7 handrun macro experiments. FEELE computerized two of them.
|-
|[http://website.fsu.edu/djcooper/teaching.html David J. Cooper's Experimental Economics Class Material]
| The site offers both links and a series of handrun classroom experiments some original and some standard.
|-
|[http://www.marietta.edu/%7Edelemeeg/expernom.html Classroom Expernomics]
|A web-based journal on classroom experiments published until 2003.
|-
|[http://www.marietta.edu/%7Edelemeeg/games/ Games Economists Play: Non-Computerized Classroom Experiments for College Economics by Greg Delemeester and Jurgen Brauer]
|One hundred and sixty classroom experiments described!
|-
|[http://www.marietta.edu/%7Edelemeeg/classroom.html Greg Delemeester's links to Classroom Experiments, Internet Experiments and Internet Simulation]
|Check for additional links.
|-
|[http://gametheory.tau.ac.il/ Rubinstein's Course in Game Theory]
|Plenty of questions on decision theory and game theory.  Very easy to use. Select your own problem set and let students work on it via the web.
|-
|[http://www.econ.ucsb.edu/%7Etedb/eep/eep.html Ted Bergstrom and John H. Miller's textbook &quot;Experiments with Economic Principles: Microeconomics&quot;]
|Experiments-based elementary microeconomics course. See note on ClassEx, below.
|-
|[https://econclassexperiments.com/  ClassEx    Freely available apps for using cell phones or laptops to run experiments from Bergstrom and Miller's Experiments with Economic Principles.]   
|-
|[http://www.moblab.com MobLab-- interactive social games for classrooms through mobile devices]
|Popular economic games on all major browsers, iPhone, iPad, and Android smartphones.
|-
|[http://www.aireconsim.com airECONsim, a &quot;long&quot; market game for teaching Industrial Organization]
|Highlights microeconomics notions such as marginal/average cost, variable/sunk costs, short run/long run costs, price elasticity of demand, demand shocks, impact of production capacity on price competition, oligopoly/monopoly and the logic behind competition, price discrimination, collusion, ... (also includes advanced features such as auctions for capacity or CO2 permits, mergers and takeovers, differentiation, ...)
|-
|[http://www.economics-games.com Economics Games, Free Multiplayer Online Games for Teaching Economics]
|Several short games for teaching economics (market games, prisoner's dilemma, public goods, Cournot and Stackelberg....). Students play with their smartphones, tablets or laptops.
|-
|[http://www.finecolab.com FinEcoLab, Free interactive Economics Games in French for tablets and laptops ]
|18 interactive games to teach concepts in financial education and economics in a playful, stimulating, meaningful and practical environment. FinÉcoLab is targeted at high school and college students. It provides teachers with a pedagogical guide. Students play with their tablets or laptops.
|}

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This is a collection of study problems related to rates of change.

== Example ==
a coned-shaped paper drinking cup is to be made to hold 27cu. cm. of water. Find the height and radius of the cup that will use the smallest amount of paper.

== Solution ==

First, we have to find a formula which relates the volume of the container, and the height. One possible formula is
:&lt;math&gt;V = \pi r^2 h \;\,.&lt;/math&gt;

We can put in the time dependence explicitly:
:&lt;math&gt;V(t) = \pi [r(t)]^2 h(t) \;\,.&lt;/math&gt;

So, differentiating with respect to time (using the product rule), we get

:&lt;math&gt;\frac{dV(t)}{dt} = \pi [r(t)]^2 \frac{dh(t)}{dt} + 2\pi r h \frac{dr(t)}{dt}&lt;/math&gt;

Now, one of the crucial observations here is that the radius of the container is not changing. So we know that

:&lt;math&gt;\frac{dr(t)}{dt} = 0&lt;/math&gt;

Hence,
:&lt;math&gt;\frac{dV(t)}{dt} = \pi [r(t)]^2 \frac{dh(t)}{dt}&lt;/math&gt;

Substituting in all our quantities, we can get the answer!


== Questions ==

* A ladder 5 m long is falling down along the side of a wall without slipping. When the top is 3 m from the ground, how fast is the end of the ladder moving away from the wall?

* A cylindrical cone is filled with water at a rate of 2 cm&lt;sup&gt;3&lt;/sup&gt;/s. When the height of the water is 10 cm, both the diameter and the height of the water is expanding at a rate of 1 cm/s. What is the slope of the cone?
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    <title>Privacy, Security, and Implied Mutual Exclusion</title>
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There are many lives. Each life is as the next, and each is observed by ever-vigilant eyes and ears, whose purpose is to safeguard against danger. A man, like any other man, lives a life like any other life. He sleeps, and his house is monitored for danger, lest he be disturbed. He awakens, and his actions are watched, lest he endanger himself or another. He is watched in the street, as he walks to the car, and he is watched in his car, again, for the safety of all concerned.

This man is watched, as all men are watched, for the safety of all men. If he were to commit a crime, he could be easily apprehended. If he were to be the victim of an accident or crime, he may be swiftly saved. His every gesture, expression, and word are perused in search of intent. It is hoped that, when he shows signs of danger, he may be apprehended before he has acted. Thus ensuring the safety of all concerned. The man, like all men, knows he is safe, because his neighbors are watched as well as he.

Why then, does he feel vulnerable? Why does he still feel unsafe?

In today's world it is accepted that privacy must be sacrificed for the sake of well-being and safety, both national and personal. People are told they are safer watched than alone, and that secrecy is the shield of those who intend harm. If someone has something to hide, they are of ill intent. &quot;After all, you have nothing to hide, do you comrade?&quot;

Unfortunately, the lives above are not works of fiction. They are a manifestation of reality. Humanity is now presented with a question of power and trust, and something must be decided and acted upon before this irreversible state becomes a universal norm, humanity must at least decide to do nothing, if this is that to which they aspire.

The United States has been watching telecommunications for decades both legally and illegally. (Poole) In the United Kingdom, it is estimated there are only 14 people for every surveillance camera. As dense as the surveillance is it is estimated that the average person is recorded on camera about 300 times in a single day. (George) Additionally, vehicle movements have been watched and recorded by a combination of GPS satellites and license plate reading cameras since 2006. (Connor) Possibly most foreboding is the increasing trend in proposed legislature toward data-mining. The Smith Data Retention Act has been cited as a prime example of this most disturbing tendency:

&quot;Sec. 6. Record Retention Requirements for Internet Service Providers.
(a) REGULATIONS.---Not later than 90 days after the date of the enactment of this section the   Attorney General shall issue regulation governing the retention of records by Internet Service  Providers. Such regulations shall, at minimum, require retention of records, such as the name and  address of the subscriber or registered user to whom an Internet Protocol address, user address, or  telephone number was assigned, in order to permit compliance with court orders that may require  production of such information.&quot;

Further provisions in the same bill effectively require ISPs and internet hosts to retain not only the specified information, but also hosted content for the use of law enforcement and judicial personnel. (Smith DRA)

Due to advances in telecommunications and information technology the availability of information, in both diversity and sheer volume, has reached a previously unfathomable level in recent years. Never before has so much information been available with so little effort in so little time. Humanity is no longer bound by the speed of physical travel, and subsequently new networks and systems have been formed as people have learned to cope with such an onslaught of data.

While the sheer scope of available knowledge is an academician's dream, it is a security nightmare. Privacy becomes sorely at risk as personal information, finances, even everyday communiques are transferred to a medium that is almost entirely public.

The mentality and openness are best surmised by this succinct statement. &quot;'The Internet treats censorship as though it were a malfunction and routes around it.' -John Gilmore&quot; (Barlow)

The migration of everyday life to this very open medium allows for those who would invade privacy, whether they be conmen or security forces, to do so with minimum effort and danger.

The same advances that have allowed humanity to move a piece of information from one side of the globe to another in a split second allow for the large-scale recording of what little isn't already resident in the digital world. Sensor technology, such as cameras, microphones, and scanners, is being employed everywhere for purposes legitimate and otherwise. In the age of information technology, anyone can see or hear anything on this planet.

With the vast resources at their disposal, nation-states are in a prime position to commit invasions of privacy, and many if not all have motive to do so. 

The government claims that in the face of threats such as terrorism, safety is dependent on the ability of law enforcement agencies to track and prevent criminal activity. However, this is in direct contradiction to a tenant long held among both military and civilian peoples, that information is among the most potent of weapons. Children have long been admonished, &quot;Don't talk to strangers,&quot; and Sun Tzu devoted over a tenth of his famous treatise to the use and warding of spies and scouts, even going so far as to state: &quot;Thus, what enables the wise sovereign and the good general to strike and conquer, and achieve things beyond the reach of ordinary men, is foreknowledge.&quot; (Giles XIII) Thus, there are two contending postulations concerning safety, that which exemplifies privacy and that which exemplifies openness.

&quot;The less you know about something, the harder it is to kill.&quot; This is the postulate behind the age-old doctrine we are all familiar with. This is the same assumption Sun Tzu made 26 centuries ago. The other assumption is that the more the government knows about, well, everything, the safer the citizens of that government are.

Obviously, one cannot withhold information about oneself, and subsequently ensure one's safety while simultaneously disclosing any and all information to another entity. It is simply not logically valid. Therefore, one of these statements must be incorrect.

The latter postulation is easily traceable to the first, on the grounds that the more knowledge, and therefore power a nation-state has, the better it can protect its people. However, power, being the potential of action, can also be used against the people. This can occur directly, in instances such as Stalin's crackdowns in Soviet Russia or McCarthyism in the United States, or indirectly, in instances where improper leadership imposes adverse conditions upon the populace.

Therefore, although the greater resources and coordination of an informed government can yield greater defense than simple non-disclosure of information, the assumption that well informed government is intrinsically protective is valid only under the assumption that the government in question holds the best-interests of its citizens as a priority.

It can be concluded given that our government is by nature transient in its intent, having elected (and therefore shifting) leadership in addition to other, more ambiguous, flaws, it cannot be held as a certainty that our government will always have the best interests of its citizens as its first priority. 

Given the capacity for information retrieval and abuse available to both our government and independent entities, it is important that humanity prevent the further development of an information infrastructure that is already large enough to allow power to fall into the hands of one who would use it adversely to public safety or progress. Privacy is a person's only shield against those who would cause them harm. To put it in the hands of another is to give that other control of one's life. The question is, can an institution be trusted with the lives of an entire nation?

Bibliography
Barlow, John Perry. “Censorship 2000.” On the Internet. 2000. ISOC. 26 March 2007 &lt;http://www,isoc.org.oti/articles/1000/barlow.html&gt;

Connor, Steve. “Britain Will Be First Country to Monitor Every Car Journey.” The Independent. 22 December 2005. 26 March 2007 &lt;http://news.independent.co.uk/uk/transport/article334686.exe&gt;

Giles, Lionel. Sun Tzu on the Art of War. 1994. Project Gutenburg, 26 March 2007. &lt;http://www.gutenburg.org/etext/132&gt;

“George Orwell, Big Brother Is Watching Your House.” This Is London. 31 March 2007. Evening Standard. 31 March 2007 &lt;http://www.thisislondon.co.uk&gt;

“&gt;&gt; Introduction to NSA/CSS.” 2007. National Security Agency. 26 March 2007 &lt;http://web.archive.org/20040307142240/www.nsa.gov/about/index.cfm&gt;

Poole, Patrick. “ECHELON: America’s Security Global Surveillance Network.” 2000. 26 March 2007 &lt;http://hly.hiwaay.net/~pspoole/echelon.html&gt;

United Kingdom of Great Britain and Northern Ireland. ACPO ANPR Steering Group, ANPR Strategy For Police Service

United Kingdom of Great Britain and Northern Ireland. ACPO National ANPR User Group, E.C.H.R, Data Protection &amp; RIPA Guidance Relating to the Police use of A.N.P.R.

United States of America. Rep. Smith, Smith Data Retention Act. 110th Congress, 1st Session. Washington D.C. 2007

[[Category:Papers]]</text>
      <sha1>c7j20lyf23jhpzt27etg4qomb1249f2</sha1>
    </revision>
  </page>
  <page>
    <title>MediaWiki:Gadget-popups.js</title>
    <ns>8</ns>
    <id>47646</id>
    <revision>
      <id>2810145</id>
      <parentid>2365582</parentid>
      <timestamp>2026-05-18T19:05:21Z</timestamp>
      <contributor>
        <username>WikiBayer</username>
        <id>2181512</id>
      </contributor>
      <origin>2810145</origin>
      <model>javascript</model>
      <format>text/javascript</format>
      <text bytes="246544" sha1="ccjy2a2nk6or0yp1zn8q6ri4sypjy88" xml:space="preserve">// STARTFILE: main.js
// **********************************************************************
// **                                                                  **
// **             changes to this file affect many users.              **
// **           please discuss on the talk page before editing         **
// **                                                                  **
// **********************************************************************
// **                                                                  **
// ** if you do edit this file, be sure that your editor recognizes it **
// ** as utf8, or the weird and wonderful characters in the namespaces **
// **   below will be completely broken. You can check with the show   **
// **            changes button before submitting the edit.            **
// **                      test: مدیا מיוחד Мэдыя                      **
// **                                                                  **
// **********************************************************************

//////////////////////////////////////////////////
// Globals
//
//&lt;nowiki&gt;
// Trying to shove as many of these as possible into the pg (popup globals) object
function pg(){}; // dummy to stop errors
window.pg = {
	re: {},               // regexps
	ns: {},               // namespaces
	string: {},           // translatable strings
	wiki: {},             // local site info
	misc: {},             // YUCK PHOOEY
	option: {},           // options, see newOption etc
	optionDefault: {},    // default option values
	flag: {},             // misc flags
	cache: {},            // page and image cache
	structures: {},       // navlink structures
	timer: {},            // all sorts of timers (too damn many)
	counter: {},          // .. and all sorts of counters
	current: {},          // state info
	endoflist: null
};
window.pop = {          // wrap various functions in here
	init: {},
	util: {},
	endoflist: null
};
function popupsReady() {
	if (!window.pg) { return false; }
	if (!pg.flag) { return false; }
	if (!pg.flag.finishedLoading) { return false; }
	return true;
}

/// Local Variables: ///
/// mode:c ///
/// End: ///
// ENDFILE: main.js
// STARTFILE: actions.js
function setupTooltips(container, remove, force, popData) {
	log('setupTooltips, container='+container+', remove='+remove);
	if (!container) {
//&lt;NOLITE&gt;
		// the main initial call
		if (getValueOf('popupOnEditSelection') &amp;&amp; window.doSelectionPopup &amp;&amp; document &amp;&amp; document.editform &amp;&amp; document.editform.wpTextbox1) {
			document.editform.wpTextbox1.onmouseup=doSelectionPopup;
		}
//&lt;/NOLITE&gt;
		// article/content is a structure-dependent thing
		container = defaultPopupsContainer();
	}

	if (!remove &amp;&amp; !force &amp;&amp; container.ranSetupTooltipsAlready) { return; }
	container.ranSetupTooltipsAlready = !remove;

	var anchors;
	anchors=container.getElementsByTagName('A');
	setupTooltipsLoop(anchors, 0, 250, 100, remove, popData);
}

function defaultPopupsContainer() {
    if (getValueOf('popupOnlyArticleLinks')) {
	    return document.getElementById('mw_content') || 
		    document.getElementById('content') ||
		    document.getElementById('article') || document;
    }
    return  document;
}

function setupTooltipsLoop(anchors,begin,howmany,sleep, remove, popData) {
	log(simplePrintf('setupTooltipsLoop(%s,%s,%s,%s,%s)', arguments));
	var finish=begin+howmany;
	var loopend = min(finish, anchors.length);
	var j=loopend - begin;
	log ('setupTooltips: anchors.length=' + anchors.length + ', begin=' + begin +
	     ', howmany=' + howmany + ', loopend=' + loopend + ', remove=' + remove);
	var doTooltip= remove ? removeTooltip : addTooltip;
	// try a faster (?) loop construct
	if (j &gt; 0) {
		do {
			var a=anchors[loopend - j];
			if (typeof a=='undefined' || !a || !a.href) {
				log('got null anchor at index ' + loopend - j);
				continue;
			}
			doTooltip(a, popData);
		} while (--j);
	}
	if (finish &lt; anchors.length) {
		setTimeout(function() {
				setupTooltipsLoop(anchors,finish,howmany,sleep,remove,popData);},
			sleep);
	} else {
		if ( !remove &amp;&amp; ! getValueOf('popupTocLinks')) { rmTocTooltips(); }
		pg.flag.finishedLoading=true;
	}
}

// eliminate popups from the TOC
// This also kills any onclick stuff that used to be going on in the toc
function rmTocTooltips() {
	var toc=document.getElementById('toc');
	if (toc) {
		var tocLinks=toc.getElementsByTagName('A');
		var tocLen = tocLinks.length;
		for (j=0; j&lt;tocLen; ++j) {
			removeTooltip(tocLinks[j], true);
		}
	}
}

function addTooltip(a, popData) {
	if ( !isPopupLink(a) ) { return; }
	a.onmouseover=mouseOverWikiLink;
	a.onmouseout= mouseOutWikiLink;
	a.onmousedown = killPopup;
	a.hasPopup = true;
	a.popData = popData;
}

function removeTooltip(a) {
	if ( !a.hasPopup ) { return; }
	a.onmouseover = null;
	a.onmouseout = null;
	if (a.originalTitle) { a.title = a.originalTitle; }
	a.hasPopup=false;
}

function removeTitle(a) {
	a.title='';
	if (a.originalTitle) { return; }
	a.originalTitle=a.title;
}

function restoreTitle(a) {
	if ( a.title || !a.originalTitle ) { return; }
	a.title = a.originalTitle;
}

function registerHooks(np) {
	var popupMaxWidth=getValueOf('popupMaxWidth');

	if (typeof popupMaxWidth == 'number') {
		var setMaxWidth = function () {
			np.mainDiv.style.maxWidth = popupMaxWidth + 'px';
			np.maxWidth = popupMaxWidth;

            try {
				// hack for IE
				// see http://www.svendtofte.com/code/max_width_in_ie/
				// use setExpression as documented here on msdn: http://tinyurl dot com/dqljn
	
				if (np.mainDiv.style.setExpression) {
					np.mainDiv.style.setExpression(
						'width', 'document.body.clientWidth &gt; ' +
						popupMaxWidth + ' ? &quot;' +popupMaxWidth + 'px&quot;: &quot;auto&quot;');
				}
            }
            catch (errors) {
            	errlog( &quot;Running on IE8 are we not?: &quot; + errors );
            }
		};
		np.addHook(setMaxWidth, 'unhide', 'before');
	}
//&lt;NOLITE&gt;
	if (window.addPopupShortcuts &amp;&amp; window.rmPopupShortcuts) {
	    np.addHook(addPopupShortcuts, 'unhide', 'after');
	    np.addHook(rmPopupShortcuts, 'hide', 'before');
	}
//&lt;/NOLITE&gt;
}


function mouseOverWikiLink(evt) {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	if (!evt &amp;&amp; window.event) {evt=window.event}
	return mouseOverWikiLink2(this, evt);
}

function footnoteTarget(a) {
	var aTitle=Title.fromAnchor(a);
	// We want &quot;.3A&quot; rather than &quot;%3A&quot; or &quot;?&quot; here, so use the anchor property directly
	var anch = aTitle.anchor;
	if ( ! /^(cite_note-|_note-|endnote)/.test(anch) ) { return false;	}

	var lTitle=Title.fromURL(location.href);
	if ( lTitle.toString(true) != aTitle.toString(true) ) {	return false; }

	var el=document.getElementById(anch);
	while ( el &amp;&amp; typeof el.nodeName == 'string') {
		var nt = el.nodeName.toLowerCase();
		if ( nt == 'li' ) { return el; }
		else if ( nt == 'body' ) { return false; }
		else if ( el.parentNode ) { el=el.parentNode; }
		else { return false; }
	}
	return false;
}

function footnotePreview(x, navpop) {
	setPopupHTML('&lt;hr&gt;' + x.innerHTML, 'popupPreview',  navpop.idNumber,
		     getValueOf('popupSubpopups') ? function() {
		setupTooltips(document.getElementById('popupPreview' + navpop.idNumber));
	} : null);
}

// var modid=0;
// if(!window.opera) { window.opera={postError: console.log}; }

function modifierKeyHandler(a) {
	return function(evt) {
		//		opera.postError('modifierKeyHandler called' + (++modid));
		//		opera.postError(''+evt + modid);
		//		for (var i in evt) {
		//			opera.postError('' + modid + ' ' + i + ' ' + evt[i]);
		//		}
		//		opera.postError(''+evt.ctrlKey + modid);
		var mod=getValueOf('popupModifier');
		if (!mod) { return true; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
		//		opera.postError('And now....'+modid);
		//		opera.postError(''+evt+modid);
		//		opera.postError(''+evt.ctrlKey+modid);

		var modPressed = modifierPressed(evt);
		var action = getValueOf('popupModifierAction');

		// FIXME: probable bug - modifierPressed should be modPressed below?
		if ( action == 'disable' &amp;&amp; modifierPressed ) { return true; }
		if ( action == 'enable' &amp;&amp; !modifierPressed ) { return true; }

		mouseOverWikiLink2(a, evt);
	};
}

function modifierPressed(evt) {
		var mod=getValueOf('popupModifier');
		if (!mod) { return false; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
//		opera.postError('And now....'+modid);
//		opera.postError(''+evt+modid);
//		opera.postError(''+evt.ctrlKey+modid);

		return ( evt &amp;&amp; mod &amp;&amp; evt[mod.toLowerCase() + 'Key'] );

}

function dealWithModifier(a,evt) {
	if (!getValueOf('popupModifier')) { return false; }
	var action = getValueOf('popupModifierAction');
	if ( action == 'enable' &amp;&amp; !modifierPressed(evt) ||
	     action == 'disable' &amp;&amp; modifierPressed(evt) ) {
		// if the modifier is needed and not pressed, listen for it until
		// we mouseout of this link.
		restoreTitle(a);
		var addHandler='addEventListener';
		var rmHandler='removeEventListener';
		var on='';
		if (!document.addEventListener) {
			addHandler='attachEvent';
			rmHandler='detachEvent';
			on='on';
		}
		if (!document[addHandler]) { // forget it
			return;
		}

		a.modifierKeyHandler=modifierKeyHandler(a);

		switch (action) {
		case 'enable':
			document[addHandler](on+'keydown', a.modifierKeyHandler, false);
			a[addHandler](on+'mouseout', function() {
					document[rmHandler](on+'keydown',
							    a.modifierKeyHandler, false);
				}, true);
			break;
		case 'disable':
			document[addHandler](on+'keyup', a.modifierKeyHandler, false);
		}

		return true;
	}
	return false;
}

function mouseOverWikiLink2(a, evt) {
	if (dealWithModifier(a,evt)) { return; }
	if ( getValueOf('removeTitles') ) { removeTitle(a); }
	if ( a==pg.current.link &amp;&amp; a.navpopup &amp;&amp; a.navpopup.isVisible() ) { return; }
	pg.current.link=a;

	if (getValueOf('simplePopups') &amp;&amp; pg.option.popupStructure===null) {
		// reset *default value* of popupStructure
		setDefault('popupStructure', 'original');
	}

	var article=(new Title()).fromAnchor(a);
	// set global variable (ugh) to hold article (wikipage)
	pg.current.article = article;

	if (!a.navpopup) {
		// FIXME: this doesn't behave well if you mouse out of a popup
		// directly into a link with the same href
		if (pg.current.linksHash[a.href] &amp;&amp; false) {
			a.navpopup = pg.current.linksHash[a.href];
		}
		else {
			a.navpopup=newNavpopup(a, article);
			pg.current.linksHash[a.href] = a.navpopup;
			pg.current.links.push(a);
		}
	}
	if (a.navpopup.pending===null || a.navpopup.pending!==0) {
		// either fresh popups or those with unfinshed business are redone from scratch
		simplePopupContent(a, article);
	}
	a.navpopup.showSoonIfStable(a.navpopup.delay);

	getValueOf('popupInitialWidth');

	clearInterval(pg.timer.checkPopupPosition);
	pg.timer.checkPopupPosition=setInterval(checkPopupPosition, 600);

	if(getValueOf('simplePopups')) {
		if (getValueOf('popupPreviewButton') &amp;&amp; !a.simpleNoMore) {
			var d=document.createElement('div');
			d.className='popupPreviewButtonDiv';
			var s=document.createElement('span');
			d.appendChild(s);
			s.className='popupPreviewButton';
			s['on' + getValueOf('popupPreviewButtonEvent')] = function() {
				a.simpleNoMore=true;
				nonsimplePopupContent(a,article);
			}
			s.innerHTML=popupString('show preview');
			setPopupHTML(d, 'popupPreview', a.navpopup.idNumber);
		}
		return;
	}

	if (a.navpopup.pending!==0 ) {
	    nonsimplePopupContent(a, article);
	}
}

// simplePopupContent: the content that is shown even when simplePopups is true
function simplePopupContent(a, article) {
	/* FIXME hack */ a.navpopup.hasPopupMenu=false;
	a.navpopup.setInnerHTML(popupHTML(a));
	fillEmptySpans({navpopup:a.navpopup});

	if (getValueOf('popupDraggable'))
	{
		var dragHandle = getValueOf('popupDragHandle') || null;
		if (dragHandle &amp;&amp; dragHandle != 'all') {
			dragHandle += a.navpopup.idNumber;
		}
		setTimeout(function(){a.navpopup.makeDraggable(dragHandle);}, 150);
	}

//&lt;NOLITE&gt;
	if (getValueOf('popupRedlinkRemoval') &amp;&amp; a.className=='new') {
		setPopupHTML('&lt;br&gt;'+popupRedlinkHTML(article), 'popupRedlink', a.navpopup.idNumber);
	}
//&lt;/NOLITE&gt;
}

function debugData(navpopup) {
	if(getValueOf('popupDebugging') &amp;&amp; navpopup.idNumber) {
		setPopupHTML('idNumber='+navpopup.idNumber + ', pending=' + navpopup.pending,
			     'popupError', navpopup.idNumber);
	}
}

function newNavpopup(a, article) {
	var navpopup = new Navpopup();
	navpopup.fuzz=5;
	navpopup.delay=getValueOf('popupDelay')*1000;
	// increment global counter now
	navpopup.idNumber = ++pg.idNumber;
	navpopup.parentAnchor = a;
	navpopup.parentPopup = (a.popData &amp;&amp; a.popData.owner);
	navpopup.article = article;
	registerHooks(navpopup);
	return navpopup;
}


function nonsimplePopupContent(a, article) {
	var diff=null, history=null;
	var params=parseParams(a.href);
	var oldid=(typeof params.oldid=='undefined' ? null : params.oldid);
//&lt;NOLITE&gt;
	if(getValueOf('popupPreviewDiffs') &amp;&amp; window.loadDiff) {
		diff=params.diff;
	}
	if(getValueOf('popupPreviewHistory')) {
		history=(params.action=='history');
	}
//&lt;/NOLITE&gt;
	a.navpopup.pending=0;
	var x;
	
	if (x=footnoteTarget(a)) {
		footnotePreview(x, a.navpopup);
//&lt;NOLITE&gt;
	} else if ( diff || diff === 0 ) {
		loadDiff(article, oldid, diff, a.navpopup);
	} else if ( history ) {
		loadAPIPreview('history', article, a.navpopup);
	} else if ( pg.re.contribs.test(a.href) ) {
		loadAPIPreview('contribs', article, a.navpopup);
	} else if ( pg.re.backlinks.test(a.href) ) {
		loadAPIPreview('backlinks', article, a.navpopup);
    } else if ( // FIXME should be able to get all preview combinations with options
		article.namespaceId()==pg.nsImageId &amp;&amp;
		( getValueOf('imagePopupsForImages') || ! anchorContainsImage(a) )
		) {
		loadAPIPreview('imagepagepreview', article, a.navpopup);
		loadImage(article, a.navpopup);
//&lt;/NOLITE&gt;
	} else {
		if (article.namespaceId() == pg.nsCategoryId &amp;&amp;
				getValueOf('popupCategoryMembers')) {
			loadAPIPreview('category', article, a.navpopup);
		} else if ((article.namespaceId() == pg.nsUserId || article.namespaceId() == pg.nsUsertalkId) &amp;&amp;
				getValueOf('popupUserInfo')) {
			loadAPIPreview('userinfo', article, a.navpopup);
		}
		startArticlePreview(article, oldid, a.navpopup);
	}
}

function pendingNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending===null) { navpop.pending=0; }
	++navpop.pending;
	debugData(navpop);
}

function completedNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending) { --navpop.pending; }
	debugData(navpop);
}

function startArticlePreview(article, oldid, navpop) {
	navpop.redir=0;
	loadPreview(article, oldid, navpop);
}

function loadPreview(article, oldid, navpop) {
	pendingNavpopTask(navpop);
	if (!navpop.redir) { navpop.originalArticle=article; }
	if (!navpop.visible &amp;&amp; getValueOf('popupLazyDownloads')) {
		var id=(navpop.redir) ? 'DOWNLOAD_PREVIEW_REDIR_HOOK' : 'DOWNLOAD_PREVIEW_HOOK';
		navpop.addHook(function() {
				getWiki(article, insertPreview, oldid, navpop);
				return true; }, 'unhide', 'before', id);
	} else {
		getWiki(article, insertPreview, oldid, navpop);
	}
}

function loadPreviewFromRedir(redirMatch, navpop) {
	// redirMatch is a regex match
	var target = new Title().fromWikiText(redirMatch[2]);
	// overwrite (or add) anchor from original target
	// mediawiki does overwrite; eg [[User:Lupin/foo3#Done]]
	if ( navpop.article.anchor ) { target.anchor = navpop.article.anchor; }
	var trailingRubbish=redirMatch[4];
	navpop.redir++;
	navpop.redirTarget=target;
//&lt;NOLITE&gt;
	if (window.redirLink) {
		var warnRedir = redirLink(target, navpop.article);
		setPopupHTML(warnRedir, 'popupWarnRedir', navpop.idNumber);
	}
//&lt;/NOLITE&gt;
	navpop.article=target;
	fillEmptySpans({redir: true, redirTarget: target, navpopup:navpop});
	return loadPreview(target, null,  navpop);
}

function insertPreview(download) {
	if (!download.owner) { return; }

	var redirMatch = pg.re.redirect.exec(download.data);
	if (download.owner.redir===0 &amp;&amp; redirMatch) {
		completedNavpopTask(download.owner);
		loadPreviewFromRedir(redirMatch, download.owner);
		return;
	}

	if (download.owner.visible || !getValueOf('popupLazyPreviews')) {
	    insertPreviewNow(download);
	} else {
		var id=(download.owner.redir) ? 'PREVIEW_REDIR_HOOK' : 'PREVIEW_HOOK';
		download.owner.addHook( function(){insertPreviewNow(download); return true;},
					'unhide', 'after', id );
	}
}

function insertPreviewNow(download) {
	if (!download.owner) { return; }
	var wikiText=download.data;
	var navpop=download.owner;
	completedNavpopTask(navpop);
	var art=navpop.redirTarget || navpop.originalArticle;

//&lt;NOLITE&gt;
	makeFixDabs(wikiText, navpop);
	if (getValueOf('popupSummaryData') &amp;&amp; window.getPageInfo) {
		var info=getPageInfo(wikiText, download);
		setPopupTrailer(getPageInfo(wikiText, download), navpop.idNumber);
	}

	var imagePage='';
	if (art.namespaceId()==pg.nsImageId) { imagePage=art.toString(); }
	else { imagePage=getValidImageFromWikiText(wikiText); }
	if(imagePage) { loadImage(Title.fromWikiText(imagePage), navpop); }
//&lt;/NOLITE&gt;

	if (getValueOf('popupPreviews')) { insertArticlePreview(download, art, navpop); }

}

function insertArticlePreview(download, art, navpop) {
	if (download &amp;&amp; typeof download.data == typeof ''){
		if (art.namespaceId()==pg.nsTemplateId &amp;&amp; getValueOf('popupPreviewRawTemplates')) {
			// FIXME compare/consolidate with diff escaping code for wikitext
			var h='&lt;hr&gt;&lt;tt&gt;' + download.data.entify().split('\\n').join('&lt;br&gt;\\n') + '&lt;/tt&gt;';
			setPopupHTML(h, 'popupPreview', navpop.idNumber);
		}
		else {
			var p=prepPreviewmaker(download.data, art, navpop);
			p.showPreview();
		}
	}
}

function prepPreviewmaker(data, article, navpop) {
	// deal with tricksy anchors
	var d=anchorize(data, article.anchorString());
	var urlBase=joinPath([pg.wiki.articlebase, article.urlString()]);
	var p=new Previewmaker(d, urlBase, navpop);
	return p;
}


// Try to imitate the way mediawiki generates HTML anchors from section titles
function anchorize(d, anch) {
	if (!anch) { return d; }
	var anchRe=RegExp('(?:=+\\s*' + literalizeRegex(anch).replace(/[_ ]/g, '[_ ]') + '\\s*=+|\\{\\{\\s*'+getValueOf('popupAnchorRegexp')+'\\s*(?:\\|[^|}]*)*?\\s*'+literalizeRegex(anch)+'\\s*(?:\\|[^}]*)?\}\})');
	var match=d.match(anchRe);
	if(match &amp;&amp; match.length &gt; 0 &amp;&amp; match[0]) { return d.substring(d.indexOf(match[0])); }

	// now try to deal with == foo [[bar|baz]] boom == -&gt; #foo_baz_boom
	var lines=d.split('\n');
	for (var i=0; i&lt;lines.length; ++i) {
		lines[i]=lines[i].replace(RegExp('[[]{2}([^|\\]]*?[|])?(.*?)[\\]]{2}', 'g'), '$2')
			.replace(/'''([^'])/g, '$1').replace(RegExp(&quot;''([^'])&quot;, 'g'), '$1');
		if (lines[i].match(anchRe)) {
			return d.split('\n').slice(i).join('\n').replace(RegExp('^[^=]*'), '');
		}
	}
	return d;
}

function killPopup() {
	if (getValueOf('popupShortcutKeys') &amp;&amp; window.rmPopupShortcuts) { rmPopupShortcuts(); }
	if (!pg) { return; }
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp; pg.current.link.navpopup.banish();
	pg.current.link=null;
	abortAllDownloads();
	if (pg.timer.checkPopupPosition !== null) {
		clearInterval(pg.timer.checkPopupPosition);
		pg.timer.checkPopupPosition=null;
	}
	return true; // preserve default action
}
// ENDFILE: actions.js
// STARTFILE: domdrag.js
/**
   @fileoverview
   The {@link Drag} object, which enables objects to be dragged around.

   &lt;pre&gt;
   *************************************************
   dom-drag.js
   09.25.2001
   www.youngpup.net
   **************************************************
   10.28.2001 - fixed minor bug where events
   sometimes fired off the handle, not the root.
   *************************************************
   Pared down, some hooks added by [[User:Lupin]]

   Copyright Aaron Boodman.
   Saying stupid things daily since March 2001.
   &lt;/pre&gt;
*/

/**
   Creates a new Drag object. This is used to make various DOM elements draggable.
   @constructor
*/
function Drag () {
	/**
	   Condition to determine whether or not to drag. This function should take one parameter, an Event.
	   To disable this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.startCondition = null;
	/**
	   Hook to be run when the drag finishes. This is passed the final coordinates of
	   the dragged object (two integers, x and y). To disables this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.endHook = null;
}

/**
   Gets an event in a cross-browser manner.
   @param {Event} e
   @private
*/
Drag.prototype.fixE = function(e) {
	if (typeof e == 'undefined') { e = window.event; }
	if (typeof e.layerX == 'undefined') { e.layerX = e.offsetX; }
	if (typeof e.layerY == 'undefined') { e.layerY = e.offsetY; }
	return e;
};
/**
   Initialises the Drag instance by telling it which object you want to be draggable, and what you want to drag it by.
   @param {DOMElement} o The &quot;handle&quot; by which &lt;code&gt;oRoot&lt;/code&gt; is dragged.
   @param {DOMElement} oRoot The object which moves when &lt;code&gt;o&lt;/code&gt; is dragged, or &lt;code&gt;o&lt;/code&gt; if omitted.
*/
Drag.prototype.init = function(o, oRoot) {
	var dragObj      = this;
	this.obj = o;
	o.onmousedown    = function(e) { dragObj.start.apply( dragObj, [e]); };
	o.dragging       = false;
	o.popups_draggable      = true;
	o.hmode          = true;
	o.vmode          = true;

	o.root = oRoot &amp;&amp; oRoot !== null ? oRoot : o ;

	if (isNaN(parseInt(o.root.style.left, 10))) { o.root.style.left   = &quot;0px&quot;; }
	if (isNaN(parseInt(o.root.style.top,  10))) { o.root.style.top    = &quot;0px&quot;; }

	o.root.onthisStart  = function(){};
	o.root.onthisEnd    = function(){};
	o.root.onthis       = function(){};
};

/**
   Starts the drag.
   @private
   @param {Event} e
*/
Drag.prototype.start = function(e) {
	var o = this.obj; // = this;
	e = this.fixE(e);
	if (this.startCondition &amp;&amp; !this.startCondition(e)) { return; }
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10);
	o.root.onthisStart(x, y);

	o.lastMouseX    = e.clientX;
	o.lastMouseY    = e.clientY;

	var dragObj      = this;
	o.onmousemoveDefault    = document.onmousemove;
	o.dragging              = true;
	document.onmousemove    = function(e) { dragObj.drag.apply( dragObj, [e] ); };
	document.onmouseup      = function(e) { dragObj.end.apply( dragObj, [e] ); };
	return false;
};
/**
   Does the drag.
   @param {Event} e
   @private
*/
Drag.prototype.drag = function(e) {
	e = this.fixE(e);
	var o = this.obj;

	var ey    = e.clientY;
	var ex    = e.clientX;
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10 );
	var nx, ny;

	nx = x + ((ex - o.lastMouseX) * (o.hmode ? 1 : -1));
	ny = y + ((ey - o.lastMouseY) * (o.vmode ? 1 : -1));

	this.obj.root.style[o.hmode ? &quot;left&quot; : &quot;right&quot;] = nx + &quot;px&quot;;
	this.obj.root.style[o.vmode ? &quot;top&quot; : &quot;bottom&quot;] = ny + &quot;px&quot;;
	this.obj.lastMouseX    = ex;
	this.obj.lastMouseY    = ey;

	this.obj.root.onthis(nx, ny);
	return false;
};

/**
   Ends the drag.
   @private
*/
Drag.prototype.end = function()  {
	document.onmousemove=this.obj.onmousemoveDefault;
	document.onmouseup   = null;
	this.obj.dragging    = false;
	if (this.endHook) {
		this.endHook( parseInt(this.obj.root.style[this.obj.hmode ? &quot;left&quot; : &quot;right&quot;], 10),
			      parseInt(this.obj.root.style[this.obj.vmode ? &quot;top&quot; : &quot;bottom&quot;], 10));
	}
};
// ENDFILE: domdrag.js
// STARTFILE: structures.js
//&lt;NOLITE&gt;
pg.structures.original={};
pg.structures.original.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle',
		'popupData', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks',
			       'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
pg.structures.original.popupRedirSpans=function () {
	return ['popupRedir', 'popupWarnRedir', 'popupRedirTopLinks',
		'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'];
};
pg.structures.original.popupTitle=function (x) {
	log ('defaultstructure.popupTitle');
	if (!getValueOf('popupNavLinks')) {
		return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	}
	return '';
};
pg.structures.original.popupTopLinks=function (x) {
	log ('defaultstructure.popupTopLinks');
	if (getValueOf('popupNavLinks')) { return navLinksHTML(x.article, x.hint, x.params); }
	return '';
};
pg.structures.original.popupImage=function(x) {
	log ('original.popupImage, x.article='+x.article+', x.navpop.idNumber='+x.navpop.idNumber);
	return imageHTML(x.article, x.navpop.idNumber);
};
pg.structures.original.popupRedirTitle=pg.structures.original.popupTitle;
pg.structures.original.popupRedirTopLinks=pg.structures.original.popupTopLinks;


function copyStructure(oldStructure, newStructure) {
	pg.structures[newStructure]={};
	for (var prop in pg.structures[oldStructure]) {
		pg.structures[newStructure][prop]=pg.structures[oldStructure][prop];
	}
}

copyStructure('original', 'nostalgia');
pg.structures.nostalgia.popupTopLinks=function(x)  {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;';
	str+='if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{'
	+ editstr + '}'
	var historystr='&lt;&lt;history|shortcut=h&gt;&gt;';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;';
	str += 'if(admin){&lt;br&gt;}else{*}&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){*&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*' +
	'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;}';
	return navlinkStringToHTML(str, x.article, x.params);
};
pg.structures.nostalgia.popupRedirTopLinks=pg.structures.nostalgia.popupTopLinks;

/** -- fancy -- **/
copyStructure('original', 'fancy');
pg.structures.fancy.popupTitle=function (x) {
	return navlinkStringToHTML('&lt;font size=+0&gt;&lt;&lt;mainlink&gt;&gt;&lt;/font&gt;',x.article,x.params);
};
pg.structures.fancy.popupTopLinks=function(x) {
	var hist='&lt;&lt;history|shortcut=h|hist&gt;&gt;|&lt;&lt;lastEdit|shortcut=/|last&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|eds&gt;&gt;}';
	var watch='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';
	var move='&lt;&lt;move|shortcut=m|move&gt;&gt;';
	return navlinkStringToHTML('if(talk){' +
				   '&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;new|shortcut=+|+&gt;&gt;*' + hist + '*' +
				   '&lt;&lt;article|shortcut=a&gt;&gt;|&lt;&lt;editArticle|edit&gt;&gt;' + '*' + watch + '*' + move +
				   '}else{&lt;&lt;edit|shortcut=e&gt;&gt;*' + hist +
				   '*&lt;&lt;talk|shortcut=t|&gt;&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;' +
				   '*' + watch + '*' + move+'}&lt;br&gt;', x.article, x.params);
};
pg.structures.fancy.popupOtherLinks=function(x) {
	var admin='&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d|del&gt;&gt;';
	var user='&lt;&lt;contribs|shortcut=c&gt;&gt;if(wikimedia){|&lt;&lt;count|shortcut=#|#&gt;&gt;}';
	user+='if(ipuser){|&lt;&lt;arin&gt;&gt;}else{*&lt;&lt;email|shortcut=E|'+
	popupString('email')+'&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}';

	var normal='&lt;&lt;whatLinksHere|shortcut=l|links here&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r|related&gt;&gt;';
	return navlinkStringToHTML('&lt;br&gt;if(user){' + user + '*}if(admin){'+admin+'if(user){&lt;br&gt;}else{*}}' + normal,
				   x.article, x.params);
};
pg.structures.fancy.popupRedirTitle=pg.structures.fancy.popupTitle;
pg.structures.fancy.popupRedirTopLinks=pg.structures.fancy.popupTopLinks;
pg.structures.fancy.popupRedirOtherLinks=pg.structures.fancy.popupOtherLinks;


/** -- fancy2 -- **/
// hack for [[User:MacGyverMagic]]
copyStructure('fancy', 'fancy2');
pg.structures.fancy2.popupTopLinks=function(x) { // hack out the &lt;br&gt; at the end and put one at the beginning
	return '&lt;br&gt;'+pg.structures.fancy.popupTopLinks(x).replace(RegExp('&lt;br&gt;$','i'),'');
};
pg.structures.fancy2.popupLayout=function () { // move toplinks to after the title
	return ['popupError', 'popupImage', 'popupTitle', 'popupData', 'popupTopLinks', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};

/** -- menus -- **/
copyStructure('original', 'menus');
pg.structures.menus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
function toggleSticky(uid) {
	var popDiv=document.getElementById('navpopup_maindiv'+uid);
	if (!popDiv) { return; }
	if (!popDiv.navpopup.sticky) { popDiv.navpopup.stick(); }
	else {
		popDiv.navpopup.unstick();
		popDiv.navpopup.hide();
	}
}
pg.structures.menus.popupTopLinks = function (x, shorter) {
	// FIXME maybe this stuff should be cached
	var s=[];
	var dropdiv='&lt;div class=&quot;popup_drop&quot;&gt;';
	var enddiv='&lt;/div&gt;';
	var endspan='&lt;/span&gt;';
	var hist='&lt;&lt;history|shortcut=h&gt;&gt;';
	if (!shorter) { hist = '&lt;menurow&gt;' + hist +
			'|&lt;&lt;historyfeed|rss&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E&gt;&gt;}&lt;/menurow&gt;'; }
	var lastedit='&lt;&lt;lastEdit|shortcut=/|show last edit&gt;&gt;';
	var jsHistory='&lt;&lt;lastContrib|last set of edits&gt;&gt;&lt;&lt;sinceMe|changes since mine&gt;&gt;';
	var linkshere='&lt;&lt;whatLinksHere|shortcut=l|what links here&gt;&gt;';
	var related='&lt;&lt;relatedChanges|shortcut=r|related changes&gt;&gt;';
	var search='&lt;menurow&gt;&lt;&lt;search|shortcut=s&gt;&gt;if(wikimedia){|&lt;&lt;globalsearch|shortcut=g|global&gt;&gt;}' +
	'|&lt;&lt;google|shortcut=G|web&gt;&gt;&lt;/menurow&gt;';
	var watch='&lt;menurow&gt;&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;&lt;/menurow&gt;';
	var protect='&lt;menurow&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|' +
	'&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;&lt;/menurow&gt;';
	var del='&lt;menurow&gt;&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|' +
	'&lt;&lt;deletelog|log&gt;&gt;&lt;/menurow&gt;';
	var move='&lt;&lt;move|shortcut=m|move page&gt;&gt;';
	var nullPurge='&lt;menurow&gt;&lt;&lt;nullEdit|shortcut=n|null edit&gt;&gt;|&lt;&lt;purge|shortcut=P&gt;&gt;&lt;/menurow&gt;';
	var viewOptions='&lt;menurow&gt;&lt;&lt;view|shortcut=v&gt;&gt;|&lt;&lt;render|shortcut=S&gt;&gt;|&lt;&lt;raw&gt;&gt;&lt;/menurow&gt;';
	var editRow='if(oldid){' +
	'&lt;menurow&gt;&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;editOld|shortcut=e|this&amp;nbsp;revision&gt;&gt;&lt;/menurow&gt;' +
	'&lt;menurow&gt;&lt;&lt;revert|shortcut=v&gt;&gt;|&lt;&lt;undo&gt;&gt;&lt;/menurow&gt;' + '}else{&lt;&lt;edit|shortcut=e&gt;&gt;}';
	var markPatrolled='if(rcid){&lt;&lt;markpatrolled|mark patrolled&gt;&gt;}';
	var newTopic='if(talk){&lt;&lt;new|shortcut=+|new topic&gt;&gt;}';
	var protectDelete='if(admin){' + protect + del + '}';

	if (getValueOf('popupActionsMenu')) {
		s.push( '&lt;&lt;mainlink&gt;&gt;*' + dropdiv + menuTitle('actions'));
	} else {
		s.push( dropdiv + '&lt;&lt;mainlink&gt;&gt;');
	}
	s.push( '&lt;menu&gt;')
	s.push( editRow + markPatrolled + newTopic + hist + lastedit )
	if (!shorter) { s.push(jsHistory); }
	s.push( move + linkshere + related)
	if (!shorter) { s.push(nullPurge + search); }
	if (!shorter) { s.push(viewOptions); }
	s.push('&lt;hr&gt;' + watch + protectDelete);
	s.push('&lt;hr&gt;' +
	       'if(talk){&lt;&lt;article|shortcut=a|view article&gt;&gt;&lt;&lt;editArticle|edit article&gt;&gt;}' +
	       'else{&lt;&lt;talk|shortcut=t|talk page&gt;&gt;&lt;&lt;editTalk|edit talk&gt;&gt;' +
	       '&lt;&lt;newTalk|shortcut=+|new topic&gt;&gt;}&lt;/menu&gt;' + enddiv);

	// user menu starts here
	var email='&lt;&lt;email|shortcut=E|email user&gt;&gt;';
	var contribs=	'if(wikimedia){&lt;menurow&gt;}&lt;&lt;contribs|shortcut=c|contributions&gt;&gt;if(wikimedia){&lt;/menurow&gt;}' +
	'if(admin){&lt;menurow&gt;&lt;&lt;deletedContribs&gt;&gt;&lt;/menurow&gt;}';


	s.push('if(user){*' + dropdiv + menuTitle('user'));
	s.push('&lt;menu&gt;'); +
	s.push('&lt;menurow&gt;&lt;&lt;userPage|shortcut=u|user&amp;nbsp;page&gt;&gt;|&lt;&lt;userSpace|space&gt;&gt;&lt;/menurow&gt;');
	s.push('&lt;&lt;userTalk|shortcut=t|user talk&gt;&gt;&lt;&lt;editUserTalk|edit user talk&gt;&gt;' +
	       '&lt;&lt;newUserTalk|shortcut=+|leave comment&gt;&gt;');
	if(!shorter) { s.push( 'if(ipuser){&lt;&lt;arin&gt;&gt;}else{' + email + '}') }
	else { s.push( 'if(ipuser){}else{' + email + '}') }
	s.push('&lt;hr&gt;' + contribs + '&lt;&lt;userlog|shortcut=L|user log&gt;&gt;');
	s.push('if(wikimedia){&lt;&lt;count|shortcut=#|edit counter&gt;&gt;}');
	s.push('if(admin){&lt;menurow&gt;&lt;&lt;unblock|unblockShort&gt;&gt;|&lt;&lt;block|shortcut=b|block user&gt;&gt;&lt;/menurow&gt;}');
	s.push('&lt;&lt;blocklog|shortcut=B|block log&gt;&gt;' + getValueOf('popupExtraUserMenu'));
	s.push('&lt;/menu&gt;'  + enddiv + '}');

	// popups menu starts here
	if (getValueOf('popupSetupMenu') &amp;&amp; !x.navpop.hasPopupMenu /* FIXME: hack */) {
		x.navpop.hasPopupMenu=true;
		s.push('*' + dropdiv + menuTitle('popupsMenu') + '&lt;menu&gt;');
		s.push('&lt;&lt;togglePreviews|toggle previews&gt;&gt;');
		s.push('&lt;&lt;purgePopups|reset&gt;&gt;');
		s.push('&lt;&lt;disablePopups|disable&gt;&gt;');
		s.push('&lt;/menu&gt;'+enddiv);
	}
	return navlinkStringToHTML(s.join(''), x.article, x.params);
};

function menuTitle(s) {
	return '&lt;a href=&quot;#&quot; noPopup=1&gt;' + popupString(s) + '&lt;/a&gt;';
}

pg.structures.menus.popupRedirTitle=pg.structures.menus.popupTitle;
pg.structures.menus.popupRedirTopLinks=pg.structures.menus.popupTopLinks;

copyStructure('menus', 'shortmenus');
pg.structures.shortmenus.popupTopLinks=function(x) {
	return pg.structures.menus.popupTopLinks(x,true);
};
pg.structures.shortmenus.popupRedirTopLinks=pg.structures.shortmenus.popupTopLinks;

copyStructure('shortmenus', 'dabshortmenus');
pg.structures.dabshortmenus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'], 'popupFixDab',
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview'];
};

copyStructure('menus', 'dabmenus');
pg.structures.dabmenus.popupLayout=pg.structures.dabshortmenus.popupLayout;


//&lt;/NOLITE&gt;
pg.structures.lite={};
pg.structures.lite.popupLayout=function () {
	return ['popupTitle', 'popupPreview' ];
};
pg.structures.lite.popupTitle=function (x) {
	log (x.article + ': structures.lite.popupTitle');
	//return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	return '&lt;div&gt;&lt;span class=&quot;popup_mainlink&quot;&gt;&lt;b&gt;' + x.article.toString() + '&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;';
};
// ENDFILE: structures.js
// STARTFILE: autoedit.js
//&lt;NOLITE&gt;
function getParamValue(paramName, h) {
	if (typeof h == 'undefined' ) { h = document.location.href; }
	var cmdRe=RegExp('[&amp;?]'+paramName+'=([^&amp;]*)');
	var m=cmdRe.exec(h);
	if (m) {
		try {
			return decodeURIComponent(m[1]);
		} catch (someError) {}
	}
	return null;
}

function substitute(data,cmdBody) {
	// alert('sub\nfrom: '+cmdBody.from+'\nto: '+cmdBody.to+'\nflags: '+cmdBody.flags);
	var fromRe=RegExp(cmdBody.from, cmdBody.flags);
	return data.replace(fromRe, cmdBody.to);
}

function execCmds(data, cmdList) {
	for (var i=0; i&lt;cmdList.length; ++i) {
		data=cmdList[i].action(data, cmdList[i]);
	}
	return data;
}

function parseCmd(str) {
	// returns a list of commands
	if (!str.length) { return []; }
	var p=false;
	switch (str[0]) {
	case 's':
		p=parseSubstitute(str);
		break;
	default:
		return false;
	}
	if (p) { return [p].concat(parseCmd(p.remainder)); }
	return false;
}

function unEscape(str, sep) {
	return str.split('\\\\').join('\\').split('\\'+sep).join(sep).split('\\n').join('\n');
}


function parseSubstitute(str) {
	// takes a string like s/a/b/flags;othercmds and parses it

	var from,to,flags,tmp;

	if (str.length&lt;4) { return false; }
	var sep=str.charAt(1);
	str=str.substring(2);

	tmp=skipOver(str,sep);
	if (tmp) { from=tmp.segment; str=tmp.remainder; }
	else { return false; }

	tmp=skipOver(str,sep);
	if (tmp) { to=tmp.segment; str=tmp.remainder; }
	else { return false; }

	flags='';
	if (str.length) {
		tmp=skipOver(str,';') || skipToEnd(str, ';');
		if (tmp) {flags=tmp.segment; str=tmp.remainder; }
	}

	return {action: substitute, from: from, to: to, flags: flags, remainder: str};

}

function skipOver(str,sep) {
	var endSegment=findNext(str,sep);
	if (endSegment&lt;0) { return false; }
	var segment=unEscape(str.substring(0,endSegment), sep);
	return {segment: segment, remainder: str.substring(endSegment+1)};
}

function skipToEnd(str,sep) {
	return {segment: str, remainder: ''};
}

function findNext(str, ch) {
	for (var i=0; i&lt;str.length; ++i) {
		if (str.charAt(i)=='\\') { i+=2; }
		if (str.charAt(i)==ch) { return i; }
	}
	return -1;
}

function setCheckbox(param, box) {
	var val=getParamValue(param);
	if (val!==null) {
		switch (val) {
		case '1': case 'yes': case 'true':
			box.checked=true;
			break;
		case '0': case 'no':  case 'false':
			box.checked=false;
		}
	}
}

function autoEdit() {
	if (!setupPopups.completed) { setupPopups(); }
	if (!document.editform) { return false; }
	if (window.autoEdit.alreadyRan) { return false; }
	window.autoEdit.alreadyRan=true;
	var cmdString=getParamValue('autoedit');
	if (cmdString) {
		try {
			var editbox=document.editform.wpTextbox1;
		} catch (dang) { return; }
		var cmdList=parseCmd(cmdString);
		var input=editbox.value;
		var output=execCmds(input, cmdList);
		editbox.value=output;
		// wikEd user script compatibility
		if (typeof(wikEdUseWikEd) != 'undefined') {
			if (wikEdUseWikEd == true) {
				WikEdUpdateFrame();
			}
		}
	}
	setCheckbox('autominor', document.editform.wpMinoredit);
	setCheckbox('autowatch', document.editform.wpWatchthis);

	var rvid = getParamValue('autorv');
	if (rvid) {
		var url=pg.wiki.apiwikibase + '?action=query&amp;format=json&amp;prop=revisions&amp;revids='+rvid;
		startDownload(url, null, autoEdit2);
	} else { autoEdit2(); }
}

function autoEdit2(d) {
	var summary=getParamValue('autosummary');
	var summaryprompt=getParamValue('autosummaryprompt');
	var summarynotice='';
	if (d &amp;&amp; d.data &amp;&amp; getParamValue('autorv')) {
		var s = getRvSummary(summary, d.data);
		if (s===false) {
			summaryprompt=true;
			summarynotice=popupString('Failed to get revision information, please edit manually.\n\n');
			summary = simplePrintf(summary, [getParamValue('autorv'), '(unknown)', '(unknown)']);
		} else { summary = s; }
	}
	if (summaryprompt) {
		var txt= summarynotice +
			popupString('Enter a non-empty edit summary or press cancel to abort');
		var response=prompt(txt, summary);
		if (response) { summary=response; }
		else { return; }
	}
	if (summary) { document.editform.wpSummary.value=summary; }
	// Attempt to avoid possible premature clicking of the save button
	// (maybe delays in updates to the DOM are to blame?? or a red herring)
	setTimeout(autoEdit3, 100);
}

function autoClickToken() {
    return mw.user.sessionId();
}

function autoEdit3() {
    if( getParamValue('actoken') != autoClickToken()) return;

	var btn=getParamValue('autoclick');
	if (btn) {
		if (document.editform &amp;&amp; document.editform[btn]) {
			var button=document.editform[btn];
			var msg=tprintf('The %s button has been automatically clicked. Please wait for the next page to load.',
					[ button.value ]);
			bannerMessage(msg);
			document.title='('+document.title+')';
			button.click();
		} else {
			alert(tprintf('Could not find button %s. Please check the settings in your javascript file.',
				      [ btn ]));
		}
	}
}

function bannerMessage(s) {
	var headings=document.getElementsByTagName('h1');
	if (headings) {
		var div=document.createElement('div');
		div.innerHTML='&lt;font size=+1&gt;&lt;b&gt;' + s + '&lt;/b&gt;&lt;/font&gt;';
		headings[0].parentNode.insertBefore(div, headings[0]);
	}
}

function getRvSummary(template, json) {
	try {
	    var o=getJsObj(json);
	    var edit = anyChild(o.query.pages).revisions[0];
	} catch (badness) {return false;}
	var timestamp = edit.timestamp.split(/[A-Z]/g).join(' ').replace(/^ *| *$/g, '');
	return simplePrintf(template, [edit.revid, timestamp, edit.userhidden === undefined ? edit.user : '(hidden)']);
}

//&lt;/NOLITE&gt;
// ENDFILE: autoedit.js
// STARTFILE: downloader.js
/**
   @fileoverview
   {@link Downloader}, a xmlhttprequest wrapper, and helper functions.
*/

/**
   Creates a new Downloader
   @constructor
   @class The Downloader class. Create a new instance of this class to download stuff.
   @param {String} url The url to download. This can be omitted and supplied later.
*/
function Downloader(url) {
	// Source: http://jibbering.com/2002/4/httprequest.html
	/** xmlhttprequest object which we're wrapping */
	this.http = false;

	/*@cc_on @*/
	/*@if (@_jscript_version &gt;= 5)
	// JScript gives us Conditional compilation,
	// we can cope with old IE versions.
	// and security blocked creation of the objects.
	try {
	this.http = new ActiveXObject(&quot;Msxml2.XMLHTTP&quot;);
	} catch (e) {
	try {
	this.http = new ActiveXObject(&quot;Microsoft.XMLHTTP&quot;);
	} catch (E) {
	// this.http = false;
	}
	}
	@end @*/

	if (! this.http &amp;&amp; typeof XMLHttpRequest!='undefined') { this.http = new XMLHttpRequest(); }
	/**
	    The url to download
	    @type String
	*/
	this.url = url;
	/**
	    A universally unique ID number
	    @type integer
	*/
	this.id=null;
	/**
	    Modification date, to be culled from the incoming headers
	    @type Date
	    @private
	*/
	this.lastModified = null;
	/**
	    What to do when the download completes successfully
	    @type Function
	    @private
	*/
	this.callbackFunction = null;
	/**
	    What to do on failure
	    @type Function
	    @private
	*/
	this.onFailure = null;
	/**
	    Flag set on &lt;code&gt;abort&lt;/code&gt;
	    @type boolean
	*/
	this.aborted = false;
	/**
	   HTTP method. See http://www.w3.org/Protocols/rfc2616/rfc2616-sec9.html for possibilities.
	   @type String
	*/
	this.method='GET';
	/**
	    Async flag.
	    @type boolean
	*/
	this.async=true;
}

new Downloader();

/** Submits the http request. */
Downloader.prototype.send = function (x) {
	if (!this.http) { return null; }
	return this.http.send(x);
};
/** Aborts the download, setting the &lt;code&gt;aborted&lt;/code&gt; field to true.  */
Downloader.prototype.abort = function () {
	if (!this.http) { return null; }
	this.aborted=true;
	return this.http.abort();
};
/** Returns the downloaded data. */
Downloader.prototype.getData = function () {if (!this.http) { return null; } return this.http.responseText;};
/** Prepares the download. */
Downloader.prototype.setTarget = function () {
	if (!this.http) { return null; }
	this.http.open(this.method, this.url, this.async);
};
/** Gets the state of the download. */
Downloader.prototype.getReadyState=function () {if (!this.http) { return null; } return this.http.readyState;};

pg.misc.downloadsInProgress = { };

/** Starts the download.
    Note that setTarget {@link Downloader#setTarget} must be run first
*/
Downloader.prototype.start=function () {
	if (!this.http) { return; }
	pg.misc.downloadsInProgress[this.id] = this;
	this.http.send(null);
};

/** Gets the 'Last-Modified' date from the download headers.
    Should be run after the download completes.
    Returns &lt;code&gt;null&lt;/code&gt; on failure.
    @return {Date}
*/
Downloader.prototype.getLastModifiedDate=function () {
	if(!this.http) { return null; }
	var lastmod=null;
	try {
		lastmod=this.http.getResponseHeader('Last-Modified');
	} catch (err) {}
	if (lastmod) { return new Date(lastmod); }
	return null;
};

/** Sets the callback function.
    @param {Function} f callback function, called as &lt;code&gt;f(this)&lt;/code&gt; on success
*/
Downloader.prototype.setCallback = function (f) {
	if(!this.http) { return; }
	this.http.onreadystatechange = f;
};

Downloader.prototype.getStatus = function() { if (!this.http) { return null; } return this.http.status; };

//////////////////////////////////////////////////
// helper functions

/** Creates a new {@link Downloader} and prepares it for action.
    @param {String} url The url to download
    @param {integer} id The ID of the {@link Downloader} object
    @param {Function} callback The callback function invoked on success
    @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function newDownload(url, id, callback, onfailure) {
	var d=new Downloader(url);
	if (!d.http) { return 'ohdear'; }
	d.id=id;
	d.setTarget();
	if (!onfailure) {
		onfailure=2;
	}
	var f = function () {
		if (d.getReadyState() == 4) {
			delete pg.misc.downloadsInProgress[this.id];
			try {
				if ( d.getStatus() == 200 ) {
					d.data=d.getData();
					d.lastModified=d.getLastModifiedDate();
					callback(d);
				} else if (typeof onfailure == typeof 1) {
					if (onfailure &gt; 0) {
						// retry
						newDownload(url, id, callback, onfailure - 1);
					}
				} else if (typeof onfailure == 'function') {
					onfailure(d,url,id,callback);
				}
			} catch (somerr) { /* ignore it */ }
		}
	};
	d.setCallback(f);
	return d;
}
/** Simulates a download from cached data.
    The supplied data is put into a {@link Downloader} as if it had downloaded it.
    @param {String} url The url.
    @param {integer} id The ID.
    @param {Function} callback The callback, which is invoked immediately as &lt;code&gt;callback(d)&lt;/code&gt;,
    where &lt;code&gt;d&lt;/code&gt; is the new {@link Downloader}.
    @param {String} data The (cached) data.
    @param {Date} lastModified The (cached) last modified date.
*/
function fakeDownload(url, id, callback, data, lastModified, owner) {
	var d=newDownload(url,callback);
	d.owner=owner;
	d.id=id; d.data=data;
	d.lastModified=lastModified;
	return callback(d);
}

/**
   Starts a download.
   @param {String} url The url to download
   @param {integer} id The ID of the {@link Downloader} object
   @param {Function} callback The callback function invoked on success
   @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function startDownload(url, id, callback) {
	var d=newDownload(url, id, callback);
	if (typeof d == typeof '' ) { return d; }
	d.start();
	return d;
}

/**
   Aborts all downloads which have been started.
*/
function abortAllDownloads() {
	for ( var x in pg.misc.downloadsInProgress ) {
		try {
			pg.misc.downloadsInProgress[x].aborted=true;
			pg.misc.downloadsInProgress[x].abort();
			delete pg.misc.downloadsInProgress[x];
		} catch (e) { }
	}
}
// ENDFILE: downloader.js
// STARTFILE: livepreview.js
// TODO: location is often not correct (eg relative links in previews)

/**
 * InstaView - a Mediawiki to HTML converter in JavaScript
 * Version 0.6.1
 * Copyright (C) Pedro Fayolle 2005-2006
 * //en.wikipedia.org/wiki/User:Pilaf
 * Distributed under the BSD license
 *
 * Changelog:
 *
 * 0.6.1
 * - Fixed problem caused by \r characters
 * - Improved inline formatting parser
 *
 * 0.6
 * - Changed name to InstaView
 * - Some major code reorganizations and factored out some common functions
 * - Handled conversion of relative links (i.e. [[/foo]])
 * - Fixed misrendering of adjacent definition list items
 * - Fixed bug in table headings handling
 * - Changed date format in signatures to reflect Mediawiki's
 * - Fixed handling of [[:Image:...]]
 * - Updated MD5 function (hopefully it will work with UTF-8)
 * - Fixed bug in handling of links inside images
 *
 * To do:
 * - Better support for &lt;math&gt;
 * - Full support for &lt;nowiki&gt;
 * - Parser-based (as opposed to RegExp-based) inline wikicode handling (make it one-pass and bullet-proof)
 * - Support for templates (through AJAX)
 * - Support for coloured links (AJAX)
 */


var Insta = {}

function setupLivePreview() {

    // options
    Insta.conf =
	{
	    baseUrl: '',

	    user: {},

	    wiki: {
		lang: pg.wiki.lang,
		interwiki: pg.wiki.interwiki,
		default_thumb_width: 180
	    },

	    paths: {
		articles: pg.wiki.articlePath + '/',
		// Only used for Insta previews with images. (not in popups)
		math: '/math/',
		images: '//upload.wikimedia.org/wikiversity/en/', // FIXME ( window.getImageUrlStart ? getImageUrlStart(pg.wiki.hostname) : ''),
		images_fallback: '//upload.wikimedia.org/wikipedia/commons/',
		magnify_icon: 'skins/common/images/magnify-clip.png'
	    },

	    locale: {
		user: mw.config.get('wgFormattedNamespaces')[pg.nsUserId],
		image: mw.config.get('wgFormattedNamespaces')[pg.nsImageId],
		category: mw.config.get('wgFormattedNamespaces')[pg.nsCategoryId],
		// shouldn't be used in popup previews, i think
		months: ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec']
	    }
	}

    // options with default values or backreferences
    with (Insta.conf) {
	user.name = user.name || 'Wikiversity participant'
	user.signature = '[['+locale.user+':'+user.name+'|'+user.name+']]'
    }

    // define constants
    Insta.BLOCK_IMAGE = new RegExp('^\\[\\[(?:File|Image|'+Insta.conf.locale.image+
				       '):.*?\\|.*?(?:frame|thumbnail|thumb|none|right|left|center)', 'i');

}


Insta.dump = function(from, to)
{
	if (typeof from == 'string') from = document.getElementById(from)
	if (typeof to == 'string') to = document.getElementById(to)
	to.innerHTML = this.convert(from.value)
}

Insta.convert = function(wiki)
{
	var	ll = (typeof wiki == 'string')? wiki.replace(/\r/g,'').split(/\n/): wiki, // lines of wikicode
		o='',	// output
		p=0,	// para flag
		$r	// result of passing a regexp to $()

	// some shorthands
	function remain() { return ll.length }
	function sh() { return ll.shift() } // shift
	function ps(s) { o+=s } // push

	function f() // similar to C's printf, uses ? as placeholders, ?? to escape question marks
	{
		var i=1,a=arguments,f=a[0],o='',c,p
		for (;i&lt;a.length; i++) if ((p=f.indexOf('?'))+1) {
			// allow character escaping
			i -= c=f.charAt(p+1)=='?'?1:0
			o += f.substring(0,p)+(c?'?':a[i])
			f=f.substr(p+1+c)
		} else break;
		return o+f
	}

	function html_entities(s) { return s.replace(/&amp;/g,&quot;&amp;amp;&quot;).replace(/&lt;/g,&quot;&amp;lt;&quot;).replace(/&gt;/g,&quot;&amp;gt;&quot;) }

	function max(a,b) { return (a&gt;b)?a:b }
	function min(a,b) { return (a&lt;b)?a:b }

	// return the first non matching character position between two strings
	function str_imatch(a, b)
	{
		for (var i=0, l=min(a.length, b.length); i&lt;l; i++) if (a.charAt(i)!=b.charAt(i)) break
		return i
	}

	// compare current line against a string or regexp
	// if passed a string it will compare only the first string.length characters
	// if passed a regexp the result is stored in $r
	function $(c) { return (typeof c == 'string') ? (ll[0].substr(0,c.length)==c) : ($r = ll[0].match(c)) }

	function $$(c) { return ll[0]==c } // compare current line against a string
	function _(p) { return ll[0].charAt(p) } // return char at pos p

	function endl(s) { ps(s); sh() }

	function parse_list()
	{
		var prev='';

		while (remain() &amp;&amp; $(/^([*#:;]+)(.*)$/)) {

			var l_match = $r

			sh()

			var ipos = str_imatch(prev, l_match[1])

			// close uncontinued lists
			for (var i=prev.length-1; i &gt;= ipos; i--) {

				var pi = prev.charAt(i)

				if (pi=='*') ps('&lt;/ul&gt;')
				else if (pi=='#') ps('&lt;/ol&gt;')
				// close a dl only if the new item is not a dl item (:, ; or empty)
				else switch (l_match[1].charAt(i)) { case'':case'*':case'#': ps('&lt;/dl&gt;') }
			}

			// open new lists
			for (var i=ipos; i&lt;l_match[1].length; i++) {

				var li = l_match[1].charAt(i)

				if (li=='*') ps('&lt;ul&gt;')
				else if (li=='#') ps('&lt;ol&gt;')
				// open a new dl only if the prev item is not a dl item (:, ; or empty)
				else switch(prev.charAt(i)) { case'':case'*':case'#': ps('&lt;dl&gt;') }
			}

			switch (l_match[1].charAt(l_match[1].length-1)) {

				case '*': case '#':
					ps('&lt;li&gt;' + parse_inline_nowiki(l_match[2])); break

				case ';':
					ps('&lt;dt&gt;')

					var dt_match

					// handle ;dt :dd format
					if (dt_match = l_match[2].match(/(.*?)(:.*?)$/)) {

						ps(parse_inline_nowiki(dt_match[1]))
						ll.unshift(dt_match[2])

					} else ps(parse_inline_nowiki(l_match[2]))

					break

				case ':':
					ps('&lt;dd&gt;' + parse_inline_nowiki(l_match[2]))
			}

			prev=l_match[1]
		}

		// close remaining lists
		for (var i=prev.length-1; i&gt;=0; i--)
			ps(f('&lt;/?&gt;', (prev.charAt(i)=='*')? 'ul': ((prev.charAt(i)=='#')? 'ol': 'dl')))
	}

	function parse_table()
	{
		endl(f('&lt;table?&gt;', $(/^\{\|( .*)$/)? $r[1]: ''))

		for (;remain();) if ($('|')) switch (_(1)) {
			case '}': endl('&lt;/table&gt;'); return
			case '-': endl(f('&lt;tr ?&gt;', $(/\|-*(.*)/)[1])); break
			default: parse_table_data()
		}
		else if ($('!')) parse_table_data()
		else sh()
	}

	function parse_table_data()
	{
		var td_line, match_i

		// 1: &quot;|+&quot;, '|' or '+'
		// 2: ??
		// 3: attributes ??
		// TODO: finish commenting this regexp
		var td_match = sh().match(/^(\|\+|\||!)((?:([^[|]*?)\|(?!\|))?(.*))$/)

		if (td_match[1] == '|+') ps('&lt;caption');
		else ps('&lt;t' + ((td_match[1]=='|')?'d':'h'))

		if (typeof td_match[3] != 'undefined') {

			ps(' ' + td_match[3])
			match_i = 4

		} else match_i = 2

		ps('&gt;')

		if (td_match[1] != '|+') {

			// use || or !! as a cell separator depending on context
			// NOTE: when split() is passed a regexp make sure to use non-capturing brackets
			td_line = td_match[match_i].split((td_match[1] == '|')? '||': /(?:\|\||!!)/)

			ps(parse_inline_nowiki(td_line.shift()))

			while (td_line.length) ll.unshift(td_match[1] + td_line.pop())

		} else ps(td_match[match_i])

		var tc = 0, td = []

		for (;remain(); td.push(sh()))
		if ($('|')) {
			if (!tc) break // we're at the outer-most level (no nested tables), skip to td parse
			else if (_(1)=='}') tc--
		}
		else if (!tc &amp;&amp; $('!')) break
		else if ($('{|')) tc++

		if (td.length) ps(Insta.convert(td))
	}

	function parse_pre()
	{
		ps('&lt;pre&gt;')
		do endl(parse_inline_nowiki(ll[0].substring(1)) + &quot;\n&quot;); while (remain() &amp;&amp; $(' '))
		ps('&lt;/pre&gt;')
	}

	function parse_block_image()
	{
		ps(parse_image(sh()))
	}

	function parse_image(str)
	{
//&lt;NOLITE&gt;
		// get what's in between &quot;[[Image:&quot; and &quot;]]&quot;
		var tag = str.substring(str.indexOf(':') + 1, str.length - 2);

		var width;
		var attr = [], filename, caption = '';
		var thumb=0, frame=0, center=0;
		var align='';

		if (tag.match(/\|/)) {
			// manage nested links
			var nesting = 0;
			var last_attr;
			for (var i = tag.length-1; i &gt; 0; i--) {
				if (tag.charAt(i) == '|' &amp;&amp; !nesting) {
					last_attr = tag.substr(i+1);
					tag = tag.substring(0, i);
					break;
				} else switch (tag.substr(i-1, 2)) {
					case ']]':
						nesting++;
						i--;
						break;
					case '[[':
						nesting--;
						i--;
				}
			}

			attr = tag.split(/\s*\|\s*/);
			attr.push(last_attr);
			filename = attr.shift();

			var w_match;

			for (;attr.length; attr.shift())
			if (w_match = attr[0].match(/^(\d*)(?:[px]*\d*)?px$/)) width = w_match[1]
			else switch(attr[0]) {
				case 'thumb':
				case 'thumbnail':
					thumb=true;
				case 'frame':
					frame=true;
					break;
				case 'none':
				case 'right':
				case 'left':
					center=false;
					align=attr[0];
					break;
				case 'center':
					center=true;
					align='none';
					break;
				default:
					if (attr.length == 1) caption = attr[0];
			}

		} else filename = tag;


		var o='';

		if (frame) {

			if (align=='') align = 'right';

			o += f(&quot;&lt;div class='thumb t?'&gt;&quot;, align);

			if (thumb) {
				if (!width) width = Insta.conf.wiki.default_thumb_width;

				o += f(&quot;&lt;div style='width:?px;'&gt;?&quot;, 2+width*1, make_image(filename, caption, width)) +
					f(&quot;&lt;div class='thumbcaption'&gt;&lt;div class='magnify' style='float:right'&gt;&lt;a href='?' class='internal' title='Enlarge'&gt;&lt;img src='?'&gt;&lt;/a&gt;&lt;/div&gt;?&lt;/div&gt;&quot;,
						Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename,
						Insta.conf.paths.magnify_icon,
						parse_inline_nowiki(caption)
					)
			} else {
				o += '&lt;div&gt;' + make_image(filename, caption) + f(&quot;&lt;div class='thumbcaption'&gt;?&lt;/div&gt;&quot;, parse_inline_nowiki(caption))
			}

			o += '&lt;/div&gt;&lt;/div&gt;';

		} else if (align != '') {
			o += f(&quot;&lt;div class='float?'&gt;&lt;span&gt;?&lt;/span&gt;&lt;/div&gt;&quot;, align, make_image(filename, caption, width));
		} else {
			return make_image(filename, caption, width);
		}

		return center? f(&quot;&lt;div class='center'&gt;?&lt;/div&gt;&quot;, o): o;
//&lt;/NOLITE&gt;
	}

	function parse_inline_nowiki(str)
	{
		var start, lastend=0
		var substart=0, nestlev=0, open, close, subloop;
		var html='';

		while (-1 != (start = str.indexOf('&lt;nowiki&gt;', substart))) {
			html += parse_inline_wiki(str.substring(lastend, start));
			start += 8;
			substart = start;
			subloop = true;
			do {
				open = str.indexOf('&lt;nowiki&gt;', substart);
				close = str.indexOf('&lt;/nowiki&gt;', substart);
				if (close&lt;=open || open==-1) {
					if (close==-1) {
						return html + html_entities(str.substr(start));
					}
					substart = close+9;
					if (nestlev) {
						nestlev--;
					} else {
						lastend = substart;
						html += html_entities(str.substring(start, lastend-9));
						subloop = false;
					}
				} else {
					substart = open+8;
					nestlev++;
				}
			} while (subloop)
		}

		return html + parse_inline_wiki(str.substr(lastend));
	}

	function make_image(filename, caption, width)
	{
//&lt;NOLITE&gt;
		// uppercase first letter in file name
		filename = filename[0].toUpperCase() + filename.substr(1);
		// replace spaces with underscores
		filename = filename.replace(/ /g, '_');

		caption = strip_inline_wiki(caption);

		var md5 = hex_md5(filename);

		var source = md5[0] + '/' + md5.substr(0,2) + '/' + filename;

		if (width) width = &quot;width='&quot; + width + &quot;px'&quot;;

		var img = f(&quot;&lt;img onerror=\&quot;this.onerror=null;this.src='?'\&quot; src='?' ? ?&gt;&quot;, Insta.conf.paths.images_fallback + source, Insta.conf.paths.images + source, (caption!='')? &quot;alt='&quot; + caption + &quot;'&quot; : '', width);

		return f(&quot;&lt;a class='image' ? href='?'&gt;?&lt;/a&gt;&quot;, (caption!='')? &quot;title='&quot; + caption + &quot;'&quot; : '', Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename, img);
//&lt;/NOLITE&gt;
	}

	function parse_inline_images(str)
	{
//&lt;NOLITE&gt;
		var start, substart=0, nestlev=0;
		var loop, close, open, wiki, html;

		while (-1 != (start=str.indexOf('[[', substart))) {
			if(str.substr(start+2).match(RegExp('^(Image|File|' + Insta.conf.locale.image + '):','i'))) {
				loop=true;
				substart=start;
				do {
					substart+=2;
					close=str.indexOf(']]',substart);
					open=str.indexOf('[[',substart);
					if (close&lt;=open||open==-1) {
						if (close==-1) return str;
						substart=close;
						if (nestlev) {
							nestlev--;
						} else {
							wiki=str.substring(start,close+2);
							html=parse_image(wiki);
							str=str.replace(wiki,html);
							substart=start+html.length;
							loop=false;
						}
					} else {
						substart=open;
						nestlev++;
					}
				} while (loop)

			} else break;
		}

//&lt;/NOLITE&gt;
		return str;
	}

	// the output of this function doesn't respect the FILO structure of HTML
	// but since most browsers can handle it I'll save myself the hassle
	function parse_inline_formatting(str)
	{
		var em,st,i,li,o='';
		while ((i=str.indexOf(&quot;''&quot;,li))+1) {
			o += str.substring(li,i);
			li=i+2;
			if (str.charAt(i+2)==&quot;'&quot;) {
				li++;
				st=!st;
				o+=st?'&lt;strong&gt;':'&lt;/strong&gt;';
			} else {
				em=!em;
				o+=em?'&lt;em&gt;':'&lt;/em&gt;';
			}
		}
		return o+str.substr(li);
	}

	function parse_inline_wiki(str)
	{
		var aux_match;

		str = parse_inline_images(str);
		str = parse_inline_formatting(str);

		// math
		while (aux_match = str.match(/&lt;(?:)math&gt;(.*?)&lt;\/math&gt;/i)) {
			var math_md5 = hex_md5(aux_match[1]);
			str = str.replace(aux_match[0], f(&quot;&lt;img src='?.png'&gt;&quot;, Insta.conf.paths.math+math_md5));
		}

		// Build a Mediawiki-formatted date string
		var date = new Date;
		var minutes = date.getUTCMinutes();
		if (minutes &lt; 10) minutes = '0' + minutes;
		var date = f(&quot;?:?, ? ? ? (UTC)&quot;, date.getUTCHours(), minutes, date.getUTCDate(), Insta.conf.locale.months[date.getUTCMonth()], date.getUTCFullYear());

		// text formatting
		return str.
			// signatures
			replace(/~{5}(?!~)/g, date).
			replace(/~{4}(?!~)/g, Insta.conf.user.name+' '+date).
			replace(/~{3}(?!~)/g, Insta.conf.user.name).

			// [[:Category:...]], [[:Image:...]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):[^|]*?)\\]\\](\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$1$2&lt;/a&gt;&quot;).
			// remove straight category and interwiki tags
			replace(RegExp('\\[\\[(?:'+Insta.conf.locale.category+'|'+Insta.conf.wiki.interwiki+'):.*?\\]\\]','gi'),'').

			// [[:Category:...|Links]], [[:Image:...|Links]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):.*?)\\|([^\\]]+?)\\]\\](\\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$2$3&lt;/a&gt;&quot;).

			// [[/Relative links]]
			replace(/\[\[(\/[^|]*?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$1&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[/Replaced|Relative links]]
			replace(/\[\[(\/.*?)\|(.+?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$2&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[Common links]]
			replace(/\[\[([^|]*?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$1$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Replaced|Links]]
			replace(/\[\[(.*?)\|([^\]]+?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$2$3&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Stripped:Namespace|Namespace]]
			replace(/\[\[([^\]]*?:)?(.*?)( *\(.*?\))?\|\]\]/g, f(&quot;&lt;a href='?$1$2$3'&gt;$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// External links
			replace(/\[(https?|news|ftp|mailto|gopher|irc):(\/*)([^\]]*?) (.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$4&lt;/a&gt;&quot;).
			replace(/\[http:\/\/(.*?)\]/g, &quot;&lt;a class='external' href='http://$1'&gt;[#]&lt;/a&gt;&quot;).
			replace(/\[(news|ftp|mailto|gopher|irc):(\/*)(.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$1:$2$3&lt;/a&gt;&quot;).
			replace(/(^| )(https?|news|ftp|mailto|gopher|irc):(\/*)([^ $]*[^.,!?;: $])/g, &quot;$1&lt;a class='external' href='$2:$3$4'&gt;$2:$3$4&lt;/a&gt;&quot;).

			replace('__NOTOC__','').
			replace('__NOEDITSECTION__','');
	}
/*
*/
	function strip_inline_wiki(str)
	{
		return str
			.replace(/\[\[[^\]]*\|(.*?)\]\]/g,'$1')
			.replace(/\[\[(.*?)\]\]/g,'$1')
			.replace(/''(.*?)''/g,'$1');
	}

	// begin parsing
	for (;remain();) if ($(/^(={1,6})(.*)\1(.*)$/)) {
		p=0
		endl(f('&lt;h?&gt;?&lt;/h?&gt;?', $r[1].length, parse_inline_nowiki($r[2]), $r[1].length, $r[3]))

	} else if ($(/^[*#:;]/)) {
		p=0
		parse_list()

	} else if ($(' ')) {
		p=0
		parse_pre()

	} else if ($('{|')) {
		p=0
		parse_table()

	} else if ($(/^----+$/)) {
		p=0
		endl('&lt;hr&gt;')

	} else if ($(Insta.BLOCK_IMAGE)) {
		p=0
		parse_block_image()

	} else {

		// handle paragraphs
		if ($$('')) {
			if (p = (remain()&gt;1 &amp;&amp; ll[1]==(''))) endl('&lt;p&gt;&lt;br&gt;')
		} else {
			if(!p) {
				ps('&lt;p&gt;')
				p=1
			}
			ps(parse_inline_nowiki(ll[0]) + ' ')
		}

		sh();
	}

	return o
};

window.wiki2html=function(txt,baseurl) {
    Insta.conf.baseUrl=baseurl;
    return Insta.convert(txt);
};
// ENDFILE: livepreview.js
// STARTFILE: pageinfo.js
//&lt;NOLITE&gt;
function popupFilterPageSize(data) {
	return formatBytes(data.length);
}

function popupFilterCountLinks(data) {
	var num=countLinks(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('wikiLinks'):popupString('wikiLink'));
}

function popupFilterCountImages(data) {
	var num=countImages(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('images'):popupString('image'));
}

function popupFilterCountCategories(data) {
	var num=countCategories(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('categories'):popupString('category'));
}


function popupFilterLastModified(data,download) {
	var lastmod=download.lastModified;
	var now=new Date();
	var age=now-lastmod;
	if (lastmod &amp;&amp; getValueOf('popupLastModified')) {
		return (tprintf('%s old', [formatAge(age)])).replace(RegExp(' ','g'), '&amp;nbsp;');
	}
	return '';
}

function formatAge(age) {
	// coerce into a number
	var a=0+age, aa=a;

	var seclen  = 1000;
	var minlen  = 60*seclen;
	var hourlen = 60*minlen;
	var daylen  = 24*hourlen;
	var weeklen = 7*daylen;

	var numweeks = (a-a%weeklen)/weeklen; a = a-numweeks*weeklen; var sweeks = addunit(numweeks, 'week');
	var numdays  = (a-a%daylen)/daylen;   a = a-numdays*daylen;   var sdays  = addunit(numdays, 'day');
	var numhours = (a-a%hourlen)/hourlen; a = a-numhours*hourlen; var shours = addunit(numhours,'hour');
	var nummins  = (a-a%minlen)/minlen;   a = a-nummins*minlen;   var smins  = addunit(nummins, 'minute');
	var numsecs  = (a-a%seclen)/seclen;   a = a-numsecs*seclen;   var ssecs  = addunit(numsecs, 'second');

	if (aa &gt; 4*weeklen) { return sweeks; }
	if (aa &gt; weeklen)   { return sweeks + ' ' + sdays; }
	if (aa &gt; daylen)    { return sdays  + ' ' + shours; }
	if (aa &gt; 6*hourlen) { return shours; }
	if (aa &gt; hourlen)   { return shours + ' ' + smins; }
	if (aa &gt; 10*minlen) { return smins; }
	if (aa &gt; minlen)    { return smins  + ' ' + ssecs; }
	return ssecs;
}

function addunit(num,str) { return '' + num + ' ' + ((num!=1) ? popupString(str+'s') : popupString(str)) ;}

function runPopupFilters(list, data, download) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i] &amp;&amp; typeof list[i] == 'function') {
			var s=list[i](data, download, download.owner.article);
			if (s) { ret.push(s); }
		}
	}
	return ret;
}

function getPageInfo(data, download) {
	if (!data || data.length === 0) { return popupString('Empty page'); }

	var popupFilters=getValueOf('popupFilters') || [];
	var extraPopupFilters = getValueOf('extraPopupFilters') || [];
	var pageInfoArray = runPopupFilters(popupFilters.concat(extraPopupFilters), data, download);

	var pageInfo=pageInfoArray.join(', ');
	if (pageInfo !== '' ) { pageInfo = upcaseFirst(pageInfo); }
	return pageInfo;
}


// this could be improved!
function countLinks(wikiText) { return wikiText.split('[[').length - 1; }

// if N = # matches, n = # brackets, then
// String.parenSplit(regex) intersperses the N+1 split elements
// with Nn other elements. So total length is
// L= N+1 + Nn = N(n+1)+1. So N=(L-1)/(n+1).

function countImages(wikiText) {
	return (wikiText.parenSplit(pg.re.image).length - 1) / (pg.re.imageBracketCount + 1);
}

function countCategories(wikiText) {
	return (wikiText.parenSplit(pg.re.category).length - 1) / (pg.re.categoryBracketCount + 1);
}

function popupFilterStubDetect(data, download, article)     {
	var counts=stubCount(data, article);
	if (counts.real) { return popupString('stub'); }
	if (counts.sect) { return popupString('section stub'); }
	return '';
}

function popupFilterDisambigDetect(data, download, article) {
	if (getValueOf('popupOnlyArticleDabStub') &amp;&amp; article.namespace()) { return ''; }
	return (isDisambig(data, article)) ? popupString('disambig') : '';
}

function formatBytes(num) {
	return (num &gt; 949) ? (Math.round(num/100)/10+popupString('kB')) : (num +'&amp;nbsp;' + popupString('bytes')) ;
}
//&lt;/NOLITE&gt;
// ENDFILE: pageinfo.js
// STARTFILE: titles.js
/**
   @fileoverview Defines the {@link Title} class, and associated crufty functions.

   &lt;code&gt;Title&lt;/code&gt; deals with article titles and their various
   forms.  {@link Stringwrapper} is the parent class of
   &lt;code&gt;Title&lt;/code&gt;, which exists simply to make things a little
   neater.

*/

/**
   Creates a new Stringwrapper.
   @constructor

   @class the Stringwrapper class. This base class is not really
   useful on its own; it just wraps various common string operations.
*/
function Stringwrapper() {
	/**
	   Wrapper for this.toString().indexOf()
	   @param {String} x
	   @type integer
	*/
	this.indexOf=function(x){return this.toString().indexOf(x);};
	/**
	   Returns this.value.
	   @type String
	*/
	this.toString=function(){return this.value;};
	/**
	   Wrapper for {@link String#parenSplit} applied to this.toString()
	   @param {RegExp} x
	   @type Array
	*/
	this.parenSplit=function(x){return this.toString().parenSplit(x);};
	/**
	   Wrapper for this.toString().substring()
	   @param {String} x
	   @param {String} y (optional)
	   @type String
	*/
	this.substring=function(x,y){
		if (typeof y=='undefined') { return this.toString().substring(x); }
		return this.toString().substring(x,y);
	};
	/**
	   Wrapper for this.toString().split()
	   @param {String} x
	   @type Array
	*/
	this.split=function(x){return this.toString().split(x);};
	/**
	   Wrapper for this.toString().replace()
	   @param {String} x
	   @param {String} y
	   @type String
	*/
	this.replace=function(x,y){ return this.toString().replace(x,y); };
}


/**
   Creates a new &lt;code&gt;Title&lt;/code&gt;.
   @constructor

   @class The Title class. Holds article titles and converts them into
   various forms. Also deals with anchors, by which we mean the bits
   of the article URL after a # character, representing locations
   within an article.

   @param {String} value The initial value to assign to the
   article. This must be the canonical title (see {@link
   Title#value}. Omit this in the constructor and use another function
   to set the title if this is unavailable.
*/
function Title(val) {
	/**
	   The canonical article title. This must be in UTF-8 with no
	   entities, escaping or nasties. Also, underscores should be
	   replaced with spaces.
	   @type String
	   @private
	*/
	this.value=null;
	/**
	   The canonical form of the anchor. This should be exactly as
	   it appears in the URL, i.e. with the .C3.0A bits in.
	   @type String
	*/
	this.anchor='';

	this.setUtf(val);
}
Title.prototype=new Stringwrapper();
/**
   Returns the canonical representation of the article title, optionally without anchor.
   @param {boolean} omitAnchor
   @fixme Decide specs for anchor
   @return String The article title and the anchor.
*/
Title.prototype.toString=function(omitAnchor) {
	return this.value + ( (!omitAnchor &amp;&amp; this.anchor) ? '#' + this.anchorString() : '' );
};
Title.prototype.anchorString=function() {
	if (!this.anchor) { return ''; }
	var split=this.anchor.parenSplit(/((?:[.][0-9A-F]{2})+)/);
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		// FIXME s/decodeURI/decodeURIComponent/g ?
		split[j]=decodeURIComponent(split[j].split('.').join('%')).split('_').join(' ');
	}
	return split.join('');
};
Title.prototype.urlAnchor=function() {
	var split=this.anchor.parenSplit('/((?:[%][0-9A-F]{2})+)/');
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		split[j]=split[j].split('%').join('.');
	}
	return split.join('');
};
Title.prototype.anchorFromUtf=function(str) {
	this.anchor=encodeURIComponent(str.split(' ').join('_'))
	.split('%3A').join(':').split(&quot;'&quot;).join('%27').split('%').join('.');
};
Title.fromURL=function(h) {
	return new Title().fromURL(h);
};
Title.prototype.fromURL=function(h) {
	if (typeof h != 'string') {
		this.value=null;
		return this;
	}

	// NOTE : playing with decodeURI, encodeURI, escape, unescape,
	// we seem to be able to replicate the IE borked encoding

	// IE doesn't do this new-fangled utf-8 thing.
	// and it's worse than that.
	// IE seems to treat the query string differently to the rest of the url
	// the query is treated as bona-fide utf8, but the first bit of the url is pissed around with

	// we fix up &amp; for all browsers, just in case.
	var splitted=h.split('?');
	splitted[0]=splitted[0].split('&amp;').join('%26');

	if (pg.flag.linksLikeIE6) {
		splitted[0]=encodeURI(decode_utf8(splitted[0]));
	}

	h=splitted.join('?');

	var contribs=pg.re.contribs.exec(h);
	if (contribs !== null) {
		if (contribs[1]=='title=') { contribs[3]=contribs[3].split('+').join(' '); }
		var u=new Title(contribs[3]);
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + u.stripNamespace()));
		return this;
	}

	var email=pg.re.email.exec(h);
	if (email !== null) {
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(email[3]).stripNamespace()));
		return this;
	}

	var backlinks=pg.re.backlinks.exec(h);
	if (backlinks) {
		this.setUtf(this.decodeNasties(new Title(backlinks[3])));
		return this;
	}

	// no more special cases to check --
	// hopefully it's not a disguised user-related or specially treated special page
	var m=pg.re.main.exec(h);
	if(m===null) { this.value=null; }
	else {
        var fromBotInterface = /[?](.+[&amp;])?title=/.test(h);
        if (fromBotInterface) {
            m[2]=m[2].split('+').join('_');
        }
        var extracted = m[2] + (m[3] ? '#' + m[3] : '');
        if (pg.flag.isSafari &amp;&amp; /%25[0-9A-Fa-f]{2}/.test(extracted)) {
            // Fix Safari issue
            // Safari sometimes encodes % as %25 in UTF-8 encoded strings like %E5%A3 -&gt; %25E5%25A3.
            this.setUtf(decodeURIComponent(unescape(extracted)));
        } else {
            this.setUtf(this.decodeNasties(extracted));
        }
    }
	return this;
};
Title.prototype.decodeNasties=function(txt) {
	var ret= this.decodeEscapes(decodeURI(txt));
	ret = ret.replace(/[_ ]*$/, '');
	return ret;
};
Title.prototype.decodeEscapes=function(txt) {
	var split=txt.parenSplit(/((?:[%][0-9A-Fa-f]{2})+)/);
	var len=split.length;
	for (var i=1; i&lt;len; i=i+2) {
		// FIXME is decodeURIComponent better?
		split[i]=unescape(split[i]);
	}
	return split.join('');
};
Title.fromAnchor=function(a) {
	return new Title().fromAnchor(a);
};
Title.prototype.fromAnchor=function(a) {
	if (!a) { this.value=null; return this; }
	return this.fromURL(a.href);
};
Title.fromWikiText=function(txt) {
	return new Title().fromWikiText(txt);
};
Title.prototype.fromWikiText=function(txt) {
	// FIXME - testing needed
	if (!pg.flag.linksLikeIE6) { txt=myDecodeURI(txt); }
	this.setUtf(txt);
	return this;
};
Title.prototype.hintValue=function(){
	if(!this.value) { return ''; }
	return safeDecodeURI(this.value);
};
//&lt;NOLITE&gt;
Title.prototype.toUserName=function(withNs) {
	if (this.namespaceId() != pg.nsUserId &amp;&amp; this.namespaceId() != pg.nsUsertalkId) {
		this.value=null;
		return;
	}
	this.value = (withNs ? mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' : '') + this.stripNamespace().split('/')[0];
};
Title.prototype.userName=function(withNs) {
	var t=(new Title(this.value));
	t.toUserName(withNs);
	if (t.value) { return t; }
	return null;
};
Title.prototype.toTalkPage=function() {
	// convert article to a talk page, or if we can't, return null
	// In other words: return null if this ALREADY IS a talk page
	// and return the corresponding talk page otherwise
	//
	// Per //www.mediawiki.org/wiki/Manual:Namespace#Subject_and_talk_namespaces
	// * All discussion namespaces have odd-integer indices
	// * The discussion namespace index for a specific namespace with index n is n + 1
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 0) //non-special and subject namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId+1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
//&lt;/NOLITE&gt;
// Return canonical, localized namespace
Title.prototype.namespace=function() {
	return mw.config.get('wgFormattedNamespaces')[this.namespaceId()];
};
Title.prototype.namespaceId=function() {
	var n=this.value.indexOf(':');
	if (n&lt;0) { return 0; } //mainspace
	var namespaceId = mw.config.get('wgNamespaceIds')[this.value.substring(0,n).split(' ').join('_').toLowerCase()];
	if (typeof namespaceId=='undefined') return 0; //mainspace
	return namespaceId;
};
//&lt;NOLITE&gt;
Title.prototype.talkPage=function() {
	var t=new Title(this.value);
	t.toTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.isTalkPage=function() {
	if (this.talkPage()===null) { return true; }
	return false;
};
Title.prototype.toArticleFromTalkPage=function() {
	//largely copy/paste from toTalkPage above.
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 1) //non-special and talk namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId-1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
Title.prototype.articleFromTalkPage=function() {
	var t=new Title(this.value);
	t.toArticleFromTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.articleFromTalkOrArticle=function() {
	var t=new Title(this.value);
	if ( t.toArticleFromTalkPage() ) { return t; }
	return this;
};
Title.prototype.isIpUser=function() {
	return pg.re.ipUser.test(this.userName());
};
//&lt;/NOLITE&gt;
Title.prototype.stripNamespace=function(){ // returns a string, not a Title
	var n=this.value.indexOf(':');
	if (n&lt;0) { return this.value; }
	var namespaceId = this.namespaceId();
	if (typeof namespaceId==='undefined') return this.value;
	return this.value.substring(n+1);
};
Title.prototype.setUtf=function(value){
	if (!value) { this.value=''; return; }
	var anch=value.indexOf('#');
	if(anch &lt; 0) { this.value=value.split('_').join(' '); this.anchor=''; return; }
	this.value=value.substring(0,anch).split('_').join(' ');
	this.anchor=value.substring(anch+1);
	this.ns=null; // wait until namespace() is called
};
Title.prototype.setUrl=function(urlfrag) {
	var anch=urlfrag.indexOf('#');
	this.value=safeDecodeURI(urlfrag.substring(0,anch));
	this.anchor=value.substring(anch+1);
};
Title.prototype.append=function(x){
	this.setUtf(this.value + x);
};
Title.prototype.urlString=function(x) {
	x || ( x={} );
	var v=this.toString(true);
	if (!x.omitAnchor &amp;&amp; this.anchor) { v+= '#' + this.urlAnchor(); }
	if (!x.keepSpaces) { v=v.split(' ').join('_'); }
	return encodeURI(v).split('&amp;').join('%26').split('?').join('%3F').split('+').join('%2B');
};
Title.prototype.removeAnchor=function() {
	return new Title(this.toString(true));
};
Title.prototype.toUrl=function() {
	return pg.wiki.titlebase + this.urlString();
};


function paramValue(param, url) {
	var s=url.parenSplit(RegExp('[?&amp;]' + literalizeRegex(param) + '=([^?&amp;]*)'));
	if (!url) { return null; }
	return s[1] || null;
}

function parseParams(url) {
	var ret={};
	if (url.indexOf('?')==-1) { return ret; }
	var s=url.split('?').slice(1).join();
	var t=s.split('&amp;');
	for (var i=0; i&lt;t.length; ++i) {
		var z=t[i].split('=');
		z.push(null);
		ret[z[0]]=z[1];
	}
	return ret;
}

// all sorts of stuff here
// FIXME almost everything needs to be rewritten

function oldidFromAnchor(a) { return paramValue('oldid', a.href); }
//function diffFromAnchor(a) { return paramValue('diff', a.href); }


function wikiMarkupToAddressFragment (str) { // for images
	var ret = safeDecodeURI(str);
	ret = ret.split(' ').join('_');
	ret = encodeURI(ret);
	return ret;
}

// (a) myDecodeURI (first standard decodeURI, then pg.re.urlNoPopup)
// (b) change spaces to underscores
// (c) encodeURI (just the straight one, no pg.re.urlNoPopup)

function myDecodeURI (str) {
	var ret;
	// FIXME decodeURIComponent??
	try { ret=decodeURI(str.toString()); }
	catch (summat) { return str; }
	for (var i=0; i&lt;pg.misc.decodeExtras.length; ++i) {
		var from=pg.misc.decodeExtras[i].from;
		var to=pg.misc.decodeExtras[i].to;
		ret=ret.split(from).join(to);
	}
	return ret;
}

function safeDecodeURI(str) { var ret=myDecodeURI(str); return ret || str; }

///////////
// TESTS //
///////////

//&lt;NOLITE&gt;
function isIpUser(user) {return pg.re.ipUser.test(user);}

function isDisambig(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	return ! article.isTalkPage() &amp;&amp; pg.re.disambig.test(data);
}

function stubCount(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	var sectStub=0;
	var realStub=0;
	if (pg.re.stub.test(data)) {
		var s=data.parenSplit(pg.re.stub);
		for (var i=1; i&lt;s.length; i=i+2) {
			if (s[i]) { ++sectStub; }
			else { ++realStub; }
		}
	}
	return { real: realStub, sect: sectStub };
}

function isValidImageName(str){ // extend as needed...
	return ( str.indexOf('{') == -1 );
}

function isInStrippableNamespace(article) {
	//I believe that this method means to return whether the given article is in a namspace without subpages. Meaning, it's broken.
	return ( article.namespace() !== '' );
}

function isInMainNamespace(article) { return !isInStrippableNamespace(article); }

function anchorContainsImage(a) {
	// iterate over children of anchor a
	// see if any are images
	if (a===null) { return false; }
	kids=a.childNodes;
	for (var i=0; i&lt;kids.length; ++i) { if (kids[i].nodeName=='IMG') { return true; } }
	return false;
}
//&lt;/NOLITE&gt;
function isPopupLink(a) {
	// NB for performance reasons, TOC links generally return true
	// they should be stripped out later

	if (!markNopopupSpanLinks.done) { markNopopupSpanLinks(); }
	if (a.inNopopupSpan || a.className=='sortheader') { return false; }

	// FIXME is this faster inline?
	if (a.onmousedown || a.getAttribute('nopopup')) { return false; }
	var h=a.href;
	if (!pg.re.basenames.test(h)) { return false; }
	if ( !pg.re.urlNoPopup.test(h) ) { return true;	}
	return (
		(pg.re.email.test(h) || pg.re.contribs.test(h) || pg.re.backlinks.test(h)) &amp;&amp;
		h.indexOf('&amp;limit=') == -1 );
}

function markNopopupSpanLinks() {
	if( !getValueOf('popupOnlyArticleLinks'))
		fixVectorMenuPopups();

	var s=getElementsByClassName(document, '*', &quot;nopopups&quot;)
	for (var i=0; i&lt;s.length; ++i) {
		var as=s[i].getElementsByTagName('a');
		for (var j=0; j&lt;as.length; ++j) {
			as[j].inNopopupSpan=true;
		}
	}
	
	markNopopupSpanLinks.done=true;
}

function fixVectorMenuPopups() {
	var vmenus = getElementsByClassName( document, 'div', 'vectorMenu');
	for( i= 0; vmenus &amp;&amp; i&lt; vmenus.length; i++ ) {
		var h5 = vmenus[i].getElementsByTagName('h5')[0];
		if( h5) var a = h5.getElementsByTagName('a')[0];
		if( a ) a.inNopopupSpan=true;
	}
}
// ENDFILE: titles.js
// STARTFILE: cookies.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Cookie handling
// from http://www.quirksmode.org/js/cookies.html

var Cookie= {
	create: function(name,value,days)
	{
		var expires;
		if (days)
		{
			var date = new Date();
			date.setTime(date.getTime()+(days*24*60*60*1000));
			expires = &quot;; expires=&quot;+date.toGMTString();
		}
		else { expires = &quot;&quot;; }
		document.cookie = name+&quot;=&quot;+value+expires+&quot;; path=/&quot;;
	},

	read: function(name)
	{
		var nameEQ = name + &quot;=&quot;;
		var ca = document.cookie.split(';');
		for(var i=0;i &lt; ca.length;i++)
		{
			var c = ca[i];
			while (c[0]==' ') { c = c.substring(1,c.length); }
			if (c.indexOf(nameEQ) === 0) { return c.substring(nameEQ.length,c.length); }
		}
		return null;
	},

	erase: function(name)
	{
		Cookie.create(name,&quot;&quot;,-1);
	}
};
//&lt;/NOLITE&gt;
// ENDFILE: cookies.js
// STARTFILE: getpage.js
//////////////////////////////////////////////////
// Wiki-specific downloading
//

// Schematic for a getWiki call
//
//   getWiki-&gt;-getPageWithCaching
//                    |
//       false        |          true
// getPage&lt;-[findPictureInCache]-&gt;-onComplete(a fake download)
//   \.
//     (async)-&gt;addPageToCache(download)-&gt;-onComplete(download)


/** @todo {document}
    @param {Title} article
    @param {Function} onComplete
    @param {integer} oldid
    @param {Navapopup} owner
*/
function getWiki(article, onComplete, oldid, owner) {
	// set ctype=text/css to get around opera gzip bug
	var url = pg.wiki.titlebase + article.removeAnchor().urlString() +
	    '&amp;action=raw&amp;ctype=text/css';
	if (oldid || oldid===0 || oldid==='0') { url += '&amp;oldid='+oldid; }
	url += '';

	getPageWithCaching(url, onComplete, owner);
}

// check cache to see if page exists

function getPageWithCaching(url, onComplete, owner) {
	log('getPageWithCaching, url='+url);
	var i=findInPageCache(url);
	if (i &gt; -1) {
		var d=fakeDownload(url, owner.idNumber, onComplete,
				   pg.cache.pages[i].data, pg.cache.pages[i].lastModified,
				   owner);
	} else {
		var d=getPage(url, onComplete, owner);
		if (d &amp;&amp; owner &amp;&amp; owner.addDownload) {
			owner.addDownload(d);
			d.owner=owner;
		}
	}
}

function getPage(url, onComplete, owner) {
	log('getPage');
	var callback= function (d) { if (!d.aborted) {addPageToCache(d); onComplete(d);} };
	return startDownload(url, owner.idNumber, callback);
}

function findInPageCache(url) {
	for (var i=0; i&lt;pg.cache.pages.length; ++i) {
		if (url==pg.cache.pages[i].url) { return i; }
	}
	return -1;
}

function addPageToCache(download) {
	log('addPageToCache '+download.url);
	var page = {url: download.url, data: download.data, lastModified: download.lastModified};
	return pg.cache.pages.push(page);
}
// ENDFILE: getpage.js
// STARTFILE: md5-2.2alpha.js
//&lt;NOLITE&gt;
/*
 * A JavaScript implementation of the RSA Data Security, Inc. MD5 Message
 * Digest Algorithm, as defined in {{RFC|1321}}.
 * Version 2.2-alpha Copyright (C) Paul Johnston 1999 - 2005
 * Other contributors: Greg Holt, Andrew Kepert, Ydnar, Lostinet
 * Distributed under the BSD License
 * See http://pajhome.org.uk/crypt/md5 for more info.
 */

/*
 * Configurable variables. You may need to tweak these to be compatible with
 * the server-side, but the defaults work in most cases.
 */
var hexcase = 0;   /* hex output format. 0 - lowercase; 1 - uppercase	     */
var b64pad  = &quot;&quot;; /* base-64 pad character. &quot;=&quot; for strict RFC compliance   */

/*
 * These are the functions you'll usually want to call
 * They take string arguments and return either hex or base-64 encoded strings
 */
function hex_md5(s)    { return rstr2hex(rstr_md5(str2rstr_utf8(s))); }
function b64_md5(s)    { return rstr2b64(rstr_md5(str2rstr_utf8(s))); }
function any_md5(s, e) { return rstr2any(rstr_md5(str2rstr_utf8(s)), e); }
function hex_hmac_md5(k, d)
  { return rstr2hex(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function b64_hmac_md5(k, d)
  { return rstr2b64(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function any_hmac_md5(k, d, e)
  { return rstr2any(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d)), e); }

/*
 * Perform a simple self-test to see if the VM is working
 */
function md5_vm_test()
{
  return hex_md5(&quot;abc&quot;) == &quot;900150983cd24fb0d6963f7d28e17f72&quot;;
}

/*
 * Calculate the MD5 of a raw string
 */
function rstr_md5(s)
{
  return binl2rstr(binl_md5(rstr2binl(s), s.length * 8));
}

/*
 * Calculate the HMAC-MD5, of a key and some data (raw strings)
 */
function rstr_hmac_md5(key, data)
{
  var bkey = rstr2binl(key);
  if(bkey.length &gt; 16) bkey = binl_md5(bkey, key.length * 8);

  var ipad = Array(16), opad = Array(16);
  for(var i = 0; i &lt; 16; i++)
  {
    ipad[i] = bkey[i] ^ 0x36363636;
    opad[i] = bkey[i] ^ 0x5C5C5C5C;
  }

  var hash = binl_md5(ipad.concat(rstr2binl(data)), 512 + data.length * 8);
  return binl2rstr(binl_md5(opad.concat(hash), 512 + 128));
}

/*
 * Convert a raw string to a hex string
 */
function rstr2hex(input)
{
  var hex_tab = hexcase ? &quot;0123456789ABCDEF&quot; : &quot;0123456789abcdef&quot;;
  var output = &quot;&quot;;
  var x;
  for(var i = 0; i &lt; input.length; i++)
  {
    x = input.charCodeAt(i);
    output += hex_tab.charAt((x &gt;&gt;&gt; 4) &amp; 0x0F)
	   +  hex_tab.charAt( x	       &amp; 0x0F);
  }
  return output;
}

/*
 * Convert a raw string to a base-64 string
 */
function rstr2b64(input)
{
  var tab = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
  var output = &quot;&quot;;
  var len = input.length;
  for(var i = 0; i &lt; len; i += 3)
  {
    var triplet = (input.charCodeAt(i) &lt;&lt; 16)
		| (i + 1 &lt; len ? input.charCodeAt(i+1) &lt;&lt; 8 : 0)
		| (i + 2 &lt; len ? input.charCodeAt(i+2)	    : 0);
    for(var j = 0; j &lt; 4; j++)
    {
      if(i * 8 + j * 6 &gt; input.length * 8) output += b64pad;
      else output += tab.charAt((triplet &gt;&gt;&gt; 6*(3-j)) &amp; 0x3F);
    }
  }
  return output;
}

/*
 * Convert a raw string to an arbitrary string encoding
 */
function rstr2any(input, encoding)
{
  var divisor = encoding.length;
  var remainders = Array();
  var i, q, x, quotient;

  /* Convert to an array of 16-bit big-endian values, forming the dividend */
  var dividend = Array(input.length / 2);
  for(i = 0; i &lt; dividend.length; i++)
  {
    dividend[i] = (input.charCodeAt(i * 2) &lt;&lt; 8) | input.charCodeAt(i * 2 + 1);
  }

  /*
   * Repeatedly perform a long division. The binary array forms the dividend,
   * the length of the encoding is the divisor. Once computed, the quotient
   * forms the dividend for the next step. We stop when the dividend is zero.
   * All remainders are stored for later use.
   */
  while(dividend.length &gt; 0)
  {
    quotient = Array();
    x = 0;
    for(i = 0; i &lt; dividend.length; i++)
    {
      x = (x &lt;&lt; 16) + dividend[i];
      q = Math.floor(x / divisor);
      x -= q * divisor;
      if(quotient.length &gt; 0 || q &gt; 0)
	quotient[quotient.length] = q;
    }
    remainders[remainders.length] = x;
    dividend = quotient;
  }

  /* Convert the remainders to the output string */
  var output = &quot;&quot;;
  for(i = remainders.length - 1; i &gt;= 0; i--)
    output += encoding.charAt(remainders[i]);

  return output;
}

/*
 * Encode a string as utf-8.
 * For efficiency, this assumes the input is valid utf-16.
 */
function str2rstr_utf8(input)
{
  var output = &quot;&quot;;
  var i = -1;
  var x, y;

  while(++i &lt; input.length)
  {
    /* Decode utf-16 surrogate pairs */
    x = input.charCodeAt(i);
    y = i + 1 &lt; input.length ? input.charCodeAt(i + 1) : 0;
    if(0xD800 &lt;= x &amp;&amp; x &lt;= 0xDBFF &amp;&amp; 0xDC00 &lt;= y &amp;&amp; y &lt;= 0xDFFF)
    {
      x = 0x10000 + ((x &amp; 0x03FF) &lt;&lt; 10) + (y &amp; 0x03FF);
      i++;
    }

    /* Encode output as utf-8 */
    if(x &lt;= 0x7F)
      output += String.fromCharCode(x);
    else if(x &lt;= 0x7FF)
      output += String.fromCharCode(0xC0 | ((x &gt;&gt;&gt; 6 ) &amp; 0x1F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0xFFFF)
      output += String.fromCharCode(0xE0 | ((x &gt;&gt;&gt; 12) &amp; 0x0F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0x1FFFFF)
      output += String.fromCharCode(0xF0 | ((x &gt;&gt;&gt; 18) &amp; 0x07),
				    0x80 | ((x &gt;&gt;&gt; 12) &amp; 0x3F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
  }
  return output;
}

/*
 * Encode a string as utf-16
 */
function str2rstr_utf16le(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode( input.charCodeAt(i)	      &amp; 0xFF,
				  (input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF);
  return output;
}

function str2rstr_utf16be(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode((input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF,
				   input.charCodeAt(i)	      &amp; 0xFF);
  return output;
}

/*
 * Convert a raw string to an array of little-endian words
 * Characters &gt;255 have their high-byte silently ignored.
 */
function rstr2binl(input)
{
  var output = Array(input.length &gt;&gt; 2);
  for(var i = 0; i &lt; output.length; i++)
    output[i] = 0;
  for(var i = 0; i &lt; input.length * 8; i += 8)
    output[i&gt;&gt;5] |= (input.charCodeAt(i / 8) &amp; 0xFF) &lt;&lt; (i%32);
  return output;
}

/*
 * Convert an array of little-endian words to a string
 */
function binl2rstr(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length * 32; i += 8)
    output += String.fromCharCode((input[i&gt;&gt;5] &gt;&gt;&gt; (i % 32)) &amp; 0xFF);
  return output;
}

/*
 * Calculate the MD5 of an array of little-endian words, and a bit length.
 */
function binl_md5(x, len)
{
  /* append padding */
  x[len &gt;&gt; 5] |= 0x80 &lt;&lt; ((len) % 32);
  x[(((len + 64) &gt;&gt;&gt; 9) &lt;&lt; 4) + 14] = len;

  var a =  1732584193;
  var b = -271733879;
  var c = -1732584194;
  var d =  271733878;

  for(var i = 0; i &lt; x.length; i += 16)
  {
    var olda = a;
    var oldb = b;
    var oldc = c;
    var oldd = d;

    a = md5_ff(a, b, c, d, x[i+ 0], 7 , -680876936);
    d = md5_ff(d, a, b, c, x[i+ 1], 12, -389564586);
    c = md5_ff(c, d, a, b, x[i+ 2], 17,	 606105819);
    b = md5_ff(b, c, d, a, x[i+ 3], 22, -1044525330);
    a = md5_ff(a, b, c, d, x[i+ 4], 7 , -176418897);
    d = md5_ff(d, a, b, c, x[i+ 5], 12,	 1200080426);
    c = md5_ff(c, d, a, b, x[i+ 6], 17, -1473231341);
    b = md5_ff(b, c, d, a, x[i+ 7], 22, -45705983);
    a = md5_ff(a, b, c, d, x[i+ 8], 7 ,	 1770035416);
    d = md5_ff(d, a, b, c, x[i+ 9], 12, -1958414417);
    c = md5_ff(c, d, a, b, x[i+10], 17, -42063);
    b = md5_ff(b, c, d, a, x[i+11], 22, -1990404162);
    a = md5_ff(a, b, c, d, x[i+12], 7 ,	 1804603682);
    d = md5_ff(d, a, b, c, x[i+13], 12, -40341101);
    c = md5_ff(c, d, a, b, x[i+14], 17, -1502002290);
    b = md5_ff(b, c, d, a, x[i+15], 22,	 1236535329);

    a = md5_gg(a, b, c, d, x[i+ 1], 5 , -165796510);
    d = md5_gg(d, a, b, c, x[i+ 6], 9 , -1069501632);
    c = md5_gg(c, d, a, b, x[i+11], 14,	 643717713);
    b = md5_gg(b, c, d, a, x[i+ 0], 20, -373897302);
    a = md5_gg(a, b, c, d, x[i+ 5], 5 , -701558691);
    d = md5_gg(d, a, b, c, x[i+10], 9 ,	 38016083);
    c = md5_gg(c, d, a, b, x[i+15], 14, -660478335);
    b = md5_gg(b, c, d, a, x[i+ 4], 20, -405537848);
    a = md5_gg(a, b, c, d, x[i+ 9], 5 ,	 568446438);
    d = md5_gg(d, a, b, c, x[i+14], 9 , -1019803690);
    c = md5_gg(c, d, a, b, x[i+ 3], 14, -187363961);
    b = md5_gg(b, c, d, a, x[i+ 8], 20,	 1163531501);
    a = md5_gg(a, b, c, d, x[i+13], 5 , -1444681467);
    d = md5_gg(d, a, b, c, x[i+ 2], 9 , -51403784);
    c = md5_gg(c, d, a, b, x[i+ 7], 14,	 1735328473);
    b = md5_gg(b, c, d, a, x[i+12], 20, -1926607734);

    a = md5_hh(a, b, c, d, x[i+ 5], 4 , -378558);
    d = md5_hh(d, a, b, c, x[i+ 8], 11, -2022574463);
    c = md5_hh(c, d, a, b, x[i+11], 16,	 1839030562);
    b = md5_hh(b, c, d, a, x[i+14], 23, -35309556);
    a = md5_hh(a, b, c, d, x[i+ 1], 4 , -1530992060);
    d = md5_hh(d, a, b, c, x[i+ 4], 11,	 1272893353);
    c = md5_hh(c, d, a, b, x[i+ 7], 16, -155497632);
    b = md5_hh(b, c, d, a, x[i+10], 23, -1094730640);
    a = md5_hh(a, b, c, d, x[i+13], 4 ,	 681279174);
    d = md5_hh(d, a, b, c, x[i+ 0], 11, -358537222);
    c = md5_hh(c, d, a, b, x[i+ 3], 16, -722521979);
    b = md5_hh(b, c, d, a, x[i+ 6], 23,	 76029189);
    a = md5_hh(a, b, c, d, x[i+ 9], 4 , -640364487);
    d = md5_hh(d, a, b, c, x[i+12], 11, -421815835);
    c = md5_hh(c, d, a, b, x[i+15], 16,	 530742520);
    b = md5_hh(b, c, d, a, x[i+ 2], 23, -995338651);

    a = md5_ii(a, b, c, d, x[i+ 0], 6 , -198630844);
    d = md5_ii(d, a, b, c, x[i+ 7], 10,	 1126891415);
    c = md5_ii(c, d, a, b, x[i+14], 15, -1416354905);
    b = md5_ii(b, c, d, a, x[i+ 5], 21, -57434055);
    a = md5_ii(a, b, c, d, x[i+12], 6 ,	 1700485571);
    d = md5_ii(d, a, b, c, x[i+ 3], 10, -1894986606);
    c = md5_ii(c, d, a, b, x[i+10], 15, -1051523);
    b = md5_ii(b, c, d, a, x[i+ 1], 21, -2054922799);
    a = md5_ii(a, b, c, d, x[i+ 8], 6 ,	 1873313359);
    d = md5_ii(d, a, b, c, x[i+15], 10, -30611744);
    c = md5_ii(c, d, a, b, x[i+ 6], 15, -1560198380);
    b = md5_ii(b, c, d, a, x[i+13], 21,	 1309151649);
    a = md5_ii(a, b, c, d, x[i+ 4], 6 , -145523070);
    d = md5_ii(d, a, b, c, x[i+11], 10, -1120210379);
    c = md5_ii(c, d, a, b, x[i+ 2], 15,	 718787259);
    b = md5_ii(b, c, d, a, x[i+ 9], 21, -343485551);

    a = safe_add(a, olda);
    b = safe_add(b, oldb);
    c = safe_add(c, oldc);
    d = safe_add(d, oldd);
  }
  return Array(a, b, c, d);
}

/*
 * These functions implement the four basic operations the algorithm uses.
 */
function md5_cmn(q, a, b, x, s, t)
{
  return safe_add(bit_rol(safe_add(safe_add(a, q), safe_add(x, t)), s),b);
}
function md5_ff(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; c) | ((~b) &amp; d), a, b, x, s, t);
}
function md5_gg(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; d) | (c &amp; (~d)), a, b, x, s, t);
}
function md5_hh(a, b, c, d, x, s, t)
{
  return md5_cmn(b ^ c ^ d, a, b, x, s, t);
}
function md5_ii(a, b, c, d, x, s, t)
{
  return md5_cmn(c ^ (b | (~d)), a, b, x, s, t);
}

/*
 * Add integers, wrapping at 2^32. This uses 16-bit operations internally
 * to work around bugs in some JS interpreters.
 */
function safe_add(x, y)
{
  var lsw = (x &amp; 0xFFFF) + (y &amp; 0xFFFF);
  var msw = (x &gt;&gt; 16) + (y &gt;&gt; 16) + (lsw &gt;&gt; 16);
  return (msw &lt;&lt; 16) | (lsw &amp; 0xFFFF);
}

/*
 * Bitwise rotate a 32-bit number to the left.
 */
function bit_rol(num, cnt)
{
  return (num &lt;&lt; cnt) | (num &gt;&gt;&gt; (32 - cnt));
}
//&lt;/NOLITE&gt;
// ENDFILE: md5-2.2alpha.js
// STARTFILE: parensplit.js
//////////////////////////////////////////////////
// parenSplit

// String.prototype.parenSplit should do what ECMAscript says
// String.prototype.split does, interspersing paren matches between
// the split elements

if (String('abc'.split(/(b)/))!='a,b,c') {
	// broken String.split, e.g. konq, IE
	String.prototype.parenSplit=function (re) {
		re=nonGlobalRegex(re);
		var s=this;
		var m=re.exec(s);
		var ret=[];
		while (m &amp;&amp; s) {
			// without the following loop, we have
			// 'ab'.parenSplit(/a|(b)/) != 'ab'.split(/a|(b)/)
			for(var i=0; i&lt;m.length; ++i) {
				if (typeof m[i]=='undefined') m[i]='';
			}
			ret.push(s.substring(0,m.index));
			ret = ret.concat(m.slice(1));
			s=s.substring(m.index + m[0].length);
			m=re.exec(s);
		}
		ret.push(s);
		return ret;
	};
} else {
	String.prototype.parenSplit=function (re) { return this.split(re); };
	String.prototype.parenSplit.isNative=true;
}

function nonGlobalRegex(re) {
	var s=re.toString();
	flags='';
	for (var j=s.length; s.charAt(j) != '/'; --j) {
		if (s.charAt(j) != 'g') { flags += s.charAt(j); }
	}
	var t=s.substring(1,j);
	return RegExp(t,flags);
}
// ENDFILE: parensplit.js
// STARTFILE: tools.js
// IE madness with encoding
// ========================
//
// suppose throughout that the page is in utf8, like wikipedia
//
// if a is an anchor DOM element and a.href should consist of
//
// http://host.name.here/wiki/foo?bar=baz
//
// then IE gives foo as &quot;latin1-encoded&quot; utf8; we have foo = decode_utf8(decodeURI(foo_ie))
// but IE gives bar=baz correctly as plain utf8
//
// ---------------------------------
//
// IE's xmlhttp doesn't understand utf8 urls. Have to use encodeURI here.
//
// ---------------------------------
//
// summat else

// Source: http://aktuell.de.selfhtml.org/artikel/javascript/utf8b64/utf8.htm

//&lt;NOLITE&gt;
function encode_utf8(rohtext) {
	// dient der Normalisierung des Zeilenumbruchs
	rohtext = rohtext.replace(/\r\n/g,&quot;\n&quot;);
	var utftext = &quot;&quot;;
	for(var n=0; n&lt;rohtext.length; n++)
	{
		// ermitteln des Unicodes des  aktuellen Zeichens
		var c=rohtext.charCodeAt(n);
		// alle Zeichen von 0-127 =&gt; 1byte
		if (c&lt;128)
			utftext += String.fromCharCode(c);
		// alle Zeichen von 127 bis 2047 =&gt; 2byte
		else if((c&gt;127) &amp;&amp; (c&lt;2048)) {
			utftext += String.fromCharCode((c&gt;&gt;6)|192);
			utftext += String.fromCharCode((c&amp;63)|128);}
		// alle Zeichen von 2048 bis 66536 =&gt; 3byte
		else {
			utftext += String.fromCharCode((c&gt;&gt;12)|224);
			utftext += String.fromCharCode(((c&gt;&gt;6)&amp;63)|128);
			utftext += String.fromCharCode((c&amp;63)|128);}
	}
	return utftext;
}

function getJsObj(json) {
	try {
		var json_ret = eval('(' + json + ')');
	} catch (someError) {
		errlog('Something went wrong with getJsobj, json='+json);
		return 1;
	}
	if( json_ret['warnings'] ) {
		for( var w=0; w &lt; json_ret['warnings'].length; w++ ) {
			log( json_ret['warnings'][w]['*'] );
		}
	} else if ( json_ret['error'] ) {
		errlog( json_ret['error'].code + ': ' + json_ret['error'].info );
	}
	return json_ret;
}

function anyChild(obj) {
	for (var p in obj) {
		return obj[p];
	}
	return null;
}

//&lt;/NOLITE&gt;

function decode_utf8(utftext) {
	var plaintext = &quot;&quot;; var i=0, c=0, c1=0, c2=0;
	// while-Schleife, weil einige Zeichen uebersprungen werden
	while(i&lt;utftext.length)
	{
		c = utftext.charCodeAt(i);
		if (c&lt;128) {
			plaintext += String.fromCharCode(c);
			i++;}
		else if((c&gt;191) &amp;&amp; (c&lt;224)) {
			c2 = utftext.charCodeAt(i+1);
			plaintext += String.fromCharCode(((c&amp;31)&lt;&lt;6) | (c2&amp;63));
			i+=2;}
		else {
			c2 = utftext.charCodeAt(i+1); c3 = utftext.charCodeAt(i+2);
			plaintext += String.fromCharCode(((c&amp;15)&lt;&lt;12) | ((c2&amp;63)&lt;&lt;6) | (c3&amp;63));
			i+=3;}
	}
	return plaintext;
}


function upcaseFirst(str) {
	if (typeof str != typeof '' || str=='') return '';
	return str[0].toUpperCase() + str.substring(1);
}


function findInArray(arr, foo) {
	if (!arr || !arr.length) { return -1; }
	var len=arr.length;
	for (var i=0; i&lt;len; ++i) { if (arr[i]==foo) { return i; } }
	return -1;
}

function nextOne (array, value) {
	// NB if the array has two consecutive entries equal
	//    then this will loop on successive calls
	var i=findInArray(array, value);
	if (i&lt;0) { return null; }
	return array[i+1];
}

function literalizeRegex(str){
	return str.replace(RegExp('([-.|()\\\\+?*^${}\\[\\]])', 'g'), '\\$1');
}

String.prototype.entify=function() {
	//var shy='&amp;shy;';
	return this.split('&amp;').join('&amp;amp;').split('&lt;').join('&amp;lt;').split('&gt;').join('&amp;gt;'/*+shy*/).split('&quot;').join('&amp;quot;');
};

function findThis(array, value) {
	if (typeof array.length == 'undefined') { return null; }
	for (var i=0; i&lt;array.length; ++i) {
		if (array[i]==value) { return i; }
	}
	return null;
}

function removeNulls(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i]) {
			ret.push(list[i]);
		}
	}
	return ret;
}
function joinPath(list) {
	return removeNulls(list).join('/');
}


function simplePrintf(str, subs) {
	if (!str || !subs) { return str; }
	var ret=[];
	var s=str.parenSplit(/(%s|\$[0-9]+)/);
	var i=0;
	do {
		ret.push(s.shift());
		if ( !s.length ) { break; }
		var cmd=s.shift();
		if (cmd == '%s') {
			if ( i &lt; subs.length ) { ret.push(subs[i]); } else { ret.push(cmd); }
			++i;
		} else {
			var j=parseInt( cmd.replace('$', ''), 10 ) - 1;
			if ( j &gt; -1 &amp;&amp; j &lt; subs.length ) { ret.push(subs[j]); } else { ret.push(cmd); }
		}
	} while (s.length &gt; 0);
	return ret.join('');
}

function max(a,b){return a&lt;b ? b : a;}
function min(a,b){return a&gt;b ? b : a;}

function isString(x) { return (typeof x === 'string' || x instanceof String); }
//function isNumber(x) { return (typeof x === 'number' || x instanceof Number); }
function isRegExp(x) { return x instanceof RegExp; }
function isArray (x) { return x instanceof Array; }
function isObject(x) { return x instanceof Object; }
function isFunction(x) {
    return !isRegExp(x) &amp;&amp; (typeof x === 'function' || x instanceof Function);
}

function repeatString(s,mult) {
	var ret='';
	for (var i=0; i&lt;mult; ++i) { ret += s; }
	return ret;
}

function zeroFill(s, min) {
	min = min || 2;
	var t=s.toString();
	return repeatString('0', min - t.length) + t;
}

function map(f, o) {
	if (isArray(o)) { return map_array(f,o); }
	return map_object(f,o);
}
function map_array(f,o) {
	var ret=[];
	for (var i=0; i&lt;o.length; ++i) {
		ret.push(f(o[i]));
	}
	return ret;
}
function map_object(f,o) {
	var ret={};
	for (var i in o) { ret[o]=f(o[i]); }
	return ret;
}
// ENDFILE: tools.js
// STARTFILE: dab.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Dab-fixing code
//


function retargetDab(newTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) {
	log('retargetDab: newTarget='+newTarget + ' oldTarget=' + oldTarget);
	return changeLinkTargetLink(
	{newTarget: newTarget,
			text: newTarget.split(' ').join('&amp;nbsp;'),
			hint: tprintf('disambigHint', [newTarget]),
			summary: simplePrintf(
				    getValueOf('popupFixDabsSummary'), [friendlyCurrentArticleName, newTarget ]),
			clickButton: 'wpDiff', minor: true, oldTarget: oldTarget,
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit});
}

function listLinks(wikitext, oldTarget, titleToEdit) {
	// mediawiki strips trailing spaces, so we do the same
	// testcase: //en.wikipedia.org/w/index.php?title=Radial&amp;oldid=97365633
	var reg=RegExp('\\[\\[([^|]*?) *(\\||\\]\\])', 'gi');
	var ret=[];
	var splitted=wikitext.parenSplit(reg);
	// ^[a-z]+ should match interwiki links, hopefully (case-insensitive)
	// and ^[a-z]* should match those and [[:Category...]] style links too
	var omitRegex=RegExp('^[a-z]*:|^[Ss]pecial:|^[Ii]mage|^[Cc]ategory');
	var friendlyCurrentArticleName= oldTarget.toString();
	var wikPos = getValueOf('popupDabWiktionary');

	for (var i=1; i&lt;splitted.length; i=i+3) {
		if (typeof splitted[i] == typeof 'string' &amp;&amp; splitted[i].length&gt;0 &amp;&amp; !omitRegex.test(splitted[i])) {
			ret.push( retargetDab(splitted[i], oldTarget, friendlyCurrentArticleName, titleToEdit) );
		} /* if */
	} /* for loop */

	ret = rmDupesFromSortedList(ret.sort());

	if (wikPos) {
		var wikTarget='wiktionary:' +
			friendlyCurrentArticleName.replace( RegExp('^(.+)\\s+[(][^)]+[)]\\s*$'), '$1' );

		var meth;
		if (wikPos.toLowerCase() == 'first') { meth = 'unshift'; }
		else { meth = 'push'; }

		ret[meth]( retargetDab(wikTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) );
	}

	ret.push(changeLinkTargetLink(
	{ newTarget: null,
			text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this disambig page from this article&quot;),
			clickButton: &quot;wpDiff&quot;, oldTarget: oldTarget,
			summary: simplePrintf(getValueOf('popupRmDabLinkSummary'), [friendlyCurrentArticleName]),
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit
			}));
	return ret;
}

function rmDupesFromSortedList(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (ret.length===0 || list[i]!=ret[ret.length-1]) { ret.push(list[i]); }
	}
	return ret;
}

function makeFixDab(data, navpop) {
	// grab title from parent popup if there is one; default exists in changeLinkTargetLink
	var titleToEdit=(navpop.parentPopup &amp;&amp; navpop.parentPopup.article.toString());
	var list=listLinks(data, navpop.originalArticle, titleToEdit);
	if (list.length===0) { log('listLinks returned empty list'); return null; }
	var html='&lt;hr&gt;' + popupString('Click to disambiguate this link to:') + '&lt;br&gt;';
	html+=list.join(', ');
	return html;
}


function makeFixDabs(wikiText, navpop) {
	if (getValueOf('popupFixDabs') &amp;&amp; isDisambig(wikiText, navpop.article) &amp;&amp;
	    Title.fromURL(location.href).namespaceId() != pg.nsSpecialId &amp;&amp;
	    navpop.article.talkPage() ) {
		setPopupHTML(makeFixDab(wikiText, navpop), 'popupFixDab', navpop.idNumber);
	}
}

function popupRedlinkHTML(article) {
	return changeLinkTargetLink(
		{ newTarget: null, text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this page from this article&quot;),
			clickButton: &quot;wpDiff&quot;,
			oldTarget: article.toString(),
			summary: simplePrintf(getValueOf('popupRedlinkSummary'), [article.toString()])});
}
//&lt;/NOLITE&gt;
// ENDFILE: dab.js
// STARTFILE: htmloutput.js

function appendPopupContent(obj, elementId, popupId, onSuccess) {
	return setPopupHTML(obj, elementId, popupId, onSuccess, true);
}

// this has to use a timer loop as we don't know if the DOM element exists when we want to set the text
function setPopupHTML (str, elementId, popupId, onSuccess, append) {
	if (elementId=='popupPreview') {
	}
	if (typeof popupId === 'undefined') {
		//console.error('popupId is not defined in setPopupHTML, html='+str.substring(0,100));
		popupId = pg.idNumber;
	}

	var popupElement=document.getElementById(elementId+popupId);
	if (popupElement) {
		if (!append) { popupElement.innerHTML=''; }
		if (isString(str)) {
			popupElement.innerHTML+=str;
		} else {
			popupElement.appendChild(str);
		}
		if (onSuccess) { onSuccess(); }
		setTimeout(checkPopupPosition, 100);
		return true;
	} else {
		// call this function again in a little while...
		setTimeout(function(){
				setPopupHTML(str,elementId,popupId,onSuccess);
			}, 600);
	}
	return null;
}

//&lt;NOLITE&gt;
function setPopupTrailer(str,id) {return setPopupHTML(str, 'popupData', id);}
//&lt;/NOLITE&gt;


function fillEmptySpans(args) { return fillEmptySpans2(args); }

// args.navpopup is mandatory
// optional: args.redir, args.redirTarget
// FIXME: ye gods, this is ugly stuff
function fillEmptySpans2(args) { // if redir is present and true then redirTarget is mandatory
	var redir=true;
	if (typeof args != 'object' || typeof args.redir == 'undefined' || !args.redir) { redir=false; }
	var a=args.navpopup.parentAnchor;

	var article, hint=null, oldid=null, params={};
	if (redir &amp;&amp; typeof args.redirTarget == typeof {}) {
		article=args.redirTarget;
		//hint=article.hintValue();
	} else {
		article=(new Title()).fromAnchor(a);
		hint=a.originalTitle || article.hintValue();
		params=parseParams(a.href);
		oldid=(getValueOf('popupHistoricalLinks')) ? params.oldid : null;
		rcid=params.rcid;
	}
	var x={ article:article, hint: hint, oldid: oldid, rcid: rcid, navpop:args.navpopup, params:params };

	var structure=pg.structures[getValueOf('popupStructure')];
	if (typeof structure != 'object') {
		setPopupHTML('popupError', 'Unknown structure (this should never happen): '+
			     pg.option.popupStructure, args.navpopup.idNumber);
		return;
	}
	var spans=flatten(pg.misc.layout);
	var numspans = spans.length;
	var redirs=pg.misc.redirSpans;

	for (var i=0; i&lt;numspans; ++i) {
		var f=findThis(redirs, spans[i]);
		//log('redir='+redir+', f='+f+', spans[i]='+spans[i]);
		if ( (f!==null &amp;&amp; !redir) || (f===null &amp;&amp; redir) ) {
			//log('skipping this set of the loop');
			continue;
		}
		var structurefn=structure[spans[i]];
		var setfn = setPopupHTML;
		if (getValueOf('popupActiveNavlinks') &amp;&amp; 
		    (spans[i].indexOf('popupTopLinks')==0 || spans[i].indexOf('popupRedirTopLinks')==0)
			    ) {
			setfn = setPopupTipsAndHTML;
		}
		switch (typeof structurefn) {
		case 'function':
			//log('running '+spans[i]+'({article:'+x.article+', hint:'+x.hint+', oldid: '+x.oldid+'})');
			setfn(structurefn(x), spans[i], args.navpopup.idNumber);
			break;
		case 'string':
			setfn(structurefn, spans[i], args.navpopup.idNumber);
			break;
		default:
			errlog('unknown thing with label '+spans[i]);
			break;
		}
	}
}

// flatten an array
function flatten(list, start) {
	var ret=[];
	if (typeof start == 'undefined') { start=0; }
	for (var i=start; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof []) {
			return ret.concat(flatten(list[i])).concat(flatten(list, i+1));
		}
		else { ret.push(list[i]); }
	}
	return ret;
}

// Generate html for whole popup
function popupHTML (a) {
	getValueOf('popupStructure');
	var structure=pg.structures[pg.option.popupStructure];
	if (typeof structure != 'object') {
		//return 'Unknown structure: '+pg.option.popupStructure;
		// override user choice
		pg.option.popupStructure=pg.optionDefault.popupStructure;
		return popupHTML(a);
	}
	if (typeof structure.popupLayout != 'function') { return 'Bad layout'; }
	pg.misc.layout=structure.popupLayout();
	if (typeof structure.popupRedirSpans == 'function') { pg.misc.redirSpans=structure.popupRedirSpans(); }
	else { pg.misc.redirSpans=[]; }
	return makeEmptySpans(pg.misc.layout, a.navpopup);
}

function makeEmptySpans (list, navpop) {
	var ret='';
	for (var i=0; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof '') {
		    ret += emptySpanHTML(list[i], navpop.idNumber, 'div');
		} else if (typeof list[i] == typeof [] &amp;&amp; list[i].length &gt; 0 ) {
			ret = ret.parenSplit(RegExp('(&lt;/[^&gt;]*?&gt;$)')).join(makeEmptySpans(list[i], navpop));
		} else if (typeof list[i] == typeof {} &amp;&amp; list[i].nodeType ) {
			ret += emptySpanHTML(list[i].name, navpop.idNumber, list[i].nodeType);
		}
	}
	return ret;
}


function emptySpanHTML(name, id, tag, classname) {
	tag = tag || 'span';
	if (!classname) { classname = emptySpanHTML.classAliases[name]; }
	classname = classname || name;
	if (name == getValueOf('popupDragHandle')) { classname += ' popupDragHandle'; }
	return simplePrintf('&lt;%s id=&quot;%s&quot; class=&quot;%s&quot;&gt;&lt;/%s&gt;', [tag, name + id, classname, tag]);
}
emptySpanHTML.classAliases={ 'popupSecondPreview': 'popupPreview' };

// generate html for popup image
// &lt;a id=&quot;popupImageLinkn&quot;&gt;&lt;img id=&quot;popupImagen&quot;&gt;
// where n=idNumber
function imageHTML(article, idNumber) {
	return simplePrintf('&lt;a id=&quot;popupImageLink$1&quot;&gt;' +
			    '&lt;img align=&quot;right&quot; valign=&quot;top&quot; id=&quot;popupImg$1&quot; style=&quot;display: none;&quot;&gt;&lt;/img&gt;' +
			    '&lt;/a&gt;', [ idNumber ]);
}

function popTipsSoonFn(id, when, popData) {
	when || ( when=250 );
	var popTips=function(){ setupTooltips(document.getElementById(id), false, true, popData); };
	return function() { setTimeout( popTips, when, popData ); };
}

function setPopupTipsAndHTML(html, divname, idnumber, popData) {
	setPopupHTML(html, divname, idnumber,
		     getValueOf('popupSubpopups') ? 
		     popTipsSoonFn(divname + idnumber, null, popData) : 
		     null);
}
// ENDFILE: htmloutput.js
// STARTFILE: mouseout.js
//////////////////////////////////////////////////
// fuzzy checks

function fuzzyCursorOffMenus(x,y, fuzz, parent) {
	if (!parent) { return null; }
	var uls=parent.getElementsByTagName('ul');
	for (var i=0; i&lt;uls.length; ++i) {
		if (uls[i].className=='popup_menu') {
			if (uls[i].offsetWidth &gt; 0) return false;
		} // else {document.title+='.';}
	}
	return true;
}

function checkPopupPosition () { // stop the popup running off the right of the screen
	// FIXME avoid pg.current.link
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp;
	    pg.current.link.navpopup.limitHorizontalPosition();
}

function mouseOutWikiLink () {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	//console ('mouseOutWikiLink');
	var a=this;
	if (a.navpopup==null) return;
	if ( ! a.navpopup.isVisible() ) {
		a.navpopup.banish();
		return;
	}
        restoreTitle(a);
	Navpopup.tracker.addHook(posCheckerHook(a.navpopup));
}

function posCheckerHook(navpop) {
	return function() {
		if (!navpop.isVisible()) { return true; /* remove this hook */ }
		if (Navpopup.tracker.dirty) {
		    return false;
		}
		var x=Navpopup.tracker.x, y=Navpopup.tracker.y;
		var mouseOverNavpop = navpop.isWithin(x,y,navpop.fuzz, navpop.mainDiv) ||
		    !fuzzyCursorOffMenus(x,y,navpop.fuzz, navpop.mainDiv);

		// FIXME it'd be prettier to do this internal to the Navpopup objects
		var t=getValueOf('popupHideDelay');
		if (t) { t = t * 1000; }
		if (!t) {
			if(!mouseOverNavpop) {
			    navpop.banish();
			    return true; /* remove this hook */
			}
			return false;
		}
		// we have a hide delay set
		var d=+(new Date());
		if ( !navpop.mouseLeavingTime ) {
			navpop.mouseLeavingTime = d;
			return false;
		}
		if ( mouseOverNavpop ) {
			navpop.mouseLeavingTime=null;
			return false;
		}
		if (d - navpop.mouseLeavingTime &gt; t) {
			navpop.mouseLeavingTime=null;
			navpop.banish(); return true; /* remove this hook */
		}
		return false;
	};
}

function runStopPopupTimer(navpop) {
	// at this point, we should have left the link but remain within the popup
	// so we call this function again until we leave the popup.
	if (!navpop.stopPopupTimer) {
		navpop.stopPopupTimer=setInterval(posCheckerHook(navpop), 500);
		navpop.addHook(function(){clearInterval(navpop.stopPopupTimer);},
			       'hide', 'before');
	}
}
// ENDFILE: mouseout.js
// STARTFILE: previewmaker.js
/**
   @fileoverview
   Defines the {@link Previewmaker} object, which generates short previews from wiki markup.
*/

/**
   Creates a new Previewmaker
   @constructor
   @class The Previewmaker class. Use an instance of this to generate short previews from Wikitext.
   @param {String} wikiText The Wikitext source of the page we wish to preview.
   @param {String} baseUrl The url we should prepend when creating relative urls.
   @param {Navpopup} owner The navpop associated to this preview generator
*/
function Previewmaker(wikiText, baseUrl, owner) {
	/** The wikitext which is manipulated to generate the preview. */
	this.originalData=wikiText;
	this.setData();
	this.baseUrl=baseUrl;
	this.owner=owner;
	this.maxCharacters=getValueOf('popupMaxPreviewCharacters');
	this.maxSentences=getValueOf('popupMaxPreviewSentences');
}
Previewmaker.prototype.setData=function() {
	var maxSize=max(10000, 2*this.maxCharacters);
	this.data=this.originalData.substring(0,maxSize);
};
/** Remove HTML comments
    @private
*/
Previewmaker.prototype.killComments = function () {
	// this also kills one trailing newline, eg [[diamyo]]
	this.data=this.data.replace(RegExp('&lt;!--[\\s\\S]*?--&gt;\\n?', 'g'), ''); 
};
/**
   @private
*/
Previewmaker.prototype.killDivs = function () {
	// say goodbye, divs (can be nested, so use * not *?)
	this.data=this.data.replace(RegExp('&lt; *div[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *div *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killGalleries = function () {
	this.data=this.data.replace(RegExp('&lt; *gallery[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *gallery *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.kill = function(opening, closing, subopening, subclosing, repl) {
	var oldk=this.data;
	var k=this.killStuff(this.data, opening, closing, subopening, subclosing, repl);
	while (k.length &lt; oldk.length) {
		oldk=k;
		k=this.killStuff(k, opening, closing, subopening, subclosing, repl);
	}
	this.data=k;
};
/**
   @private
*/
Previewmaker.prototype.killStuff = function (txt, opening, closing, subopening, subclosing, repl) {
	var op=this.makeRegexp(opening);
	var cl=this.makeRegexp(closing, '^');
	var sb=subopening ? this.makeRegexp(subopening, '^') : null;
	var sc=subclosing ? this.makeRegexp(subclosing, '^') : cl;
	if (!op || !cl) {
	    alert('Navigation Popups error: op or cl is null! something is wrong.');
	    return;
	}
	if (!op.test(txt)) { return txt; }
	var ret='';
	var opResult = op.exec(txt);
	ret = txt.substring(0,opResult.index);
	txt=txt.substring(opResult.index+opResult[0].length);
	var depth = 1;
	while (txt.length &gt; 0) {
		var removal=0;
		if (depth==1 &amp;&amp; cl.test(txt)) {
			depth--;
			removal=cl.exec(txt)[0].length;
		} else if (depth &gt; 1 &amp;&amp; sc.test(txt)) {
			depth--;
			removal=sc.exec(txt)[0].length;
		}else if (sb &amp;&amp; sb.test(txt)) {
			depth++;
			removal=sb.exec(txt)[0].length;
		}
		if ( !removal ) { removal = 1; }
		txt=txt.substring(removal);
		if (depth==0) { break; }
	}
	return ret + (repl || '') + txt;
};
/**
   @private
*/
Previewmaker.prototype.makeRegexp = function (x, prefix, suffix) {
	prefix = prefix || '';
	suffix = suffix || '';
	var reStr='';
	var flags='';
	if (isString(x)) {
		reStr=prefix + literalizeRegex(x) + suffix;
	} else if (isRegExp(x)) {
		var s=x.toString().substring(1);
		var sp=s.split('/');
		flags=sp[sp.length-1];
		sp[sp.length-1]='';
		s=sp.join('/');
		s=s.substring(0,s.length-1);
		reStr= prefix + s + suffix;
	} else {
		log ('makeRegexp failed');
	}

	log ('makeRegexp: got reStr=' + reStr + ', flags=' + flags);
	return RegExp(reStr, flags);
};
/**
   @private
*/
Previewmaker.prototype.killBoxTemplates = function () {

	// taxobox removal... in fact, there's a saudiprincebox_begin, so let's be more general
	// also, have float_begin, ... float_end
	this.kill(RegExp('[{][{][^{}\\s|]*?(float|box)[_ ](begin|start)', 'i'),	/[}][}]\s*/, '{{');

	// infoboxes etc
	// from [[User:Zyxw/popups.js]]: kill frames too
	this.kill(RegExp('[{][{][^{}\\s|]*?(infobox|elementbox|frame)[_ ]', 'i'), /[}][}]\s*/, '{{');

};
/**
   @private
*/
Previewmaker.prototype.killTemplates = function () {
	this.kill('{{', '}}', '{', '}', ' ');
};
/**
   @private
*/
Previewmaker.prototype.killTables = function () {
	// tables are bad, too
	// this can be slow, but it's an inprovement over a browser hang
	// torture test: [[Comparison_of_Intel_Central_Processing_Units]]
	this.kill('{|', /[|]}\s*/, '{|');
	this.kill(/&lt;table.*?&gt;/i, /&lt;\/table.*?&gt;/i, /&lt;table.*?&gt;/i);
	// remove lines starting with a pipe for the hell of it (?)
	this.data=this.data.replace(RegExp('^[|].*$', 'mg'), '');
};
/**
   @private
*/
Previewmaker.prototype.killImages = function () {
	var forbiddenNamespaceAliases = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=pg.nsImageId &amp;&amp; _namespaceId!=pg.nsCategoryId) return;
		forbiddenNamespaceAliases.push(_localizedNamespaceLc.split(' ').join('[ _]')); //todo: escape regexp fragments!
	});
	
	// images and categories are a nono
	this.kill(RegExp('[[][[]\\s*(' + forbiddenNamespaceAliases.join('|') + ')\\s*:', 'i'),
		  /\]\]\s*/, '[', ']');
};
/**
   @private
*/
Previewmaker.prototype.killHTML = function () {
	// kill &lt;ref ...&gt;...&lt;/ref&gt;
	this.kill(/&lt;ref\b[^/&gt;]*?&gt;/i, /&lt;\/ref&gt;/i);

	// let's also delete entire lines starting with &lt;. it's worth a try.
	this.data=this.data.replace(RegExp('(^|\\n) *&lt;.*', 'g'), '\n');

	// and those pesky html tags, but not &lt;nowiki&gt; or &lt;blockquote&gt;
	var splitted=this.data.parenSplit(/(&lt;.*?&gt;)/);
	var len=splitted.length;
	for (var i=1; i&lt;len; i=i+2) {
		switch (splitted[i]) {
		case '&lt;nowiki&gt;':
		case '&lt;/nowiki&gt;':
			break;
		default:
			if (! /^&lt; *\/? *blockquote\b/i.test(splitted[i])) {
				splitted[i]='';
			}
		}
	}
	this.data=splitted.join('');
};
/**
   @private
*/
Previewmaker.prototype.killChunks = function() { // heuristics alert
	// chunks of italic text? you crazy, man?
	var italicChunkRegex=new RegExp
	(&quot;((^|\\n)\\s*:*\\s*''[^']([^']|'''|'[^']){20}(.|\\n[^\\n])*''[.!?\\s]*\\n)+&quot;, 'g');
	// keep stuff separated, though, so stick in \n (fixes [[Union Jack]]?
	this.data=this.data.replace(italicChunkRegex, '\n');
};
/**
   @private
*/
Previewmaker.prototype.mopup = function () {
	// we simply *can't* be doing with horizontal rules right now
	this.data=this.data.replace(RegExp('^-{4,}','mg'),'');

	// no indented lines
	this.data=this.data.replace(RegExp('(^|\\n) *:[^\\n]*','g'), '');

	// replace __TOC__, __NOTOC__ and whatever else there is
	// this'll probably do
	this.data=this.data.replace(RegExp('^__[A-Z_]*__ *$', 'gmi'),'');
};
/**
   @private
*/
Previewmaker.prototype.firstBit = function () {
	// dont't be givin' me no subsequent paragraphs, you hear me?
	/// first we &quot;normalize&quot; section headings, removing whitespace after, adding before
	var d=this.data;

	if (getValueOf('popupPreviewCutHeadings')) {
		this.data=this.data.replace(RegExp('\\s*(==+[^=]*==+)\\s*', 'g'), '\n\n$1 ');
		/// then we want to get rid of paragraph breaks whose text ends badly
		this.data=this.data.replace(RegExp('([:;]) *\\n{2,}', 'g'), '$1\n');

		this.data=this.data.replace(RegExp('^[\\s\\n]*'), '');
		stuff=(RegExp('^([^\\n]|\\n[^\\n\\s])*')).exec(this.data);
		if (stuff) { d = stuff[0]; }
		if (!getValueOf('popupPreviewFirstParOnly')) { d = this.data; }

		/// now put \n\n after sections so that bullets and numbered lists work
		d=d.replace(RegExp('(==+[^=]*==+)\\s*', 'g'), '$1\n\n');
	}


	// superfluous sentences are RIGHT OUT.
	// note: exactly 1 set of parens here needed to make the slice work
	d = d.parenSplit(RegExp('([!?.]+[&quot;'+&quot;'&quot;+']*\\s)','g'));
	// leading space is bad, mmkay?
	d[0]=d[0].replace(RegExp('^\\s*'), '');

	var notSentenceEnds=RegExp('([^.][a-z][.] *[a-z]|etc|sic|Dr|Mr|Mrs|Ms|St|no|op|cit|\\[[^\\]]*|\\s[A-Zvclm])$', 'i');
	d = this.fixSentenceEnds(d, notSentenceEnds);

	this.fullLength=d.join('').length;
	var maxChars=getValueOf('popupMaxPreviewCharacters') + this.extraCharacters;
	var n=this.maxSentences;
	var dd=this.firstSentences(d,n); 

	do {
		dd=this.firstSentences(d,n); --n;
	} while ( dd.length &gt; this.maxCharacters &amp;&amp; n != 0 );

	this.data = dd;
};
/**
   @private
*/
Previewmaker.prototype.fixSentenceEnds = function(strs, reg) {
	// take an array of strings, strs
	// join strs[i] to strs[i+1] &amp; strs[i+2] if strs[i] matches regex reg

	var abbrevRe=/\b[a-z][^a-z]*$/i;

	for (var i=0; i&lt;strs.length-2; ++i) {
		if (reg.test(strs[i])) {
			a=[];
			for (var j=0; j&lt;strs.length; ++j) {
				if (j&lt;i)   a[j]=strs[j];
				if (j==i)  a[i]=strs[i]+strs[i+1]+strs[i+2];
				if (j&gt;i+2) a[j-2]=strs[j];
			}
			return this.fixSentenceEnds(a,reg);
		}
		// BUGGY STUFF - trying to fix up [[S. C. Johnson &amp; Son]] preview
		if (false &amp;&amp; abbrevRe.test(strs[i])) {
			var j=i, buf='';
			do {
				buf=buf+strs[i]+strs[i+1];
				i=i+2;
			} while (i&lt;strs.length-2 &amp;&amp; abbrevRe.test(strs[i]));
			strs[i]=buf+strs[i];
			var a=(j?strs.slice(0,j-1):[]).concat(strs.slice(i));
			return this.fixSentenceEnds(a,reg);
		}
	}
	return strs;
};
/**
   @private
*/
Previewmaker.prototype.firstSentences = function(strs, howmany) {
	var t=strs.slice(0, 2*howmany);
	return t.join('');
};
/**
   @private
*/
Previewmaker.prototype.killBadWhitespace = function() {
	// also cleans up isolated '''', eg [[Suntory Sungoliath]]
	this.data=this.data.replace(RegExp('^ *\'+ *$', 'gm'), '');
};
/**
   Runs the various methods to generate the preview.
   The preview is stored in the &lt;code&gt;html&lt;/html&gt; field.
   @private
*/
Previewmaker.prototype.makePreview = function() {
	if (this.owner.article.namespaceId()!=pg.nsTemplateId &amp;&amp;
				this.owner.article.namespaceId()!=pg.nsImageId ) {
		this.killComments();
		this.killDivs();
		this.killGalleries();
		this.killBoxTemplates();

		if (getValueOf('popupPreviewKillTemplates')) {
			this.killTemplates();
		} else {
			this.killMultilineTemplates();
		}
		this.killTables();
		this.killImages();
		this.killHTML();
		this.killChunks();
		this.mopup();

		this.firstBit();
		this.killBadWhitespace();
	}
	else
	{
		this.killHTML();
	}
	this.html=wiki2html(this.data, this.baseUrl); // needs livepreview
	this.fixHTML();
	this.stripLongTemplates();
};
/**
   @private
*/
Previewmaker.prototype.esWiki2HtmlPart = function(data) {
  var reLinks = /(?:\[\[([^|\]]*)(?:\|([^|\]]*))*]]([a-z]*))/gi; //match a wikilink
  reLinks.lastIndex = 0; //reset regex

  var match;
  var result = &quot;&quot;;
  var postfixIndex = 0;
  while ((match = reLinks.exec(data)) != null) //match all wikilinks
  {
    //FIXME: the way that link is built here isn't perfect. It is clickable, but popups preview won't recognize it in some cases.
    result += mw.html.escape(data.substring(postfixIndex, match.index)) + 
              '&lt;a href=&quot;'+Insta.conf.paths.articles+mw.html.escape(match[1])+'&quot;&gt;'+mw.html.escape((match[2]?match[2]:match[1])+match[3])+&quot;&lt;/a&gt;&quot;;
    postfixIndex = reLinks.lastIndex;
  }
  //append the rest
  result += mw.html.escape(data.substring(postfixIndex));
  
  return result;
};
Previewmaker.prototype.editSummaryPreview=function() {
	var reAes   = /\/\* *(.*?) *\*\//g; //match the first section marker
	reAes.lastIndex = 0; //reset regex
	
	var match;
	
	match = reAes.exec(this.data);
	if (match)
	{
		//we have a section link. Split it, process it, combine it.
		var prefix = this.data.substring(0,match.index-1);
		var section = match[1];
		var postfix = this.data.substring(reAes.lastIndex);
		
		var start = &quot;&lt;span class='autocomment'&gt;&quot;;
		var end = &quot;&lt;/span&gt;&quot;;
		if (prefix.length&gt;0) start = this.esWiki2HtmlPart(prefix) + &quot; &quot; + start + &quot;- &quot;;
		if (postfix.length&gt;0) end = &quot;: &quot; + end + this.esWiki2HtmlPart(postfix);
		

		var t=new Title().fromURL(this.baseUrl);
		t.anchorFromUtf(section);
		var sectionLink = Insta.conf.paths.articles + mw.html.escape(t.toString(true)) + '#' + mw.html.escape(t.anchor);
		return start + '&lt;a href=&quot;'+sectionLink+'&quot;&gt;&amp;rarr;&lt;/a&gt; '+mw.html.escape(section) + end;
	}
	
	//else there's no section link, htmlify the whole thing.
	return this.esWiki2HtmlPart(this.data);
};

//&lt;NOLITE&gt;
/** Test function for debugging preview problems one step at a time.
 */
function previewSteps(txt) {
	try {
		txt=txt || document.editform.wpTextbox1.value;
	} catch (err) {
		if (pg.cache.pages.length &gt; 0) {
			txt=pg.cache.pages[pg.cache.pages.length-1].data;
		} else {
			alert('provide text or use an edit page');
		}
	}
	txt=txt.substring(0,10000);
	var base=pg.wiki.articlebase + Title.fromURL(document.location.href).urlString();
	var p=new Previewmaker(txt, base, pg.current.link.navpopup);
	if (this.owner.article.namespaceId() != pg.nsTemplateId) {
		p.killComments(); if (!confirm('done killComments(). Continue?\n---\n' + p.data)) { return; }
		p.killDivs(); if (!confirm('done killDivs(). Continue?\n---\n' + p.data)) { return; }
		p.killGalleries(); if (!confirm('done killGalleries(). Continue?\n---\n' + p.data)) { return; }
		p.killBoxTemplates(); if (!confirm('done killBoxTemplates(). Continue?\n---\n' + p.data)) { return; }

		if (getValueOf('popupPreviewKillTemplates')) {
			p.killTemplates(); if (!confirm('done killTemplates(). Continue?\n---\n' + p.data)) { return; }
		} else {
			p.killMultilineTemplates(); if (!confirm('done killMultilineTemplates(). Continue?\n---\n' + p.data)) { return; }
		}

		p.killTables(); if (!confirm('done killTables(). Continue?\n---\n' + p.data)) { return; }
		p.killImages(); if (!confirm('done killImages(). Continue?\n---\n' + p.data)) { return; }
		p.killHTML(); if (!confirm('done killHTML(). Continue?\n---\n' + p.data)) { return; }
		p.killChunks(); if (!confirm('done killChunks(). Continue?\n---\n' + p.data)) { return; }
		p.mopup(); if (!confirm('done mopup(). Continue?\n---\n' + p.data)) { return; }

		p.firstBit(); if (!confirm('done firstBit(). Continue?\n---\n' + p.data)) { return; }
		p.killBadWhitespace(); if (!confirm('done killBadWhitespace(). Continue?\n---\n' + p.data)) { return; }
	}

	p.html=wiki2html(p.data, base); // needs livepreview
	p.fixHTML(); if (!confirm('done fixHTML(). Continue?\n---\n' + p.html)) { return; }
	p.stripLongTemplates(); if (!confirm('done stripLongTemplates(). Continue?\n---\n' + p.html)) { return; }
	alert('finished preview - end result follows.\n---\n' + p.html);
}
//&lt;/NOLITE&gt;

/**
   Works around a quoting bug in livepreview.
   &lt;code&gt;wiki2html('[[Foo\'s &quot;bar&quot;]]')&lt;/code&gt; gives @literal{&lt;a href='Foo's &quot;bar&quot;'&gt;}
   which doesn't do very well. We change this into @literal{&lt;a href=&quot;Foo's %22bar%22&quot;&gt;}
   @private
*/
Previewmaker.prototype.fixHTML = function() {
	if(!this.html) return;
	// all links seem to have potential issues with quotation marks
	var splitted=this.html.parenSplit(/href='([^&gt;]*)'/g);
	var ret='';
	for (var i=0; i&lt;splitted.length; ++i) {
		if(i%2==0) { ret += splitted[i]; continue; }
		if(i%2==1) { ret += 'href=&quot;' + splitted[i].split('&quot;').join('%22') + '&quot;'; }
	}
	// fix question marks in wiki links
	// maybe this'll break some stuff :-(
	ret=ret.replace(RegExp('\(&lt;a href=&quot;' + pg.wiki.articlePath + '/[^&quot;]*\)[?]\(.*?&quot;\)', 'g'), '$1%3F$2');
	// FIXME fix up % too
	this.html=ret;
};
/**
   Generates the preview and displays it in the current popup.

   Does nothing if the generated preview is invalid or consists of whitespace only.
   Also activates wikilinks in the preview for subpopups if the popupSubpopups option is true.
*/
Previewmaker.prototype.showPreview = function () {
	this.makePreview();
	if (typeof this.html != typeof '') return;
	if (RegExp('^\\s*$').test(this.html)) return;
	setPopupHTML('&lt;hr&gt;', 'popupPrePreviewSep', this.owner.idNumber);
	setPopupTipsAndHTML(this.html, 'popupPreview', this.owner.idNumber, { owner: this.owner });
	var more = (this.fullLength &gt; this.data.length) ? this.moreLink() : '';
	setPopupHTML(more, 'popupPreviewMore', this.owner.idNumber);
};
/**
   @private
*/
Previewmaker.prototype.moreLink=function() {
	var a=document.createElement('a');
	a.className='popupMoreLink';
	a.innerHTML=popupString('more...');
	var savedThis=this;
	a.onclick=function() {
		savedThis.maxCharacters+=2000;
		savedThis.maxSentences+=20;
		savedThis.setData();
		savedThis.showPreview();
	}
	return a;
}

/**
   @private
*/
Previewmaker.prototype.stripLongTemplates = function() {
	// operates on the HTML!
	this.html=this.html.replace(RegExp('^.{0,1000}[{][{][^}]*?(&lt;(p|br)( /)?&gt;\\s*){2,}([^{}]*?[}][}])?', 'gi'), '');
	this.html=this.html.split('\n').join(' '); // workaround for &lt;pre&gt; templates
	this.html=this.html.replace(RegExp('[{][{][^}]*&lt;pre&gt;[^}]*[}][}]','gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killMultilineTemplates = function() {
	this.kill('{{{', '}}}');
	this.kill(RegExp('\\s*[{][{][^{}]*\\n'), '}}', '{{');
};
// ENDFILE: previewmaker.js
// STARTFILE: querypreview.js
function loadAPIPreview(queryType, article, navpop) {
	var art=new Title(article).urlString();
	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;';
	var htmlGenerator=function(a,d){alert('invalid html generator');};
	switch (queryType) {
	case 'history':
		url += 'meta=userinfo&amp;uiprop=options&amp;titles=' + art + '&amp;prop=revisions&amp;rvlimit=' +
			getValueOf('popupHistoryPreviewLimit');
		htmlGenerator=APIhistoryPreviewHTML;
		break;
	case 'category':
		url += 'list=categorymembers&amp;rawcontinue=&amp;cmtitle=' + art;
		htmlGenerator=APIcategoryPreviewHTML;
		break;
	case 'userinfo':
	  var username = new Title( article ).userName();
		var usernameart = encodeURIComponent( username );
		if (pg.re.ipUser.test(username)) {
			url += 'list=blocks&amp;bkprop=range&amp;bkip=' + usernameart;
		} else {
			url += 'list=users&amp;usprop=blockinfo|groups|editcount|registration&amp;ususers=' + usernameart + &quot;&amp;meta=globaluserinfo&amp;guiprop=groups|unattached&amp;guiuser=&quot;+ usernameart;
		}
		htmlGenerator=APIuserInfoPreviewHTML;
		break;
	case 'contribs':
		var usernameart = encodeURIComponent( new Title( article ).userName() );
		url += 'list=usercontribs&amp;meta=userinfo&amp;uiprop=options&amp;ucuser=' + usernameart +
			'&amp;uclimit=' + getValueOf('popupContribsPreviewLimit');
		htmlGenerator=APIcontribsPreviewHTML;
		break;
	case 'imagepagepreview':
		var trail='';
		if (getValueOf('popupImageLinks')) { trail = '&amp;list=imageusage&amp;iutitle=' + art; }
		url += 'titles=' + art + '&amp;prop=revisions|imageinfo&amp;rvprop=content' + trail;
		htmlGenerator=APIimagepagePreviewHTML;
		break;
	case 'backlinks':
		url += 'list=backlinks&amp;rawcontinue=&amp;bltitle=' + art;
		htmlGenerator=APIbacklinksPreviewHTML;
		break;
	}
	pendingNavpopTask(navpop);
	var callback=function(d){
	    log( &quot;callback of API functions was hit&quot; );
		showAPIPreview(queryType, htmlGenerator(article,d,navpop), navpop.idNumber, navpop, d);
	};
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_'+queryType+'_QUERY_DATA'); }
}

function linkList(list) {
	list.sort(function(x,y) { return (x==y ? 0 : (x&lt;y ? -1 : 1)); });
	var buf=[];
	for (var i=0; i&lt;list.length; ++i) {
		buf.push(wikiLink({article: new Title(list[i]),
				   text:    list[i].split(' ').join('&amp;nbsp;'),
				   action:  'view'}));
	}
	return buf.join(', ');
}

function getTimeOffset(tz) {
	if( tz ) {
		if( tz.indexOf('|') &gt; -1 ) {
			// New format
			return parseInt(tz.split('|')[1],10);
		} else if ( tz.indexOf(':') &gt; -1 ) {
			// Old format
			return( parseInt(tz,10)*60 + parseInt(tz.split(':')[1],10) );
		}
	}
	return 0;
}

function editPreviewTable(article, h, reallyContribs, timeOffset) {
	var html=['&lt;table&gt;'];
	var day=null;
	var curart=article;
	for (var i=0; i&lt;h.length; ++i) {
		if (reallyContribs) { 
		    var page=h[i]['title']; curart = new Title(page);
		}
		var minor=typeof h[i]['minor']=='undefined' ? '' : '&lt;b&gt;m &lt;/b&gt;';
		var editDate=adjustDate(getDateFromTimestamp(h[i].timestamp), timeOffset);
		var thisDay = dayFormat(editDate);
		var thisTime = timeFormat(editDate);
		if (thisDay==day) { thisDay=''; }
		else { day=thisDay; }
		if (thisDay) {
			html.push( '&lt;tr&gt;&lt;td colspan=3&gt;&lt;span class=&quot;popup_history_date&quot;&gt;' +
				  thisDay+'&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;' );
		}
		html.push('&lt;tr class=&quot;popup_history_row_' + ( (i%2) ? 'odd' : 'even') + '&quot;&gt;');
		html.push('&lt;td&gt;(&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;diff=prev&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + popupString('last') + '&lt;/a&gt;)&lt;/td&gt;');
		html.push('&lt;td&gt;' +
			'&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + thisTime + '&lt;/a&gt;&lt;/td&gt;');
		var col3url='', col3txt='';
		if (!reallyContribs) {
			var user=h[i]['user'];
			if( typeof h[i]['userhidden'] == &quot;undefined&quot; ) {
				if( pg.re.ipUser.test(user) ) {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId] + ':Contributions&amp;target=' + new Title(user).urlString();
				} else {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(user).urlString();
				}
				col3txt=mw.html.escape(user);
			} else {
				col3url=getValueOf('popupRevDelUrl');
				col3txt=mw.html.escape( popupString('revdel'));
			}
		} else {
			col3url=pg.wiki.titlebase + curart.urlString();
			col3txt=mw.html.escape(page);
		}
		html.push('&lt;td&gt;' + (reallyContribs ? minor : '') +
			'&lt;a href=&quot;' + col3url + '&quot;&gt;' + col3txt + '&lt;/a&gt;&lt;/td&gt;');
		var comment='';
		var c=h[i].comment || h[i]['*'];
		if (c) {
			comment=new Previewmaker(c, new Title(curart).toUrl()).editSummaryPreview();
		} else if (typeof h[i]['commenthidden'] != &quot;undefined&quot; ) {
			comment=popupString('revdel');
		}
		html.push('&lt;td&gt;' + (!reallyContribs ? minor : '') + comment + '&lt;/td&gt;');
		html.push('&lt;/tr&gt;');
		html=[html.join('')];
	}
	html.push('&lt;/table&gt;');
	return html.join('');
}

function getDateFromTimestamp(t) {
	var s=t.split(/[^0-9]/);
	switch(s.length) {
	case 0: return null;
	case 1: return new Date(s[0]);
	case 2: return new Date(s[0], s[1]-1);
	case 3: return new Date(s[0], s[1]-1, s[2]);
	case 4: return new Date(s[0], s[1]-1, s[2], s[3]);
	case 5: return new Date(s[0], s[1]-1, s[2], s[3], s[4]);
	case 6: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5]);
	default: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5], s[6]);
	}
}

function adjustDate(d, offset) {
	// offset is in minutes
	var o=offset * 60 * 1000;
	return new Date( +d + o);
}

function dayFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCFullYear(), editDate.getUTCMonth()+1, editDate.getUTCDate()]).join('-'); }
	return map(zeroFill, [editDate.getFullYear(), editDate.getMonth()+1, editDate.getDate()]).join('-');
}

function timeFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCHours(), editDate.getUTCMinutes(), editDate.getUTCSeconds()]).join(':'); }
	return map(zeroFill, [editDate.getHours(), editDate.getMinutes(), editDate.getSeconds()]).join(':');
}

function showAPIPreview(queryType, html, id, navpop, download) {
    // DJ: done
	var target='popupPreview';
	switch (queryType) {
	case 'imagelinks':
	case 'category':
	case 'userinfo':
		target='popupPostPreview'; break;
	}
	setPopupTipsAndHTML(html, target, id);
	completedNavpopTask(navpop);
}

function APIbacklinksPreviewHTML(article, download, navpop) {
    try {
	    var jsObj=getJsObj(download.data);
   	    var list=jsObj.query.backlinks;
	} catch (someError) { return 'backlinksPreviewHTML went wonky'; }
	var html=[];
	if (!list) { return popupString('No backlinks found'); }
	for ( var i=0; i &lt; list.length; i++ ) {
		var t=new Title(list[i]['title']);
		html.push('&lt;a href=&quot;' + pg.wiki.titlebase + t.urlString() + '&quot;&gt;' + t + '&lt;/a&gt;');
	}
	html=html.join(', ');
	if (jsObj['query-continue'] &amp;&amp; jsObj['query-continue'].backlinks &amp;&amp; jsObj['query-continue'].backlinks.blcontinue) {
		html += popupString(' and more');
	}
	return html;
}

function APIsharedImagePagePreviewHTML(obj) {
	log( &quot;APIsharedImagePagePreviewHTML&quot; );
	var popupid = obj['requestid'];
	if( obj['query'] &amp;&amp; obj['query']['pages'] )
	{
		var page=anyChild(obj['query']['pages']);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
		if( content ) 
		{
			/* Not entirely safe, but the best we can do */
			var p=new Previewmaker(content, pg.current.link.navpopup.article, pg.current.link.navpopup);
			p.makePreview();
			setPopupHTML( p.html, &quot;popupSecondPreview&quot;, popupid );
		}
	}
}

function APIimagepagePreviewHTML(article, download, navpop) {
	try {
	    var jsObj=getJsObj(download.data);
		var page=anyChild(jsObj.query.pages);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
	} catch (someError) {
		return 'API imagepage preview failed :(';
	}
	var ret='';
	var alt='';
	try{alt=navpop.parentAnchor.childNodes[0].alt;} catch(e){}
	if (alt) {
		ret = ret + '&lt;hr&gt;&lt;b&gt;' + popupString('Alt text:') + '&lt;/b&gt; ' + mw.html.escape(alt);
	}
	if (content) {
		var p=prepPreviewmaker(content, article, navpop);
		p.makePreview();
		if (p.html) { ret += '&lt;hr&gt;' + p.html; }
	}
	if (content!==null &amp;&amp; getValueOf('popupSummaryData')) {
		var info=getPageInfo(content, download);
		log(info);
		setPopupTrailer(info, navpop.idNumber);
	}
	if (page &amp;&amp; page.imagerepository == &quot;shared&quot; ) {
		var art=new Title(article);
		var encart = encodeURIComponent( &quot;File:&quot; + art.stripNamespace() );
		var shared_url =  pg.wiki.apicommonsbase + '?format=json&amp;callback=APIsharedImagePagePreviewHTML' +
							'&amp;requestid=' + navpop.idNumber +
							'&amp;action=query&amp;prop=revisions&amp;rvprop=content&amp;titles=' + encart;
		if (pg.flag.isIE) {
			shared_url = shared_url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
		}

		ret = ret +'&lt;hr&gt;' + popupString( 'Image from Commons') +
				': &lt;a href=&quot;' + pg.wiki.commonsbase + '?title=' + encart + '&quot;&gt;' +
				popupString( 'Description page') + '&lt;/a&gt;';
		mw.loader.load( shared_url );
	}
	showAPIPreview('imagelinks', APIimagelinksPreviewHTML(article,download), navpop.idNumber, download);
	return ret;
}

function APIimagelinksPreviewHTML(article, download) {
	try {
		var jsobj=getJsObj(download.data);
		var list=jsobj.query.imageusage;
		if (!list) { return popupString('No image links found'); }
	} catch(someError) { return 'Image links preview generation failed :('; }
	var ret=[];
	for (var i=0; i &lt; list.length; i++) {
		ret.push(list[i]['title']);
	}
	if (ret.length === 0) { return popupString('No image links found'); }
	return '&lt;h2&gt;' + popupString('File links') + '&lt;/h2&gt;' + linkList(ret);
}

function APIcategoryPreviewHTML(article, download) {
    try{
        var jsobj=getJsObj(download.data);
        var list=jsobj.query.categorymembers;
    } catch(someError) { return 'Category preview failed :('; }
	var ret=[];
	for (var p=0; p &lt; list.length; p++) { 
	   ret.push(list[p]['title']); 
	}
	if (ret.length === 0) { return popupString('Empty category'); }
	ret = '&lt;h2&gt;' + tprintf('Category members (%s shown)', [ret.length]) + '&lt;/h2&gt;' +linkList(ret);
	if (jsobj['query-continue'] &amp;&amp; jsobj['query-continue'].categorymembers &amp;&amp; jsobj['query-continue'].categorymembers.cmcontinue) {
		ret += popupString(' and more');
	}
	return ret;
}

function APIuserInfoPreviewHTML(article, download) {
	var ret=[];
	try{
		var queryobj=getJsObj(download.data).query;
	} catch(someError) { return 'Userinfo preview failed :('; }
	
	var user=anyChild(queryobj.users);
	if (user) {
		var globaluserinfo=queryobj.globaluserinfo;
		if (user.invalid == '') {
			ret.push( popupString( 'Invalid user') );
		} else if (user.missing == '') {
			ret.push( popupString( 'Not a registered username') );
		}
		if( user.blockedby )
			ret.push('&lt;b&gt;' + popupString('BLOCKED') + '&lt;/b&gt;');
		if( globaluserinfo &amp;&amp; (globaluserinfo.locked != null || globaluserinfo.hidden != null) ) {
			var lockedSulAccountIsAttachedToThis = true;
			for( var i=0; globaluserinfo.unattached &amp;&amp; i &lt; globaluserinfo.unattached.length; i++) {
				if (globaluserinfo.unattached[i].wiki===mw.config.get('wgDBname')) { lockedSulAccountIsAttachedToThis=false; break; }
			}
			if (lockedSulAccountIsAttachedToThis) {
				if (globaluserinfo.locked != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('LOCKED') + '&lt;/i&gt;&lt;/b&gt;');
				if (globaluserinfo.hidden != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('HIDDEN') + '&lt;/i&gt;&lt;/b&gt;');
			}
		}
		for( var i=0; (user.groups &amp;&amp; i &lt; user.groups.length); i++) {
			switch (user.groups[i]) {
				case '*':
				case 'user':
				case 'autoconfirmed':
					break;
				default:
					ret.push( mw.html.escape(user.groups[i]) );
			}
		}
		for( var i=0; (globaluserinfo &amp;&amp; globaluserinfo.groups &amp;&amp; i &lt; globaluserinfo.groups.length); i++) {
			ret.push( '&lt;i&gt;'+mw.html.escape(globaluserinfo.groups[i])+'&lt;/i&gt;' );
		}
		if( user.editcount || user.registration )
			ret.push( mw.html.escape((user.editcount?user.editcount:'') + popupString(' edits since: ') + (user.registration?dayFormat(getDateFromTimestamp(user.registration)):'')) );
	}
	
	if (queryobj.blocks) {
		ret.push( popupString( 'IP user') ); //we only request list=blocks for IPs
		for (var i=0; i&lt;queryobj.blocks.length; i++) {
			ret.push('&lt;b&gt;' + popupString(queryobj.blocks[i].rangestart===queryobj.blocks[i].rangeend ? 'BLOCKED' : 'RANGEBLOCKED') + '&lt;/b&gt;' );
		}
	}
	
	ret = '&lt;hr&gt;' + ret.join( ', ' );
	return ret;
}

function APIcontribsPreviewHTML(article, download, navpop) {
    return APIhistoryPreviewHTML(article, download, navpop, true);
}

function APIhistoryPreviewHTML(article, download, navpop, reallyContribs) {
    try {
		var jsobj=getJsObj(download.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
		if( reallyContribs )
		    var edits=jsobj.query.usercontribs;
		else 
		    var edits=anyChild(jsobj.query.pages)['revisions'];
	} catch (someError) {
		return 'History preview failed :-(';
	}
	var timeOffset = getTimeOffset(tz);
	Cookie.create('popTz', timeOffset, 1);

	var ret=editPreviewTable(article, edits, reallyContribs, timeOffset);
	return ret;
}


//&lt;/NOLITE&gt;
// ENDFILE: querypreview.js
// STARTFILE: debug.js
////////////////////////////////////////////////////////////////////
// Debugging functions
////////////////////////////////////////////////////////////////////

function log(){}; // dummy to stop errors
function setupDebugging() {
//&lt;NOLITE&gt;
	if (window.popupDebug) { // popupDebug is set from .version
		window.log=function(x) { //if(gMsg!='')gMsg += '\n'; gMsg+=time() + ' ' + x; };
			window.console.log(x);
		}
		window.errlog=function(x) {
			window.console.error(x);
		}
		log('Initializing logger');
	} else {
//&lt;/NOLITE&gt;
		window.log = function(x) {};
		window.errlog = function(x) {};
//&lt;NOLITE&gt;
	}
//&lt;/NOLITE&gt;
}
// ENDFILE: debug.js
// STARTFILE: images.js

// load image of type Title.
function loadImage(image, navpop) {
	if (typeof image.stripNamespace != 'function') { alert('loadImages bad'); }
    // API call to retrieve image info.

	if (!getValueOf('popupImages')) return;
	if (!isValidImageName(image)) return false;
	
	var art=image.urlString();

	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query';
	url += '&amp;prop=imageinfo&amp;iiprop=url|mime&amp;iiurlwidth=' + getValueOf('popupImageSizeLarge');;
	url += '&amp;titles=' + art;
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}

	pendingNavpopTask(navpop);
	var callback=function(d){
		popupsInsertImage(navpop.idNumber, navpop, d);
	};
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'after', 'DOWNLOAD_IMAGE_QUERY_DATA'); }

}

function popupsInsertImage(id, navpop, download) {
	log( &quot;popupsInsertImage&quot;);
	try {
		var jsObj=getJsObj(download.data);
		var imagepage=anyChild(jsObj.query.pages);
		if (typeof imagepage.imageinfo === 'undefined') return;
		var imageinfo = imagepage.imageinfo[0];
	} catch (someError) {
		log( &quot;popupsInsertImage failed :(&quot; );
		return;
	}

	var popupImage = document.getElementById(&quot;popupImg&quot;+id);
	if (!popupImage) {
		log( &quot;could not find insertion point for image&quot;);
		return;
	}

	popupImage.width=getValueOf('popupImageSize');
	popupImage.style.display='inline';

	// Set the source for the image.
	if( imageinfo.thumburl )
		popupImage.src=imageinfo.thumburl;
	else if( imageinfo.mime.indexOf(&quot;image&quot;) == 0 ){
		popupImage.src=imageinfo.url;
		log( &quot;a thumb could not be found, using original image&quot; );
	} else log( &quot;fullsize imagethumb, but not sure if it's an image&quot;);


	var a=document.getElementById(&quot;popupImageLink&quot;+id);
	if (a === null) { return null; }

    // Determine the action of the surrouding imagelink.
	switch (getValueOf('popupThumbAction')) {
	case 'imagepage':
		if (pg.current.article.namespaceId()!=pg.nsImageId) {
			a.href=imageinfo.descriptionurl;
			// FIXME: unreliable pg.idNumber
			popTipsSoonFn('popupImage' + id)();
			break;
		} // else fall through
	case 'sizetoggle':
		a.onclick=toggleSize;
		a.title=popupString('Toggle image size');
		return;
	case 'linkfull':
		a.href = imageinfo.url;
		a.title=popupString('Open full-size image');
		return;
	}

}

// Toggles the image between inline small and navpop fullwidth.
// It's the same image, no actual sizechange occurs, only display width.
function toggleSize() {
	var imgContainer=this;
	if (!imgContainer) { alert('imgContainer is null :/'); return;}
	img=imgContainer.firstChild;
	if (!img) { alert('img is null :/'); return;}
	if (!img.style.width || img.style.width=='') { img.style.width='100%'; }
	else { img.style.width=''; }
}

// Returns one title of an image from wikiText.
function getValidImageFromWikiText(wikiText) {
	// nb in pg.re.image we're interested in the second bracketed expression
	// this may change if the regex changes :-(
	//var match=pg.re.image.exec(wikiText);
	var matched=null;
	var match;
	// strip html comments, used by evil bots :-(
	var t = removeMatchesUnless(wikiText, RegExp('(&lt;!--[\\s\\S]*?--&gt;)'), 1,
				    RegExp('^&lt;!--[^[]*popup', 'i'));

	while ( match = pg.re.image.exec(t) ) {
		// now find a sane image name - exclude templates by seeking {
		var m = match[2] || match[6];
		if ( isValidImageName(m) ) {
			matched=m;
			break;
		}
	}
	pg.re.image.lastIndex=0;
	if (!matched) { return null; }
	return mw.config.get('wgFormattedNamespaces')[pg.nsImageId]+':'+upcaseFirst(matched);
}

function removeMatchesUnless(str, re1, parencount, re2) {
    var split=str.parenSplit(re1);
    var c=parencount + 1;
    for (var i=0; i&lt;split.length; ++i) {
	if ( i%c === 0 || re2.test(split[i]) ) { continue; }
	split[i]='';
    }
    return split.join('');
}

//&lt;/NOLITE&gt;
// ENDFILE: images.js
// STARTFILE: namespaces.js
// Set up namespaces and other non-strings.js localization
// (currently that means redirs too)


function namespaceListToRegex(list) {return RegExp('^('+list.join('|').split(' ').join('[ _]')+'):');};

function setNamespaces() {
	pg.nsSpecialId   = -1;
	pg.nsImageId     = 6;
	pg.nsUserId      = 2;
	pg.nsUsertalkId  = 3;
	pg.nsCategoryId  = 14;
	pg.nsTemplateId  = 10;
}


function setRedirs() {
	var r='redirect';
	var R='REDIRECT';
	var redirLists={
//&lt;NOLITE&gt;
		'ar':  [ R, 'تحويل' ],
		'be':  [ r, 'перанакіраваньне' ],
		'bg':  [ r, 'пренасочване', 'виж' ],
		'bs':  [ r, 'Preusmjeri', 'preusmjeri', 'PREUSMJERI' ],
		'cs':  [ R, 'PŘESMĚRUJ' ],
		'cy':  [ r, 'ail-cyfeirio' ],
		'de':  [ R, 'WEITERLEITUNG' ],
		'eo':  [ R, 'ALIDIREKTU', 'ALIDIREKTI' ],
		'es':  [ R, 'REDIRECCIÓN' ],
		'et':  [ r, 'suuna' ],
		'ga':  [ r, 'athsheoladh' ],
		'gl':  [ r, 'REDIRECCIÓN', 'REDIRECIONAMENTO'],
		'he':  [ R, 'הפניה' ],
		'hu':  [ R, 'ÁTIRÁNYÍTÁS' ],
		'is':  [ r, 'tilvísun', 'TILVÍSUN' ],
		'it':  [ R, 'RINVIA', 'Rinvia'],
		'mk':  [ r, 'пренасочување', 'види' ],
		'nds': [ r, 'wiederleiden' ],
		'nl':  [ R, 'DOORVERWIJZING' ],
		'nn':  [ r, 'omdiriger' ],
		'pl':  [ R, 'PATRZ', 'PRZEKIERUJ', 'TAM' ],
		'pt':  [ R, 'redir' ],
		'ru':  [ R, 'ПЕРЕНАПРАВЛЕНИЕ', 'ПЕРЕНАПР' ],
		'sk':  [ r, 'presmeruj' ],
		'sr':  [ r, 'Преусмери', 'преусмери', 'ПРЕУСМЕРИ', 'Preusmeri', 'preusmeri', 'PREUSMERI' ],
		'tt':  [ R, 'yünältü', 'перенаправление', 'перенапр' ],
		'uk': [ R, 'ПЕРЕНАПРАВЛЕННЯ', 'ПЕРЕНАПР' ],
		'vi':  [ r, 'đổi' ] // no comma
//&lt;/NOLITE&gt;
	};
	var redirList=redirLists[ pg.wiki.lang ] || [r, R];
	// Mediawiki is very tolerant about what comes after the #redirect at the start
	pg.re.redirect=RegExp('^\\s*[#](' + redirList.join('|') + ').*?\\[{2}([^\\|\\]]*)(|[^\\]]*)?\\]{2}\\s*(.*)', 'i');
}

function setInterwiki() {
	if (pg.wiki.wikimedia) {
		// From //meta.wikimedia.org/wiki/List_of_Wikipedias
		pg.wiki.interwiki='aa|ab|ace|af|ak|als|am|an|ang|ar|arc|arz|as|ast|av|ay|az|ba|bar|bat-smg|bcl|be|be-x-old|bg|bh|bi|bjn|bm|bn|bo|bpy|br|bs|bug|bxr|ca|cbk-zam|cdo|ce|ceb|ch|cho|chr|chy|ckb|co|cr|crh|cs|csb|cu|cv|cy|da|de|diq|dsb|dv|dz|ee|el|eml|en|eo|es|et|eu|ext|fa|ff|fi|fiu-vro|fj|fo|fr|frp|frr|fur|fy|ga|gag|gan|gd|gl|glk|gn|got|gu|gv|ha|hak|haw|he|hi|hif|ho|hr|hsb|ht|hu|hy|hz|ia|id|ie|ig|ii|ik|ilo|io|is|it|iu|ja|jbo|jv|ka|kaa|kab|kbd|kg|ki|kj|kk|kl|km|kn|ko|koi|kr|krc|ks|ksh|ku|kv|kw|ky|la|lad|lb|lbe|lg|li|lij|lmo|ln|lo|lt|ltg|lv|map-bms|mdf|mg|mh|mhr|mi|mk|ml|mn|mo|mr|mrj|ms|mt|mus|mwl|my|myv|mzn|na|nah|nap|nds|nds-nl|ne|new|ng|nl|nn|no|nov|nrm|nv|ny|oc|om|or|os|pa|pag|pam|pap|pcd|pdc|pfl|pi|pih|pl|pms|pnb|pnt|ps|pt|qu|rm|rmy|rn|ro|roa-rup|roa-tara|ru|rue|rw|sa|sah|sc|scn|sco|sd|se|sg|sh|si|simple|sk|sl|sm|sn|so|sq|sr|srn|ss|st|stq|su|sv|sw|szl|ta|te|tet|tg|th|ti|tk|tl|tn|to|tpi|tr|ts|tt|tum|tw|ty|udm|ug|uk|ur|uz|ve|vec|vi|vls|vo|wa|war|wo|wuu|xal|xh|yi|yo|za|zea|zh|zh-classical|zh-min-nan|zh-yue|zu';
		pg.re.interwiki=RegExp('^'+pg.wiki.interwiki+':');
	} else {
		pg.wiki.interwiki=null;
		pg.re.interwiki=RegExp('^$');
	}
}

// return a regexp pattern matching all variants to write the given namespace
function nsRe(namespaceId) {
	var imageNamespaceVariants = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=namespaceId) return;
		//todo: escape regexp fragments!
		_localizedNamespaceLc = upcaseFirst(_localizedNamespaceLc);
		imageNamespaceVariants.push(_localizedNamespaceLc.split(' ').join('[ _]'));
		imageNamespaceVariants.push(encodeURI(_localizedNamespaceLc));
	});

	return '(?:' + imageNamespaceVariants.join('|') + ')';
}

function nsReImage() {
	return nsRe(pg.nsImageId);
}

// ENDFILE: namespaces.js
// STARTFILE: selpop.js
//&lt;NOLITE&gt;
function getEditboxSelection() {
	// see http://www.webgurusforum.com/8/12/0
	try {
		var editbox=document.editform.wpTextbox1;
	} catch (dang) { return; }
	// IE, Opera
	if (document.selection) { return document.selection.createRange().text; }
	// Mozilla
	var selStart = editbox.selectionStart;
	var selEnd = editbox.selectionEnd;
	return (editbox.value).substring(selStart, selEnd);
}

function doSelectionPopup() {
	// popup if the selection looks like [[foo|anything afterwards at all
	// or [[foo|bar]]text without ']]'
	// or [[foo|bar]]
	var sel=getEditboxSelection();
	var open=sel.indexOf('[[');
	var pipe=sel.indexOf('|');
	var close=sel.indexOf(']]');
	if (open == -1 || ( pipe == -1 &amp;&amp; close == -1) ) { return; }
	if (pipe != -1 &amp;&amp; open &gt; pipe || close != -1 &amp;&amp; open &gt; close) { return; }
	if (getValueOf('popupOnEditSelection')=='boxpreview') {
		return doSeparateSelectionPopup(sel);
	}
	var article=new Title(sel.substring(open+2, (pipe &lt; 0) ? close : pipe)).urlString();
	if (close &gt; 0 &amp;&amp; sel.substring(close+2).indexOf('[[') &gt;= 0) { 
		return; 
	}
	var a=document.createElement('a');
	a.href=pg.wiki.titlebase + article;
	mouseOverWikiLink2(a);
	if (a.navpopup) {
		a.navpopup.addHook(function(){runStopPopupTimer(a.navpopup);}, 'unhide', 'after');
	}
}

function doSeparateSelectionPopup(str) {
	var div=document.getElementById('selectionPreview');
	if (!div) {
		div = document.createElement('div');
		div.id='selectionPreview';
		try { var box=document.editform.wpTextbox1; }
		catch (oopsie) { return; }
		box.parentNode.insertBefore(div, box);
	}
	div.innerHTML=wiki2html(str);
	div.ranSetupTooltipsAlready = false;
	popTipsSoonFn('selectionPreview')();
}
//&lt;/NOLITE&gt;
// ENDFILE: selpop.js
// STARTFILE: navpopup.js
/**
   @fileoverview  Defines two classes: {@link Navpopup} and {@link Mousetracker}.

   &lt;code&gt;Navpopup&lt;/code&gt; describes popups: when they appear, where, what
   they look like and so on.

   &lt;code&gt;Mousetracker&lt;/code&gt; &quot;captures&quot; the mouse using
   &lt;code&gt;document.onmousemove&lt;/code&gt;.
*/


/**
   Creates a new Mousetracker.
   @constructor
   @class The Mousetracker class. This monitors mouse movements and manages associated hooks.
*/
function Mousetracker() {
	/**
	   Interval to regularly run the hooks anyway, in milliseconds.
	   @type Integer
	*/
	this.loopDelay=400;

	/**
	   Timer for the loop.
	   @type Timer
	*/
	this.timer=null;

	/**
	   Flag - are we switched on?
	   @type Boolean
	*/
	this.active=false;
	/**
	   Flag - are we probably inaccurate, i.e. not reflecting the actual mouse position?
	*/
	this.dirty=true;
	/**
	   Array of hook functions.
	   @private
	   @type Array
	*/
	this.hooks=[];
}

/**
   Adds a hook, to be called when we get events.
   @param {Function} f A function which is called as
   &lt;code&gt;f(x,y)&lt;/code&gt;. It should return &lt;code&gt;true&lt;/code&gt; when it
   wants to be removed, and &lt;code&gt;false&lt;/code&gt; otherwise.
*/
Mousetracker.prototype.addHook = function (f) {
	this.hooks.push(f);
};

/**
   Runs hooks, passing them the x
   and y coords of the mouse.  Hook functions that return true are
   passed to {@link Mousetracker#removeHooks} for removal.
   @private
*/
Mousetracker.prototype.runHooks = function () {
	if (!this.hooks || !this.hooks.length) { return; }
	//log('Mousetracker.runHooks; we got some hooks to run');
	var remove=false;
	var removeObj={};
	// this method gets called a LOT -
	// pre-cache some variables
	var x=this.x, y=this.y, len = this.hooks.length;

	for (var i=0; i&lt;len; ++i) {
		//~ run the hook function, and remove it if it returns true
		if (this.hooks[i](x, y)===true) {
			remove=true;
			removeObj[i]=true;
		}
	}
	if (remove) { this.removeHooks(removeObj); }
};

/**
   Removes hooks.
   @private
   @param {Object} removeObj An object whose keys are the index
   numbers of functions for removal, with values that evaluate to true
*/
Mousetracker.prototype.removeHooks = function(removeObj) {
	var newHooks=[];
	var len = this.hooks.length;
	for (var i=0; i&lt;len; ++i) {
		if (! removeObj[i]) { newHooks.push(this.hooks[i]); }
	}
	this.hooks=newHooks;
};


/**
   Event handler for mouse wiggles.
   We simply grab the event, set x and y and run the hooks.
   This makes the cpu all hot and bothered :-(
   @private
   @param {Event} e Mousemove event
*/
Mousetracker.prototype.track=function (e) {
	//~ Apparently this is needed in IE.
	e = e || window.event;
	var x, y;
	if (e) {
		if (e.pageX) { x=e.pageX; y=e.pageY; }
		else if (typeof e.clientX!='undefined') {
			var left, top, docElt = window.document.documentElement;

			if (docElt) { left=docElt.scrollLeft; }
			left = left || window.document.body.scrollLeft || window.document.scrollLeft || 0;

			if (docElt) { top=docElt.scrollTop; }
			top = top || window.document.body.scrollTop || window.document.scrollTop || 0;

			x=e.clientX + left;
			y=e.clientY + top;
		} else { return; }
		this.setPosition(x,y);
	}
};

/**
   Sets the x and y coordinates stored and takes appropriate action,
   running hooks as appropriate.
   @param {Integer} x, y Screen coordinates to set
*/

Mousetracker.prototype.setPosition=function(x,y) {
	this.x = x;
	this.y = y;
	if (this.dirty || this.hooks.length === 0) { this.dirty=false; return; }
	if (typeof this.lastHook_x != 'number') { this.lastHook_x = -100; this.lastHook_y=-100; }
	var diff = (this.lastHook_x - x)*(this.lastHook_y - y);
	diff = (diff &gt;= 0) ? diff : -diff;
	if ( diff &gt; 1 ) {
		this.lastHook_x=x;
		this.lastHook_y=y;
		if (this.dirty) { this.dirty = false; }
		else { this.runHooks(); }
	}
}

/**
   Sets things in motion, unless they are already that is, registering an event handler on &lt;code&gt;document.onmousemove&lt;/code&gt;.
   A half-hearted attempt is made to preserve the old event handler if there is one.
*/
Mousetracker.prototype.enable = function () {
	if (this.active) { return; }
	this.active=true;
	//~ Save the current handler for mousemove events. This isn't too
	//~ robust, of course.
	this.savedHandler=document.onmousemove;
	//~ Gotta save @tt{this} again for the closure, and use apply for
	//~ the member function.
	var savedThis=this;
	document.onmousemove=function (e) {savedThis.track.apply(savedThis, [e]);};
	if (this.loopDelay) { this.timer = setInterval(function() { //log('loop delay in mousetracker is working');
								    savedThis.runHooks();}, this.loopDelay); }
};

/**
   Disables the tracker, removing the event handler.
*/
Mousetracker.prototype.disable = function () {
	if (!this.active) { return; }
	if (typeof this.savedHandler=='function') {
		document.onmousemove=this.savedHandler;
	} else { delete document.onmousemove; }
	if (this.timer) { clearInterval(this.timer); }
	this.active=false;
};

/**
   Creates a new Navpopup.
   Gets a UID for the popup and
   @param init Contructor object. If &lt;code&gt;init.draggable&lt;/code&gt; is true or absent, the popup becomes draggable.
   @constructor
   @class The Navpopup class. This generates popup hints, and does some management of them.
*/
function Navpopup(init) {
	//alert('new Navpopup(init)');
	/** UID for each Navpopup instance.
	    Read-only.
	    @type integer
	*/
	this.uid=Navpopup.uid++;
	/**
	   Read-only flag for current visibility of the popup.
	   @type boolean
	   @private
	*/
	this.visible=false;
	/** Flag to be set when we want to cancel a previous request to
	    show the popup in a little while.
	    @private
	    @type boolean
	*/
	this.noshow=false;
	/** Categorised list of hooks.
	    @see #runHooks
	    @see #addHook
	    @private
	    @type Object
	*/
	this.hooks={
		'create': [],
		'unhide': [],
		'hide': []
	};
	/** list of unique IDs of hook functions, to avoid duplicates
	    @private
	*/
	this.hookIds={};
	/** List of downloads associated with the popup.
	    @private
	    @type Array
	*/
	this.downloads=[];
	/** Number of uncompleted downloads.
	    @type integer
	*/
	this.pending=null;
	/** Tolerance in pixels when detecting whether the mouse has left the popup.
	    @type integer
	*/
	this.fuzz=5;
	/** Flag to toggle running {@link #limitHorizontalPosition} to regulate the popup's position.
	    @type boolean
	*/
	this.constrained=true;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.width=0;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.height=0;
	/** The main content DIV element.
	    @type HTMLDivElement
	*/
	this.mainDiv=null;
	this.createMainDiv();

//	if (!init || typeof init.popups_draggable=='undefined' || init.popups_draggable) {
//		this.makeDraggable(true);
//	}
}

/**
   A UID for each Navpopup. This constructor property is just a counter.
   @type integer
   @private
*/
Navpopup.uid=0;

/**
   Retrieves the {@link #visible} attribute, indicating whether the popup is currently visible.
   @type boolean
*/
Navpopup.prototype.isVisible=function() {
	return this.visible;
};

/**
   Repositions popup using CSS style.
   @private
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @param {boolean} noLimitHor Don't call {@link #limitHorizontalPosition}
*/
Navpopup.prototype.reposition= function (x,y, noLimitHor) {
	log ('reposition('+x+','+y+','+noLimitHor+')');
	if (typeof x != 'undefined' &amp;&amp; x!==null) { this.left=x; }
	if (typeof y != 'undefined' &amp;&amp; y!==null) { this.top=y; }
	if (typeof this.left != 'undefined' &amp;&amp; typeof this.top != 'undefined') {
		this.mainDiv.style.left=this.left + 'px';
		this.mainDiv.style.top=this.top + 'px';
	}
	if (!noLimitHor) { this.limitHorizontalPosition(); }
	//console.log('navpop'+this.uid+' - (left,top)=(' + this.left + ',' + this.top + '), css=('
	//+ this.mainDiv.style.left + ',' + this.mainDiv.style.top + ')');
};

/**
   Prevents popups from being in silly locations. Hopefully.
   Should not be run if {@link #constrained} is true.
   @private
*/
Navpopup.prototype.limitHorizontalPosition=function() {
	if (!this.constrained || this.tooWide) { return; }
	this.updateDimensions();
	var x=this.left;
	var w=this.width;
	var cWidth=document.body.clientWidth;


//	log('limitHorizontalPosition: x='+x+
//		    ', this.left=' + this.left +
//		    ', this.width=' + this.width +
//		    ', cWidth=' + cWidth);


	if ( (x+w) &gt;= cWidth ||
	     ( x &gt; 0 &amp;&amp; this.maxWidth &amp;&amp; this.width &lt; this.maxWidth &amp;&amp; this.height &gt; this.width
	       &amp;&amp; x &gt; cWidth - this.maxWidth ) ) {
		// This is a very nasty hack. There has to be a better way!
		// We find the &quot;natural&quot; width of the div by positioning it at the far left
		// then reset it so that it should be flush right (well, nearly)
		this.mainDiv.style.left='-10000px';
		this.mainDiv.style.width = this.maxWidth + 'px';
		var naturalWidth=parseInt(this.mainDiv.offsetWidth, 10);
		var newLeft=cWidth - naturalWidth - 1;
		if (newLeft &lt; 0) { newLeft = 0; this.tooWide=true; } // still unstable for really wide popups?
		log ('limitHorizontalPosition: moving to ('+newLeft + ','+ this.top+');' + ' naturalWidth=' + naturalWidth + ', clientWidth=' + cWidth);
		this.reposition(newLeft, null, true);
	}
};

/**
   Counter indicating the z-order of the &quot;highest&quot; popup.
   We start the z-index at 1000 so that popups are above everything
   else on the screen.
   @private
   @type integer
*/
Navpopup.highest=1000;

/**
   Brings popup to the top of the z-order.
   We increment the {@link #highest} property of the contructor here.
   @private
*/
Navpopup.prototype.raise = function () {
	this.mainDiv.style.zIndex=Navpopup.highest + 1;
	++Navpopup.highest;
};

/**
   Shows the popup provided {@link #noshow} is not true.
   Updates the position, brings the popup to the top of the z-order and unhides it.
*/
Navpopup.prototype.show = function () {
	//document.title+='s';
	if (this.noshow) { return; }
	//document.title+='t';
	this.reposition();
	this.raise();
	this.unhide();
};


/**
   Runs the {@link #show} method in a little while, unless we're
   already visible.
   @param {integer} time Delay in milliseconds
   @see #showSoonIfStable
*/
Navpopup.prototype.showSoon = function (time) {
	if (this.visible) { return; }
	this.noshow=false;
	//~ We have to save the value of @tt{this} so that the closure below
	//~ works.
	var savedThis=this;
	//this.start_x = Navpopup.tracker.x;
	//this.start_y = Navpopup.tracker.y;
	setTimeout(function () {
		if (Navpopup.tracker.active) {
			savedThis.reposition.apply(savedThis, [Navpopup.tracker.x + 2, Navpopup.tracker.y + 2]);
		}
		//~ Have to use apply to invoke his member function here
		savedThis.show.apply(savedThis, []);
	}, time);
};

/**
   Checks to see if the mouse pointer has
   stabilised (checking every &lt;code&gt;time&lt;/code&gt;/2 milliseconds) and runs the
   {@link #show} method if it has. This method makes {@link #showSoon} redundant.
   @param {integer} time The minimum time (ms) before the popup may be shown.
*/
Navpopup.prototype.showSoonIfStable = function (time) {
	log ('showSoonIfStable, time='+time);
	if (this.visible) { return; }
	this.noshow = false;

	//~ initialize these variables so that we never run @tt{show} after
	//~ just half the time
	this.stable_x = -10000; this.stable_y = -10000;

	var stableShow = function() {
		log('stableShow called');
		var new_x = Navpopup.tracker.x, new_y = Navpopup.tracker.y;
		var dx = savedThis.stable_x - new_x, dy = savedThis.stable_y - new_y;
		var fuzz2 = 0; // savedThis.fuzz * savedThis.fuzz;
		//document.title += '[' + [savedThis.stable_x,new_x, savedThis.stable_y,new_y, dx, dy, fuzz2].join(',') + '] ';
		if ( dx * dx &lt;= fuzz2 &amp;&amp; dy * dy &lt;= fuzz2 ) {
			log ('mouse is stable');
			clearInterval(savedThis.showSoonStableTimer);
			savedThis.reposition.apply(savedThis, [new_x + 2, new_y + 2]);
			savedThis.show.apply(savedThis, []);
			return;
		}
		savedThis.stable_x = new_x; savedThis.stable_y = new_y;
	};
	var savedThis = this;
	this.showSoonStableTimer = setInterval(stableShow, time/2);
};

/**
   Makes the popup unhidable until we call {@link #unstick}.
*/
Navpopup.prototype.stick=function() {
	this.noshow=false;
	this.sticky=true;
};

/**
   Allows the popup to be hidden.
*/
Navpopup.prototype.unstick=function() {
	this.sticky=false;
};

/**
   Sets the {@link #noshow} flag and hides the popup. This should be called
   when the mouse leaves the link before
   (or after) it's actually been displayed.
*/
Navpopup.prototype.banish = function () {
	log ('banish called');
	// hide and prevent showing with showSoon in the future
	this.noshow=true;
	if (this.showSoonStableTimer) {
		log('clearing showSoonStableTimer');
		clearInterval(this.showSoonStableTimer);
	}
	this.hide();
};

/**
   Runs hooks added with {@link #addHook}.
   @private
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
*/
Navpopup.prototype.runHooks = function (key, when) {
	if (!this.hooks[key]) { return; }
	var keyHooks=this.hooks[key];
	var len=keyHooks.length;
	for (var i=0; i&lt; len; ++i) {
		if (keyHooks[i] &amp;&amp; keyHooks[i].when == when) {
			if (keyHooks[i].hook.apply(this, [])) {
				// remove the hook
				if (keyHooks[i].hookId) {
					delete this.hookIds[keyHooks[i].hookId];
				}
				keyHooks[i]=null;
			}
		}
	}
};

/**
   Adds a hook to the popup. Hook functions are run with &lt;code&gt;this&lt;/code&gt; set to refer to the Navpopup instance, and no arguments.
   @param {Function} hook The hook function. Functions that return true are deleted.
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
   @param {String} uid A truthy string identifying the hook function; if it matches another hook in this position, it won't be added again.
*/
Navpopup.prototype.addHook = function ( hook, key, when, uid ) {
	when = when || 'after';
	if (!this.hooks[key]) { return; }
	// if uid is specified, don't add duplicates
	var hookId=null;
	if (uid) {
		hookId=[key,when,uid].join('|');
		if (this.hookIds[hookId]) {
			return;
		}
		this.hookIds[hookId]=true;
	}
	this.hooks[key].push( {hook: hook, when: when, hookId: hookId} );
};

/**
   Creates the main DIV element, which contains all the actual popup content.
   Runs hooks with key 'create'.
   @private
*/
Navpopup.prototype.createMainDiv = function () {
	if (this.mainDiv) { return; }
	this.runHooks('create', 'before');
	var mainDiv=document.createElement('div');

	var savedThis=this;
	mainDiv.onclick=function(e) {savedThis.onclickHandler(e);};
	mainDiv.className=(this.className) ? this.className : 'navpopup_maindiv';
	mainDiv.id=mainDiv.className + this.uid;

	mainDiv.style.position='absolute';
	mainDiv.style.display='none';
	mainDiv.className='navpopup';

	// easy access to javascript object through DOM functions
	mainDiv.navpopup=this;

	this.mainDiv=mainDiv;
	document.body.appendChild(mainDiv);
	this.runHooks('create', 'after');
};
/**
   Calls the {@link #raise} method.
   @private
*/
Navpopup.prototype.onclickHandler=function(e) {
	this.raise();
};
/**
   Makes the popup draggable, using a {@link Drag} object.
   @private
*/
Navpopup.prototype.makeDraggable=function(handleName) {
	if (!this.mainDiv) { this.createMainDiv(); }
	var drag=new Drag();
	if (!handleName) {
	    drag.startCondition=function(e) {
		try { if (!e.shiftKey) { return false; } } catch (err) { return false; }
		return true;
	    };
	}
	var dragHandle;
	if (handleName) dragHandle = document.getElementById(handleName);
	if (!dragHandle) dragHandle = this.mainDiv;
	var np=this;
	drag.endHook=function(x,y) {
		Navpopup.tracker.dirty=true;
		np.reposition(x,y);
	};
	drag.init(dragHandle,this.mainDiv);
};

/** Hides the popup using CSS. Runs hooks with key 'hide'.
    Sets {@link #visible} appropriately.     {@link #banish} should be called externally instead of this method.

    @private
*/
Navpopup.prototype.hide = function () {
	this.runHooks('hide', 'before');
	this.abortDownloads();
	if (this.sticky) { return; }
	if (typeof this.visible != 'undefined' &amp;&amp; this.visible) {
		this.mainDiv.style.display='none';
		this.visible=false;
	}
	this.runHooks('hide', 'after');
};

/** Shows the popup using CSS. Runs hooks with key 'unhide'.
    Sets {@link #visible} appropriately.   {@link #show} should be called externally instead of this method.
    @private
*/
Navpopup.prototype.unhide = function () {
	this.runHooks('unhide', 'before');
	if (typeof this.visible != 'undefined' &amp;&amp; !this.visible) {
		this.mainDiv.style.display='inline';
		this.visible=true;
	}
	this.runHooks('unhide', 'after');
};

/**
   Sets the &lt;code&gt;innerHTML&lt;/code&gt; attribute of the main div containing the popup content.
   @param {String} html The HTML to set.
*/
Navpopup.prototype.setInnerHTML = function (html) {
	this.mainDiv.innerHTML = html;
};

/**
   Updates the {@link #width} and {@link #height} attributes with the CSS properties.
   @private
*/
Navpopup.prototype.updateDimensions = function () {
	this.width=parseInt(this.mainDiv.offsetWidth, 10);
	this.height=parseInt(this.mainDiv.offsetHeight, 10);
};

/**
   Checks if the point (x,y) is within {@link #fuzz} of the
   {@link #mainDiv}.
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @type boolean
*/
Navpopup.prototype.isWithin = function(x,y) {
	//~ If we're not even visible, no point should be considered as
	//~ being within the popup.
	if (!this.visible) { return false; }
	this.updateDimensions();
	var fuzz=this.fuzz || 0;
	//~ Use a simple box metric here.
	return (x+fuzz &gt;= this.left &amp;&amp; x-fuzz &lt;= this.left + this.width &amp;&amp;
		y+fuzz &gt;= this.top  &amp;&amp; y-fuzz &lt;= this.top  + this.height);
};

/**
   Adds a download to {@link #downloads}.
   @param {Downloader} download
*/
Navpopup.prototype.addDownload=function(download) {
	if (!download) { return; }
	this.downloads.push(download);
};
/**
   Aborts the downloads listed in {@link #downloads}.
   @see Downloader#abort
*/
Navpopup.prototype.abortDownloads=function() {
	for(var i=0; i&lt;this.downloads.length; ++i) {
		var d=this.downloads[i];
		if (d &amp;&amp; d.abort) { d.abort(); }
	}
	this.downloads=[];
};


/**
   A {@link Mousetracker} instance which is a property of the constructor (pseudo-global).
*/
Navpopup.tracker=new Mousetracker();
// ENDFILE: navpopup.js
// STARTFILE: diff.js
//&lt;NOLITE&gt;
/*
 * Javascript Diff Algorithm
 *  By John Resig (http://ejohn.org/) and [[:en:User:Lupin]]
 *
 * More Info:
 *  http://ejohn.org/projects/javascript-diff-algorithm/
 */

function delFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;del class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/del&gt;&quot;;
}
function insFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;ins class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/ins&gt;&quot;;
}

function countCrossings(a, b, i, eject) {
	// count the crossings on the edge starting at b[i]
	if (!b[i].row &amp;&amp; b[i].row !== 0) { return -1; }
	var count=0;
	for (var j=0; j&lt;a.length; ++j) {
		if (!a[j].row &amp;&amp; a[j].row !== 0) { continue; }
		if ( (j-b[i].row)*(i-a[j].row) &gt; 0) {
			if(eject) { return true; }
			count++;
		}
	}
	return count;
}

function shortenDiffString(str, context) {
	var re=RegExp('(&lt;del[\\s\\S]*?&lt;/del&gt;|&lt;ins[\\s\\S]*?&lt;/ins&gt;)');
	var splitted=str.parenSplit(re);
	var ret=[''];
	for (var i=0; i&lt;splitted.length; i+=2) {
		if (splitted[i].length &lt; 2*context) {
			ret[ret.length-1] += splitted[i];
			if (i+1&lt;splitted.length) { ret[ret.length-1] += splitted[i+1]; }
			continue;
		}
		else {
			if (i &gt; 0) { ret[ret.length-1] += splitted[i].substring(0,context); }
			if (i+1 &lt; splitted.length) {
			    ret.push(splitted[i].substring(splitted[i].length-context) +
				     splitted[i+1]);
			}
		}
	}
	while (ret.length &gt; 0 &amp;&amp; !ret[0]) { ret = ret.slice(1); }
	return ret;
}


function diffString( o, n, simpleSplit ) {
	var splitRe=RegExp('([[]{2}|[\\]]{2}|[{]{2,3}|[}]{2,3}|[|]|=|&lt;|&gt;|[*:]+|\\s|\\b)');

	//  We need to split the strings o and n first, and entify() the parts
	//  individually, so that the HTML entities are never cut apart. (AxelBoldt)
	var out, i, oSplitted, nSplitted;
	if (simpleSplit) { 
		oSplitted=o.split(/\b/); 
		nSplitted=n.split(/\b/); 
	} else { 
		oSplitted=o.parenSplit(splitRe); 
		nSplitted=n.parenSplit(splitRe); 
	}
	for (i=0; i&lt;oSplitted.length; ++i) {oSplitted[i]=oSplitted[i].entify();}
	for (i=0; i&lt;nSplitted.length; ++i) {nSplitted[i]=nSplitted[i].entify();}
		
	out = diff (oSplitted, nSplitted);
	var str = &quot;&quot;;
	var acc=[]; // accumulator for prettier output

	// crossing pairings -- eg 'A B' vs 'B A' -- cause problems, so let's iron them out
	// this doesn't always do things optimally but it should be fast enough
	var maxOutputPair=0;
	for (i=0; i&lt;out.n.length; ++i) {
	    if ( out.n[i].paired ) {
		if( maxOutputPair &gt; out.n[i].row ) {
		    // tangle - delete pairing
		    out.o[ out.n[i].row ]=out.o[ out.n[i].row ].text;
		    out.n[i]=out.n[i].text;
		}
		if (maxOutputPair &lt; out.n[i].row) { maxOutputPair = out.n[i].row; }
	    }
	}

	// output the stuff preceding the first paired old line
	for (i=0; i&lt;out.o.length &amp;&amp; !out.o[i].paired; ++i) { acc.push( out.o[i] ); }
	str += delFmt(acc); acc=[];

	// main loop
	for ( i = 0; i &lt; out.n.length; ++i ) {
		// output unpaired new &quot;lines&quot;
		while ( i &lt; out.n.length &amp;&amp; !out.n[i].paired ) { acc.push( out.n[i++] ); }
		str += insFmt(acc); acc=[];
		if ( i &lt; out.n.length ) { // this new &quot;line&quot; is paired with the (out.n[i].row)th old &quot;line&quot;
			str += out.n[i].text;
			// output unpaired old rows starting after this new line's partner
			var m = out.n[i].row + 1;
			while ( m &lt; out.o.length &amp;&amp; !out.o[m].paired ) { acc.push ( out.o[m++] ); }
			str += delFmt(acc); acc=[];
		}
	}
	return str;
}

// see http://developer.mozilla.org/en/docs/Core_JavaScript_1.5_Reference:Global_Objects:Object
// FIXME: use obj.hasOwnProperty instead of this kludge!
window.jsReservedProperties=RegExp('^(constructor|prototype|__((define|lookup)[GS]etter)__' +
				   '|eval|hasOwnProperty|propertyIsEnumerable' +
				   '|to(Source|String|LocaleString)|(un)?watch|valueOf)$');
function diffBugAlert(word) {
	if (!diffBugAlert.list[word]) {
		diffBugAlert.list[word]=1;
		alert('Bad word: '+word+'\n\nPlease report this bug.');
	}
}
diffBugAlert.list={};

function makeDiffHashtable(src) {
	var ret={};
	for ( var i = 0; i &lt; src.length; i++ ) {
		if ( jsReservedProperties.test(src[i]) ) { src[i] += '&lt;!-- --&gt;'; }
		if ( !ret[ src[i] ] ) {	ret[ src[i] ] = []; }
		try { ret[ src[i] ].push( i ); } catch (err) { diffBugAlert(src[i]); }
	}
	return ret;
}

function diff( o, n ) {

	// pass 1: make hashtable ns with new rows as keys
	var ns = makeDiffHashtable(n);

	// pass 2: make hashtable os with old rows as keys
	var os = makeDiffHashtable(o);

	// pass 3: pair unique new rows and matching unique old rows
	var i;
	for ( i in ns ) {
		if ( ns[i].length == 1 &amp;&amp; os[i] &amp;&amp; os[i].length == 1 ) {
			n[ ns[i][0] ] = { text: n[ ns[i][0] ], row: os[i][0], paired: true };
			o[ os[i][0] ] = { text: o[ os[i][0] ], row: ns[i][0], paired: true };
		}
	}

	// pass 4: pair matching rows immediately following paired rows (not necessarily unique)
	for ( i = 0; i &lt; n.length - 1; i++ ) {
		if ( n[i].paired &amp;&amp; ! n[i+1].paired &amp;&amp; n[i].row + 1 &lt; o.length &amp;&amp; ! o[ n[i].row + 1 ].paired &amp;&amp;
		     n[i+1] == o[ n[i].row + 1 ] ) {
			n[i+1] = { text: n[i+1], row: n[i].row + 1, paired: true };
			o[n[i].row+1] = { text: o[n[i].row+1], row: i + 1, paired: true };
		}
	}

	// pass 5: pair matching rows immediately preceding paired rows (not necessarily unique)
	for ( i = n.length - 1; i &gt; 0; i-- ) {
		if ( n[i].paired &amp;&amp; ! n[i-1].paired &amp;&amp; n[i].row &gt; 0 &amp;&amp; ! o[ n[i].row - 1 ].paired &amp;&amp;
		     n[i-1] == o[ n[i].row - 1 ] ) {
			n[i-1] = { text: n[i-1], row: n[i].row - 1, paired: true };
			o[n[i].row-1] = { text: o[n[i].row-1], row: i - 1, paired: true };
		}
	}

	return { o: o, n: n };
}
//&lt;/NOLITE&gt;
// ENDFILE: diff.js
// STARTFILE: init.js
function setSiteInfo() {
	if (window.popupLocalDebug) {
		pg.wiki.hostname = 'en.wikiversity.org';
	} else {
		pg.wiki.hostname = location.hostname; // use in preference to location.hostname for flexibility (?)
	}
	pg.wiki.wikimedia=RegExp('(wiki([pm]edia|source|books|news|quote|versity)|wiktionary|mediawiki)[.]org').test(pg.wiki.hostname);
	pg.wiki.wikia=RegExp('[.]wikia[.]com$', 'i').test(pg.wiki.hostname);
	pg.wiki.isLocal=RegExp('^localhost').test(pg.wiki.hostname);
	pg.wiki.commons=( pg.wiki.wikimedia &amp;&amp; pg.wiki.hostname != 'commons.wikimedia.org') ? 'commons.wikimedia.org' : null;
	pg.wiki.lang = mw.config.get('wgContentLanguage');
	var port = location.port ? ':' + location.port : '';
	pg.wiki.sitebase = pg.wiki.hostname + port;
}

function setTitleBase() {
	var protocol = ( window.popupLocalDebug ? 'http:' : location.protocol );
	pg.wiki.articlePath = mw.config.get('wgArticlePath').replace(/\/\$1/, &quot;&quot;);   // as in http://some.thing.com/wiki/Article
	pg.wiki.botInterfacePath = mw.config.get('wgScript');
	pg.wiki.APIPath = wgScriptPath +&quot;/api.php&quot;;
	// default mediawiki setting is paths like http://some.thing.com/articlePath/index.php?title=foo

	var titletail = pg.wiki.botInterfacePath + '?title=';
	//var titletail2 = joinPath([pg.wiki.botInterfacePath, 'wiki.phtml?title=']);

	// other sites may need to add code here to set titletail depending on how their urls work

	pg.wiki.titlebase   = protocol + '//' + pg.wiki.sitebase + titletail;
	//pg.wiki.titlebase2  = protocol + '//' + joinPath([pg.wiki.sitebase, titletail2]);
	pg.wiki.wikibase    = protocol + '//' + pg.wiki.sitebase + pg.wiki.botInterfacePath;
	pg.wiki.apiwikibase = protocol + '//' + pg.wiki.sitebase + pg.wiki.APIPath;
	pg.wiki.articlebase = protocol + '//' + pg.wiki.sitebase + pg.wiki.articlePath;
	pg.wiki.commonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.botInterfacePath;
	pg.wiki.apicommonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.APIPath;
	pg.re.basenames = RegExp( '^(' +
				  map( literalizeRegex, [ pg.wiki.titlebase, //pg.wiki.titlebase2,
							  pg.wiki.articlebase ]).join('|') + ')' );
}


//////////////////////////////////////////////////
// Global regexps

function setMainRegex() {
	var reStart='[^:]*://';
	var preTitles = literalizeRegex(wgScriptPath) + '/(?:index[.]php|wiki[.]phtml)[?]title=';
	// slightly ugly hack when pg.wiki.articlePath is empty
	preTitles += '|' + literalizeRegex( ( pg.wiki.articlePath ? pg.wiki.articlePath + '/': ''));

	var reEnd='(' + preTitles + ')([^&amp;?#]*)[^#]*(?:#(.+))?';
	pg.re.main = RegExp(reStart + literalizeRegex(pg.wiki.sitebase) + reEnd);
}

function setRegexps() {
	setMainRegex();
	var sp=nsRe(pg.nsSpecialId);
	pg.re.urlNoPopup=RegExp('((title=|/)' + sp + '(?:%3A|:)|section=[0-9])') ;
	pg.re.contribs  =RegExp('(title=|/)'  + sp + '(?:%3A|:)Contributions' + '(&amp;target=|/|/' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)(.*)') ;
	pg.re.email     =RegExp('(title=|/)'  + sp + '(?:%3A|:)EmailUser'     + '(&amp;target=|/|/(?:' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)?)(.*)') ;
	pg.re.backlinks =RegExp('(title=|/)'  + sp + '(?:%3A|:)WhatLinksHere' + '(&amp;target=|/)([^&amp;]*)');

//&lt;NOLITE&gt;
	var im=nsReImage();
	// note: tries to get images in infobox templates too, e.g. movie pages, album pages etc
	//                      (^|\[\[)image: *([^|\]]*[^|\] ]) *
	//                      (^|\[\[)image: *([^|\]]*[^|\] ])([^0-9\]]*([0-9]+) *px)?
	//                                                        $4 = 120 as in 120px
	pg.re.image = RegExp('(^|\\[\\[)' + im + ': *([^|\\]]*[^|\\] ])' +
			     '([^0-9\\]]*([0-9]+) *px)?|(?:\\n *[|]?|[|]) *' +
			     '(' + getValueOf('popupImageVarsRegexp') + ')' +
			     ' *= *(?:\\[\\[ *)?(?:' + im + ':)?' +
			     '([^|]*?)(?:\\]\\])? *[|]? *\\n', 'img') ;
	pg.re.imageBracketCount = 6;

	pg.re.category = RegExp('\\[\\[' +nsRe(pg.nsCategoryId) +
				': *([^|\\]]*[^|\\] ]) *', 'i');
	pg.re.categoryBracketCount = 1;

	pg.re.ipUser=RegExp('('+nsRe(pg.nsUserId)+':)?' +
			    '((25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}' +
			    '(25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])');

	pg.re.stub= RegExp(getValueOf('popupStubRegexp'), 'im');
	pg.re.disambig=RegExp(getValueOf('popupDabRegexp'), 'im');

//&lt;/NOLITE&gt;
	// FIXME replace with general parameter parsing function, this is daft
	pg.re.oldid=RegExp('[?&amp;]oldid=([^&amp;]*)');
	pg.re.diff=RegExp('[?&amp;]diff=([^&amp;]*)');
}


//////////////////////////////////////////////////
// miscellany

function setupCache() {
	// page caching
	pg.cache.pages = [];
}

function setMisc() {
	pg.current.link=null;
	pg.current.links=[];
	pg.current.linksHash={};

	setupCache();

	pg.timer.checkPopupPosition=null;
	pg.counter.loop=0;

	// ids change with each popup: popupImage0, popupImage1 etc
	pg.idNumber=0;

	// for myDecodeURI
	pg.misc.decodeExtras = [
		{from: '%2C', to: ',' },
		{from: '_',   to: ' ' },
		{from: '%24', to: '$'},
		{from: '%26',   to: '&amp;' } // no ,
		];

}

function leadingInteger(s){
	var n=s.match(/^(\d*)/)[1];
	if (n) { return +n; }
	return null;
}

function setBrowserHacks() {
	var useOriginal=false;
	// browser-specific hacks
	if (typeof window.opera != 'undefined') {
		//if (leadingInteger(opera.version()) &lt; 9)
		{ useOriginal=true; } // v9 beta still seems to have buggy css
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
	} else if (navigator.appName=='Konqueror') {
		setDefault('popupNavLinkSeparator', ' &amp;bull; ');
		pg.flag.isKonq=true;
	} else if ( navigator.vendor &amp;&amp; navigator.vendor.toLowerCase().indexOf('apple computer')===0) {
		pg.flag.isSafari=true;
		var webkit=+navigator.userAgent.replace(RegExp('^.*AppleWebKit[/](\\d+).*', 'i'), '$1');
		if (webkit &lt; 420) { useOriginal=true; }
	} else if (navigator.appName.indexOf(&quot;Microsoft&quot;)!=-1) {
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
		var ver=+navigator.userAgent.replace(RegExp('^.*MSIE (\\d+).*'), '$1');
		pg.flag.isIE=true;
		pg.flag.IEVersion=ver;
	}
	if (pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 8) {
		useOriginal=true;
	}
	if ((pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 7) || pg.flag.isKonq || (pg.flag.isSafari &amp;&amp; webkit &lt; 420)) {
		pg.flag.linksLikeIE6=true;
	}
	if (useOriginal &amp;&amp; pg.structures.original) {
		setDefault('popupStructure','original');
	}
}

function setupPopups() {
	// NB translatable strings should be set up first (strings.js)
	// basics
	setupDebugging();
	setSiteInfo();
	setTitleBase();
	setOptions(); // see options.js

	// namespaces etc
	setNamespaces();
	setInterwiki();

	// regexps
	setRegexps();
	setRedirs();

	// other stuff
	setBrowserHacks();
	setMisc();
	setupLivePreview();

	// main deal here
	setupTooltips();
	Navpopup.tracker.enable();

	setupPopups.completed = true;
}
// ENDFILE: init.js
// STARTFILE: navlinks.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// navlinks... let the fun begin
//

function defaultNavlinkSpec() {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';
	if (getValueOf('popupLastEditLink')) {
		str += '*&lt;&lt;lastEdit|shortcut=/&gt;&gt;|&lt;&lt;lastContrib&gt;&gt;|&lt;&lt;sinceMe&gt;&gt;if(oldid){|&lt;&lt;oldEdit&gt;&gt;|&lt;&lt;diffCur&gt;&gt;}';
	}

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;*&lt;&lt;userlog|shortcut=L|log&gt;&gt;';
	str+='if(ipuser){*&lt;&lt;arin&gt;&gt;}if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;|&lt;&lt;blocklog|log&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{' + editstr + '}'
		var historystr='&lt;&lt;history|shortcut=h&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|&gt;&gt;}';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;*&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){&lt;br&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;*' +
		'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|&lt;&lt;deletelog|log&gt;&gt;}';
	return str;
}

function navLinksHTML (article, hint, params) { //oldid, rcid) {
	var str = '&lt;span class=&quot;popupNavLinks&quot;&gt;' + defaultNavlinkSpec() + '&lt;/span&gt;';
	// BAM
	return navlinkStringToHTML(str, article, params);
}

function expandConditionalNavlinkString(s,article,z,recursionCount) {
	var oldid=z.oldid, rcid=z.rcid, diff=z.diff;
	// nested conditionals (up to 10 deep) are ok, hopefully! (work from the inside out)
	if (typeof recursionCount!=typeof 0) { recursionCount=0; }
	var conditionalSplitRegex=RegExp(
		//(1     if    \\(    (2    2)    \\)      {(3    3)}  (4   else      {(5     5)}  4)1)
		'(;?\\s*if\\s*\\(\\s*([\\w]*)\\s*\\)\\s*\\{([^{}]*)\\}(\\s*else\\s*\\{([^{}]*?)\\}|))', 'i');
	var splitted=s.parenSplit(conditionalSplitRegex);
	// $1: whole conditional
	// $2: test condition
	// $3: true expansion
	// $4: else clause (possibly empty)
	// $5: false expansion (possibly null)
	var numParens=5;
	var ret = splitted[0];
	for (var i=1; i&lt;splitted.length; i=i+numParens+1) {

		var testString=splitted[i+2-1];
		var trueString=splitted[i+3-1];
		var falseString=splitted[i+5-1];
		if (typeof falseString=='undefined' || !falseString) { falseString=''; }
		var testResult=null;

		switch (testString) {
		case 'user':
			testResult=(article.userName())?true:false;
			break;
		case 'talk':
			testResult=(article.talkPage())?false:true; // talkPage converts _articles_ to talkPages
			break;
		case 'admin':
			testResult=getValueOf('popupAdminLinks')?true:false;
			break;
		case 'oldid':
			testResult=(typeof oldid != 'undefined' &amp;&amp; oldid)?true:false;
			break;
		case 'rcid':
			testResult=(typeof rcid != 'undefined' &amp;&amp; rcid)?true:false;
			break;
		case 'ipuser':
			testResult=(article.isIpUser())?true:false;
			break;
		case 'mainspace_en':
			testResult=isInMainNamespace(article) &amp;&amp;
				pg.wiki.hostname=='en.wikiversity.org';
			break;
		case 'wikimedia':
			testResult=(pg.wiki.wikimedia) ? true : false;
			break;
		case 'diff':
			testResult=(typeof diff != 'undefined' &amp;&amp; diff)?true:false;
			break;
		}

		switch(testResult) {
		case null: ret+=splitted[i];  break;
		case true: ret+=trueString;   break;
		case false: ret+=falseString; break;
		}

		// append non-conditional string
		ret += splitted[i+numParens];
	}
	if (conditionalSplitRegex.test(ret) &amp;&amp; recursionCount &lt; 10) {
		return expandConditionalNavlinkString(ret,article,z,recursionCount+1);
	}
	return ret;
}

function navlinkStringToArray(s, article, params) {
	s=expandConditionalNavlinkString(s,article,params);
	var splitted=s.parenSplit(RegExp('&lt;&lt;(.*?)&gt;&gt;'));
	var ret=[];
	for (var i=0; i&lt;splitted.length; ++i) {
		if (i%2) { // i odd, so s is a tag
			var t=new navlinkTag();
			var ss=splitted[i].split('|');
			t.id=ss[0];
			for (var j=1; j&lt;ss.length; ++j) {
				var sss=ss[j].split('=');
				if (sss.length&gt;1) {
					t[sss[0]]=sss[1];
				}
				else { // no assignment (no &quot;=&quot;), so treat this as a title (overwriting the last one)
					t.text=popupString(sss[0]);
				}
			}
			t.article=article;
			var oldid=params.oldid, rcid=params.rcid, diff=params.diff;
			if (typeof oldid != 'undefined' &amp;&amp; oldid != null) { t.oldid=oldid; }
			if (typeof rcid != 'undefined' &amp;&amp; rcid != null) { t.rcid=rcid; }
			if (typeof diff != 'undefined' &amp;&amp; diff != null) { t.diff=diff; }
			if (!t.text &amp;&amp; t.id != 'mainlink') { t.text=popupString(t.id); }
			ret.push(t);
		}
		else { // plain HTML
			ret.push(splitted[i]);
		}
	}
	return ret;
}


function navlinkSubstituteHTML(s) {
	return s.split('*').join(getValueOf('popupNavLinkSeparator'))
		.split('&lt;menurow&gt;').join('&lt;li class=&quot;popup_menu_row&quot;&gt;')
		.split('&lt;/menurow&gt;').join('&lt;/li&gt;')
		.split('&lt;menu&gt;').join('&lt;ul class=&quot;popup_menu&quot;&gt;')
		.split('&lt;/menu&gt;').join('&lt;/ul&gt;');

}

function navlinkDepth(magic,s) {
	return s.split('&lt;' + magic + '&gt;').length - s.split('&lt;/' + magic + '&gt;').length;
}


// navlinkString: * becomes the separator
//                &lt;&lt;foo|bar=baz|fubar&gt;&gt; becomes a foo-link with attribute bar='baz'
//                                      and visible text 'fubar'
//                if(test){...} and if(test){...}else{...} work too (nested ok)

function navlinkStringToHTML(s,article,params) {
	//limitAlert(navlinkStringToHTML, 5, 'navlinkStringToHTML\n' + article + '\n' + (typeof article));
	var p=navlinkStringToArray(s,article,params);
	var html='';
	var menudepth = 0; // nested menus not currently allowed, but doesn't do any harm to code for it
	var menurowdepth = 0;
	var wrapping = null;
	for (var i=0; i&lt;p.length; ++i) {
		if (typeof p[i] == typeof '') {
			html+=navlinkSubstituteHTML(p[i]);
			menudepth += navlinkDepth('menu', p[i]);
			menurowdepth += navlinkDepth('menurow', p[i]);
//			if (menudepth === 0) {
//				tagType='span';
//			} else if (menurowdepth === 0) {
//				tagType='li';
//			} else {
//				tagType = null;
//			}
		} else if (typeof p[i].type != 'undefined' &amp;&amp; p[i].type=='navlinkTag') {
			if (menudepth &gt; 0 &amp;&amp; menurowdepth === 0) {
				html += '&lt;li class=&quot;popup_menu_item&quot;&gt;' + p[i].html() + '&lt;/li&gt;';
			} else {
				html+=p[i].html();
			}
		}
	}
	return html;
}

function navlinkTag() {
	this.type='navlinkTag';
}

navlinkTag.prototype.html=function () {
	this.getNewWin();
	this.getPrintFunction();
	var html='';
	var opening, closing;
	var tagType='span';
	if (!tagType) {
		opening = ''; closing = '';
	} else {
		opening = '&lt;' + tagType + ' class=&quot;popup_' + this.id + '&quot;&gt;';
		closing = '&lt;/' + tagType + '&gt;';
	}
	if (typeof this.print!='function') {
		errlog ('Oh dear - invalid print function for a navlinkTag, id='+this.id);
	} else {
		html=this.print(this);
		if (typeof html != typeof '') {html='';}
		else if (typeof this.shortcut!='undefined') html=addPopupShortcut(html, this.shortcut);
	}
	return opening + html + closing;
};

navlinkTag.prototype.getNewWin=function() {
	getValueOf('popupLinksNewWindow');
	if (typeof pg.option.popupLinksNewWindow[this.id] === 'undefined') { this.newWin=null; }
	this.newWin=pg.option.popupLinksNewWindow[this.id];
}

navlinkTag.prototype.getPrintFunction=function() { //think about this some more
	// this.id and this.article should already be defined
	if (typeof this.id!=typeof '' || typeof this.article!=typeof {} ) { return; }
	var html='';
	var a,t;

	this.noPopup=1;
	switch (this.id) {
	case 'contribs': case 'history': case 'whatLinksHere':
	case 'userPage': case 'monobook': case 'userTalk':
	case 'talk': case 'article': case 'lastEdit':
		this.noPopup=null;
	}
	switch (this.id) {
	case 'email':     case 'contribs':  case 'block':     case 'unblock':
	case 'userlog':   case 'userSpace': case 'deletedContribs':
		this.article=this.article.userName();
	}

	switch (this.id) {
	case 'userTalk': case 'newUserTalk': case 'editUserTalk':
	case 'userPage': case 'monobook': case 'editMonobook': case 'blocklog':
		this.article=this.article.userName(true);
	// fall through; no break
	case 'pagelog': case 'deletelog': case 'protectlog':
	delete this.oldid;
	}

	if (this.id=='editMonobook' || this.id=='monobook') { this.article.append('/monobook.js'); }

	if (this.id != 'mainlink') {
		// FIXME anchor handling should be done differently with Title object
		this.article=this.article.removeAnchor();
		// if (typeof this.text=='undefined') this.text=popupString(this.id);
	}

	switch (this.id) {
	case 'undelete':       this.print=specialLink; this.specialpage='Undelete'; this.sep='/'; break;
	case 'whatLinksHere':  this.print=specialLink; this.specialpage='Whatlinkshere'; break;
	case 'relatedChanges': this.print=specialLink; this.specialpage='Recentchangeslinked'; break;
	case 'move':           this.print=specialLink; this.specialpage='Movepage'; break;
	case 'contribs':       this.print=specialLink; this.specialpage='Contributions'; break;
	case 'deletedContribs':this.print=specialLink; this.specialpage='Deletedcontributions'; break;
	case 'email':          this.print=specialLink; this.specialpage='EmailUser'; this.sep='/'; break;
	case 'block':          this.print=specialLink; this.specialpage='Blockip'; this.sep='&amp;ip='; break;
	case 'unblock':        this.print=specialLink; this.specialpage='Ipblocklist'; this.sep='&amp;action=unblock&amp;ip='; break;
	case 'userlog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;user='; break;
	case 'blocklog':       this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=block&amp;page='; break;
	case 'pagelog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;page='; break;
	case 'protectlog':     this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=protect&amp;page='; break;
	case 'deletelog':      this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=delete&amp;page='; break;
	case 'userSpace':      this.print=specialLink; this.specialpage='PrefixIndex'; this.sep='&amp;namespace=2&amp;prefix='; break;
	case 'search':         this.print=specialLink; this.specialpage='Search'; this.sep='&amp;fulltext=Search&amp;search='; break;
	case 'history': case 'historyfeed': case 'unwatch': case 'watch':
	case 'unprotect': case 'protect':
	this.print=wikiLink; this.action=this.id; break;

	case 'delete':
	this.print=wikiLink; this.action='delete';
	if (this.article.namespaceId()==pg.nsImageId) {
	    var img=this.article.stripNamespace();
	    this.action+='&amp;image='+img;
	}
	break;

	case 'markpatrolled':
	case 'edit': // editOld should keep the oldid, but edit should not.
	delete this.oldid; // fall through
	case 'view': case 'purge': case 'render':
	this.print=wikiLink;
	this.action=this.id; break;
	case 'raw':
	this.print=wikiLink; this.action='raw&amp;ctype=text/css'; break;
	case 'new':
	this.print=wikiLink; this.action='edit&amp;section=new'; break;
	case 'mainlink':
	if (typeof this.text=='undefined') { this.text=this.article.toString().entify(); }
	if (getValueOf('popupSimplifyMainLink') &amp;&amp; isInStrippableNamespace(this.article)) {
	    var s=this.text.split('/'); this.text=s[s.length-1];
	    if (this.text=='' &amp;&amp; s.length &gt; 1) { this.text=s[s.length-2]; }
	}
	this.print=titledWikiLink;
	if (typeof this.title=='undefined' &amp;&amp; pg.current.link &amp;&amp; typeof pg.current.link.href != 'undefined') {
	    this.title=safeDecodeURI((pg.current.link.originalTitle)?pg.current.link.originalTitle:this.article);
	    if (typeof this.oldid != 'undefined' &amp;&amp; this.oldid) {
		this.title=tprintf('Revision %s of %s', [this.oldid, this.title]);
	    }
	}
	this.action='view'; break;
	case 'userPage':
	case 'article':
	case 'monobook':
	case 'editMonobook':
	case 'editArticle':
	delete this.oldid;
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.article=this.article.articleFromTalkOrArticle();
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.print=wikiLink;
	if (this.id.indexOf('edit')==0) {
	    this.action='edit';
	} else { this.action='view';}
	break;
	case 'userTalk':
	case 'talk':
	this.article=this.article.talkPage();
	delete this.oldid;
	this.print=wikiLink;
	this.action='view'; break;
	case 'arin':
	this.print=arinLink; break;
	case 'count':
	this.print=editCounterLink; break;
	case 'google':
	this.print=googleLink; break;
	case 'editors':
	this.print=editorListLink; break;
	case 'globalsearch':
	this.print=globalSearchLink; break;
	case 'lastEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the last edit');
	this.from='prev'; this.to='cur'; break;
	case 'oldEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the edit made to get revision') + ' ' + this.oldid;
	this.from='prev'; this.to=this.oldid; break;
	case 'editOld':
	this.print=wikiLink; this.action='edit'; break;
	case 'undo':
	this.print=wikiLink; this.action='edit&amp;undo='; break;
	case 'markpatrolled':
	this.print=wikiLink; this.action='markpatrolled';
	case 'revert':
	this.print=wikiLink; this.action='revert'; break;
	case 'nullEdit':
	this.print=wikiLink; this.action='nullEdit'; break;
	case 'diffCur':
	this.print=titledDiffLink;
	this.title=tprintf('Show changes since revision %s', [this.oldid]);
	this.from=this.oldid; this.to='cur'; break;
	case 'editUserTalk':
	case 'editTalk':
	delete this.oldid;
	this.article=this.article.talkPage();
	this.action='edit'; this.print=wikiLink; break;
	case 'newUserTalk':
	case 'newTalk':
	this.article=this.article.talkPage();
	this.action='edit&amp;section=new'; this.print=wikiLink; break;
	case 'lastContrib':
	case 'sinceMe':
	this.print=magicHistoryLink;
	break;
	case 'togglePreviews':
	this.text=popupString(pg.option.simplePopups ? 'enable previews' : 'disable previews');
	case 'disablePopups': case 'purgePopups':
	this.print=popupMenuLink;
	break;
	default:
	this.print=function () {return 'Unknown navlink type: '+this.id+''};
	}
};
//
//  end navlinks
//////////////////////////////////////////////////
//&lt;/NOLITE&gt;
// ENDFILE: navlinks.js
// STARTFILE: shortcutkeys.js
//&lt;NOLITE&gt;
function popupHandleKeypress(evt) {
	var keyCode = window.event ? window.event.keyCode : ( evt.keyCode ? evt.keyCode : evt.which);
	if (!keyCode || !pg.current.link || !pg.current.link.navpopup) { return; }
	if (keyCode==27) { // escape
		killPopup();
		return false; // swallow keypress
	}

	var letter=String.fromCharCode(keyCode);
	var links=pg.current.link.navpopup.mainDiv.getElementsByTagName('A');
	var startLink=0;
	var i,j;

	if (popupHandleKeypress.lastPopupLinkSelected) {
		for (i=0; i&lt;links.length; ++i) {
			if (links[i]==popupHandleKeypress.lastPopupLinkSelected) { startLink=i; }
		}
	}
	for (j=0; j&lt;links.length; ++j) {
		i=(startLink + j + 1) % links.length;
		if (links[i].getAttribute('popupkey')==letter) {
			if (evt &amp;&amp; evt.preventDefault) evt.preventDefault();
			links[i].focus();
			popupHandleKeypress.lastPopupLinkSelected=links[i];
			return false; // swallow keypress
		}
	}

	// pass keypress on
	if (document.oldPopupOnkeypress) { return document.oldPopupOnkeypress(evt); }
	return true;
}

function addPopupShortcuts() {
	if (document.onkeypress!=popupHandleKeypress) {
		document.oldPopupOnkeypress=document.onkeypress;
	}
	document.onkeypress=popupHandleKeypress;
}

function rmPopupShortcuts() {
	popupHandleKeypress.lastPopupLinkSelected=null;
	try {
		if (document.oldPopupOnkeypress &amp;&amp; document.oldPopupOnkeypress==popupHandleKeypress) {
			// panic
			document.onkeypress=null; //function () {};
			return;
		}
		document.onkeypress=document.oldPopupOnkeypress;
	} catch (nasties) { /* IE goes here */ }
}


function addLinkProperty(html, property) {
	// take &quot;&lt;a href=...&gt;...&lt;/a&gt; and add a property
	// not sophisticated at all, easily broken
	var i=html.indexOf('&gt;');
	if (i&lt;0) { return html; }
	return html.substring(0,i) + ' ' + property + html.substring(i);
}

function addPopupShortcut(html, key) {
	if (!getValueOf('popupShortcutKeys')) { return html; }
	var ret= addLinkProperty(html, 'popupkey=&quot;'+key+'&quot;');
	if (key==' ') { key=popupString('spacebar'); }
	return ret.replace(RegExp('^(.*?)(title=&quot;)(.*?)(&quot;.*)$', 'i'),'$1$2$3 ['+key+']$4');
}
//&lt;/NOLITE&gt;
// ENDFILE: shortcutkeys.js
// STARTFILE: diffpreview.js
//&lt;NOLITE&gt;
function loadDiff(article, oldid, diff, navpop) {
	navpop.diffData={};
	var oldRev, newRev;
	switch (diff) {
	case 'cur':
		switch ( oldid ) {
		case null:
		case '':
		case 'prev':
			// eg newmessages diff link
			oldRev='0&amp;direction=prev';
			newRev=0;
			break;
		default:
			oldRev = oldid;
			newRev = 0;
		}
		break;
	case 'prev':
		oldRev = ( oldid || 0 ) + '&amp;direction=prev'; newRev = oldid; break;
	case 'next':
		oldRev = oldid; newRev = oldid + '&amp;direction=next';
		break;
	default:
		oldRev = oldid || 0; newRev = diff || 0; break;
	}
	oldRev = oldRev || 0;
	newRev = newRev || 0;

	var go = function() {
		pendingNavpopTask(navpop);
		getWiki(article, doneDiffNew, newRev, navpop);

		pendingNavpopTask(navpop);
		getWiki(article, doneDiffOld, oldRev, navpop);

		var tz = Cookie.read('popTz');
		if (getValueOf('popupAdjustDiffDates') &amp;&amp; tz===null) {
		    pendingNavpopTask(navpop);
		    getPageWithCaching(pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;meta=userinfo&amp;uiprop=options',
				       function(d) {
					       completedNavpopTask(navpop);
					       setTimecorrectionCookie(d);
					       if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
				       },  navpop);
		}
		return true; // remove hook once run
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_DIFFS'); }
}

function setTimecorrectionCookie(d) {
	try {
		var jsobj=getJsObj(d.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
	} catch (someError) {
		logerr( 'setTimecorretion failed' );
		return;
	}
    Cookie.create( 'popTz', getTimeOffset(tz), 1);
}

function doneDiff(download, isOld) {
	if (!download.owner || !download.owner.diffData) { return; }
	var navpop=download.owner;
	var label= (isOld) ? 'Old' : 'New';
	var otherLabel=(isOld) ? 'New' : 'Old';
	navpop.diffData[label]=download;
	completedNavpopTask(download.owner);
	if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
}

function diffDownloadsComplete(navpop) {
	if ( Cookie.read('popTz')===null) { return false; }
	return navpop.diffData.Old &amp;&amp; navpop.diffData.New;
}

function doneDiffNew(download) { doneDiff(download, false); }
function doneDiffOld(download) { doneDiff(download, true);  }

function rmBoringLines(a,b,context) {

	if (typeof context == 'undefined') { context=2; }
	// this is fairly slow... i think it's quicker than doing a word-based diff from the off, though
	var aa=[], aaa=[];
	var bb=[], bbb=[];
	var i, j;

	// first, gather all disconnected nodes in a and all crossing nodes in a and b
	for (i=0; i&lt;a.length; ++i ) {
		if(!a[i].paired) { aa[i]=1; }
		else if (countCrossings(b,a,i, true)) {
			aa[i]=1;
			bb[ a[i].row ] = 1;
		}
	}

	// pick up remaining disconnected nodes in b
	for (i=0; i&lt;b.length; ++i ) {
		if (bb[i]==1) { continue; }
		if(!b[i].paired) { bb[i]=1; }
	}

	// another pass to gather context: we want the neighbours of included nodes which are not yet included
	// we have to add in partners of these nodes, but we don't want to add context for *those* nodes in the next pass
	for (i=0; i&lt;b.length; ++i) {
		if ( bb[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(b.length, i+context); ++j) {
				if ( !bb[j] ) { bb[j] = 1; aa[ b[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;a.length; ++i) {
		if ( aa[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(a.length, i+context); ++j) {
				if ( !aa[j] ) { aa[j] = 1; bb[ a[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;bb.length; ++i) {
		if (bb[i] &gt; 0) { // it's a row we need
			if (b[i].paired) { bbb.push(b[i].text); } // joined; partner should be in aa
			else {
				bbb.push(b[i]);
			}
		}
	}
	for (i=0; i&lt;aa.length; ++i) {
		if (aa[i] &gt; 0) { // it's a row we need
			if (a[i].paired) { aaa.push(a[i].text); } // joined; partner should be in aa
			else {
				aaa.push(a[i]);
			}
		}
	}

	return { a: aaa, b: bbb};
}

function stripOuterCommonLines(a,b,context) {
	var i=0;
	while (i&lt;a.length &amp;&amp; i &lt; b.length &amp;&amp; a[i]==b[i]) { ++i; }
	var j=a.length-1; var k=b.length-1;
	while ( j&gt;=0 &amp;&amp; k&gt;=0 &amp;&amp; a[j]==b[k] ) { --j; --k; }

	return { a: a.slice(max(0,i - 1 - context), min(a.length+1, j + context+1)),
			    b: b.slice(max(0,i - 1 - context), min(b.length+1, k + context+1)) };
}

function insertDiff(navpop) {
	// for speed reasons, we first do a line-based diff, discard stuff that seems boring, then do a word-based diff
	// FIXME: sometimes this gives misleading diffs as distant chunks are squashed together
	var oldlines=navpop.diffData.Old.data.split('\n');
	var newlines=navpop.diffData.New.data.split('\n');
	var inner=stripOuterCommonLines(oldlines,newlines,getValueOf('popupDiffContextLines'));
	oldlines=inner.a; newlines=inner.b;
	var truncated=false;
	getValueOf('popupDiffMaxLines');
	if (oldlines.length &gt; pg.option.popupDiffMaxLines || newlines.length &gt; pg.option.popupDiffMaxLines) {
		// truncate
		truncated=true;
		inner=stripOuterCommonLines(oldlines.slice(0,pg.option.popupDiffMaxLines),
					    newlines.slice(0,pg.option.popupDiffMaxLines),
					    pg.option.popupDiffContextLines);
		oldlines=inner.a; newlines=inner.b;
	}

	var lineDiff=diff(oldlines, newlines);
	var lines2=rmBoringLines(lineDiff.o, lineDiff.n);
	var oldlines2=lines2.a; var newlines2=lines2.b;

	var simpleSplit = !String.prototype.parenSplit.isNative;
	var html='&lt;hr&gt;';
	if (getValueOf('popupDiffDates')) {
		html += diffDatesTable(navpop.diffData.Old, navpop.diffData.New);
		html += '&lt;hr&gt;';
	}
	html += shortenDiffString(
		diffString(oldlines2.join('\n'), newlines2.join('\n'), simpleSplit),
		getValueOf('popupDiffContextCharacters') ).join('&lt;hr&gt;');
	setPopupTipsAndHTML(html.split('\n').join('&lt;br&gt;') +
		     (truncated ? '&lt;hr&gt;&lt;b&gt;'+popupString('Diff truncated for performance reasons')+'&lt;/b&gt;' : '') ,
			    'popupPreview', navpop.idNumber);
}

function diffDatesTable( oldDl, newDl ) {
	var html='&lt;table class=&quot;popup_diff_dates&quot;&gt;';
	html += diffDatesTableRow( newDl, tprintf('New revision'));
	html += diffDatesTableRow( oldDl, tprintf('Old revision'));
	html += '&lt;/table&gt;';
	return html;
}
function diffDatesTableRow( dl, label ) {
	var txt='';
	if (!dl) {
		txt=popupString('Something went wrong :-(');
	} else if (!dl.lastModified) {
		txt= (/^\s*$/.test(dl.data)) ?
			popupString('Empty revision, maybe non-existent') : popupString('Unknown date');
	} else {
		var datePrint=getValueOf('popupDiffDatePrinter');
		if (typeof dl.lastModified[datePrint] == 'function') {
			if (getValueOf('popupAdjustDiffDates')) {
				var off;
				if (off=Cookie.read('popTz')) {
					var d2=adjustDate(dl.lastModified, off);
					txt = dayFormat(d2, true) + ' ' + timeFormat(d2, true);
				}
			} else {
				txt = dl.lastModified[datePrint]();
			}
		} else {
			txt = tprintf('Invalid %s %s', ['popupDiffDatePrinter', datePrint]);
		}
	}
	var revlink = generalLink({url: dl.url.replace(/&amp;.*?(oldid=[0-9]+(?:&amp;direction=[^&amp;]*)?).*/, '&amp;$1'),
				   text: label, title: label});
	return simplePrintf('&lt;tr&gt;&lt;td&gt;%s&lt;/td&gt;&lt;td&gt;%s&lt;/td&gt;&lt;/tr&gt;', [ revlink, txt ]);
}
//&lt;/NOLITE&gt;
// ENDFILE: diffpreview.js
// STARTFILE: links.js
//&lt;NOLITE&gt;
/////////////////////
// LINK GENERATION //
/////////////////////

// titledDiffLink --&gt; titledWikiLink --&gt; generalLink
// wikiLink       --&gt; titledWikiLink --&gt; generalLink
// editCounterLink --&gt; generalLink

function titledDiffLink(l) { // article, text, title, from, to) {
	return titledWikiLink({article: l.article, action: l.to + '&amp;oldid=' + l.from,
				newWin: l.newWin,
				noPopup: l.noPopup,
				text: l.text, title: l.title,
				/* hack: no oldid here */
				actionName: 'diff'});
}


function wikiLink(l) {
	//{article:article, action:action, text:text, oldid, newid}) {
	if (! (typeof l.article == typeof {}
	       &amp;&amp; typeof l.action == typeof '' &amp;&amp; typeof l.text==typeof '')) return null;
	if (typeof l.oldid == 'undefined') { l.oldid=null; }
	var savedOldid = l.oldid;
	if (!/^(edit|view|revert|render)$|^raw/.test(l.action)) { l.oldid=null; }
	var hint=popupString(l.action + 'Hint'); // revertHint etc etc etc
	var oldidData=[l.oldid, safeDecodeURI(l.article)];
	var revisionString = tprintf('revision %s of %s', oldidData);
	log('revisionString='+revisionString);
	switch (l.action) {
	case 'edit&amp;section=new': hint = popupString('newSectionHint');  break;
	case 'edit&amp;undo=':
		if (l.diff &amp;&amp; l.diff != 'prev' &amp;&amp; savedOldid ) {
		  l.action += l.diff + '&amp;undoafter=' + savedOldid;
		} else if (savedOldid) {
		  l.action += savedOldid;
		}
		hint = popupString('undoHint');
		break;
	case 'raw&amp;ctype=text/css': hint=popupString('rawHint'); break;
	case 'revert':
		var p=parseParams(pg.current.link.href);
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=' + revertSummary(l.oldid, p.diff);
		if (p.diff=='prev') {
			l.action += '&amp;direction=prev';
			revisionString = tprintf('the revision prior to revision %s of %s', oldidData);
		}
		if (getValueOf('popupRevertSummaryPrompt')) { l.action += '&amp;autosummaryprompt=true'; }
		if (getValueOf('popupMinorReverts')) { l.action += '&amp;autominor=true'; }
		log('revisionString is now '+revisionString);
		break;
	case 'nullEdit':
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=null';
		break;
	case 'historyfeed':
		l.action='history&amp;feed=rss';
		break;
	case 'markpatrolled':
		l.action='markpatrolled&amp;rcid='+l.rcid;
	}

	if (hint) {
		if (l.oldid) {
			hint = simplePrintf(hint, [revisionString]);
		}
		else {
			hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
		}
	}
	else {
		hint = safeDecodeURI(l.article + '&amp;action=' + l.action) + (l.oldid) ? '&amp;oldid='+l.oldid : '';
	}

	return titledWikiLink({article: l.article, action: l.action, text: l.text, newWin:l.newWin,
				title: hint, oldid: l.oldid, noPopup: l.noPopup});
}

function revertSummary(oldid, diff) {
	var ret='';
	if (diff == 'prev') {
		ret=getValueOf('popupQueriedRevertToPreviousSummary');
	} else { ret = getValueOf('popupQueriedRevertSummary'); }
	return ret + '&amp;autorv=' + oldid;
}

function titledWikiLink(l) {
	// possible properties of argument:
	// article, action, text, title, oldid, actionName, className, noPopup
	// oldid = null is fine here

	// article and action are mandatory args

	if (typeof l.article == 'undefined' || typeof l.action=='undefined') {
		errlog('got undefined article or action in titledWikiLink');
		return null;
	}

	var base = pg.wiki.titlebase +  l.article.urlString();
	var url=base;

	if (typeof l.actionName=='undefined' || !l.actionName) { l.actionName='action'; }

	// no need to add &amp;action=view, and this confuses anchors
	if (l.action != 'view') { url = base + '&amp;' + l.actionName + '=' + l.action; }

	if (typeof l.oldid!='undefined' &amp;&amp; l.oldid) { url+='&amp;oldid='+l.oldid; }

	var cssClass=pg.misc.defaultNavlinkClassname;
	if (typeof l.className!='undefined' &amp;&amp; l.className) { cssClass=l.className; }

	return generalNavLink({url: url, newWin: l.newWin,
				title: (typeof l.title != 'undefined') ? l.title : null,
				text: (typeof l.text!='undefined')?l.text:null,
				className: cssClass, noPopup:l.noPopup});
}

function getLastContrib(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processLastContribInfo(x,{page: wikipage, newWin: newWin})});
}
function processLastContribInfo(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: an odd thing happened. Please retry.'); return; }
	if(!info.firstNewEditor) {
		alert(tprintf('Only found one editor: %s made %s edits', [info.edits[0].editor,info.edits.length]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+info.firstNewEditor.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function getDiffSinceMyEdit(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processDiffSinceMyEdit(x,{page: wikipage, newWin: newWin})});
}
function processDiffSinceMyEdit(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: something fishy happened. Please try again.'); return; }
	var friendlyName=stuff.page.split('_').join(' ');
	if(!info.myLastEdit) {
		alert(tprintf('Couldn\'t find an edit by %s\nin the last %s edits to\n%s',
			      [info.userName, getValueOf('popupHistoryLimit'), friendlyName]));
		return;
	}
	if(info.myLastEdit.index==0) {
		alert(tprintf(&quot;%s seems to be the last editor to the page %s&quot;, [info.userName, friendlyName]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+ info.myLastEdit.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function displayUrl(url, newWin){
	if(newWin) { window.open(url); }
	else { document.location=url; }
}

function purgePopups() {
	processAllPopups(true);
	setupCache(); // deletes all cached items (not browser cached, though...)
	pg.option={};
	abortAllDownloads();
}

function processAllPopups(nullify, banish) {
	for (var i=0; i&lt;pg.current.links.length; ++i) {
		if (!pg.current.links[i].navpopup) { continue; }
		(nullify || banish) &amp;&amp; pg.current.links[i].navpopup.banish();
		pg.current.links[i].simpleNoMore=false;
		nullify &amp;&amp; (pg.current.links[i].navpopup=null);
	}
}

function disablePopups(){
	processAllPopups(false, true);
	setupTooltips(null, true);
}

function togglePreviews() {
	processAllPopups(true, true);
	pg.option.simplePopups=!pg.option.simplePopups;
	abortAllDownloads();
}

function magicHistoryLink(l) {
	// FIXME use onclick change href trick to sort this out instead of window.open

	var jsUrl='', title='';
	switch(l.id) {
	case 'lastContrib':
		jsUrl=simplePrintf('javascript:getLastContrib(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('lastContribHint');
		break;
	case 'sinceMe':
		jsUrl=simplePrintf('javascript:getDiffSinceMyEdit(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('sinceMeHint');
		break;
	}

	return generalNavLink({url: jsUrl, newWin: false, // can't have new windows with JS links, I think
				title: title, text: l.text, noPopup: l.noPopup});
}

function popupMenuLink(l) {
	var jsUrl=simplePrintf('javascript:%s()', [l.id]);
	var title=popupString(simplePrintf('%sHint', [l.id]));
	return generalNavLink({url: jsUrl, newWin:false, title:title, text:l.text, noPopup:l.noPopup});
}

function specialLink(l) {
	// properties: article, specialpage, text, sep
	if (typeof l.specialpage=='undefined'||!l.specialpage) return null;
	var base = pg.wiki.titlebase +  mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId]+':'+l.specialpage;
	if (typeof l.sep == 'undefined' || l.sep===null) l.sep='&amp;target=';
	var article=l.article.urlString({keepSpaces: l.specialpage=='Search'});
	var hint=popupString(l.specialpage+'Hint');
	switch (l.specialpage) {
	case 'Log':
	    switch (l.sep) {
	    case '&amp;user=': hint=popupString('userLogHint'); break;
	    case '&amp;type=block&amp;page=': hint=popupString('blockLogHint'); break;
	    case '&amp;page=': hint=popupString('pageLogHint'); break;
	    case '&amp;type=protect&amp;page=': hint=popupString('protectLogHint'); break;
	    case '&amp;type=delete&amp;page=': hint=popupString('deleteLogHint'); break;
	    default: log('Unknown log type, sep=' + l.sep); hint='Missing hint (FIXME)';
	    }
	    break;
	case 'PrefixIndex': article += '/'; break;
	}
	if (hint) hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
	else hint = safeDecodeURI(l.specialpage+':'+l.article) ;

	var url = base + l.sep + article;
	return generalNavLink({url: url, title: hint, text: l.text, newWin:l.newWin, noPopup:l.noPopup});
}

function generalLink(l) {
	// l.url, l.text, l.title, l.newWin, l.className, l.noPopup
	if (typeof l.url=='undefined') return null;

	// only quotation marks in the url can screw us up now... I think
	var url=l.url.split('&quot;').join('%22');

	var ret='&lt;a href=&quot;' + url + '&quot;';
	if (typeof l.title!='undefined' &amp;&amp; l.title) { ret += ' title=&quot;' + mw.html.escape(l.title) + '&quot;'; }
	if (l.noPopup) { ret += ' noPopup=1'; }
	var newWin;
	if (typeof l.newWin=='undefined' || l.newWin===null) { newWin=getValueOf('popupNewWindows'); }
	else { newWin=l.newWin; }
	if (newWin) { ret += ' target=&quot;_blank&quot;'; }
	if (typeof l.className!='undefined'&amp;&amp;l.className) { ret+=' class=&quot;'+l.className+'&quot;'; }
	ret += '&gt;';
	if (typeof l.text==typeof '') { ret+= l.text; }
	ret +='&lt;/a&gt;';
	return ret;
}

function appendParamsToLink(linkstr, params) {
	var sp=linkstr.parenSplit(RegExp('(href=&quot;[^&quot;]+?)&quot;', 'i'));
	if (sp.length&lt;2) return null;
	var ret=sp.shift() + sp.shift();
	ret += '&amp;' + params + '&quot;';
	ret += sp.join('');
	return ret;
}

function changeLinkTargetLink(x) { // newTarget, text, hint, summary, clickButton, minor, title (optional) {
	if (x.newTarget) {
		log ('changeLinkTargetLink: newTarget=' + x.newTarget);
	}
	// optional: oldTarget (in wikitext)
	// if x.newTarget omitted or null, remove the link

	x.clickButton=encodeURI(x.clickButton);

	// FIXME: first character of page title as well as namespace should be case insensitive
	// eg [[category:foo]] and [[Category:Foo]] are equivalent
	// this'll break if charAt(0) is nasty
	var cA=literalizeRegex(x.oldTarget);
	var chs=cA[0].toUpperCase();
	chs='['+chs + chs.toLowerCase()+']';
	var currentArticleRegexBit=encodeURIComponent(chs+cA.substring(1));
	currentArticleRegexBit=currentArticleRegexBit
		.split(RegExp('[_ ]+', 'g')).join('[_ ]+')
		.split( &quot;%20&quot; ).join('[_ ]+')
		.split('\\(').join('(?:%2528|\\()')
		.split('\\)').join('(?:%2529|\\))');
	// leading and trailing space should be ignored, and anchor bits optional:
	currentArticleRegexBit = '\\s*(' + currentArticleRegexBit + '(?:#[^\\[\\|]*)?)\\s*';
	// e.g. Computer (archaic) -&gt; \s*([Cc]omputer[_ ](?:%2528|\()archaic(?:%2528|\)))\s*

	// autoedit=s~\[\[([Cc]ad)\]\]~[[Computer-aided%20design|$1]]~g;s~\[\[([Cc]AD)[|]~[[Computer-aided%20design|~g

	var title=x.title || mw.config.get('wgPageName').split('_').join(' ');
	var lk=titledWikiLink({article: new Title(title), newWin:x.newWin,
						action:  'edit',
						text:    x.text,
						title:   x.hint,
						className: 'popup_change_title_link'
						});
	var cmd='';
	if (x.newTarget) {
		// escape '&amp;' and other nasties
		var t=encodeURIComponent(x.newTarget);
		var s=encodeURIComponent(literalizeRegex(x.newTarget));
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~[['+t+'|$1]]~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|]~[['+t+'|~g;';
		cmd += 's~\\[\\['+s + '\\|' + s + '\\]\\]~[[' + t + ']]~g';
	} else {
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~$1~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|](.*?)\\]\\]~$2~g';
	}
	cmd += '&amp;autoclick='+x.clickButton + '&amp;actoken=' + autoClickToken();
	cmd += ( x.minor == null ) ? '' : '&amp;autominor='+x.minor;
	cmd += ( x.watch == null ) ? '' : '&amp;autowatch='+x.watch;
	cmd += '&amp;autosummary='+encodeURIComponent(x.summary);
	return appendParamsToLink(lk, 'autoedit='+cmd);
}


function redirLink(redirMatch, article) {
	// NB redirMatch is in wikiText
	var ret='';

	if (getValueOf('popupAppendRedirNavLinks') &amp;&amp; getValueOf('popupNavLinks')) {
		ret += '&lt;hr&gt;';
		if (getValueOf('popupFixRedirs') &amp;&amp; typeof autoEdit != 'undefined' &amp;&amp; autoEdit) {
			log('redirLink: newTarget=' + redirMatch);
			ret += addPopupShortcut(
				changeLinkTargetLink(
				{newTarget: redirMatch, text: popupString('Redirects'),
					hint: popupString('Fix this redirect'),
						summary: simplePrintf(getValueOf('popupFixRedirsSummary'),
								      [article.toString(), redirMatch ]),
						oldTarget: article.toString(),
						clickButton: getValueOf('popupRedirAutoClick'), minor: true,
						watch: getValueOf('popupWatchRedirredPages')})
				, 'R');
			ret += popupString(' to ');
		}
		else ret += popupString('Redirects') + popupString(' to ');
		return ret;
	}

	else return '&lt;br&gt; ' + popupString('Redirects') + popupString(' to ') +
		     titledWikiLink({article: new Title().fromWikiText(redirMatch), action: 'view',  /* FIXME: newWin */
						      text: safeDecodeURI(redirMatch), title: popupString('Bypass redirect')});
}

function arinLink(l) {
	if (!saneLinkCheck(l)) { return null; }
	if ( ! l.article.isIpUser() || ! pg.wiki.wikimedia) return null;

	var uN=l.article.userName();

	return generalNavLink({url:'http://ws.arin.net/cgi-bin/whois.pl?queryinput=' + encodeURIComponent(uN), newWin:l.newWin,
				title: tprintf('Look up %s in ARIN whois database', [uN]),
				text: l.text, noPopup:1});
}

function toolDbName(cookieStyle) {
	var ret = mw.config.get('wgDBname');
	if (!cookieStyle) { ret+= '_p'; }
	return ret;
}

function saneLinkCheck(l) {
	if (typeof l.article != typeof {} || typeof l.text != typeof '') { return false; }
	return true;
}
function editCounterLink(l) {
	if(!saneLinkCheck(l)) return null;
	if (! pg.wiki.wikimedia) return null;
	var uN=l.article.userName();
	var tool=getValueOf('popupEditCounterTool');
	var url;
	var soxredToolUrl='http://toolserver.org/~soxred93/count/index.php?name=$1&amp;lang=$2&amp;wiki=$3';
	var kateToolUrl='http://toolserver.org/~$3/cgi-bin/Tool1/wannabe_kate?username=$1&amp;site=en.wikiversity.org&amp;$2';

	switch(tool) {
	case 'custom':
		url=simplePrintf(getValueOf('popupEditCounterUrl'), [ encodeURIComponent(uN), toolDbName() ]);
		break;
	case 'kate':
	case 'interiot':
		url=simplePrintf(kateToolUrl, [ encodeURIComponent(uN), toolDbName(), tool ]);
		break;
	default:
	    var theWiki=pg.wiki.hostname.split('.');
		url=simplePrintf(soxredToolUrl, [ encodeURIComponent(uN), theWiki[0], theWiki[1] ]);
	}
	return generalNavLink({url:url, title: tprintf('editCounterLinkHint', [uN]),
				newWin:l.newWin, text: l.text, noPopup:1});
}


function globalSearchLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://vs.aka-online.de/cgi-bin/globalwpsearch.pl?timeout=120&amp;search=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + article, newWin:l.newWin,
				title: tprintf('globalSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function googleLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://www.google.com/search?q=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + '%22' + article + '%22', newWin:l.newWin,
				title: tprintf('googleSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function editorListLink(l) {
	if(!saneLinkCheck(l)) return null;
	var article= l.article.articleFromTalkPage() || l.article;
        var theWiki=pg.wiki.hostname.split('.');
        var base='http://toolserver.org/~soxred93/articleinfo/index.php?&amp;uselang=' + wgUserLanguage +
            'lang=' + theWiki[0] + '&amp;wiki=' + theWiki[1] + '&amp;begin=&amp;end=&amp;article='
	return generalNavLink({url:base+article.urlString(),
				title: tprintf('editorListHint', [article]),
				newWin:l.newWin, text: l.text, noPopup:1});
}

function generalNavLink(l) {
	l.className = (l.className==null) ? 'popupNavLink' : l.className;
	return generalLink(l);
}

//////////////////////////////////////////////////
// magic history links
//

function getHistoryInfo(wikipage, whatNext) {
	log('getHistoryInfo');
	getHistory(wikipage, whatNext ? function(d){whatNext(processHistory(d));} : processHistory);
}

// FIXME eliminate pg.idNumber ... how? :-(

function getHistory(wikipage, onComplete) {
	log('getHistory');
	var url = pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;prop=revisions&amp;titles=' +
			new Title(wikipage).urlString() + '&amp;rvlimit=' + getValueOf('popupHistoryLimit');
	log('getHistory: url='+url);
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	return startDownload(url, pg.idNumber+'history', onComplete);
}

function processHistory(download) {
	var jsobj = getJsObj(download.data);
	try {
		window.x=jsobj;
		var p=jsobj['query']['pages']
		for (var pageid in p) {
			var revisions=p[pageid]['revisions'];
			// we only get the first one
			break;
		}
	} catch (someError) {
		log('Something went wrong with JSON business');
		return finishProcessHistory([]);
	}
	var edits=[];
	for (var i=0; i&lt;revisions.length; ++i) {
		edits.push({ oldid: revisions[i]['revid'], editor: revisions[i]['user'] });
	}
	log('processed ' + edits.length + ' edits');
	return finishProcessHistory(edits, mw.config.get('wgUserName'));
}


function finishProcessHistory(edits, userName) {
	var histInfo={};

	histInfo.edits=edits;
	histInfo.userName=userName;

	for (var i=0; i&lt;edits.length; ++i) {
		if (typeof histInfo.myLastEdit == 'undefined' &amp;&amp; userName &amp;&amp; edits[i].editor==userName) {
			histInfo.myLastEdit={index: i, oldid: edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
		if (typeof histInfo.firstNewEditor == 'undefined' &amp;&amp; edits[i].editor != edits[0].editor) {
			histInfo.firstNewEditor={index:i, oldid:edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
	}
	//pg.misc.historyInfo=histInfo;
	return histInfo;
}
//&lt;/NOLITE&gt;
// ENDFILE: links.js
// STARTFILE: options.js
//////////////////////////////////////////////////
// options

// check for cookies and existing value, else use default
function defaultize(x) {
	var val=null;
	if (x!='popupCookies') {
		defaultize('popupCookies');
		if (pg.option.popupCookies &amp;&amp; (val=Cookie.read(x))) {
			pg.option[x]=val;
			return;
		}
	}
	if (pg.option[x]===null || typeof pg.option[x]=='undefined') {
		if (typeof window[x] != 'undefined' ) pg.option[x]=window[x];
		else pg.option[x]=pg.optionDefault[x];
	}
}

function newOption(x, def) {
	pg.optionDefault[x]=def;
}

function setDefault(x, def) {
	return newOption(x, def);
}

function getValueOf(varName) {
	defaultize(varName);
	return pg.option[varName];
}

function useDefaultOptions() { // for testing
	for (var p in pg.optionDefault) {
		pg.option[p]=pg.optionDefault[p];
		if (typeof window[p]!='undefined') { delete window[p]; }
	}
}

function setOptions() {
	// user-settable parameters and defaults
	var userIsSysop = false;
	if ( mw.config.get('wgUserGroups') ) {
		for ( var g = 0; g &lt; mw.config.get('wgUserGroups').length; ++g ) {
			if ( mw.config.get('wgUserGroups')[g] == &quot;sysop&quot; )
				userIsSysop = true
		}
	}

	// Basic options
	newOption('popupDelay',               0.5);
	newOption('popupHideDelay',           0.5);
	newOption('simplePopups',             false);
	newOption('popupStructure',           'shortmenus');   // see later - default for popupStructure is 'original' if simplePopups is true
	newOption('popupActionsMenu',         true);
	newOption('popupSetupMenu',           true);
	newOption('popupAdminLinks',          userIsSysop);
	newOption('popupShortcutKeys',        false);
	newOption('popupHistoricalLinks',     true);
	newOption('popupOnlyArticleLinks',    true);
	newOption('removeTitles',             true);
	newOption('popupMaxWidth',            350);
	newOption('popupInitialWidth',        false); // integer or false
	newOption('popupSimplifyMainLink',    true);
	newOption('popupAppendRedirNavLinks', true);
	newOption('popupTocLinks',            false);
	newOption('popupSubpopups',           true);
	newOption('popupDragHandle',          false /* 'popupTopLinks'*/);
	newOption('popupLazyPreviews',        true);
	newOption('popupLazyDownloads',       true);
	newOption('popupAllDabsStubs',        false);
	newOption('popupDebugging',           false);
	newOption('popupAdjustDiffDates',     true);
	newOption('popupActiveNavlinks',      true);
	newOption('popupModifier',            false); // ctrl, shift, alt or meta
	newOption('popupModifierAction',      'enable'); // or 'disable'
	newOption('popupDraggable',           true);

//&lt;NOLITE&gt;
	// images
	newOption('popupImages',                 true);
	newOption('imagePopupsForImages',        true);
	newOption('popupNeverGetThumbs',         false);
	//newOption('popupImagesToggleSize',       true);
	newOption('popupThumbAction',            'imagepage'); //'sizetoggle');
	newOption('popupImageSize',              60);
	newOption('popupImageSizeLarge',         200);

	// redirs, dabs, reversion
	newOption('popupFixRedirs',             false);
	newOption('popupRedirAutoClick',        'wpDiff');
	newOption('popupFixDabs',               false);
	newOption('popupRevertSummaryPrompt',   false);
	newOption('popupMinorReverts',          false);
	newOption('popupRedlinkRemoval',        false);
	newOption('popupWatchDisambiggedPages', null);
	newOption('popupWatchRedirredPages',    null);
	newOption('popupDabWiktionary',         'last');

	// navlinks
	newOption('popupNavLinks',          true);
	newOption('popupNavLinkSeparator',  ' &amp;sdot; ');
	newOption('popupLastEditLink',      true);
	newOption('popupEditCounterTool',   'soxred');
	newOption('popupEditCounterUrl',    '');
	newOption('popupExtraUserMenu',     '');
//&lt;/NOLITE&gt;

	// previews etc
	newOption('popupPreviews',             true);
	newOption('popupSummaryData',          true);
	newOption('popupMaxPreviewSentences',  5);
	newOption('popupMaxPreviewCharacters', 600);
	newOption('popupLastModified',         true);
	newOption('popupPreviewKillTemplates', true);
	newOption('popupPreviewRawTemplates',  true);
	newOption('popupPreviewFirstParOnly',  true);
	newOption('popupPreviewCutHeadings',   true);
	newOption('popupPreviewButton',        false);
	newOption('popupPreviewButtonEvent',   'click');

//&lt;NOLITE&gt;
	// diffs
	newOption('popupPreviewDiffs',          true);
	newOption('popupDiffMaxLines',          100);
	newOption('popupDiffContextLines',      2);
	newOption('popupDiffContextCharacters', 40);
	newOption('popupDiffDates',             true);
	newOption('popupDiffDatePrinter',       'toLocaleString');

	// edit summaries. God, these are ugly.
	newOption('popupFixDabsSummary',           popupString('defaultpopupFixDabsSummary') );
	newOption('popupExtendedRevertSummary',    popupString('defaultpopupExtendedRevertSummary') );
	newOption('popupTimeOffset',               null);
	newOption('popupRevertSummary',            popupString('defaultpopupRevertSummary') );
	newOption('popupRevertToPreviousSummary',  popupString('defaultpopupRevertToPreviousSummary') );
	newOption('popupQueriedRevertSummary',            popupString('defaultpopupQueriedRevertSummary') );
	newOption('popupQueriedRevertToPreviousSummary',  popupString('defaultpopupQueriedRevertToPreviousSummary') );
	newOption('popupFixRedirsSummary',         popupString('defaultpopupFixRedirsSummary') );
	newOption('popupRedlinkSummary',           popupString('defaultpopupRedlinkSummary') );
	newOption('popupRmDabLinkSummary',         popupString('defaultpopupRmDabLinkSummary') );
//&lt;/NOLITE&gt;
	// misc
	newOption('popupCookies',             false);
	newOption('popupHistoryLimit',        50);
//&lt;NOLITE&gt;
	newOption('popupFilters',             [popupFilterStubDetect,     popupFilterDisambigDetect,
					       popupFilterPageSize,       popupFilterCountLinks,
					       popupFilterCountImages,    popupFilterCountCategories,
					       popupFilterLastModified]);
	newOption('extraPopupFilters',        []);
	newOption('popupOnEditSelection', 'cursor');
	newOption('popupPreviewHistory',      true);
	newOption('popupImageLinks',          true);
	newOption('popupCategoryMembers',     true);
	newOption('popupUserInfo',            true);
	newOption('popupHistoryPreviewLimit', 25);
	newOption('popupContribsPreviewLimit',25);
	newOption('popupRevDelUrl',          '//en.wikiversity.org/wiki/Wikiversity:Revision_deletion');
//&lt;/NOLITE&gt;

	// new windows
	newOption('popupNewWindows',     false);
	newOption('popupLinksNewWindow', {'lastContrib': true, 'sinceMe': true});

	// regexps
	newOption('popupDabRegexp', '([{][{]\\s*disambig|disambig\\s*[}][}]|disamb\\s*[}][}]|dab\\s*[}][}])|[{][{]\\s*(((geo|hn|road?|school|number)dis)|[234][lc][acw]|shipindex)(\\s*[|][^}]*)?\\s*[}][}]|is a .*disambiguation.*page');
	newOption('popupAnchorRegexp', 'anchors?'); //how to identify an anchors template
	newOption('popupStubRegexp', '(sect)?stub[}][}]|This .*-related article is a .*stub');
	newOption('popupImageVarsRegexp', 'image|image_(?:file|skyline|name|flag|seal)|cover|badge|logo');
}
// ENDFILE: options.js
// STARTFILE: strings.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Translatable strings
//////////////////////////////////////////////////
//
// See instructions at
// //en.wikipedia.org/wiki/Wikipedia:Tools/Navigation_popups/Translation

pg.string = {
	/////////////////////////////////////
	// summary data, searching etc.
	/////////////////////////////////////
	'article': 'article',
	'category': 'category',
	'categories': 'categories',
	'image': 'image',
	'images': 'images',
	'stub': 'stub',
	'section stub': 'section stub',
	'Empty page': 'Empty page',
	'kB': 'kB',
	'bytes': 'bytes',
	'day': 'day',
	'days': 'days',
	'hour': 'hour',
	'hours': 'hours',
	'minute': 'minute',
	'minutes': 'minutes',
	'second': 'second',
	'seconds': 'seconds',
	'week': 'week',
	'weeks': 'weeks',
	'search': 'search',
	'SearchHint': 'Find English Wikiversity resources containing %s',
	'web': 'web',
	'global': 'global',
	'globalSearchHint': 'Search across Wikiversity in different languages for %s',
	'googleSearchHint': 'Google for %s',
	/////////////////////////////////////
	// article-related actions and info
	// (some actions also apply to user pages)
	/////////////////////////////////////
	'actions': 'actions',         ///// view articles and view talk
	'popupsMenu': 'popups',
	'togglePreviewsHint': 'Toggle preview generation in popups on this page',
	'enable previews': 'enable previews',
	'disable previews': 'disable previews',
	'toggle previews': 'toggle previews',
	'show preview': 'show preview',
	'reset': 'reset',
	'more...': 'more...',
	'disable': 'disable popups',
	'disablePopupsHint': 'Disable popups on this page. Reload page to re-enable.',
	'historyfeedHint': 'RSS feed of recent changes to this page',
	'purgePopupsHint': 'Reset popups, clearing all cached popup data.',
	'PopupsHint': 'Reset popups, clearing all cached popup data.',
	'spacebar': 'space',
	'view': 'view',
	'view article': 'view article',
	'viewHint': 'Go to %s',
	'talk': 'talk',
	'talk page': 'talk page',
	'this&amp;nbsp;revision': 'this&amp;nbsp;revision',
	'revision %s of %s': 'revision %s of %s',
	'Revision %s of %s': 'Revision %s of %s',
	'the revision prior to revision %s of %s': 'the revision prior to revision %s of %s',
	'Toggle image size': 'Click to toggle image size',
	'del': 'del',                 ///// delete, protect, move
	'delete': 'delete',
	'deleteHint': 'Delete %s',
	'undeleteShort': 'un',
	'UndeleteHint': 'Show the deletion history for %s',
	'protect': 'protect',
	'protectHint': 'Restrict editing rights to %s',
	'unprotectShort': 'un',
	'unprotectHint': 'Allow %s to be edited by anyone again',
	'move': 'move',
	'move page': 'move page',
	'MovepageHint': 'Change the title of %s',
	'edit': 'edit',               ///// edit articles and talk
	'edit article': 'edit article',
	'editHint': 'Change the content of %s',
	'edit talk': 'edit talk',
	'new': 'new',
	'new topic': 'new topic',
	'newSectionHint': 'Start a new section on %s',
	'null edit': 'null edit',
	'nullEditHint': 'Submit an edit to %s, making no changes ',
	'hist': 'hist',               ///// history, diffs, editors, related
	'history': 'history',
	'historyHint': 'List the changes made to %s',
	'last': 'last',
	'lastEdit': 'lastEdit',
	'mark patrolled': 'mark patrolled',
	'markpatrolledHint': 'Mark this edit as patrolled',
	'show last edit': 'most recent edit',
	'Show the last edit': 'Show the effects of the most recent change',
	'lastContrib': 'lastContrib',
	'last set of edits': 'latest edits',
	'lastContribHint': 'Show the net effect of changes made by the last editor',
	'cur': 'cur',
	'diffCur': 'diffCur',
	'Show changes since revision %s': 'Show changes since revision %s',
	'%s old': '%s old', // as in 4 weeks old
	'oldEdit': 'oldEdit',
	'purge': 'purge',
	'purgeHint': 'Demand a fresh copy of %s',
	'raw': 'source',
	'rawHint': 'Download the source of %s',
	'render': 'simple',
	'renderHint': 'Show a plain HTML version of %s',
	'Show the edit made to get revision': 'Show the edit made to get revision',
	'sinceMe': 'sinceMe',
	'changes since mine': 'diff my edit',
	'sinceMeHint': 'Show changes since my last edit',
	'Couldn\'t find an edit by %s\nin the last %s edits to\n%s': 'Couldn\'t find an edit by %s\nin the last %s edits to\n%s',
	'eds': 'eds',
	'editors': 'editors',
	'editorListHint': 'List the users who have edited %s',
	'related': 'related',
	'relatedChanges': 'relatedChanges',
	'related changes': 'related changes',
	'RecentchangeslinkedHint': 'Show changes in articles related to %s',
	'editOld': 'editOld',          ///// edit old version, or revert
	'rv': 'rv',
	'revert': 'revert',
	'revertHint': 'Revert to %s',
	'defaultpopupRedlinkSummary': 'Removing link to empty page [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupFixDabsSummary': 'Disambiguate [[%s]] to [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupFixRedirsSummary': 'Redirect bypass from [[%s]] to [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupExtendedRevertSummary': 'Revert to revision dated %s by %s, oldid %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRevertToPreviousSummary': 'Revert to the revision prior to revision %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRevertSummary': 'Revert to revision %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupQueriedRevertToPreviousSummary': 'Revert to the revision prior to revision $1 dated $2 by $3 using [[:en:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupQueriedRevertSummary': 'Revert to revision $1 dated $2 by $3 using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRmDabLinkSummary': 'Remove link to dab page [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'Redirects': 'Redirects', // as in Redirects to ...
	' to ': ' to ',           // as in Redirects to ...
	'Bypass redirect': 'Bypass redirect',
	'Fix this redirect': 'Fix this redirect',
	'disambig': 'disambig',          ///// add or remove dab etc.
	'disambigHint': 'Disambiguate this link to [[%s]]',
	'Click to disambiguate this link to:': 'Click to disambiguate this link to:',
	'remove this link': 'remove this link',
	'remove all links to this page from this article': 'remove all links to this page from this article',
	'remove all links to this disambig page from this article': 'remove all links to this disambig page from this article',
	'mainlink': 'mainlink',          ///// links, watch, unwatch
	'wikiLink': 'wikiLink',
	'wikiLinks': 'wikiLinks',
	'links here': 'links here',
	'whatLinksHere': 'whatLinksHere',
	'what links here': 'what links here',
	'WhatlinkshereHint': 'List the pages that are hyperlinked to %s',
	'unwatchShort': 'un',
	'watchThingy': 'watch',  // called watchThingy because {}.watch is a function
	'watchHint': 'Add %s to my watchlist',
	'unwatchHint': 'Remove %s from my watchlist',
	'Only found one editor: %s made %s edits': 'Only found one editor: %s made %s edits',
	'%s seems to be the last editor to the page %s': '%s seems to be the last editor to the page %s',
	'rss': 'rss',
	/////////////////////////////////////
	// diff previews
	/////////////////////////////////////
	'Diff truncated for performance reasons': 'Diff truncated for performance reasons',
	'Old revision': 'Old revision',
	'New revision': 'New revision',
	'Something went wrong :-(': 'Something went wrong :-(',
	'Empty revision, maybe non-existent': 'Empty revision, maybe non-existent',
	'Unknown date': 'Unknown date',
	/////////////////////////////////////
	// other special previews
	/////////////////////////////////////
	'Empty category': 'Empty category',
	'Category members (%s shown)': 'Category members (%s shown)',
	'No image links found': 'No image links found',
	'File links': 'File links',
	'No image found': 'No image found',
	'Image from Commons': 'Image from Commons',
	'Description page': 'Description page',
	'Alt text:': 'Alt text:',
	'revdel':'Hidden revision',
	/////////////////////////////////////
	// user-related actions and info
	/////////////////////////////////////
	'user': 'user',               ///// user page, talk, email, space
	'user&amp;nbsp;page': 'user&amp;nbsp;page',
	'user talk': 'user talk',
	'edit user talk': 'edit user talk',
	'leave comment': 'leave comment',
	'email': 'email',
	'email user': 'email user',
	'EmailuserHint': 'Send an email to %s',
	'space': 'space', // short form for userSpace link
	'PrefixIndexHint': 'Show pages in the userspace of %s',
	'count': 'count',             ///// contributions, log
	'edit counter': 'edit counter',
	'editCounterLinkHint': 'Count the contributions made by %s',
	'contribs': 'contribs',
	'contributions': 'contributions',
	'deletedContribs': 'deleted contributions',
	'DeletedcontributionsHint': 'List deleted edits made by %s',
	'ContributionsHint': 'List the contributions made by %s',
	'log': 'log',
	'user log': 'user log',
	'userLogHint': 'Show %s\'s user log',
	'arin': 'ARIN lookup',             ///// ARIN lookup, block user or IP
	'Look up %s in ARIN whois database': 'Look up %s in the ARIN whois database',
	'unblockShort': 'un',
	'block': 'block',
	'block user': 'block user',
	'IpblocklistHint': 'Unblock %s',
	'BlockipHint': 'Prevent %s from editing',
	'block log': 'block log',
	'blockLogHint': 'Show the block log for %s',
	'protectLogHint': 'Show the protection log for %s',
	'pageLogHint': 'Show the page log for %s',
	'deleteLogHint': 'Show the deletion log for %s',
	'Invalid %s %s': 'The option %s is invalid: %s',
	'No backlinks found': 'No backlinks found',
	' and more': ' and more',
	'undo': 'undo',
	'undoHint': 'undo this edit',
	'Download preview data': 'Download preview data',
	'Invalid or IP user': 'Invalid or IP user',
	'Not a registered username': 'Not a registered username',
	'BLOCKED': 'BLOCKED',
	' edits since: ': ' edits since: ',
	/////////////////////////////////////
	// Autoediting
	/////////////////////////////////////
	'Enter a non-empty edit summary or press cancel to abort': 'Enter a non-empty edit summary or press cancel to abort',
	'Failed to get revision information, please edit manually.\n\n': 'Failed to get revision information, please edit manually.\n\n',
	'The %s button has been automatically clicked. Please wait for the next page to load.': 'The %s button has been automatically clicked. Please wait for the next page to load.',
	'Could not find button %s. Please check the settings in your javascript file.': 'Could not find button %s. Please check the settings in your javascript file.',
	/////////////////////////////////////
	// Popups setup
	/////////////////////////////////////
	'Open full-size image': 'Open full-size image',
	'zxy': 'zxy'
};


function popupString(str) {
	if (typeof popupStrings != 'undefined' &amp;&amp; popupStrings &amp;&amp; popupStrings[str]) { return popupStrings[str]; }
	if (pg.string[str]) { return pg.string[str]; }
	return str;
}


function tprintf(str,subs) {
	if (typeof subs != typeof []) { subs = [subs]; }
	return simplePrintf(popupString(str), subs);
}

//&lt;/NOLITE&gt;
// ENDFILE: strings.js


////////////////////////////////////////////////////////////////////
// Run things
////////////////////////////////////////////////////////////////////

hookEvent('load', setupPopups);
$(autoEdit);

//support for MediaWiki's live preview
$( function() {
   	if(typeof doLivePreview != &quot;function&quot; || typeof $ != &quot;function&quot;) return;
	$(&quot;#wpPreview&quot;).click(function(){
		var i = setInterval(function(){
			var p = document.getElementById(&quot;wikiPreview&quot;);
			if(p.previousSibling.className == &quot;mw-ajax-loader&quot;) return;

			p.ranSetupTooltipsAlready = false;
			setupTooltips(p);
			clearInterval(i);
		}, 500);
	});
});
// &lt;/nowiki&gt;</text>
      <sha1>ccjy2a2nk6or0yp1zn8q6ri4sypjy88</sha1>
    </revision>
    <revision>
      <id>2810147</id>
      <parentid>2810145</parentid>
      <timestamp>2026-05-18T19:08:23Z</timestamp>
      <contributor>
        <username>WikiBayer</username>
        <id>2181512</id>
      </contributor>
      <origin>2810147</origin>
      <model>javascript</model>
      <format>text/javascript</format>
      <text bytes="246577" sha1="dvlz067wiphlvragdziqjzs3956an5h" xml:space="preserve">// STARTFILE: main.js
// **********************************************************************
// **                                                                  **
// **             changes to this file affect many users.              **
// **           please discuss on the talk page before editing         **
// **                                                                  **
// **********************************************************************
// **                                                                  **
// ** if you do edit this file, be sure that your editor recognizes it **
// ** as utf8, or the weird and wonderful characters in the namespaces **
// **   below will be completely broken. You can check with the show   **
// **            changes button before submitting the edit.            **
// **                      test: مدیا מיוחד Мэдыя                      **
// **                                                                  **
// **********************************************************************

//////////////////////////////////////////////////
// Globals
//
//&lt;nowiki&gt;
// Trying to shove as many of these as possible into the pg (popup globals) object
function pg(){}; // dummy to stop errors
window.pg = {
	re: {},               // regexps
	ns: {},               // namespaces
	string: {},           // translatable strings
	wiki: {},             // local site info
	misc: {},             // YUCK PHOOEY
	option: {},           // options, see newOption etc
	optionDefault: {},    // default option values
	flag: {},             // misc flags
	cache: {},            // page and image cache
	structures: {},       // navlink structures
	timer: {},            // all sorts of timers (too damn many)
	counter: {},          // .. and all sorts of counters
	current: {},          // state info
	endoflist: null
};
window.pop = {          // wrap various functions in here
	init: {},
	util: {},
	endoflist: null
};
function popupsReady() {
	if (!window.pg) { return false; }
	if (!pg.flag) { return false; }
	if (!pg.flag.finishedLoading) { return false; }
	return true;
}

/// Local Variables: ///
/// mode:c ///
/// End: ///
// ENDFILE: main.js
// STARTFILE: actions.js
function setupTooltips(container, remove, force, popData) {
	log('setupTooltips, container='+container+', remove='+remove);
	if (!container) {
//&lt;NOLITE&gt;
		// the main initial call
		if (getValueOf('popupOnEditSelection') &amp;&amp; window.doSelectionPopup &amp;&amp; document &amp;&amp; document.editform &amp;&amp; document.editform.wpTextbox1) {
			document.editform.wpTextbox1.onmouseup=doSelectionPopup;
		}
//&lt;/NOLITE&gt;
		// article/content is a structure-dependent thing
		container = defaultPopupsContainer();
	}

	if (!remove &amp;&amp; !force &amp;&amp; container.ranSetupTooltipsAlready) { return; }
	container.ranSetupTooltipsAlready = !remove;

	var anchors;
	anchors=container.getElementsByTagName('A');
	setupTooltipsLoop(anchors, 0, 250, 100, remove, popData);
}

function defaultPopupsContainer() {
    if (getValueOf('popupOnlyArticleLinks')) {
	    return document.getElementById('mw_content') || 
		    document.getElementById('content') ||
		    document.getElementById('article') || document;
    }
    return  document;
}

function setupTooltipsLoop(anchors,begin,howmany,sleep, remove, popData) {
	log(simplePrintf('setupTooltipsLoop(%s,%s,%s,%s,%s)', arguments));
	var finish=begin+howmany;
	var loopend = min(finish, anchors.length);
	var j=loopend - begin;
	log ('setupTooltips: anchors.length=' + anchors.length + ', begin=' + begin +
	     ', howmany=' + howmany + ', loopend=' + loopend + ', remove=' + remove);
	var doTooltip= remove ? removeTooltip : addTooltip;
	// try a faster (?) loop construct
	if (j &gt; 0) {
		do {
			var a=anchors[loopend - j];
			if (typeof a=='undefined' || !a || !a.href) {
				log('got null anchor at index ' + loopend - j);
				continue;
			}
			doTooltip(a, popData);
		} while (--j);
	}
	if (finish &lt; anchors.length) {
		setTimeout(function() {
				setupTooltipsLoop(anchors,finish,howmany,sleep,remove,popData);},
			sleep);
	} else {
		if ( !remove &amp;&amp; ! getValueOf('popupTocLinks')) { rmTocTooltips(); }
		pg.flag.finishedLoading=true;
	}
}

// eliminate popups from the TOC
// This also kills any onclick stuff that used to be going on in the toc
function rmTocTooltips() {
	var toc=document.getElementById('toc');
	if (toc) {
		var tocLinks=toc.getElementsByTagName('A');
		var tocLen = tocLinks.length;
		for (j=0; j&lt;tocLen; ++j) {
			removeTooltip(tocLinks[j], true);
		}
	}
}

function addTooltip(a, popData) {
	if ( !isPopupLink(a) ) { return; }
	a.onmouseover=mouseOverWikiLink;
	a.onmouseout= mouseOutWikiLink;
	a.onmousedown = killPopup;
	a.hasPopup = true;
	a.popData = popData;
}

function removeTooltip(a) {
	if ( !a.hasPopup ) { return; }
	a.onmouseover = null;
	a.onmouseout = null;
	if (a.originalTitle) { a.title = a.originalTitle; }
	a.hasPopup=false;
}

function removeTitle(a) {
	a.title='';
	if (a.originalTitle) { return; }
	a.originalTitle=a.title;
}

function restoreTitle(a) {
	if ( a.title || !a.originalTitle ) { return; }
	a.title = a.originalTitle;
}

function registerHooks(np) {
	var popupMaxWidth=getValueOf('popupMaxWidth');

	if (typeof popupMaxWidth == 'number') {
		var setMaxWidth = function () {
			np.mainDiv.style.maxWidth = popupMaxWidth + 'px';
			np.maxWidth = popupMaxWidth;

            try {
				// hack for IE
				// see http://www.svendtofte.com/code/max_width_in_ie/
				// use setExpression as documented here on msdn: http://tinyurl dot com/dqljn
	
				if (np.mainDiv.style.setExpression) {
					np.mainDiv.style.setExpression(
						'width', 'document.body.clientWidth &gt; ' +
						popupMaxWidth + ' ? &quot;' +popupMaxWidth + 'px&quot;: &quot;auto&quot;');
				}
            }
            catch (errors) {
            	errlog( &quot;Running on IE8 are we not?: &quot; + errors );
            }
		};
		np.addHook(setMaxWidth, 'unhide', 'before');
	}
//&lt;NOLITE&gt;
	if (window.addPopupShortcuts &amp;&amp; window.rmPopupShortcuts) {
	    np.addHook(addPopupShortcuts, 'unhide', 'after');
	    np.addHook(rmPopupShortcuts, 'hide', 'before');
	}
//&lt;/NOLITE&gt;
}


function mouseOverWikiLink(evt) {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	if (!evt &amp;&amp; window.event) {evt=window.event}
	return mouseOverWikiLink2(this, evt);
}

function footnoteTarget(a) {
	var aTitle=Title.fromAnchor(a);
	// We want &quot;.3A&quot; rather than &quot;%3A&quot; or &quot;?&quot; here, so use the anchor property directly
	var anch = aTitle.anchor;
	if ( ! /^(cite_note-|_note-|endnote)/.test(anch) ) { return false;	}

	var lTitle=Title.fromURL(location.href);
	if ( lTitle.toString(true) != aTitle.toString(true) ) {	return false; }

	var el=document.getElementById(anch);
	while ( el &amp;&amp; typeof el.nodeName == 'string') {
		var nt = el.nodeName.toLowerCase();
		if ( nt == 'li' ) { return el; }
		else if ( nt == 'body' ) { return false; }
		else if ( el.parentNode ) { el=el.parentNode; }
		else { return false; }
	}
	return false;
}

function footnotePreview(x, navpop) {
	setPopupHTML('&lt;hr&gt;' + x.innerHTML, 'popupPreview',  navpop.idNumber,
		     getValueOf('popupSubpopups') ? function() {
		setupTooltips(document.getElementById('popupPreview' + navpop.idNumber));
	} : null);
}

// var modid=0;
// if(!window.opera) { window.opera={postError: console.log}; }

function modifierKeyHandler(a) {
	return function(evt) {
		//		opera.postError('modifierKeyHandler called' + (++modid));
		//		opera.postError(''+evt + modid);
		//		for (var i in evt) {
		//			opera.postError('' + modid + ' ' + i + ' ' + evt[i]);
		//		}
		//		opera.postError(''+evt.ctrlKey + modid);
		var mod=getValueOf('popupModifier');
		if (!mod) { return true; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
		//		opera.postError('And now....'+modid);
		//		opera.postError(''+evt+modid);
		//		opera.postError(''+evt.ctrlKey+modid);

		var modPressed = modifierPressed(evt);
		var action = getValueOf('popupModifierAction');

		// FIXME: probable bug - modifierPressed should be modPressed below?
		if ( action == 'disable' &amp;&amp; modifierPressed ) { return true; }
		if ( action == 'enable' &amp;&amp; !modifierPressed ) { return true; }

		mouseOverWikiLink2(a, evt);
	};
}

function modifierPressed(evt) {
		var mod=getValueOf('popupModifier');
		if (!mod) { return false; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
//		opera.postError('And now....'+modid);
//		opera.postError(''+evt+modid);
//		opera.postError(''+evt.ctrlKey+modid);

		return ( evt &amp;&amp; mod &amp;&amp; evt[mod.toLowerCase() + 'Key'] );

}

function dealWithModifier(a,evt) {
	if (!getValueOf('popupModifier')) { return false; }
	var action = getValueOf('popupModifierAction');
	if ( action == 'enable' &amp;&amp; !modifierPressed(evt) ||
	     action == 'disable' &amp;&amp; modifierPressed(evt) ) {
		// if the modifier is needed and not pressed, listen for it until
		// we mouseout of this link.
		restoreTitle(a);
		var addHandler='addEventListener';
		var rmHandler='removeEventListener';
		var on='';
		if (!document.addEventListener) {
			addHandler='attachEvent';
			rmHandler='detachEvent';
			on='on';
		}
		if (!document[addHandler]) { // forget it
			return;
		}

		a.modifierKeyHandler=modifierKeyHandler(a);

		switch (action) {
		case 'enable':
			document[addHandler](on+'keydown', a.modifierKeyHandler, false);
			a[addHandler](on+'mouseout', function() {
					document[rmHandler](on+'keydown',
							    a.modifierKeyHandler, false);
				}, true);
			break;
		case 'disable':
			document[addHandler](on+'keyup', a.modifierKeyHandler, false);
		}

		return true;
	}
	return false;
}

function mouseOverWikiLink2(a, evt) {
	if (dealWithModifier(a,evt)) { return; }
	if ( getValueOf('removeTitles') ) { removeTitle(a); }
	if ( a==pg.current.link &amp;&amp; a.navpopup &amp;&amp; a.navpopup.isVisible() ) { return; }
	pg.current.link=a;

	if (getValueOf('simplePopups') &amp;&amp; pg.option.popupStructure===null) {
		// reset *default value* of popupStructure
		setDefault('popupStructure', 'original');
	}

	var article=(new Title()).fromAnchor(a);
	// set global variable (ugh) to hold article (wikipage)
	pg.current.article = article;

	if (!a.navpopup) {
		// FIXME: this doesn't behave well if you mouse out of a popup
		// directly into a link with the same href
		if (pg.current.linksHash[a.href] &amp;&amp; false) {
			a.navpopup = pg.current.linksHash[a.href];
		}
		else {
			a.navpopup=newNavpopup(a, article);
			pg.current.linksHash[a.href] = a.navpopup;
			pg.current.links.push(a);
		}
	}
	if (a.navpopup.pending===null || a.navpopup.pending!==0) {
		// either fresh popups or those with unfinshed business are redone from scratch
		simplePopupContent(a, article);
	}
	a.navpopup.showSoonIfStable(a.navpopup.delay);

	getValueOf('popupInitialWidth');

	clearInterval(pg.timer.checkPopupPosition);
	pg.timer.checkPopupPosition=setInterval(checkPopupPosition, 600);

	if(getValueOf('simplePopups')) {
		if (getValueOf('popupPreviewButton') &amp;&amp; !a.simpleNoMore) {
			var d=document.createElement('div');
			d.className='popupPreviewButtonDiv';
			var s=document.createElement('span');
			d.appendChild(s);
			s.className='popupPreviewButton';
			s['on' + getValueOf('popupPreviewButtonEvent')] = function() {
				a.simpleNoMore=true;
				nonsimplePopupContent(a,article);
			}
			s.innerHTML=popupString('show preview');
			setPopupHTML(d, 'popupPreview', a.navpopup.idNumber);
		}
		return;
	}

	if (a.navpopup.pending!==0 ) {
	    nonsimplePopupContent(a, article);
	}
}

// simplePopupContent: the content that is shown even when simplePopups is true
function simplePopupContent(a, article) {
	/* FIXME hack */ a.navpopup.hasPopupMenu=false;
	a.navpopup.setInnerHTML(popupHTML(a));
	fillEmptySpans({navpopup:a.navpopup});

	if (getValueOf('popupDraggable'))
	{
		var dragHandle = getValueOf('popupDragHandle') || null;
		if (dragHandle &amp;&amp; dragHandle != 'all') {
			dragHandle += a.navpopup.idNumber;
		}
		setTimeout(function(){a.navpopup.makeDraggable(dragHandle);}, 150);
	}

//&lt;NOLITE&gt;
	if (getValueOf('popupRedlinkRemoval') &amp;&amp; a.className=='new') {
		setPopupHTML('&lt;br&gt;'+popupRedlinkHTML(article), 'popupRedlink', a.navpopup.idNumber);
	}
//&lt;/NOLITE&gt;
}

function debugData(navpopup) {
	if(getValueOf('popupDebugging') &amp;&amp; navpopup.idNumber) {
		setPopupHTML('idNumber='+navpopup.idNumber + ', pending=' + navpopup.pending,
			     'popupError', navpopup.idNumber);
	}
}

function newNavpopup(a, article) {
	var navpopup = new Navpopup();
	navpopup.fuzz=5;
	navpopup.delay=getValueOf('popupDelay')*1000;
	// increment global counter now
	navpopup.idNumber = ++pg.idNumber;
	navpopup.parentAnchor = a;
	navpopup.parentPopup = (a.popData &amp;&amp; a.popData.owner);
	navpopup.article = article;
	registerHooks(navpopup);
	return navpopup;
}


function nonsimplePopupContent(a, article) {
	var diff=null, history=null;
	var params=parseParams(a.href);
	var oldid=(typeof params.oldid=='undefined' ? null : params.oldid);
//&lt;NOLITE&gt;
	if(getValueOf('popupPreviewDiffs') &amp;&amp; window.loadDiff) {
		diff=params.diff;
	}
	if(getValueOf('popupPreviewHistory')) {
		history=(params.action=='history');
	}
//&lt;/NOLITE&gt;
	a.navpopup.pending=0;
	var x;
	
	if (x=footnoteTarget(a)) {
		footnotePreview(x, a.navpopup);
//&lt;NOLITE&gt;
	} else if ( diff || diff === 0 ) {
		loadDiff(article, oldid, diff, a.navpopup);
	} else if ( history ) {
		loadAPIPreview('history', article, a.navpopup);
	} else if ( pg.re.contribs.test(a.href) ) {
		loadAPIPreview('contribs', article, a.navpopup);
	} else if ( pg.re.backlinks.test(a.href) ) {
		loadAPIPreview('backlinks', article, a.navpopup);
    } else if ( // FIXME should be able to get all preview combinations with options
		article.namespaceId()==pg.nsImageId &amp;&amp;
		( getValueOf('imagePopupsForImages') || ! anchorContainsImage(a) )
		) {
		loadAPIPreview('imagepagepreview', article, a.navpopup);
		loadImage(article, a.navpopup);
//&lt;/NOLITE&gt;
	} else {
		if (article.namespaceId() == pg.nsCategoryId &amp;&amp;
				getValueOf('popupCategoryMembers')) {
			loadAPIPreview('category', article, a.navpopup);
		} else if ((article.namespaceId() == pg.nsUserId || article.namespaceId() == pg.nsUsertalkId) &amp;&amp;
				getValueOf('popupUserInfo')) {
			loadAPIPreview('userinfo', article, a.navpopup);
		}
		startArticlePreview(article, oldid, a.navpopup);
	}
}

function pendingNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending===null) { navpop.pending=0; }
	++navpop.pending;
	debugData(navpop);
}

function completedNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending) { --navpop.pending; }
	debugData(navpop);
}

function startArticlePreview(article, oldid, navpop) {
	navpop.redir=0;
	loadPreview(article, oldid, navpop);
}

function loadPreview(article, oldid, navpop) {
	pendingNavpopTask(navpop);
	if (!navpop.redir) { navpop.originalArticle=article; }
	if (!navpop.visible &amp;&amp; getValueOf('popupLazyDownloads')) {
		var id=(navpop.redir) ? 'DOWNLOAD_PREVIEW_REDIR_HOOK' : 'DOWNLOAD_PREVIEW_HOOK';
		navpop.addHook(function() {
				getWiki(article, insertPreview, oldid, navpop);
				return true; }, 'unhide', 'before', id);
	} else {
		getWiki(article, insertPreview, oldid, navpop);
	}
}

function loadPreviewFromRedir(redirMatch, navpop) {
	// redirMatch is a regex match
	var target = new Title().fromWikiText(redirMatch[2]);
	// overwrite (or add) anchor from original target
	// mediawiki does overwrite; eg [[User:Lupin/foo3#Done]]
	if ( navpop.article.anchor ) { target.anchor = navpop.article.anchor; }
	var trailingRubbish=redirMatch[4];
	navpop.redir++;
	navpop.redirTarget=target;
//&lt;NOLITE&gt;
	if (window.redirLink) {
		var warnRedir = redirLink(target, navpop.article);
		setPopupHTML(warnRedir, 'popupWarnRedir', navpop.idNumber);
	}
//&lt;/NOLITE&gt;
	navpop.article=target;
	fillEmptySpans({redir: true, redirTarget: target, navpopup:navpop});
	return loadPreview(target, null,  navpop);
}

function insertPreview(download) {
	if (!download.owner) { return; }

	var redirMatch = pg.re.redirect.exec(download.data);
	if (download.owner.redir===0 &amp;&amp; redirMatch) {
		completedNavpopTask(download.owner);
		loadPreviewFromRedir(redirMatch, download.owner);
		return;
	}

	if (download.owner.visible || !getValueOf('popupLazyPreviews')) {
	    insertPreviewNow(download);
	} else {
		var id=(download.owner.redir) ? 'PREVIEW_REDIR_HOOK' : 'PREVIEW_HOOK';
		download.owner.addHook( function(){insertPreviewNow(download); return true;},
					'unhide', 'after', id );
	}
}

function insertPreviewNow(download) {
	if (!download.owner) { return; }
	var wikiText=download.data;
	var navpop=download.owner;
	completedNavpopTask(navpop);
	var art=navpop.redirTarget || navpop.originalArticle;

//&lt;NOLITE&gt;
	makeFixDabs(wikiText, navpop);
	if (getValueOf('popupSummaryData') &amp;&amp; window.getPageInfo) {
		var info=getPageInfo(wikiText, download);
		setPopupTrailer(getPageInfo(wikiText, download), navpop.idNumber);
	}

	var imagePage='';
	if (art.namespaceId()==pg.nsImageId) { imagePage=art.toString(); }
	else { imagePage=getValidImageFromWikiText(wikiText); }
	if(imagePage) { loadImage(Title.fromWikiText(imagePage), navpop); }
//&lt;/NOLITE&gt;

	if (getValueOf('popupPreviews')) { insertArticlePreview(download, art, navpop); }

}

function insertArticlePreview(download, art, navpop) {
	if (download &amp;&amp; typeof download.data == typeof ''){
		if (art.namespaceId()==pg.nsTemplateId &amp;&amp; getValueOf('popupPreviewRawTemplates')) {
			// FIXME compare/consolidate with diff escaping code for wikitext
			var h='&lt;hr&gt;&lt;tt&gt;' + download.data.entify().split('\\n').join('&lt;br&gt;\\n') + '&lt;/tt&gt;';
			setPopupHTML(h, 'popupPreview', navpop.idNumber);
		}
		else {
			var p=prepPreviewmaker(download.data, art, navpop);
			p.showPreview();
		}
	}
}

function prepPreviewmaker(data, article, navpop) {
	// deal with tricksy anchors
	var d=anchorize(data, article.anchorString());
	var urlBase=joinPath([pg.wiki.articlebase, article.urlString()]);
	var p=new Previewmaker(d, urlBase, navpop);
	return p;
}


// Try to imitate the way mediawiki generates HTML anchors from section titles
function anchorize(d, anch) {
	if (!anch) { return d; }
	var anchRe=RegExp('(?:=+\\s*' + literalizeRegex(anch).replace(/[_ ]/g, '[_ ]') + '\\s*=+|\\{\\{\\s*'+getValueOf('popupAnchorRegexp')+'\\s*(?:\\|[^|}]*)*?\\s*'+literalizeRegex(anch)+'\\s*(?:\\|[^}]*)?\}\})');
	var match=d.match(anchRe);
	if(match &amp;&amp; match.length &gt; 0 &amp;&amp; match[0]) { return d.substring(d.indexOf(match[0])); }

	// now try to deal with == foo [[bar|baz]] boom == -&gt; #foo_baz_boom
	var lines=d.split('\n');
	for (var i=0; i&lt;lines.length; ++i) {
		lines[i]=lines[i].replace(RegExp('[[]{2}([^|\\]]*?[|])?(.*?)[\\]]{2}', 'g'), '$2')
			.replace(/'''([^'])/g, '$1').replace(RegExp(&quot;''([^'])&quot;, 'g'), '$1');
		if (lines[i].match(anchRe)) {
			return d.split('\n').slice(i).join('\n').replace(RegExp('^[^=]*'), '');
		}
	}
	return d;
}

function killPopup() {
	if (getValueOf('popupShortcutKeys') &amp;&amp; window.rmPopupShortcuts) { rmPopupShortcuts(); }
	if (!pg) { return; }
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp; pg.current.link.navpopup.banish();
	pg.current.link=null;
	abortAllDownloads();
	if (pg.timer.checkPopupPosition !== null) {
		clearInterval(pg.timer.checkPopupPosition);
		pg.timer.checkPopupPosition=null;
	}
	return true; // preserve default action
}
// ENDFILE: actions.js
// STARTFILE: domdrag.js
/**
   @fileoverview
   The {@link Drag} object, which enables objects to be dragged around.

   &lt;pre&gt;
   *************************************************
   dom-drag.js
   09.25.2001
   www.youngpup.net
   **************************************************
   10.28.2001 - fixed minor bug where events
   sometimes fired off the handle, not the root.
   *************************************************
   Pared down, some hooks added by [[User:Lupin]]

   Copyright Aaron Boodman.
   Saying stupid things daily since March 2001.
   &lt;/pre&gt;
*/

/**
   Creates a new Drag object. This is used to make various DOM elements draggable.
   @constructor
*/
function Drag () {
	/**
	   Condition to determine whether or not to drag. This function should take one parameter, an Event.
	   To disable this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.startCondition = null;
	/**
	   Hook to be run when the drag finishes. This is passed the final coordinates of
	   the dragged object (two integers, x and y). To disables this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.endHook = null;
}

/**
   Gets an event in a cross-browser manner.
   @param {Event} e
   @private
*/
Drag.prototype.fixE = function(e) {
	if (typeof e == 'undefined') { e = window.event; }
	if (typeof e.layerX == 'undefined') { e.layerX = e.offsetX; }
	if (typeof e.layerY == 'undefined') { e.layerY = e.offsetY; }
	return e;
};
/**
   Initialises the Drag instance by telling it which object you want to be draggable, and what you want to drag it by.
   @param {DOMElement} o The &quot;handle&quot; by which &lt;code&gt;oRoot&lt;/code&gt; is dragged.
   @param {DOMElement} oRoot The object which moves when &lt;code&gt;o&lt;/code&gt; is dragged, or &lt;code&gt;o&lt;/code&gt; if omitted.
*/
Drag.prototype.init = function(o, oRoot) {
	var dragObj      = this;
	this.obj = o;
	o.onmousedown    = function(e) { dragObj.start.apply( dragObj, [e]); };
	o.dragging       = false;
	o.popups_draggable      = true;
	o.hmode          = true;
	o.vmode          = true;

	o.root = oRoot &amp;&amp; oRoot !== null ? oRoot : o ;

	if (isNaN(parseInt(o.root.style.left, 10))) { o.root.style.left   = &quot;0px&quot;; }
	if (isNaN(parseInt(o.root.style.top,  10))) { o.root.style.top    = &quot;0px&quot;; }

	o.root.onthisStart  = function(){};
	o.root.onthisEnd    = function(){};
	o.root.onthis       = function(){};
};

/**
   Starts the drag.
   @private
   @param {Event} e
*/
Drag.prototype.start = function(e) {
	var o = this.obj; // = this;
	e = this.fixE(e);
	if (this.startCondition &amp;&amp; !this.startCondition(e)) { return; }
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10);
	o.root.onthisStart(x, y);

	o.lastMouseX    = e.clientX;
	o.lastMouseY    = e.clientY;

	var dragObj      = this;
	o.onmousemoveDefault    = document.onmousemove;
	o.dragging              = true;
	document.onmousemove    = function(e) { dragObj.drag.apply( dragObj, [e] ); };
	document.onmouseup      = function(e) { dragObj.end.apply( dragObj, [e] ); };
	return false;
};
/**
   Does the drag.
   @param {Event} e
   @private
*/
Drag.prototype.drag = function(e) {
	e = this.fixE(e);
	var o = this.obj;

	var ey    = e.clientY;
	var ex    = e.clientX;
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10 );
	var nx, ny;

	nx = x + ((ex - o.lastMouseX) * (o.hmode ? 1 : -1));
	ny = y + ((ey - o.lastMouseY) * (o.vmode ? 1 : -1));

	this.obj.root.style[o.hmode ? &quot;left&quot; : &quot;right&quot;] = nx + &quot;px&quot;;
	this.obj.root.style[o.vmode ? &quot;top&quot; : &quot;bottom&quot;] = ny + &quot;px&quot;;
	this.obj.lastMouseX    = ex;
	this.obj.lastMouseY    = ey;

	this.obj.root.onthis(nx, ny);
	return false;
};

/**
   Ends the drag.
   @private
*/
Drag.prototype.end = function()  {
	document.onmousemove=this.obj.onmousemoveDefault;
	document.onmouseup   = null;
	this.obj.dragging    = false;
	if (this.endHook) {
		this.endHook( parseInt(this.obj.root.style[this.obj.hmode ? &quot;left&quot; : &quot;right&quot;], 10),
			      parseInt(this.obj.root.style[this.obj.vmode ? &quot;top&quot; : &quot;bottom&quot;], 10));
	}
};
// ENDFILE: domdrag.js
// STARTFILE: structures.js
//&lt;NOLITE&gt;
pg.structures.original={};
pg.structures.original.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle',
		'popupData', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks',
			       'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
pg.structures.original.popupRedirSpans=function () {
	return ['popupRedir', 'popupWarnRedir', 'popupRedirTopLinks',
		'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'];
};
pg.structures.original.popupTitle=function (x) {
	log ('defaultstructure.popupTitle');
	if (!getValueOf('popupNavLinks')) {
		return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	}
	return '';
};
pg.structures.original.popupTopLinks=function (x) {
	log ('defaultstructure.popupTopLinks');
	if (getValueOf('popupNavLinks')) { return navLinksHTML(x.article, x.hint, x.params); }
	return '';
};
pg.structures.original.popupImage=function(x) {
	log ('original.popupImage, x.article='+x.article+', x.navpop.idNumber='+x.navpop.idNumber);
	return imageHTML(x.article, x.navpop.idNumber);
};
pg.structures.original.popupRedirTitle=pg.structures.original.popupTitle;
pg.structures.original.popupRedirTopLinks=pg.structures.original.popupTopLinks;


function copyStructure(oldStructure, newStructure) {
	pg.structures[newStructure]={};
	for (var prop in pg.structures[oldStructure]) {
		pg.structures[newStructure][prop]=pg.structures[oldStructure][prop];
	}
}

copyStructure('original', 'nostalgia');
pg.structures.nostalgia.popupTopLinks=function(x)  {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;';
	str+='if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{'
	+ editstr + '}'
	var historystr='&lt;&lt;history|shortcut=h&gt;&gt;';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;';
	str += 'if(admin){&lt;br&gt;}else{*}&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){*&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*' +
	'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;}';
	return navlinkStringToHTML(str, x.article, x.params);
};
pg.structures.nostalgia.popupRedirTopLinks=pg.structures.nostalgia.popupTopLinks;

/** -- fancy -- **/
copyStructure('original', 'fancy');
pg.structures.fancy.popupTitle=function (x) {
	return navlinkStringToHTML('&lt;font size=+0&gt;&lt;&lt;mainlink&gt;&gt;&lt;/font&gt;',x.article,x.params);
};
pg.structures.fancy.popupTopLinks=function(x) {
	var hist='&lt;&lt;history|shortcut=h|hist&gt;&gt;|&lt;&lt;lastEdit|shortcut=/|last&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|eds&gt;&gt;}';
	var watch='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';
	var move='&lt;&lt;move|shortcut=m|move&gt;&gt;';
	return navlinkStringToHTML('if(talk){' +
				   '&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;new|shortcut=+|+&gt;&gt;*' + hist + '*' +
				   '&lt;&lt;article|shortcut=a&gt;&gt;|&lt;&lt;editArticle|edit&gt;&gt;' + '*' + watch + '*' + move +
				   '}else{&lt;&lt;edit|shortcut=e&gt;&gt;*' + hist +
				   '*&lt;&lt;talk|shortcut=t|&gt;&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;' +
				   '*' + watch + '*' + move+'}&lt;br&gt;', x.article, x.params);
};
pg.structures.fancy.popupOtherLinks=function(x) {
	var admin='&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d|del&gt;&gt;';
	var user='&lt;&lt;contribs|shortcut=c&gt;&gt;if(wikimedia){|&lt;&lt;count|shortcut=#|#&gt;&gt;}';
	user+='if(ipuser){|&lt;&lt;arin&gt;&gt;}else{*&lt;&lt;email|shortcut=E|'+
	popupString('email')+'&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}';

	var normal='&lt;&lt;whatLinksHere|shortcut=l|links here&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r|related&gt;&gt;';
	return navlinkStringToHTML('&lt;br&gt;if(user){' + user + '*}if(admin){'+admin+'if(user){&lt;br&gt;}else{*}}' + normal,
				   x.article, x.params);
};
pg.structures.fancy.popupRedirTitle=pg.structures.fancy.popupTitle;
pg.structures.fancy.popupRedirTopLinks=pg.structures.fancy.popupTopLinks;
pg.structures.fancy.popupRedirOtherLinks=pg.structures.fancy.popupOtherLinks;


/** -- fancy2 -- **/
// hack for [[User:MacGyverMagic]]
copyStructure('fancy', 'fancy2');
pg.structures.fancy2.popupTopLinks=function(x) { // hack out the &lt;br&gt; at the end and put one at the beginning
	return '&lt;br&gt;'+pg.structures.fancy.popupTopLinks(x).replace(RegExp('&lt;br&gt;$','i'),'');
};
pg.structures.fancy2.popupLayout=function () { // move toplinks to after the title
	return ['popupError', 'popupImage', 'popupTitle', 'popupData', 'popupTopLinks', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};

/** -- menus -- **/
copyStructure('original', 'menus');
pg.structures.menus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
function toggleSticky(uid) {
	var popDiv=document.getElementById('navpopup_maindiv'+uid);
	if (!popDiv) { return; }
	if (!popDiv.navpopup.sticky) { popDiv.navpopup.stick(); }
	else {
		popDiv.navpopup.unstick();
		popDiv.navpopup.hide();
	}
}
pg.structures.menus.popupTopLinks = function (x, shorter) {
	// FIXME maybe this stuff should be cached
	var s=[];
	var dropdiv='&lt;div class=&quot;popup_drop&quot;&gt;';
	var enddiv='&lt;/div&gt;';
	var endspan='&lt;/span&gt;';
	var hist='&lt;&lt;history|shortcut=h&gt;&gt;';
	if (!shorter) { hist = '&lt;menurow&gt;' + hist +
			'|&lt;&lt;historyfeed|rss&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E&gt;&gt;}&lt;/menurow&gt;'; }
	var lastedit='&lt;&lt;lastEdit|shortcut=/|show last edit&gt;&gt;';
	var jsHistory='&lt;&lt;lastContrib|last set of edits&gt;&gt;&lt;&lt;sinceMe|changes since mine&gt;&gt;';
	var linkshere='&lt;&lt;whatLinksHere|shortcut=l|what links here&gt;&gt;';
	var related='&lt;&lt;relatedChanges|shortcut=r|related changes&gt;&gt;';
	var search='&lt;menurow&gt;&lt;&lt;search|shortcut=s&gt;&gt;if(wikimedia){|&lt;&lt;globalsearch|shortcut=g|global&gt;&gt;}' +
	'|&lt;&lt;google|shortcut=G|web&gt;&gt;&lt;/menurow&gt;';
	var watch='&lt;menurow&gt;&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;&lt;/menurow&gt;';
	var protect='&lt;menurow&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|' +
	'&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;&lt;/menurow&gt;';
	var del='&lt;menurow&gt;&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|' +
	'&lt;&lt;deletelog|log&gt;&gt;&lt;/menurow&gt;';
	var move='&lt;&lt;move|shortcut=m|move page&gt;&gt;';
	var nullPurge='&lt;menurow&gt;&lt;&lt;nullEdit|shortcut=n|null edit&gt;&gt;|&lt;&lt;purge|shortcut=P&gt;&gt;&lt;/menurow&gt;';
	var viewOptions='&lt;menurow&gt;&lt;&lt;view|shortcut=v&gt;&gt;|&lt;&lt;render|shortcut=S&gt;&gt;|&lt;&lt;raw&gt;&gt;&lt;/menurow&gt;';
	var editRow='if(oldid){' +
	'&lt;menurow&gt;&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;editOld|shortcut=e|this&amp;nbsp;revision&gt;&gt;&lt;/menurow&gt;' +
	'&lt;menurow&gt;&lt;&lt;revert|shortcut=v&gt;&gt;|&lt;&lt;undo&gt;&gt;&lt;/menurow&gt;' + '}else{&lt;&lt;edit|shortcut=e&gt;&gt;}';
	var markPatrolled='if(rcid){&lt;&lt;markpatrolled|mark patrolled&gt;&gt;}';
	var newTopic='if(talk){&lt;&lt;new|shortcut=+|new topic&gt;&gt;}';
	var protectDelete='if(admin){' + protect + del + '}';

	if (getValueOf('popupActionsMenu')) {
		s.push( '&lt;&lt;mainlink&gt;&gt;*' + dropdiv + menuTitle('actions'));
	} else {
		s.push( dropdiv + '&lt;&lt;mainlink&gt;&gt;');
	}
	s.push( '&lt;menu&gt;')
	s.push( editRow + markPatrolled + newTopic + hist + lastedit )
	if (!shorter) { s.push(jsHistory); }
	s.push( move + linkshere + related)
	if (!shorter) { s.push(nullPurge + search); }
	if (!shorter) { s.push(viewOptions); }
	s.push('&lt;hr&gt;' + watch + protectDelete);
	s.push('&lt;hr&gt;' +
	       'if(talk){&lt;&lt;article|shortcut=a|view article&gt;&gt;&lt;&lt;editArticle|edit article&gt;&gt;}' +
	       'else{&lt;&lt;talk|shortcut=t|talk page&gt;&gt;&lt;&lt;editTalk|edit talk&gt;&gt;' +
	       '&lt;&lt;newTalk|shortcut=+|new topic&gt;&gt;}&lt;/menu&gt;' + enddiv);

	// user menu starts here
	var email='&lt;&lt;email|shortcut=E|email user&gt;&gt;';
	var contribs=	'if(wikimedia){&lt;menurow&gt;}&lt;&lt;contribs|shortcut=c|contributions&gt;&gt;if(wikimedia){&lt;/menurow&gt;}' +
	'if(admin){&lt;menurow&gt;&lt;&lt;deletedContribs&gt;&gt;&lt;/menurow&gt;}';


	s.push('if(user){*' + dropdiv + menuTitle('user'));
	s.push('&lt;menu&gt;'); +
	s.push('&lt;menurow&gt;&lt;&lt;userPage|shortcut=u|user&amp;nbsp;page&gt;&gt;|&lt;&lt;userSpace|space&gt;&gt;&lt;/menurow&gt;');
	s.push('&lt;&lt;userTalk|shortcut=t|user talk&gt;&gt;&lt;&lt;editUserTalk|edit user talk&gt;&gt;' +
	       '&lt;&lt;newUserTalk|shortcut=+|leave comment&gt;&gt;');
	if(!shorter) { s.push( 'if(ipuser){&lt;&lt;arin&gt;&gt;}else{' + email + '}') }
	else { s.push( 'if(ipuser){}else{' + email + '}') }
	s.push('&lt;hr&gt;' + contribs + '&lt;&lt;userlog|shortcut=L|user log&gt;&gt;');
	s.push('if(wikimedia){&lt;&lt;count|shortcut=#|edit counter&gt;&gt;}');
	s.push('if(admin){&lt;menurow&gt;&lt;&lt;unblock|unblockShort&gt;&gt;|&lt;&lt;block|shortcut=b|block user&gt;&gt;&lt;/menurow&gt;}');
	s.push('&lt;&lt;blocklog|shortcut=B|block log&gt;&gt;' + getValueOf('popupExtraUserMenu'));
	s.push('&lt;/menu&gt;'  + enddiv + '}');

	// popups menu starts here
	if (getValueOf('popupSetupMenu') &amp;&amp; !x.navpop.hasPopupMenu /* FIXME: hack */) {
		x.navpop.hasPopupMenu=true;
		s.push('*' + dropdiv + menuTitle('popupsMenu') + '&lt;menu&gt;');
		s.push('&lt;&lt;togglePreviews|toggle previews&gt;&gt;');
		s.push('&lt;&lt;purgePopups|reset&gt;&gt;');
		s.push('&lt;&lt;disablePopups|disable&gt;&gt;');
		s.push('&lt;/menu&gt;'+enddiv);
	}
	return navlinkStringToHTML(s.join(''), x.article, x.params);
};

function menuTitle(s) {
	return '&lt;a href=&quot;#&quot; noPopup=1&gt;' + popupString(s) + '&lt;/a&gt;';
}

pg.structures.menus.popupRedirTitle=pg.structures.menus.popupTitle;
pg.structures.menus.popupRedirTopLinks=pg.structures.menus.popupTopLinks;

copyStructure('menus', 'shortmenus');
pg.structures.shortmenus.popupTopLinks=function(x) {
	return pg.structures.menus.popupTopLinks(x,true);
};
pg.structures.shortmenus.popupRedirTopLinks=pg.structures.shortmenus.popupTopLinks;

copyStructure('shortmenus', 'dabshortmenus');
pg.structures.dabshortmenus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'], 'popupFixDab',
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview'];
};

copyStructure('menus', 'dabmenus');
pg.structures.dabmenus.popupLayout=pg.structures.dabshortmenus.popupLayout;


//&lt;/NOLITE&gt;
pg.structures.lite={};
pg.structures.lite.popupLayout=function () {
	return ['popupTitle', 'popupPreview' ];
};
pg.structures.lite.popupTitle=function (x) {
	log (x.article + ': structures.lite.popupTitle');
	//return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	return '&lt;div&gt;&lt;span class=&quot;popup_mainlink&quot;&gt;&lt;b&gt;' + x.article.toString() + '&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;';
};
// ENDFILE: structures.js
// STARTFILE: autoedit.js
//&lt;NOLITE&gt;
function getParamValue(paramName, h) {
	if (typeof h == 'undefined' ) { h = document.location.href; }
	var cmdRe=RegExp('[&amp;?]'+paramName+'=([^&amp;]*)');
	var m=cmdRe.exec(h);
	if (m) {
		try {
			return decodeURIComponent(m[1]);
		} catch (someError) {}
	}
	return null;
}

function substitute(data,cmdBody) {
	// alert('sub\nfrom: '+cmdBody.from+'\nto: '+cmdBody.to+'\nflags: '+cmdBody.flags);
	var fromRe=RegExp(cmdBody.from, cmdBody.flags);
	return data.replace(fromRe, cmdBody.to);
}

function execCmds(data, cmdList) {
	for (var i=0; i&lt;cmdList.length; ++i) {
		data=cmdList[i].action(data, cmdList[i]);
	}
	return data;
}

function parseCmd(str) {
	// returns a list of commands
	if (!str.length) { return []; }
	var p=false;
	switch (str[0]) {
	case 's':
		p=parseSubstitute(str);
		break;
	default:
		return false;
	}
	if (p) { return [p].concat(parseCmd(p.remainder)); }
	return false;
}

function unEscape(str, sep) {
	return str.split('\\\\').join('\\').split('\\'+sep).join(sep).split('\\n').join('\n');
}


function parseSubstitute(str) {
	// takes a string like s/a/b/flags;othercmds and parses it

	var from,to,flags,tmp;

	if (str.length&lt;4) { return false; }
	var sep=str.charAt(1);
	str=str.substring(2);

	tmp=skipOver(str,sep);
	if (tmp) { from=tmp.segment; str=tmp.remainder; }
	else { return false; }

	tmp=skipOver(str,sep);
	if (tmp) { to=tmp.segment; str=tmp.remainder; }
	else { return false; }

	flags='';
	if (str.length) {
		tmp=skipOver(str,';') || skipToEnd(str, ';');
		if (tmp) {flags=tmp.segment; str=tmp.remainder; }
	}

	return {action: substitute, from: from, to: to, flags: flags, remainder: str};

}

function skipOver(str,sep) {
	var endSegment=findNext(str,sep);
	if (endSegment&lt;0) { return false; }
	var segment=unEscape(str.substring(0,endSegment), sep);
	return {segment: segment, remainder: str.substring(endSegment+1)};
}

function skipToEnd(str,sep) {
	return {segment: str, remainder: ''};
}

function findNext(str, ch) {
	for (var i=0; i&lt;str.length; ++i) {
		if (str.charAt(i)=='\\') { i+=2; }
		if (str.charAt(i)==ch) { return i; }
	}
	return -1;
}

function setCheckbox(param, box) {
	var val=getParamValue(param);
	if (val!==null) {
		switch (val) {
		case '1': case 'yes': case 'true':
			box.checked=true;
			break;
		case '0': case 'no':  case 'false':
			box.checked=false;
		}
	}
}

function autoEdit() {
	if (!setupPopups.completed) { setupPopups(); }
	if (!document.editform) { return false; }
	if (window.autoEdit.alreadyRan) { return false; }
	window.autoEdit.alreadyRan=true;
	var cmdString=getParamValue('autoedit');
	if (cmdString) {
		try {
			var editbox=document.editform.wpTextbox1;
		} catch (dang) { return; }
		var cmdList=parseCmd(cmdString);
		var input=editbox.value;
		var output=execCmds(input, cmdList);
		editbox.value=output;
		// wikEd user script compatibility
		if (typeof(wikEdUseWikEd) != 'undefined') {
			if (wikEdUseWikEd == true) {
				WikEdUpdateFrame();
			}
		}
	}
	setCheckbox('autominor', document.editform.wpMinoredit);
	setCheckbox('autowatch', document.editform.wpWatchthis);

	var rvid = getParamValue('autorv');
	if (rvid) {
		var url=pg.wiki.apiwikibase + '?action=query&amp;format=json&amp;prop=revisions&amp;revids='+rvid;
		startDownload(url, null, autoEdit2);
	} else { autoEdit2(); }
}

function autoEdit2(d) {
	var summary=getParamValue('autosummary');
	var summaryprompt=getParamValue('autosummaryprompt');
	var summarynotice='';
	if (d &amp;&amp; d.data &amp;&amp; getParamValue('autorv')) {
		var s = getRvSummary(summary, d.data);
		if (s===false) {
			summaryprompt=true;
			summarynotice=popupString('Failed to get revision information, please edit manually.\n\n');
			summary = simplePrintf(summary, [getParamValue('autorv'), '(unknown)', '(unknown)']);
		} else { summary = s; }
	}
	if (summaryprompt) {
		var txt= summarynotice +
			popupString('Enter a non-empty edit summary or press cancel to abort');
		var response=prompt(txt, summary);
		if (response) { summary=response; }
		else { return; }
	}
	if (summary) { document.editform.wpSummary.value=summary; }
	// Attempt to avoid possible premature clicking of the save button
	// (maybe delays in updates to the DOM are to blame?? or a red herring)
	setTimeout(autoEdit3, 100);
}

function autoClickToken() {
    return mw.user.sessionId();
}

function autoEdit3() {
    if( getParamValue('actoken') != autoClickToken()) return;

	var btn=getParamValue('autoclick');
	if (btn) {
		if (document.editform &amp;&amp; document.editform[btn]) {
			var button=document.editform[btn];
			var msg=tprintf('The %s button has been automatically clicked. Please wait for the next page to load.',
					[ button.value ]);
			bannerMessage(msg);
			document.title='('+document.title+')';
			button.click();
		} else {
			alert(tprintf('Could not find button %s. Please check the settings in your javascript file.',
				      [ btn ]));
		}
	}
}

function bannerMessage(s) {
	var headings=document.getElementsByTagName('h1');
	if (headings) {
		var div=document.createElement('div');
		div.innerHTML='&lt;font size=+1&gt;&lt;b&gt;' + s + '&lt;/b&gt;&lt;/font&gt;';
		headings[0].parentNode.insertBefore(div, headings[0]);
	}
}

function getRvSummary(template, json) {
	try {
	    var o=getJsObj(json);
	    var edit = anyChild(o.query.pages).revisions[0];
	} catch (badness) {return false;}
	var timestamp = edit.timestamp.split(/[A-Z]/g).join(' ').replace(/^ *| *$/g, '');
	return simplePrintf(template, [edit.revid, timestamp, edit.userhidden === undefined ? edit.user : '(hidden)']);
}

//&lt;/NOLITE&gt;
// ENDFILE: autoedit.js
// STARTFILE: downloader.js
/**
   @fileoverview
   {@link Downloader}, a xmlhttprequest wrapper, and helper functions.
*/

/**
   Creates a new Downloader
   @constructor
   @class The Downloader class. Create a new instance of this class to download stuff.
   @param {String} url The url to download. This can be omitted and supplied later.
*/
function Downloader(url) {
	// Source: http://jibbering.com/2002/4/httprequest.html
	/** xmlhttprequest object which we're wrapping */
	this.http = false;

	/*@cc_on @*/
	/*@if (@_jscript_version &gt;= 5)
	// JScript gives us Conditional compilation,
	// we can cope with old IE versions.
	// and security blocked creation of the objects.
	try {
	this.http = new ActiveXObject(&quot;Msxml2.XMLHTTP&quot;);
	} catch (e) {
	try {
	this.http = new ActiveXObject(&quot;Microsoft.XMLHTTP&quot;);
	} catch (E) {
	// this.http = false;
	}
	}
	@end @*/

	if (! this.http &amp;&amp; typeof XMLHttpRequest!='undefined') { this.http = new XMLHttpRequest(); }
	/**
	    The url to download
	    @type String
	*/
	this.url = url;
	/**
	    A universally unique ID number
	    @type integer
	*/
	this.id=null;
	/**
	    Modification date, to be culled from the incoming headers
	    @type Date
	    @private
	*/
	this.lastModified = null;
	/**
	    What to do when the download completes successfully
	    @type Function
	    @private
	*/
	this.callbackFunction = null;
	/**
	    What to do on failure
	    @type Function
	    @private
	*/
	this.onFailure = null;
	/**
	    Flag set on &lt;code&gt;abort&lt;/code&gt;
	    @type boolean
	*/
	this.aborted = false;
	/**
	   HTTP method. See http://www.w3.org/Protocols/rfc2616/rfc2616-sec9.html for possibilities.
	   @type String
	*/
	this.method='GET';
	/**
	    Async flag.
	    @type boolean
	*/
	this.async=true;
}

new Downloader();

/** Submits the http request. */
Downloader.prototype.send = function (x) {
	if (!this.http) { return null; }
	return this.http.send(x);
};
/** Aborts the download, setting the &lt;code&gt;aborted&lt;/code&gt; field to true.  */
Downloader.prototype.abort = function () {
	if (!this.http) { return null; }
	this.aborted=true;
	return this.http.abort();
};
/** Returns the downloaded data. */
Downloader.prototype.getData = function () {if (!this.http) { return null; } return this.http.responseText;};
/** Prepares the download. */
Downloader.prototype.setTarget = function () {
	if (!this.http) { return null; }
	this.http.open(this.method, this.url, this.async);
};
/** Gets the state of the download. */
Downloader.prototype.getReadyState=function () {if (!this.http) { return null; } return this.http.readyState;};

pg.misc.downloadsInProgress = { };

/** Starts the download.
    Note that setTarget {@link Downloader#setTarget} must be run first
*/
Downloader.prototype.start=function () {
	if (!this.http) { return; }
	pg.misc.downloadsInProgress[this.id] = this;
	this.http.send(null);
};

/** Gets the 'Last-Modified' date from the download headers.
    Should be run after the download completes.
    Returns &lt;code&gt;null&lt;/code&gt; on failure.
    @return {Date}
*/
Downloader.prototype.getLastModifiedDate=function () {
	if(!this.http) { return null; }
	var lastmod=null;
	try {
		lastmod=this.http.getResponseHeader('Last-Modified');
	} catch (err) {}
	if (lastmod) { return new Date(lastmod); }
	return null;
};

/** Sets the callback function.
    @param {Function} f callback function, called as &lt;code&gt;f(this)&lt;/code&gt; on success
*/
Downloader.prototype.setCallback = function (f) {
	if(!this.http) { return; }
	this.http.onreadystatechange = f;
};

Downloader.prototype.getStatus = function() { if (!this.http) { return null; } return this.http.status; };

//////////////////////////////////////////////////
// helper functions

/** Creates a new {@link Downloader} and prepares it for action.
    @param {String} url The url to download
    @param {integer} id The ID of the {@link Downloader} object
    @param {Function} callback The callback function invoked on success
    @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function newDownload(url, id, callback, onfailure) {
	var d=new Downloader(url);
	if (!d.http) { return 'ohdear'; }
	d.id=id;
	d.setTarget();
	if (!onfailure) {
		onfailure=2;
	}
	var f = function () {
		if (d.getReadyState() == 4) {
			delete pg.misc.downloadsInProgress[this.id];
			try {
				if ( d.getStatus() == 200 ) {
					d.data=d.getData();
					d.lastModified=d.getLastModifiedDate();
					callback(d);
				} else if (typeof onfailure == typeof 1) {
					if (onfailure &gt; 0) {
						// retry
						newDownload(url, id, callback, onfailure - 1);
					}
				} else if (typeof onfailure == 'function') {
					onfailure(d,url,id,callback);
				}
			} catch (somerr) { /* ignore it */ }
		}
	};
	d.setCallback(f);
	return d;
}
/** Simulates a download from cached data.
    The supplied data is put into a {@link Downloader} as if it had downloaded it.
    @param {String} url The url.
    @param {integer} id The ID.
    @param {Function} callback The callback, which is invoked immediately as &lt;code&gt;callback(d)&lt;/code&gt;,
    where &lt;code&gt;d&lt;/code&gt; is the new {@link Downloader}.
    @param {String} data The (cached) data.
    @param {Date} lastModified The (cached) last modified date.
*/
function fakeDownload(url, id, callback, data, lastModified, owner) {
	var d=newDownload(url,callback);
	d.owner=owner;
	d.id=id; d.data=data;
	d.lastModified=lastModified;
	return callback(d);
}

/**
   Starts a download.
   @param {String} url The url to download
   @param {integer} id The ID of the {@link Downloader} object
   @param {Function} callback The callback function invoked on success
   @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function startDownload(url, id, callback) {
	var d=newDownload(url, id, callback);
	if (typeof d == typeof '' ) { return d; }
	d.start();
	return d;
}

/**
   Aborts all downloads which have been started.
*/
function abortAllDownloads() {
	for ( var x in pg.misc.downloadsInProgress ) {
		try {
			pg.misc.downloadsInProgress[x].aborted=true;
			pg.misc.downloadsInProgress[x].abort();
			delete pg.misc.downloadsInProgress[x];
		} catch (e) { }
	}
}
// ENDFILE: downloader.js
// STARTFILE: livepreview.js
// TODO: location is often not correct (eg relative links in previews)

/**
 * InstaView - a Mediawiki to HTML converter in JavaScript
 * Version 0.6.1
 * Copyright (C) Pedro Fayolle 2005-2006
 * //en.wikipedia.org/wiki/User:Pilaf
 * Distributed under the BSD license
 *
 * Changelog:
 *
 * 0.6.1
 * - Fixed problem caused by \r characters
 * - Improved inline formatting parser
 *
 * 0.6
 * - Changed name to InstaView
 * - Some major code reorganizations and factored out some common functions
 * - Handled conversion of relative links (i.e. [[/foo]])
 * - Fixed misrendering of adjacent definition list items
 * - Fixed bug in table headings handling
 * - Changed date format in signatures to reflect Mediawiki's
 * - Fixed handling of [[:Image:...]]
 * - Updated MD5 function (hopefully it will work with UTF-8)
 * - Fixed bug in handling of links inside images
 *
 * To do:
 * - Better support for &lt;math&gt;
 * - Full support for &lt;nowiki&gt;
 * - Parser-based (as opposed to RegExp-based) inline wikicode handling (make it one-pass and bullet-proof)
 * - Support for templates (through AJAX)
 * - Support for coloured links (AJAX)
 */


var Insta = {}

function setupLivePreview() {

    // options
    Insta.conf =
	{
	    baseUrl: '',

	    user: {},

	    wiki: {
		lang: pg.wiki.lang,
		interwiki: pg.wiki.interwiki,
		default_thumb_width: 180
	    },

	    paths: {
		articles: pg.wiki.articlePath + '/',
		// Only used for Insta previews with images. (not in popups)
		math: '/math/',
		images: '//upload.wikimedia.org/wikiversity/en/', // FIXME ( window.getImageUrlStart ? getImageUrlStart(pg.wiki.hostname) : ''),
		images_fallback: '//upload.wikimedia.org/wikipedia/commons/',
		magnify_icon: 'skins/common/images/magnify-clip.png'
	    },

	    locale: {
		user: mw.config.get('wgFormattedNamespaces')[pg.nsUserId],
		image: mw.config.get('wgFormattedNamespaces')[pg.nsImageId],
		category: mw.config.get('wgFormattedNamespaces')[pg.nsCategoryId],
		// shouldn't be used in popup previews, i think
		months: ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec']
	    }
	}

    // options with default values or backreferences
    with (Insta.conf) {
	user.name = user.name || 'Wikiversity participant'
	user.signature = '[['+locale.user+':'+user.name+'|'+user.name+']]'
    }

    // define constants
    Insta.BLOCK_IMAGE = new RegExp('^\\[\\[(?:File|Image|'+Insta.conf.locale.image+
				       '):.*?\\|.*?(?:frame|thumbnail|thumb|none|right|left|center)', 'i');

}


Insta.dump = function(from, to)
{
	if (typeof from == 'string') from = document.getElementById(from)
	if (typeof to == 'string') to = document.getElementById(to)
	to.innerHTML = this.convert(from.value)
}

Insta.convert = function(wiki)
{
	var	ll = (typeof wiki == 'string')? wiki.replace(/\r/g,'').split(/\n/): wiki, // lines of wikicode
		o='',	// output
		p=0,	// para flag
		$r	// result of passing a regexp to $()

	// some shorthands
	function remain() { return ll.length }
	function sh() { return ll.shift() } // shift
	function ps(s) { o+=s } // push

	function f() // similar to C's printf, uses ? as placeholders, ?? to escape question marks
	{
		var i=1,a=arguments,f=a[0],o='',c,p
		for (;i&lt;a.length; i++) if ((p=f.indexOf('?'))+1) {
			// allow character escaping
			i -= c=f.charAt(p+1)=='?'?1:0
			o += f.substring(0,p)+(c?'?':a[i])
			f=f.substr(p+1+c)
		} else break;
		return o+f
	}

	function html_entities(s) { return s.replace(/&amp;/g,&quot;&amp;amp;&quot;).replace(/&lt;/g,&quot;&amp;lt;&quot;).replace(/&gt;/g,&quot;&amp;gt;&quot;) }

	function max(a,b) { return (a&gt;b)?a:b }
	function min(a,b) { return (a&lt;b)?a:b }

	// return the first non matching character position between two strings
	function str_imatch(a, b)
	{
		for (var i=0, l=min(a.length, b.length); i&lt;l; i++) if (a.charAt(i)!=b.charAt(i)) break
		return i
	}

	// compare current line against a string or regexp
	// if passed a string it will compare only the first string.length characters
	// if passed a regexp the result is stored in $r
	function $(c) { return (typeof c == 'string') ? (ll[0].substr(0,c.length)==c) : ($r = ll[0].match(c)) }

	function $$(c) { return ll[0]==c } // compare current line against a string
	function _(p) { return ll[0].charAt(p) } // return char at pos p

	function endl(s) { ps(s); sh() }

	function parse_list()
	{
		var prev='';

		while (remain() &amp;&amp; $(/^([*#:;]+)(.*)$/)) {

			var l_match = $r

			sh()

			var ipos = str_imatch(prev, l_match[1])

			// close uncontinued lists
			for (var i=prev.length-1; i &gt;= ipos; i--) {

				var pi = prev.charAt(i)

				if (pi=='*') ps('&lt;/ul&gt;')
				else if (pi=='#') ps('&lt;/ol&gt;')
				// close a dl only if the new item is not a dl item (:, ; or empty)
				else switch (l_match[1].charAt(i)) { case'':case'*':case'#': ps('&lt;/dl&gt;') }
			}

			// open new lists
			for (var i=ipos; i&lt;l_match[1].length; i++) {

				var li = l_match[1].charAt(i)

				if (li=='*') ps('&lt;ul&gt;')
				else if (li=='#') ps('&lt;ol&gt;')
				// open a new dl only if the prev item is not a dl item (:, ; or empty)
				else switch(prev.charAt(i)) { case'':case'*':case'#': ps('&lt;dl&gt;') }
			}

			switch (l_match[1].charAt(l_match[1].length-1)) {

				case '*': case '#':
					ps('&lt;li&gt;' + parse_inline_nowiki(l_match[2])); break

				case ';':
					ps('&lt;dt&gt;')

					var dt_match

					// handle ;dt :dd format
					if (dt_match = l_match[2].match(/(.*?)(:.*?)$/)) {

						ps(parse_inline_nowiki(dt_match[1]))
						ll.unshift(dt_match[2])

					} else ps(parse_inline_nowiki(l_match[2]))

					break

				case ':':
					ps('&lt;dd&gt;' + parse_inline_nowiki(l_match[2]))
			}

			prev=l_match[1]
		}

		// close remaining lists
		for (var i=prev.length-1; i&gt;=0; i--)
			ps(f('&lt;/?&gt;', (prev.charAt(i)=='*')? 'ul': ((prev.charAt(i)=='#')? 'ol': 'dl')))
	}

	function parse_table()
	{
		endl(f('&lt;table?&gt;', $(/^\{\|( .*)$/)? $r[1]: ''))

		for (;remain();) if ($('|')) switch (_(1)) {
			case '}': endl('&lt;/table&gt;'); return
			case '-': endl(f('&lt;tr ?&gt;', $(/\|-*(.*)/)[1])); break
			default: parse_table_data()
		}
		else if ($('!')) parse_table_data()
		else sh()
	}

	function parse_table_data()
	{
		var td_line, match_i

		// 1: &quot;|+&quot;, '|' or '+'
		// 2: ??
		// 3: attributes ??
		// TODO: finish commenting this regexp
		var td_match = sh().match(/^(\|\+|\||!)((?:([^[|]*?)\|(?!\|))?(.*))$/)

		if (td_match[1] == '|+') ps('&lt;caption');
		else ps('&lt;t' + ((td_match[1]=='|')?'d':'h'))

		if (typeof td_match[3] != 'undefined') {

			ps(' ' + td_match[3])
			match_i = 4

		} else match_i = 2

		ps('&gt;')

		if (td_match[1] != '|+') {

			// use || or !! as a cell separator depending on context
			// NOTE: when split() is passed a regexp make sure to use non-capturing brackets
			td_line = td_match[match_i].split((td_match[1] == '|')? '||': /(?:\|\||!!)/)

			ps(parse_inline_nowiki(td_line.shift()))

			while (td_line.length) ll.unshift(td_match[1] + td_line.pop())

		} else ps(td_match[match_i])

		var tc = 0, td = []

		for (;remain(); td.push(sh()))
		if ($('|')) {
			if (!tc) break // we're at the outer-most level (no nested tables), skip to td parse
			else if (_(1)=='}') tc--
		}
		else if (!tc &amp;&amp; $('!')) break
		else if ($('{|')) tc++

		if (td.length) ps(Insta.convert(td))
	}

	function parse_pre()
	{
		ps('&lt;pre&gt;')
		do endl(parse_inline_nowiki(ll[0].substring(1)) + &quot;\n&quot;); while (remain() &amp;&amp; $(' '))
		ps('&lt;/pre&gt;')
	}

	function parse_block_image()
	{
		ps(parse_image(sh()))
	}

	function parse_image(str)
	{
//&lt;NOLITE&gt;
		// get what's in between &quot;[[Image:&quot; and &quot;]]&quot;
		var tag = str.substring(str.indexOf(':') + 1, str.length - 2);

		var width;
		var attr = [], filename, caption = '';
		var thumb=0, frame=0, center=0;
		var align='';

		if (tag.match(/\|/)) {
			// manage nested links
			var nesting = 0;
			var last_attr;
			for (var i = tag.length-1; i &gt; 0; i--) {
				if (tag.charAt(i) == '|' &amp;&amp; !nesting) {
					last_attr = tag.substr(i+1);
					tag = tag.substring(0, i);
					break;
				} else switch (tag.substr(i-1, 2)) {
					case ']]':
						nesting++;
						i--;
						break;
					case '[[':
						nesting--;
						i--;
				}
			}

			attr = tag.split(/\s*\|\s*/);
			attr.push(last_attr);
			filename = attr.shift();

			var w_match;

			for (;attr.length; attr.shift())
			if (w_match = attr[0].match(/^(\d*)(?:[px]*\d*)?px$/)) width = w_match[1]
			else switch(attr[0]) {
				case 'thumb':
				case 'thumbnail':
					thumb=true;
				case 'frame':
					frame=true;
					break;
				case 'none':
				case 'right':
				case 'left':
					center=false;
					align=attr[0];
					break;
				case 'center':
					center=true;
					align='none';
					break;
				default:
					if (attr.length == 1) caption = attr[0];
			}

		} else filename = tag;


		var o='';

		if (frame) {

			if (align=='') align = 'right';

			o += f(&quot;&lt;div class='thumb t?'&gt;&quot;, align);

			if (thumb) {
				if (!width) width = Insta.conf.wiki.default_thumb_width;

				o += f(&quot;&lt;div style='width:?px;'&gt;?&quot;, 2+width*1, make_image(filename, caption, width)) +
					f(&quot;&lt;div class='thumbcaption'&gt;&lt;div class='magnify' style='float:right'&gt;&lt;a href='?' class='internal' title='Enlarge'&gt;&lt;img src='?'&gt;&lt;/a&gt;&lt;/div&gt;?&lt;/div&gt;&quot;,
						Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename,
						Insta.conf.paths.magnify_icon,
						parse_inline_nowiki(caption)
					)
			} else {
				o += '&lt;div&gt;' + make_image(filename, caption) + f(&quot;&lt;div class='thumbcaption'&gt;?&lt;/div&gt;&quot;, parse_inline_nowiki(caption))
			}

			o += '&lt;/div&gt;&lt;/div&gt;';

		} else if (align != '') {
			o += f(&quot;&lt;div class='float?'&gt;&lt;span&gt;?&lt;/span&gt;&lt;/div&gt;&quot;, align, make_image(filename, caption, width));
		} else {
			return make_image(filename, caption, width);
		}

		return center? f(&quot;&lt;div class='center'&gt;?&lt;/div&gt;&quot;, o): o;
//&lt;/NOLITE&gt;
	}

	function parse_inline_nowiki(str)
	{
		var start, lastend=0
		var substart=0, nestlev=0, open, close, subloop;
		var html='';

		while (-1 != (start = str.indexOf('&lt;nowiki&gt;', substart))) {
			html += parse_inline_wiki(str.substring(lastend, start));
			start += 8;
			substart = start;
			subloop = true;
			do {
				open = str.indexOf('&lt;nowiki&gt;', substart);
				close = str.indexOf('&lt;/nowiki&gt;', substart);
				// &lt;/nowiki&gt;
				if (close&lt;=open || open==-1) {
					if (close==-1) {
						return html + html_entities(str.substr(start));
					}
					substart = close+9;
					if (nestlev) {
						nestlev--;
					} else {
						lastend = substart;
						html += html_entities(str.substring(start, lastend-9));
						subloop = false;
					}
				} else {
					substart = open+8;
					nestlev++;
				}
			} while (subloop)
		}

		return html + parse_inline_wiki(str.substr(lastend));
	}

	function make_image(filename, caption, width)
	{
//&lt;NOLITE&gt;
		// uppercase first letter in file name
		filename = filename[0].toUpperCase() + filename.substr(1);
		// replace spaces with underscores
		filename = filename.replace(/ /g, '_');

		caption = strip_inline_wiki(caption);

		var md5 = hex_md5(filename);

		var source = md5[0] + '/' + md5.substr(0,2) + '/' + filename;

		if (width) width = &quot;width='&quot; + width + &quot;px'&quot;;

		var img = f(&quot;&lt;img onerror=\&quot;this.onerror=null;this.src='?'\&quot; src='?' ? ?&gt;&quot;, Insta.conf.paths.images_fallback + source, Insta.conf.paths.images + source, (caption!='')? &quot;alt='&quot; + caption + &quot;'&quot; : '', width);

		return f(&quot;&lt;a class='image' ? href='?'&gt;?&lt;/a&gt;&quot;, (caption!='')? &quot;title='&quot; + caption + &quot;'&quot; : '', Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename, img);
//&lt;/NOLITE&gt;
	}

	function parse_inline_images(str)
	{
//&lt;NOLITE&gt;
		var start, substart=0, nestlev=0;
		var loop, close, open, wiki, html;

		while (-1 != (start=str.indexOf('[[', substart))) {
			if(str.substr(start+2).match(RegExp('^(Image|File|' + Insta.conf.locale.image + '):','i'))) {
				loop=true;
				substart=start;
				do {
					substart+=2;
					close=str.indexOf(']]',substart);
					open=str.indexOf('[[',substart);
					if (close&lt;=open||open==-1) {
						if (close==-1) return str;
						substart=close;
						if (nestlev) {
							nestlev--;
						} else {
							wiki=str.substring(start,close+2);
							html=parse_image(wiki);
							str=str.replace(wiki,html);
							substart=start+html.length;
							loop=false;
						}
					} else {
						substart=open;
						nestlev++;
					}
				} while (loop)

			} else break;
		}

//&lt;/NOLITE&gt;
		return str;
	}

	// the output of this function doesn't respect the FILO structure of HTML
	// but since most browsers can handle it I'll save myself the hassle
	function parse_inline_formatting(str)
	{
		var em,st,i,li,o='';
		while ((i=str.indexOf(&quot;''&quot;,li))+1) {
			o += str.substring(li,i);
			li=i+2;
			if (str.charAt(i+2)==&quot;'&quot;) {
				li++;
				st=!st;
				o+=st?'&lt;strong&gt;':'&lt;/strong&gt;';
			} else {
				em=!em;
				o+=em?'&lt;em&gt;':'&lt;/em&gt;';
			}
		}
		return o+str.substr(li);
	}

	function parse_inline_wiki(str)
	{
		var aux_match;

		str = parse_inline_images(str);
		str = parse_inline_formatting(str);

		// math
		while (aux_match = str.match(/&lt;(?:)math&gt;(.*?)&lt;\/math&gt;/i)) {
			var math_md5 = hex_md5(aux_match[1]);
			str = str.replace(aux_match[0], f(&quot;&lt;img src='?.png'&gt;&quot;, Insta.conf.paths.math+math_md5));
		}

		// Build a Mediawiki-formatted date string
		var date = new Date;
		var minutes = date.getUTCMinutes();
		if (minutes &lt; 10) minutes = '0' + minutes;
		var date = f(&quot;?:?, ? ? ? (UTC)&quot;, date.getUTCHours(), minutes, date.getUTCDate(), Insta.conf.locale.months[date.getUTCMonth()], date.getUTCFullYear());

		// text formatting
		return str.
			// signatures
			replace(/~{5}(?!~)/g, date).
			replace(/~{4}(?!~)/g, Insta.conf.user.name+' '+date).
			replace(/~{3}(?!~)/g, Insta.conf.user.name).

			// [[:Category:...]], [[:Image:...]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):[^|]*?)\\]\\](\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$1$2&lt;/a&gt;&quot;).
			// remove straight category and interwiki tags
			replace(RegExp('\\[\\[(?:'+Insta.conf.locale.category+'|'+Insta.conf.wiki.interwiki+'):.*?\\]\\]','gi'),'').

			// [[:Category:...|Links]], [[:Image:...|Links]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):.*?)\\|([^\\]]+?)\\]\\](\\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$2$3&lt;/a&gt;&quot;).

			// [[/Relative links]]
			replace(/\[\[(\/[^|]*?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$1&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[/Replaced|Relative links]]
			replace(/\[\[(\/.*?)\|(.+?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$2&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[Common links]]
			replace(/\[\[([^|]*?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$1$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Replaced|Links]]
			replace(/\[\[(.*?)\|([^\]]+?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$2$3&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Stripped:Namespace|Namespace]]
			replace(/\[\[([^\]]*?:)?(.*?)( *\(.*?\))?\|\]\]/g, f(&quot;&lt;a href='?$1$2$3'&gt;$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// External links
			replace(/\[(https?|news|ftp|mailto|gopher|irc):(\/*)([^\]]*?) (.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$4&lt;/a&gt;&quot;).
			replace(/\[http:\/\/(.*?)\]/g, &quot;&lt;a class='external' href='http://$1'&gt;[#]&lt;/a&gt;&quot;).
			replace(/\[(news|ftp|mailto|gopher|irc):(\/*)(.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$1:$2$3&lt;/a&gt;&quot;).
			replace(/(^| )(https?|news|ftp|mailto|gopher|irc):(\/*)([^ $]*[^.,!?;: $])/g, &quot;$1&lt;a class='external' href='$2:$3$4'&gt;$2:$3$4&lt;/a&gt;&quot;).

			replace('__NOTOC__','').
			replace('__NOEDITSECTION__','');
	}
/*
*/
	function strip_inline_wiki(str)
	{
		return str
			.replace(/\[\[[^\]]*\|(.*?)\]\]/g,'$1')
			.replace(/\[\[(.*?)\]\]/g,'$1')
			.replace(/''(.*?)''/g,'$1');
	}

	// begin parsing
	for (;remain();) if ($(/^(={1,6})(.*)\1(.*)$/)) {
		p=0
		endl(f('&lt;h?&gt;?&lt;/h?&gt;?', $r[1].length, parse_inline_nowiki($r[2]), $r[1].length, $r[3]))

	} else if ($(/^[*#:;]/)) {
		p=0
		parse_list()

	} else if ($(' ')) {
		p=0
		parse_pre()

	} else if ($('{|')) {
		p=0
		parse_table()

	} else if ($(/^----+$/)) {
		p=0
		endl('&lt;hr&gt;')

	} else if ($(Insta.BLOCK_IMAGE)) {
		p=0
		parse_block_image()

	} else {

		// handle paragraphs
		if ($$('')) {
			if (p = (remain()&gt;1 &amp;&amp; ll[1]==(''))) endl('&lt;p&gt;&lt;br&gt;')
		} else {
			if(!p) {
				ps('&lt;p&gt;')
				p=1
			}
			ps(parse_inline_nowiki(ll[0]) + ' ')
		}

		sh();
	}

	return o
};

window.wiki2html=function(txt,baseurl) {
    Insta.conf.baseUrl=baseurl;
    return Insta.convert(txt);
};
// ENDFILE: livepreview.js
// STARTFILE: pageinfo.js
//&lt;NOLITE&gt;
function popupFilterPageSize(data) {
	return formatBytes(data.length);
}

function popupFilterCountLinks(data) {
	var num=countLinks(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('wikiLinks'):popupString('wikiLink'));
}

function popupFilterCountImages(data) {
	var num=countImages(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('images'):popupString('image'));
}

function popupFilterCountCategories(data) {
	var num=countCategories(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('categories'):popupString('category'));
}


function popupFilterLastModified(data,download) {
	var lastmod=download.lastModified;
	var now=new Date();
	var age=now-lastmod;
	if (lastmod &amp;&amp; getValueOf('popupLastModified')) {
		return (tprintf('%s old', [formatAge(age)])).replace(RegExp(' ','g'), '&amp;nbsp;');
	}
	return '';
}

function formatAge(age) {
	// coerce into a number
	var a=0+age, aa=a;

	var seclen  = 1000;
	var minlen  = 60*seclen;
	var hourlen = 60*minlen;
	var daylen  = 24*hourlen;
	var weeklen = 7*daylen;

	var numweeks = (a-a%weeklen)/weeklen; a = a-numweeks*weeklen; var sweeks = addunit(numweeks, 'week');
	var numdays  = (a-a%daylen)/daylen;   a = a-numdays*daylen;   var sdays  = addunit(numdays, 'day');
	var numhours = (a-a%hourlen)/hourlen; a = a-numhours*hourlen; var shours = addunit(numhours,'hour');
	var nummins  = (a-a%minlen)/minlen;   a = a-nummins*minlen;   var smins  = addunit(nummins, 'minute');
	var numsecs  = (a-a%seclen)/seclen;   a = a-numsecs*seclen;   var ssecs  = addunit(numsecs, 'second');

	if (aa &gt; 4*weeklen) { return sweeks; }
	if (aa &gt; weeklen)   { return sweeks + ' ' + sdays; }
	if (aa &gt; daylen)    { return sdays  + ' ' + shours; }
	if (aa &gt; 6*hourlen) { return shours; }
	if (aa &gt; hourlen)   { return shours + ' ' + smins; }
	if (aa &gt; 10*minlen) { return smins; }
	if (aa &gt; minlen)    { return smins  + ' ' + ssecs; }
	return ssecs;
}

function addunit(num,str) { return '' + num + ' ' + ((num!=1) ? popupString(str+'s') : popupString(str)) ;}

function runPopupFilters(list, data, download) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i] &amp;&amp; typeof list[i] == 'function') {
			var s=list[i](data, download, download.owner.article);
			if (s) { ret.push(s); }
		}
	}
	return ret;
}

function getPageInfo(data, download) {
	if (!data || data.length === 0) { return popupString('Empty page'); }

	var popupFilters=getValueOf('popupFilters') || [];
	var extraPopupFilters = getValueOf('extraPopupFilters') || [];
	var pageInfoArray = runPopupFilters(popupFilters.concat(extraPopupFilters), data, download);

	var pageInfo=pageInfoArray.join(', ');
	if (pageInfo !== '' ) { pageInfo = upcaseFirst(pageInfo); }
	return pageInfo;
}


// this could be improved!
function countLinks(wikiText) { return wikiText.split('[[').length - 1; }

// if N = # matches, n = # brackets, then
// String.parenSplit(regex) intersperses the N+1 split elements
// with Nn other elements. So total length is
// L= N+1 + Nn = N(n+1)+1. So N=(L-1)/(n+1).

function countImages(wikiText) {
	return (wikiText.parenSplit(pg.re.image).length - 1) / (pg.re.imageBracketCount + 1);
}

function countCategories(wikiText) {
	return (wikiText.parenSplit(pg.re.category).length - 1) / (pg.re.categoryBracketCount + 1);
}

function popupFilterStubDetect(data, download, article)     {
	var counts=stubCount(data, article);
	if (counts.real) { return popupString('stub'); }
	if (counts.sect) { return popupString('section stub'); }
	return '';
}

function popupFilterDisambigDetect(data, download, article) {
	if (getValueOf('popupOnlyArticleDabStub') &amp;&amp; article.namespace()) { return ''; }
	return (isDisambig(data, article)) ? popupString('disambig') : '';
}

function formatBytes(num) {
	return (num &gt; 949) ? (Math.round(num/100)/10+popupString('kB')) : (num +'&amp;nbsp;' + popupString('bytes')) ;
}
//&lt;/NOLITE&gt;
// ENDFILE: pageinfo.js
// STARTFILE: titles.js
/**
   @fileoverview Defines the {@link Title} class, and associated crufty functions.

   &lt;code&gt;Title&lt;/code&gt; deals with article titles and their various
   forms.  {@link Stringwrapper} is the parent class of
   &lt;code&gt;Title&lt;/code&gt;, which exists simply to make things a little
   neater.

*/

/**
   Creates a new Stringwrapper.
   @constructor

   @class the Stringwrapper class. This base class is not really
   useful on its own; it just wraps various common string operations.
*/
function Stringwrapper() {
	/**
	   Wrapper for this.toString().indexOf()
	   @param {String} x
	   @type integer
	*/
	this.indexOf=function(x){return this.toString().indexOf(x);};
	/**
	   Returns this.value.
	   @type String
	*/
	this.toString=function(){return this.value;};
	/**
	   Wrapper for {@link String#parenSplit} applied to this.toString()
	   @param {RegExp} x
	   @type Array
	*/
	this.parenSplit=function(x){return this.toString().parenSplit(x);};
	/**
	   Wrapper for this.toString().substring()
	   @param {String} x
	   @param {String} y (optional)
	   @type String
	*/
	this.substring=function(x,y){
		if (typeof y=='undefined') { return this.toString().substring(x); }
		return this.toString().substring(x,y);
	};
	/**
	   Wrapper for this.toString().split()
	   @param {String} x
	   @type Array
	*/
	this.split=function(x){return this.toString().split(x);};
	/**
	   Wrapper for this.toString().replace()
	   @param {String} x
	   @param {String} y
	   @type String
	*/
	this.replace=function(x,y){ return this.toString().replace(x,y); };
}


/**
   Creates a new &lt;code&gt;Title&lt;/code&gt;.
   @constructor

   @class The Title class. Holds article titles and converts them into
   various forms. Also deals with anchors, by which we mean the bits
   of the article URL after a # character, representing locations
   within an article.

   @param {String} value The initial value to assign to the
   article. This must be the canonical title (see {@link
   Title#value}. Omit this in the constructor and use another function
   to set the title if this is unavailable.
*/
function Title(val) {
	/**
	   The canonical article title. This must be in UTF-8 with no
	   entities, escaping or nasties. Also, underscores should be
	   replaced with spaces.
	   @type String
	   @private
	*/
	this.value=null;
	/**
	   The canonical form of the anchor. This should be exactly as
	   it appears in the URL, i.e. with the .C3.0A bits in.
	   @type String
	*/
	this.anchor='';

	this.setUtf(val);
}
Title.prototype=new Stringwrapper();
/**
   Returns the canonical representation of the article title, optionally without anchor.
   @param {boolean} omitAnchor
   @fixme Decide specs for anchor
   @return String The article title and the anchor.
*/
Title.prototype.toString=function(omitAnchor) {
	return this.value + ( (!omitAnchor &amp;&amp; this.anchor) ? '#' + this.anchorString() : '' );
};
Title.prototype.anchorString=function() {
	if (!this.anchor) { return ''; }
	var split=this.anchor.parenSplit(/((?:[.][0-9A-F]{2})+)/);
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		// FIXME s/decodeURI/decodeURIComponent/g ?
		split[j]=decodeURIComponent(split[j].split('.').join('%')).split('_').join(' ');
	}
	return split.join('');
};
Title.prototype.urlAnchor=function() {
	var split=this.anchor.parenSplit('/((?:[%][0-9A-F]{2})+)/');
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		split[j]=split[j].split('%').join('.');
	}
	return split.join('');
};
Title.prototype.anchorFromUtf=function(str) {
	this.anchor=encodeURIComponent(str.split(' ').join('_'))
	.split('%3A').join(':').split(&quot;'&quot;).join('%27').split('%').join('.');
};
Title.fromURL=function(h) {
	return new Title().fromURL(h);
};
Title.prototype.fromURL=function(h) {
	if (typeof h != 'string') {
		this.value=null;
		return this;
	}

	// NOTE : playing with decodeURI, encodeURI, escape, unescape,
	// we seem to be able to replicate the IE borked encoding

	// IE doesn't do this new-fangled utf-8 thing.
	// and it's worse than that.
	// IE seems to treat the query string differently to the rest of the url
	// the query is treated as bona-fide utf8, but the first bit of the url is pissed around with

	// we fix up &amp; for all browsers, just in case.
	var splitted=h.split('?');
	splitted[0]=splitted[0].split('&amp;').join('%26');

	if (pg.flag.linksLikeIE6) {
		splitted[0]=encodeURI(decode_utf8(splitted[0]));
	}

	h=splitted.join('?');

	var contribs=pg.re.contribs.exec(h);
	if (contribs !== null) {
		if (contribs[1]=='title=') { contribs[3]=contribs[3].split('+').join(' '); }
		var u=new Title(contribs[3]);
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + u.stripNamespace()));
		return this;
	}

	var email=pg.re.email.exec(h);
	if (email !== null) {
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(email[3]).stripNamespace()));
		return this;
	}

	var backlinks=pg.re.backlinks.exec(h);
	if (backlinks) {
		this.setUtf(this.decodeNasties(new Title(backlinks[3])));
		return this;
	}

	// no more special cases to check --
	// hopefully it's not a disguised user-related or specially treated special page
	var m=pg.re.main.exec(h);
	if(m===null) { this.value=null; }
	else {
        var fromBotInterface = /[?](.+[&amp;])?title=/.test(h);
        if (fromBotInterface) {
            m[2]=m[2].split('+').join('_');
        }
        var extracted = m[2] + (m[3] ? '#' + m[3] : '');
        if (pg.flag.isSafari &amp;&amp; /%25[0-9A-Fa-f]{2}/.test(extracted)) {
            // Fix Safari issue
            // Safari sometimes encodes % as %25 in UTF-8 encoded strings like %E5%A3 -&gt; %25E5%25A3.
            this.setUtf(decodeURIComponent(unescape(extracted)));
        } else {
            this.setUtf(this.decodeNasties(extracted));
        }
    }
	return this;
};
Title.prototype.decodeNasties=function(txt) {
	var ret= this.decodeEscapes(decodeURI(txt));
	ret = ret.replace(/[_ ]*$/, '');
	return ret;
};
Title.prototype.decodeEscapes=function(txt) {
	var split=txt.parenSplit(/((?:[%][0-9A-Fa-f]{2})+)/);
	var len=split.length;
	for (var i=1; i&lt;len; i=i+2) {
		// FIXME is decodeURIComponent better?
		split[i]=unescape(split[i]);
	}
	return split.join('');
};
Title.fromAnchor=function(a) {
	return new Title().fromAnchor(a);
};
Title.prototype.fromAnchor=function(a) {
	if (!a) { this.value=null; return this; }
	return this.fromURL(a.href);
};
Title.fromWikiText=function(txt) {
	return new Title().fromWikiText(txt);
};
Title.prototype.fromWikiText=function(txt) {
	// FIXME - testing needed
	if (!pg.flag.linksLikeIE6) { txt=myDecodeURI(txt); }
	this.setUtf(txt);
	return this;
};
Title.prototype.hintValue=function(){
	if(!this.value) { return ''; }
	return safeDecodeURI(this.value);
};
//&lt;NOLITE&gt;
Title.prototype.toUserName=function(withNs) {
	if (this.namespaceId() != pg.nsUserId &amp;&amp; this.namespaceId() != pg.nsUsertalkId) {
		this.value=null;
		return;
	}
	this.value = (withNs ? mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' : '') + this.stripNamespace().split('/')[0];
};
Title.prototype.userName=function(withNs) {
	var t=(new Title(this.value));
	t.toUserName(withNs);
	if (t.value) { return t; }
	return null;
};
Title.prototype.toTalkPage=function() {
	// convert article to a talk page, or if we can't, return null
	// In other words: return null if this ALREADY IS a talk page
	// and return the corresponding talk page otherwise
	//
	// Per //www.mediawiki.org/wiki/Manual:Namespace#Subject_and_talk_namespaces
	// * All discussion namespaces have odd-integer indices
	// * The discussion namespace index for a specific namespace with index n is n + 1
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 0) //non-special and subject namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId+1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
//&lt;/NOLITE&gt;
// Return canonical, localized namespace
Title.prototype.namespace=function() {
	return mw.config.get('wgFormattedNamespaces')[this.namespaceId()];
};
Title.prototype.namespaceId=function() {
	var n=this.value.indexOf(':');
	if (n&lt;0) { return 0; } //mainspace
	var namespaceId = mw.config.get('wgNamespaceIds')[this.value.substring(0,n).split(' ').join('_').toLowerCase()];
	if (typeof namespaceId=='undefined') return 0; //mainspace
	return namespaceId;
};
//&lt;NOLITE&gt;
Title.prototype.talkPage=function() {
	var t=new Title(this.value);
	t.toTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.isTalkPage=function() {
	if (this.talkPage()===null) { return true; }
	return false;
};
Title.prototype.toArticleFromTalkPage=function() {
	//largely copy/paste from toTalkPage above.
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 1) //non-special and talk namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId-1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
Title.prototype.articleFromTalkPage=function() {
	var t=new Title(this.value);
	t.toArticleFromTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.articleFromTalkOrArticle=function() {
	var t=new Title(this.value);
	if ( t.toArticleFromTalkPage() ) { return t; }
	return this;
};
Title.prototype.isIpUser=function() {
	return pg.re.ipUser.test(this.userName());
};
//&lt;/NOLITE&gt;
Title.prototype.stripNamespace=function(){ // returns a string, not a Title
	var n=this.value.indexOf(':');
	if (n&lt;0) { return this.value; }
	var namespaceId = this.namespaceId();
	if (typeof namespaceId==='undefined') return this.value;
	return this.value.substring(n+1);
};
Title.prototype.setUtf=function(value){
	if (!value) { this.value=''; return; }
	var anch=value.indexOf('#');
	if(anch &lt; 0) { this.value=value.split('_').join(' '); this.anchor=''; return; }
	this.value=value.substring(0,anch).split('_').join(' ');
	this.anchor=value.substring(anch+1);
	this.ns=null; // wait until namespace() is called
};
Title.prototype.setUrl=function(urlfrag) {
	var anch=urlfrag.indexOf('#');
	this.value=safeDecodeURI(urlfrag.substring(0,anch));
	this.anchor=value.substring(anch+1);
};
Title.prototype.append=function(x){
	this.setUtf(this.value + x);
};
Title.prototype.urlString=function(x) {
	x || ( x={} );
	var v=this.toString(true);
	if (!x.omitAnchor &amp;&amp; this.anchor) { v+= '#' + this.urlAnchor(); }
	if (!x.keepSpaces) { v=v.split(' ').join('_'); }
	return encodeURI(v).split('&amp;').join('%26').split('?').join('%3F').split('+').join('%2B');
};
Title.prototype.removeAnchor=function() {
	return new Title(this.toString(true));
};
Title.prototype.toUrl=function() {
	return pg.wiki.titlebase + this.urlString();
};


function paramValue(param, url) {
	var s=url.parenSplit(RegExp('[?&amp;]' + literalizeRegex(param) + '=([^?&amp;]*)'));
	if (!url) { return null; }
	return s[1] || null;
}

function parseParams(url) {
	var ret={};
	if (url.indexOf('?')==-1) { return ret; }
	var s=url.split('?').slice(1).join();
	var t=s.split('&amp;');
	for (var i=0; i&lt;t.length; ++i) {
		var z=t[i].split('=');
		z.push(null);
		ret[z[0]]=z[1];
	}
	return ret;
}

// all sorts of stuff here
// FIXME almost everything needs to be rewritten

function oldidFromAnchor(a) { return paramValue('oldid', a.href); }
//function diffFromAnchor(a) { return paramValue('diff', a.href); }


function wikiMarkupToAddressFragment (str) { // for images
	var ret = safeDecodeURI(str);
	ret = ret.split(' ').join('_');
	ret = encodeURI(ret);
	return ret;
}

// (a) myDecodeURI (first standard decodeURI, then pg.re.urlNoPopup)
// (b) change spaces to underscores
// (c) encodeURI (just the straight one, no pg.re.urlNoPopup)

function myDecodeURI (str) {
	var ret;
	// FIXME decodeURIComponent??
	try { ret=decodeURI(str.toString()); }
	catch (summat) { return str; }
	for (var i=0; i&lt;pg.misc.decodeExtras.length; ++i) {
		var from=pg.misc.decodeExtras[i].from;
		var to=pg.misc.decodeExtras[i].to;
		ret=ret.split(from).join(to);
	}
	return ret;
}

function safeDecodeURI(str) { var ret=myDecodeURI(str); return ret || str; }

///////////
// TESTS //
///////////

//&lt;NOLITE&gt;
function isIpUser(user) {return pg.re.ipUser.test(user);}

function isDisambig(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	return ! article.isTalkPage() &amp;&amp; pg.re.disambig.test(data);
}

function stubCount(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	var sectStub=0;
	var realStub=0;
	if (pg.re.stub.test(data)) {
		var s=data.parenSplit(pg.re.stub);
		for (var i=1; i&lt;s.length; i=i+2) {
			if (s[i]) { ++sectStub; }
			else { ++realStub; }
		}
	}
	return { real: realStub, sect: sectStub };
}

function isValidImageName(str){ // extend as needed...
	return ( str.indexOf('{') == -1 );
}

function isInStrippableNamespace(article) {
	//I believe that this method means to return whether the given article is in a namspace without subpages. Meaning, it's broken.
	return ( article.namespace() !== '' );
}

function isInMainNamespace(article) { return !isInStrippableNamespace(article); }

function anchorContainsImage(a) {
	// iterate over children of anchor a
	// see if any are images
	if (a===null) { return false; }
	kids=a.childNodes;
	for (var i=0; i&lt;kids.length; ++i) { if (kids[i].nodeName=='IMG') { return true; } }
	return false;
}
//&lt;/NOLITE&gt;
function isPopupLink(a) {
	// NB for performance reasons, TOC links generally return true
	// they should be stripped out later

	if (!markNopopupSpanLinks.done) { markNopopupSpanLinks(); }
	if (a.inNopopupSpan || a.className=='sortheader') { return false; }

	// FIXME is this faster inline?
	if (a.onmousedown || a.getAttribute('nopopup')) { return false; }
	var h=a.href;
	if (!pg.re.basenames.test(h)) { return false; }
	if ( !pg.re.urlNoPopup.test(h) ) { return true;	}
	return (
		(pg.re.email.test(h) || pg.re.contribs.test(h) || pg.re.backlinks.test(h)) &amp;&amp;
		h.indexOf('&amp;limit=') == -1 );
}

function markNopopupSpanLinks() {
	if( !getValueOf('popupOnlyArticleLinks'))
		fixVectorMenuPopups();

	var s=getElementsByClassName(document, '*', &quot;nopopups&quot;)
	for (var i=0; i&lt;s.length; ++i) {
		var as=s[i].getElementsByTagName('a');
		for (var j=0; j&lt;as.length; ++j) {
			as[j].inNopopupSpan=true;
		}
	}
	
	markNopopupSpanLinks.done=true;
}

function fixVectorMenuPopups() {
	var vmenus = getElementsByClassName( document, 'div', 'vectorMenu');
	for( i= 0; vmenus &amp;&amp; i&lt; vmenus.length; i++ ) {
		var h5 = vmenus[i].getElementsByTagName('h5')[0];
		if( h5) var a = h5.getElementsByTagName('a')[0];
		if( a ) a.inNopopupSpan=true;
	}
}
// ENDFILE: titles.js
// STARTFILE: cookies.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Cookie handling
// from http://www.quirksmode.org/js/cookies.html

var Cookie= {
	create: function(name,value,days)
	{
		var expires;
		if (days)
		{
			var date = new Date();
			date.setTime(date.getTime()+(days*24*60*60*1000));
			expires = &quot;; expires=&quot;+date.toGMTString();
		}
		else { expires = &quot;&quot;; }
		document.cookie = name+&quot;=&quot;+value+expires+&quot;; path=/&quot;;
	},

	read: function(name)
	{
		var nameEQ = name + &quot;=&quot;;
		var ca = document.cookie.split(';');
		for(var i=0;i &lt; ca.length;i++)
		{
			var c = ca[i];
			while (c[0]==' ') { c = c.substring(1,c.length); }
			if (c.indexOf(nameEQ) === 0) { return c.substring(nameEQ.length,c.length); }
		}
		return null;
	},

	erase: function(name)
	{
		Cookie.create(name,&quot;&quot;,-1);
	}
};
//&lt;/NOLITE&gt;
// ENDFILE: cookies.js
// STARTFILE: getpage.js
//////////////////////////////////////////////////
// Wiki-specific downloading
//

// Schematic for a getWiki call
//
//   getWiki-&gt;-getPageWithCaching
//                    |
//       false        |          true
// getPage&lt;-[findPictureInCache]-&gt;-onComplete(a fake download)
//   \.
//     (async)-&gt;addPageToCache(download)-&gt;-onComplete(download)


/** @todo {document}
    @param {Title} article
    @param {Function} onComplete
    @param {integer} oldid
    @param {Navapopup} owner
*/
function getWiki(article, onComplete, oldid, owner) {
	// set ctype=text/css to get around opera gzip bug
	var url = pg.wiki.titlebase + article.removeAnchor().urlString() +
	    '&amp;action=raw&amp;ctype=text/css';
	if (oldid || oldid===0 || oldid==='0') { url += '&amp;oldid='+oldid; }
	url += '';

	getPageWithCaching(url, onComplete, owner);
}

// check cache to see if page exists

function getPageWithCaching(url, onComplete, owner) {
	log('getPageWithCaching, url='+url);
	var i=findInPageCache(url);
	if (i &gt; -1) {
		var d=fakeDownload(url, owner.idNumber, onComplete,
				   pg.cache.pages[i].data, pg.cache.pages[i].lastModified,
				   owner);
	} else {
		var d=getPage(url, onComplete, owner);
		if (d &amp;&amp; owner &amp;&amp; owner.addDownload) {
			owner.addDownload(d);
			d.owner=owner;
		}
	}
}

function getPage(url, onComplete, owner) {
	log('getPage');
	var callback= function (d) { if (!d.aborted) {addPageToCache(d); onComplete(d);} };
	return startDownload(url, owner.idNumber, callback);
}

function findInPageCache(url) {
	for (var i=0; i&lt;pg.cache.pages.length; ++i) {
		if (url==pg.cache.pages[i].url) { return i; }
	}
	return -1;
}

function addPageToCache(download) {
	log('addPageToCache '+download.url);
	var page = {url: download.url, data: download.data, lastModified: download.lastModified};
	return pg.cache.pages.push(page);
}
// ENDFILE: getpage.js
// STARTFILE: md5-2.2alpha.js
//&lt;NOLITE&gt;
/*
 * A JavaScript implementation of the RSA Data Security, Inc. MD5 Message
 * Digest Algorithm, as defined in {{RFC|1321}}.
 * Version 2.2-alpha Copyright (C) Paul Johnston 1999 - 2005
 * Other contributors: Greg Holt, Andrew Kepert, Ydnar, Lostinet
 * Distributed under the BSD License
 * See http://pajhome.org.uk/crypt/md5 for more info.
 */

/*
 * Configurable variables. You may need to tweak these to be compatible with
 * the server-side, but the defaults work in most cases.
 */
var hexcase = 0;   /* hex output format. 0 - lowercase; 1 - uppercase	     */
var b64pad  = &quot;&quot;; /* base-64 pad character. &quot;=&quot; for strict RFC compliance   */

/*
 * These are the functions you'll usually want to call
 * They take string arguments and return either hex or base-64 encoded strings
 */
function hex_md5(s)    { return rstr2hex(rstr_md5(str2rstr_utf8(s))); }
function b64_md5(s)    { return rstr2b64(rstr_md5(str2rstr_utf8(s))); }
function any_md5(s, e) { return rstr2any(rstr_md5(str2rstr_utf8(s)), e); }
function hex_hmac_md5(k, d)
  { return rstr2hex(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function b64_hmac_md5(k, d)
  { return rstr2b64(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function any_hmac_md5(k, d, e)
  { return rstr2any(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d)), e); }

/*
 * Perform a simple self-test to see if the VM is working
 */
function md5_vm_test()
{
  return hex_md5(&quot;abc&quot;) == &quot;900150983cd24fb0d6963f7d28e17f72&quot;;
}

/*
 * Calculate the MD5 of a raw string
 */
function rstr_md5(s)
{
  return binl2rstr(binl_md5(rstr2binl(s), s.length * 8));
}

/*
 * Calculate the HMAC-MD5, of a key and some data (raw strings)
 */
function rstr_hmac_md5(key, data)
{
  var bkey = rstr2binl(key);
  if(bkey.length &gt; 16) bkey = binl_md5(bkey, key.length * 8);

  var ipad = Array(16), opad = Array(16);
  for(var i = 0; i &lt; 16; i++)
  {
    ipad[i] = bkey[i] ^ 0x36363636;
    opad[i] = bkey[i] ^ 0x5C5C5C5C;
  }

  var hash = binl_md5(ipad.concat(rstr2binl(data)), 512 + data.length * 8);
  return binl2rstr(binl_md5(opad.concat(hash), 512 + 128));
}

/*
 * Convert a raw string to a hex string
 */
function rstr2hex(input)
{
  var hex_tab = hexcase ? &quot;0123456789ABCDEF&quot; : &quot;0123456789abcdef&quot;;
  var output = &quot;&quot;;
  var x;
  for(var i = 0; i &lt; input.length; i++)
  {
    x = input.charCodeAt(i);
    output += hex_tab.charAt((x &gt;&gt;&gt; 4) &amp; 0x0F)
	   +  hex_tab.charAt( x	       &amp; 0x0F);
  }
  return output;
}

/*
 * Convert a raw string to a base-64 string
 */
function rstr2b64(input)
{
  var tab = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
  var output = &quot;&quot;;
  var len = input.length;
  for(var i = 0; i &lt; len; i += 3)
  {
    var triplet = (input.charCodeAt(i) &lt;&lt; 16)
		| (i + 1 &lt; len ? input.charCodeAt(i+1) &lt;&lt; 8 : 0)
		| (i + 2 &lt; len ? input.charCodeAt(i+2)	    : 0);
    for(var j = 0; j &lt; 4; j++)
    {
      if(i * 8 + j * 6 &gt; input.length * 8) output += b64pad;
      else output += tab.charAt((triplet &gt;&gt;&gt; 6*(3-j)) &amp; 0x3F);
    }
  }
  return output;
}

/*
 * Convert a raw string to an arbitrary string encoding
 */
function rstr2any(input, encoding)
{
  var divisor = encoding.length;
  var remainders = Array();
  var i, q, x, quotient;

  /* Convert to an array of 16-bit big-endian values, forming the dividend */
  var dividend = Array(input.length / 2);
  for(i = 0; i &lt; dividend.length; i++)
  {
    dividend[i] = (input.charCodeAt(i * 2) &lt;&lt; 8) | input.charCodeAt(i * 2 + 1);
  }

  /*
   * Repeatedly perform a long division. The binary array forms the dividend,
   * the length of the encoding is the divisor. Once computed, the quotient
   * forms the dividend for the next step. We stop when the dividend is zero.
   * All remainders are stored for later use.
   */
  while(dividend.length &gt; 0)
  {
    quotient = Array();
    x = 0;
    for(i = 0; i &lt; dividend.length; i++)
    {
      x = (x &lt;&lt; 16) + dividend[i];
      q = Math.floor(x / divisor);
      x -= q * divisor;
      if(quotient.length &gt; 0 || q &gt; 0)
	quotient[quotient.length] = q;
    }
    remainders[remainders.length] = x;
    dividend = quotient;
  }

  /* Convert the remainders to the output string */
  var output = &quot;&quot;;
  for(i = remainders.length - 1; i &gt;= 0; i--)
    output += encoding.charAt(remainders[i]);

  return output;
}

/*
 * Encode a string as utf-8.
 * For efficiency, this assumes the input is valid utf-16.
 */
function str2rstr_utf8(input)
{
  var output = &quot;&quot;;
  var i = -1;
  var x, y;

  while(++i &lt; input.length)
  {
    /* Decode utf-16 surrogate pairs */
    x = input.charCodeAt(i);
    y = i + 1 &lt; input.length ? input.charCodeAt(i + 1) : 0;
    if(0xD800 &lt;= x &amp;&amp; x &lt;= 0xDBFF &amp;&amp; 0xDC00 &lt;= y &amp;&amp; y &lt;= 0xDFFF)
    {
      x = 0x10000 + ((x &amp; 0x03FF) &lt;&lt; 10) + (y &amp; 0x03FF);
      i++;
    }

    /* Encode output as utf-8 */
    if(x &lt;= 0x7F)
      output += String.fromCharCode(x);
    else if(x &lt;= 0x7FF)
      output += String.fromCharCode(0xC0 | ((x &gt;&gt;&gt; 6 ) &amp; 0x1F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0xFFFF)
      output += String.fromCharCode(0xE0 | ((x &gt;&gt;&gt; 12) &amp; 0x0F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0x1FFFFF)
      output += String.fromCharCode(0xF0 | ((x &gt;&gt;&gt; 18) &amp; 0x07),
				    0x80 | ((x &gt;&gt;&gt; 12) &amp; 0x3F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
  }
  return output;
}

/*
 * Encode a string as utf-16
 */
function str2rstr_utf16le(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode( input.charCodeAt(i)	      &amp; 0xFF,
				  (input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF);
  return output;
}

function str2rstr_utf16be(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode((input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF,
				   input.charCodeAt(i)	      &amp; 0xFF);
  return output;
}

/*
 * Convert a raw string to an array of little-endian words
 * Characters &gt;255 have their high-byte silently ignored.
 */
function rstr2binl(input)
{
  var output = Array(input.length &gt;&gt; 2);
  for(var i = 0; i &lt; output.length; i++)
    output[i] = 0;
  for(var i = 0; i &lt; input.length * 8; i += 8)
    output[i&gt;&gt;5] |= (input.charCodeAt(i / 8) &amp; 0xFF) &lt;&lt; (i%32);
  return output;
}

/*
 * Convert an array of little-endian words to a string
 */
function binl2rstr(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length * 32; i += 8)
    output += String.fromCharCode((input[i&gt;&gt;5] &gt;&gt;&gt; (i % 32)) &amp; 0xFF);
  return output;
}

/*
 * Calculate the MD5 of an array of little-endian words, and a bit length.
 */
function binl_md5(x, len)
{
  /* append padding */
  x[len &gt;&gt; 5] |= 0x80 &lt;&lt; ((len) % 32);
  x[(((len + 64) &gt;&gt;&gt; 9) &lt;&lt; 4) + 14] = len;

  var a =  1732584193;
  var b = -271733879;
  var c = -1732584194;
  var d =  271733878;

  for(var i = 0; i &lt; x.length; i += 16)
  {
    var olda = a;
    var oldb = b;
    var oldc = c;
    var oldd = d;

    a = md5_ff(a, b, c, d, x[i+ 0], 7 , -680876936);
    d = md5_ff(d, a, b, c, x[i+ 1], 12, -389564586);
    c = md5_ff(c, d, a, b, x[i+ 2], 17,	 606105819);
    b = md5_ff(b, c, d, a, x[i+ 3], 22, -1044525330);
    a = md5_ff(a, b, c, d, x[i+ 4], 7 , -176418897);
    d = md5_ff(d, a, b, c, x[i+ 5], 12,	 1200080426);
    c = md5_ff(c, d, a, b, x[i+ 6], 17, -1473231341);
    b = md5_ff(b, c, d, a, x[i+ 7], 22, -45705983);
    a = md5_ff(a, b, c, d, x[i+ 8], 7 ,	 1770035416);
    d = md5_ff(d, a, b, c, x[i+ 9], 12, -1958414417);
    c = md5_ff(c, d, a, b, x[i+10], 17, -42063);
    b = md5_ff(b, c, d, a, x[i+11], 22, -1990404162);
    a = md5_ff(a, b, c, d, x[i+12], 7 ,	 1804603682);
    d = md5_ff(d, a, b, c, x[i+13], 12, -40341101);
    c = md5_ff(c, d, a, b, x[i+14], 17, -1502002290);
    b = md5_ff(b, c, d, a, x[i+15], 22,	 1236535329);

    a = md5_gg(a, b, c, d, x[i+ 1], 5 , -165796510);
    d = md5_gg(d, a, b, c, x[i+ 6], 9 , -1069501632);
    c = md5_gg(c, d, a, b, x[i+11], 14,	 643717713);
    b = md5_gg(b, c, d, a, x[i+ 0], 20, -373897302);
    a = md5_gg(a, b, c, d, x[i+ 5], 5 , -701558691);
    d = md5_gg(d, a, b, c, x[i+10], 9 ,	 38016083);
    c = md5_gg(c, d, a, b, x[i+15], 14, -660478335);
    b = md5_gg(b, c, d, a, x[i+ 4], 20, -405537848);
    a = md5_gg(a, b, c, d, x[i+ 9], 5 ,	 568446438);
    d = md5_gg(d, a, b, c, x[i+14], 9 , -1019803690);
    c = md5_gg(c, d, a, b, x[i+ 3], 14, -187363961);
    b = md5_gg(b, c, d, a, x[i+ 8], 20,	 1163531501);
    a = md5_gg(a, b, c, d, x[i+13], 5 , -1444681467);
    d = md5_gg(d, a, b, c, x[i+ 2], 9 , -51403784);
    c = md5_gg(c, d, a, b, x[i+ 7], 14,	 1735328473);
    b = md5_gg(b, c, d, a, x[i+12], 20, -1926607734);

    a = md5_hh(a, b, c, d, x[i+ 5], 4 , -378558);
    d = md5_hh(d, a, b, c, x[i+ 8], 11, -2022574463);
    c = md5_hh(c, d, a, b, x[i+11], 16,	 1839030562);
    b = md5_hh(b, c, d, a, x[i+14], 23, -35309556);
    a = md5_hh(a, b, c, d, x[i+ 1], 4 , -1530992060);
    d = md5_hh(d, a, b, c, x[i+ 4], 11,	 1272893353);
    c = md5_hh(c, d, a, b, x[i+ 7], 16, -155497632);
    b = md5_hh(b, c, d, a, x[i+10], 23, -1094730640);
    a = md5_hh(a, b, c, d, x[i+13], 4 ,	 681279174);
    d = md5_hh(d, a, b, c, x[i+ 0], 11, -358537222);
    c = md5_hh(c, d, a, b, x[i+ 3], 16, -722521979);
    b = md5_hh(b, c, d, a, x[i+ 6], 23,	 76029189);
    a = md5_hh(a, b, c, d, x[i+ 9], 4 , -640364487);
    d = md5_hh(d, a, b, c, x[i+12], 11, -421815835);
    c = md5_hh(c, d, a, b, x[i+15], 16,	 530742520);
    b = md5_hh(b, c, d, a, x[i+ 2], 23, -995338651);

    a = md5_ii(a, b, c, d, x[i+ 0], 6 , -198630844);
    d = md5_ii(d, a, b, c, x[i+ 7], 10,	 1126891415);
    c = md5_ii(c, d, a, b, x[i+14], 15, -1416354905);
    b = md5_ii(b, c, d, a, x[i+ 5], 21, -57434055);
    a = md5_ii(a, b, c, d, x[i+12], 6 ,	 1700485571);
    d = md5_ii(d, a, b, c, x[i+ 3], 10, -1894986606);
    c = md5_ii(c, d, a, b, x[i+10], 15, -1051523);
    b = md5_ii(b, c, d, a, x[i+ 1], 21, -2054922799);
    a = md5_ii(a, b, c, d, x[i+ 8], 6 ,	 1873313359);
    d = md5_ii(d, a, b, c, x[i+15], 10, -30611744);
    c = md5_ii(c, d, a, b, x[i+ 6], 15, -1560198380);
    b = md5_ii(b, c, d, a, x[i+13], 21,	 1309151649);
    a = md5_ii(a, b, c, d, x[i+ 4], 6 , -145523070);
    d = md5_ii(d, a, b, c, x[i+11], 10, -1120210379);
    c = md5_ii(c, d, a, b, x[i+ 2], 15,	 718787259);
    b = md5_ii(b, c, d, a, x[i+ 9], 21, -343485551);

    a = safe_add(a, olda);
    b = safe_add(b, oldb);
    c = safe_add(c, oldc);
    d = safe_add(d, oldd);
  }
  return Array(a, b, c, d);
}

/*
 * These functions implement the four basic operations the algorithm uses.
 */
function md5_cmn(q, a, b, x, s, t)
{
  return safe_add(bit_rol(safe_add(safe_add(a, q), safe_add(x, t)), s),b);
}
function md5_ff(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; c) | ((~b) &amp; d), a, b, x, s, t);
}
function md5_gg(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; d) | (c &amp; (~d)), a, b, x, s, t);
}
function md5_hh(a, b, c, d, x, s, t)
{
  return md5_cmn(b ^ c ^ d, a, b, x, s, t);
}
function md5_ii(a, b, c, d, x, s, t)
{
  return md5_cmn(c ^ (b | (~d)), a, b, x, s, t);
}

/*
 * Add integers, wrapping at 2^32. This uses 16-bit operations internally
 * to work around bugs in some JS interpreters.
 */
function safe_add(x, y)
{
  var lsw = (x &amp; 0xFFFF) + (y &amp; 0xFFFF);
  var msw = (x &gt;&gt; 16) + (y &gt;&gt; 16) + (lsw &gt;&gt; 16);
  return (msw &lt;&lt; 16) | (lsw &amp; 0xFFFF);
}

/*
 * Bitwise rotate a 32-bit number to the left.
 */
function bit_rol(num, cnt)
{
  return (num &lt;&lt; cnt) | (num &gt;&gt;&gt; (32 - cnt));
}
//&lt;/NOLITE&gt;
// ENDFILE: md5-2.2alpha.js
// STARTFILE: parensplit.js
//////////////////////////////////////////////////
// parenSplit

// String.prototype.parenSplit should do what ECMAscript says
// String.prototype.split does, interspersing paren matches between
// the split elements

if (String('abc'.split(/(b)/))!='a,b,c') {
	// broken String.split, e.g. konq, IE
	String.prototype.parenSplit=function (re) {
		re=nonGlobalRegex(re);
		var s=this;
		var m=re.exec(s);
		var ret=[];
		while (m &amp;&amp; s) {
			// without the following loop, we have
			// 'ab'.parenSplit(/a|(b)/) != 'ab'.split(/a|(b)/)
			for(var i=0; i&lt;m.length; ++i) {
				if (typeof m[i]=='undefined') m[i]='';
			}
			ret.push(s.substring(0,m.index));
			ret = ret.concat(m.slice(1));
			s=s.substring(m.index + m[0].length);
			m=re.exec(s);
		}
		ret.push(s);
		return ret;
	};
} else {
	String.prototype.parenSplit=function (re) { return this.split(re); };
	String.prototype.parenSplit.isNative=true;
}

function nonGlobalRegex(re) {
	var s=re.toString();
	flags='';
	for (var j=s.length; s.charAt(j) != '/'; --j) {
		if (s.charAt(j) != 'g') { flags += s.charAt(j); }
	}
	var t=s.substring(1,j);
	return RegExp(t,flags);
}
// ENDFILE: parensplit.js
// STARTFILE: tools.js
// IE madness with encoding
// ========================
//
// suppose throughout that the page is in utf8, like wikipedia
//
// if a is an anchor DOM element and a.href should consist of
//
// http://host.name.here/wiki/foo?bar=baz
//
// then IE gives foo as &quot;latin1-encoded&quot; utf8; we have foo = decode_utf8(decodeURI(foo_ie))
// but IE gives bar=baz correctly as plain utf8
//
// ---------------------------------
//
// IE's xmlhttp doesn't understand utf8 urls. Have to use encodeURI here.
//
// ---------------------------------
//
// summat else

// Source: http://aktuell.de.selfhtml.org/artikel/javascript/utf8b64/utf8.htm

//&lt;NOLITE&gt;
function encode_utf8(rohtext) {
	// dient der Normalisierung des Zeilenumbruchs
	rohtext = rohtext.replace(/\r\n/g,&quot;\n&quot;);
	var utftext = &quot;&quot;;
	for(var n=0; n&lt;rohtext.length; n++)
	{
		// ermitteln des Unicodes des  aktuellen Zeichens
		var c=rohtext.charCodeAt(n);
		// alle Zeichen von 0-127 =&gt; 1byte
		if (c&lt;128)
			utftext += String.fromCharCode(c);
		// alle Zeichen von 127 bis 2047 =&gt; 2byte
		else if((c&gt;127) &amp;&amp; (c&lt;2048)) {
			utftext += String.fromCharCode((c&gt;&gt;6)|192);
			utftext += String.fromCharCode((c&amp;63)|128);}
		// alle Zeichen von 2048 bis 66536 =&gt; 3byte
		else {
			utftext += String.fromCharCode((c&gt;&gt;12)|224);
			utftext += String.fromCharCode(((c&gt;&gt;6)&amp;63)|128);
			utftext += String.fromCharCode((c&amp;63)|128);}
	}
	return utftext;
}

function getJsObj(json) {
	try {
		var json_ret = eval('(' + json + ')');
	} catch (someError) {
		errlog('Something went wrong with getJsobj, json='+json);
		return 1;
	}
	if( json_ret['warnings'] ) {
		for( var w=0; w &lt; json_ret['warnings'].length; w++ ) {
			log( json_ret['warnings'][w]['*'] );
		}
	} else if ( json_ret['error'] ) {
		errlog( json_ret['error'].code + ': ' + json_ret['error'].info );
	}
	return json_ret;
}

function anyChild(obj) {
	for (var p in obj) {
		return obj[p];
	}
	return null;
}

//&lt;/NOLITE&gt;

function decode_utf8(utftext) {
	var plaintext = &quot;&quot;; var i=0, c=0, c1=0, c2=0;
	// while-Schleife, weil einige Zeichen uebersprungen werden
	while(i&lt;utftext.length)
	{
		c = utftext.charCodeAt(i);
		if (c&lt;128) {
			plaintext += String.fromCharCode(c);
			i++;}
		else if((c&gt;191) &amp;&amp; (c&lt;224)) {
			c2 = utftext.charCodeAt(i+1);
			plaintext += String.fromCharCode(((c&amp;31)&lt;&lt;6) | (c2&amp;63));
			i+=2;}
		else {
			c2 = utftext.charCodeAt(i+1); c3 = utftext.charCodeAt(i+2);
			plaintext += String.fromCharCode(((c&amp;15)&lt;&lt;12) | ((c2&amp;63)&lt;&lt;6) | (c3&amp;63));
			i+=3;}
	}
	return plaintext;
}


function upcaseFirst(str) {
	if (typeof str != typeof '' || str=='') return '';
	return str[0].toUpperCase() + str.substring(1);
}


function findInArray(arr, foo) {
	if (!arr || !arr.length) { return -1; }
	var len=arr.length;
	for (var i=0; i&lt;len; ++i) { if (arr[i]==foo) { return i; } }
	return -1;
}

function nextOne (array, value) {
	// NB if the array has two consecutive entries equal
	//    then this will loop on successive calls
	var i=findInArray(array, value);
	if (i&lt;0) { return null; }
	return array[i+1];
}

function literalizeRegex(str){
	return str.replace(RegExp('([-.|()\\\\+?*^${}\\[\\]])', 'g'), '\\$1');
}

String.prototype.entify=function() {
	//var shy='&amp;shy;';
	return this.split('&amp;').join('&amp;amp;').split('&lt;').join('&amp;lt;').split('&gt;').join('&amp;gt;'/*+shy*/).split('&quot;').join('&amp;quot;');
};

function findThis(array, value) {
	if (typeof array.length == 'undefined') { return null; }
	for (var i=0; i&lt;array.length; ++i) {
		if (array[i]==value) { return i; }
	}
	return null;
}

function removeNulls(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i]) {
			ret.push(list[i]);
		}
	}
	return ret;
}
function joinPath(list) {
	return removeNulls(list).join('/');
}


function simplePrintf(str, subs) {
	if (!str || !subs) { return str; }
	var ret=[];
	var s=str.parenSplit(/(%s|\$[0-9]+)/);
	var i=0;
	do {
		ret.push(s.shift());
		if ( !s.length ) { break; }
		var cmd=s.shift();
		if (cmd == '%s') {
			if ( i &lt; subs.length ) { ret.push(subs[i]); } else { ret.push(cmd); }
			++i;
		} else {
			var j=parseInt( cmd.replace('$', ''), 10 ) - 1;
			if ( j &gt; -1 &amp;&amp; j &lt; subs.length ) { ret.push(subs[j]); } else { ret.push(cmd); }
		}
	} while (s.length &gt; 0);
	return ret.join('');
}

function max(a,b){return a&lt;b ? b : a;}
function min(a,b){return a&gt;b ? b : a;}

function isString(x) { return (typeof x === 'string' || x instanceof String); }
//function isNumber(x) { return (typeof x === 'number' || x instanceof Number); }
function isRegExp(x) { return x instanceof RegExp; }
function isArray (x) { return x instanceof Array; }
function isObject(x) { return x instanceof Object; }
function isFunction(x) {
    return !isRegExp(x) &amp;&amp; (typeof x === 'function' || x instanceof Function);
}

function repeatString(s,mult) {
	var ret='';
	for (var i=0; i&lt;mult; ++i) { ret += s; }
	return ret;
}

function zeroFill(s, min) {
	min = min || 2;
	var t=s.toString();
	return repeatString('0', min - t.length) + t;
}

function map(f, o) {
	if (isArray(o)) { return map_array(f,o); }
	return map_object(f,o);
}
function map_array(f,o) {
	var ret=[];
	for (var i=0; i&lt;o.length; ++i) {
		ret.push(f(o[i]));
	}
	return ret;
}
function map_object(f,o) {
	var ret={};
	for (var i in o) { ret[o]=f(o[i]); }
	return ret;
}
// ENDFILE: tools.js
// STARTFILE: dab.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Dab-fixing code
//


function retargetDab(newTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) {
	log('retargetDab: newTarget='+newTarget + ' oldTarget=' + oldTarget);
	return changeLinkTargetLink(
	{newTarget: newTarget,
			text: newTarget.split(' ').join('&amp;nbsp;'),
			hint: tprintf('disambigHint', [newTarget]),
			summary: simplePrintf(
				    getValueOf('popupFixDabsSummary'), [friendlyCurrentArticleName, newTarget ]),
			clickButton: 'wpDiff', minor: true, oldTarget: oldTarget,
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit});
}

function listLinks(wikitext, oldTarget, titleToEdit) {
	// mediawiki strips trailing spaces, so we do the same
	// testcase: //en.wikipedia.org/w/index.php?title=Radial&amp;oldid=97365633
	var reg=RegExp('\\[\\[([^|]*?) *(\\||\\]\\])', 'gi');
	var ret=[];
	var splitted=wikitext.parenSplit(reg);
	// ^[a-z]+ should match interwiki links, hopefully (case-insensitive)
	// and ^[a-z]* should match those and [[:Category...]] style links too
	var omitRegex=RegExp('^[a-z]*:|^[Ss]pecial:|^[Ii]mage|^[Cc]ategory');
	var friendlyCurrentArticleName= oldTarget.toString();
	var wikPos = getValueOf('popupDabWiktionary');

	for (var i=1; i&lt;splitted.length; i=i+3) {
		if (typeof splitted[i] == typeof 'string' &amp;&amp; splitted[i].length&gt;0 &amp;&amp; !omitRegex.test(splitted[i])) {
			ret.push( retargetDab(splitted[i], oldTarget, friendlyCurrentArticleName, titleToEdit) );
		} /* if */
	} /* for loop */

	ret = rmDupesFromSortedList(ret.sort());

	if (wikPos) {
		var wikTarget='wiktionary:' +
			friendlyCurrentArticleName.replace( RegExp('^(.+)\\s+[(][^)]+[)]\\s*$'), '$1' );

		var meth;
		if (wikPos.toLowerCase() == 'first') { meth = 'unshift'; }
		else { meth = 'push'; }

		ret[meth]( retargetDab(wikTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) );
	}

	ret.push(changeLinkTargetLink(
	{ newTarget: null,
			text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this disambig page from this article&quot;),
			clickButton: &quot;wpDiff&quot;, oldTarget: oldTarget,
			summary: simplePrintf(getValueOf('popupRmDabLinkSummary'), [friendlyCurrentArticleName]),
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit
			}));
	return ret;
}

function rmDupesFromSortedList(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (ret.length===0 || list[i]!=ret[ret.length-1]) { ret.push(list[i]); }
	}
	return ret;
}

function makeFixDab(data, navpop) {
	// grab title from parent popup if there is one; default exists in changeLinkTargetLink
	var titleToEdit=(navpop.parentPopup &amp;&amp; navpop.parentPopup.article.toString());
	var list=listLinks(data, navpop.originalArticle, titleToEdit);
	if (list.length===0) { log('listLinks returned empty list'); return null; }
	var html='&lt;hr&gt;' + popupString('Click to disambiguate this link to:') + '&lt;br&gt;';
	html+=list.join(', ');
	return html;
}


function makeFixDabs(wikiText, navpop) {
	if (getValueOf('popupFixDabs') &amp;&amp; isDisambig(wikiText, navpop.article) &amp;&amp;
	    Title.fromURL(location.href).namespaceId() != pg.nsSpecialId &amp;&amp;
	    navpop.article.talkPage() ) {
		setPopupHTML(makeFixDab(wikiText, navpop), 'popupFixDab', navpop.idNumber);
	}
}

function popupRedlinkHTML(article) {
	return changeLinkTargetLink(
		{ newTarget: null, text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this page from this article&quot;),
			clickButton: &quot;wpDiff&quot;,
			oldTarget: article.toString(),
			summary: simplePrintf(getValueOf('popupRedlinkSummary'), [article.toString()])});
}
//&lt;/NOLITE&gt;
// ENDFILE: dab.js
// STARTFILE: htmloutput.js

function appendPopupContent(obj, elementId, popupId, onSuccess) {
	return setPopupHTML(obj, elementId, popupId, onSuccess, true);
}

// this has to use a timer loop as we don't know if the DOM element exists when we want to set the text
function setPopupHTML (str, elementId, popupId, onSuccess, append) {
	if (elementId=='popupPreview') {
	}
	if (typeof popupId === 'undefined') {
		//console.error('popupId is not defined in setPopupHTML, html='+str.substring(0,100));
		popupId = pg.idNumber;
	}

	var popupElement=document.getElementById(elementId+popupId);
	if (popupElement) {
		if (!append) { popupElement.innerHTML=''; }
		if (isString(str)) {
			popupElement.innerHTML+=str;
		} else {
			popupElement.appendChild(str);
		}
		if (onSuccess) { onSuccess(); }
		setTimeout(checkPopupPosition, 100);
		return true;
	} else {
		// call this function again in a little while...
		setTimeout(function(){
				setPopupHTML(str,elementId,popupId,onSuccess);
			}, 600);
	}
	return null;
}

//&lt;NOLITE&gt;
function setPopupTrailer(str,id) {return setPopupHTML(str, 'popupData', id);}
//&lt;/NOLITE&gt;


function fillEmptySpans(args) { return fillEmptySpans2(args); }

// args.navpopup is mandatory
// optional: args.redir, args.redirTarget
// FIXME: ye gods, this is ugly stuff
function fillEmptySpans2(args) { // if redir is present and true then redirTarget is mandatory
	var redir=true;
	if (typeof args != 'object' || typeof args.redir == 'undefined' || !args.redir) { redir=false; }
	var a=args.navpopup.parentAnchor;

	var article, hint=null, oldid=null, params={};
	if (redir &amp;&amp; typeof args.redirTarget == typeof {}) {
		article=args.redirTarget;
		//hint=article.hintValue();
	} else {
		article=(new Title()).fromAnchor(a);
		hint=a.originalTitle || article.hintValue();
		params=parseParams(a.href);
		oldid=(getValueOf('popupHistoricalLinks')) ? params.oldid : null;
		rcid=params.rcid;
	}
	var x={ article:article, hint: hint, oldid: oldid, rcid: rcid, navpop:args.navpopup, params:params };

	var structure=pg.structures[getValueOf('popupStructure')];
	if (typeof structure != 'object') {
		setPopupHTML('popupError', 'Unknown structure (this should never happen): '+
			     pg.option.popupStructure, args.navpopup.idNumber);
		return;
	}
	var spans=flatten(pg.misc.layout);
	var numspans = spans.length;
	var redirs=pg.misc.redirSpans;

	for (var i=0; i&lt;numspans; ++i) {
		var f=findThis(redirs, spans[i]);
		//log('redir='+redir+', f='+f+', spans[i]='+spans[i]);
		if ( (f!==null &amp;&amp; !redir) || (f===null &amp;&amp; redir) ) {
			//log('skipping this set of the loop');
			continue;
		}
		var structurefn=structure[spans[i]];
		var setfn = setPopupHTML;
		if (getValueOf('popupActiveNavlinks') &amp;&amp; 
		    (spans[i].indexOf('popupTopLinks')==0 || spans[i].indexOf('popupRedirTopLinks')==0)
			    ) {
			setfn = setPopupTipsAndHTML;
		}
		switch (typeof structurefn) {
		case 'function':
			//log('running '+spans[i]+'({article:'+x.article+', hint:'+x.hint+', oldid: '+x.oldid+'})');
			setfn(structurefn(x), spans[i], args.navpopup.idNumber);
			break;
		case 'string':
			setfn(structurefn, spans[i], args.navpopup.idNumber);
			break;
		default:
			errlog('unknown thing with label '+spans[i]);
			break;
		}
	}
}

// flatten an array
function flatten(list, start) {
	var ret=[];
	if (typeof start == 'undefined') { start=0; }
	for (var i=start; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof []) {
			return ret.concat(flatten(list[i])).concat(flatten(list, i+1));
		}
		else { ret.push(list[i]); }
	}
	return ret;
}

// Generate html for whole popup
function popupHTML (a) {
	getValueOf('popupStructure');
	var structure=pg.structures[pg.option.popupStructure];
	if (typeof structure != 'object') {
		//return 'Unknown structure: '+pg.option.popupStructure;
		// override user choice
		pg.option.popupStructure=pg.optionDefault.popupStructure;
		return popupHTML(a);
	}
	if (typeof structure.popupLayout != 'function') { return 'Bad layout'; }
	pg.misc.layout=structure.popupLayout();
	if (typeof structure.popupRedirSpans == 'function') { pg.misc.redirSpans=structure.popupRedirSpans(); }
	else { pg.misc.redirSpans=[]; }
	return makeEmptySpans(pg.misc.layout, a.navpopup);
}

function makeEmptySpans (list, navpop) {
	var ret='';
	for (var i=0; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof '') {
		    ret += emptySpanHTML(list[i], navpop.idNumber, 'div');
		} else if (typeof list[i] == typeof [] &amp;&amp; list[i].length &gt; 0 ) {
			ret = ret.parenSplit(RegExp('(&lt;/[^&gt;]*?&gt;$)')).join(makeEmptySpans(list[i], navpop));
		} else if (typeof list[i] == typeof {} &amp;&amp; list[i].nodeType ) {
			ret += emptySpanHTML(list[i].name, navpop.idNumber, list[i].nodeType);
		}
	}
	return ret;
}


function emptySpanHTML(name, id, tag, classname) {
	tag = tag || 'span';
	if (!classname) { classname = emptySpanHTML.classAliases[name]; }
	classname = classname || name;
	if (name == getValueOf('popupDragHandle')) { classname += ' popupDragHandle'; }
	return simplePrintf('&lt;%s id=&quot;%s&quot; class=&quot;%s&quot;&gt;&lt;/%s&gt;', [tag, name + id, classname, tag]);
}
emptySpanHTML.classAliases={ 'popupSecondPreview': 'popupPreview' };

// generate html for popup image
// &lt;a id=&quot;popupImageLinkn&quot;&gt;&lt;img id=&quot;popupImagen&quot;&gt;
// where n=idNumber
function imageHTML(article, idNumber) {
	return simplePrintf('&lt;a id=&quot;popupImageLink$1&quot;&gt;' +
			    '&lt;img align=&quot;right&quot; valign=&quot;top&quot; id=&quot;popupImg$1&quot; style=&quot;display: none;&quot;&gt;&lt;/img&gt;' +
			    '&lt;/a&gt;', [ idNumber ]);
}

function popTipsSoonFn(id, when, popData) {
	when || ( when=250 );
	var popTips=function(){ setupTooltips(document.getElementById(id), false, true, popData); };
	return function() { setTimeout( popTips, when, popData ); };
}

function setPopupTipsAndHTML(html, divname, idnumber, popData) {
	setPopupHTML(html, divname, idnumber,
		     getValueOf('popupSubpopups') ? 
		     popTipsSoonFn(divname + idnumber, null, popData) : 
		     null);
}
// ENDFILE: htmloutput.js
// STARTFILE: mouseout.js
//////////////////////////////////////////////////
// fuzzy checks

function fuzzyCursorOffMenus(x,y, fuzz, parent) {
	if (!parent) { return null; }
	var uls=parent.getElementsByTagName('ul');
	for (var i=0; i&lt;uls.length; ++i) {
		if (uls[i].className=='popup_menu') {
			if (uls[i].offsetWidth &gt; 0) return false;
		} // else {document.title+='.';}
	}
	return true;
}

function checkPopupPosition () { // stop the popup running off the right of the screen
	// FIXME avoid pg.current.link
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp;
	    pg.current.link.navpopup.limitHorizontalPosition();
}

function mouseOutWikiLink () {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	//console ('mouseOutWikiLink');
	var a=this;
	if (a.navpopup==null) return;
	if ( ! a.navpopup.isVisible() ) {
		a.navpopup.banish();
		return;
	}
        restoreTitle(a);
	Navpopup.tracker.addHook(posCheckerHook(a.navpopup));
}

function posCheckerHook(navpop) {
	return function() {
		if (!navpop.isVisible()) { return true; /* remove this hook */ }
		if (Navpopup.tracker.dirty) {
		    return false;
		}
		var x=Navpopup.tracker.x, y=Navpopup.tracker.y;
		var mouseOverNavpop = navpop.isWithin(x,y,navpop.fuzz, navpop.mainDiv) ||
		    !fuzzyCursorOffMenus(x,y,navpop.fuzz, navpop.mainDiv);

		// FIXME it'd be prettier to do this internal to the Navpopup objects
		var t=getValueOf('popupHideDelay');
		if (t) { t = t * 1000; }
		if (!t) {
			if(!mouseOverNavpop) {
			    navpop.banish();
			    return true; /* remove this hook */
			}
			return false;
		}
		// we have a hide delay set
		var d=+(new Date());
		if ( !navpop.mouseLeavingTime ) {
			navpop.mouseLeavingTime = d;
			return false;
		}
		if ( mouseOverNavpop ) {
			navpop.mouseLeavingTime=null;
			return false;
		}
		if (d - navpop.mouseLeavingTime &gt; t) {
			navpop.mouseLeavingTime=null;
			navpop.banish(); return true; /* remove this hook */
		}
		return false;
	};
}

function runStopPopupTimer(navpop) {
	// at this point, we should have left the link but remain within the popup
	// so we call this function again until we leave the popup.
	if (!navpop.stopPopupTimer) {
		navpop.stopPopupTimer=setInterval(posCheckerHook(navpop), 500);
		navpop.addHook(function(){clearInterval(navpop.stopPopupTimer);},
			       'hide', 'before');
	}
}
// ENDFILE: mouseout.js
// STARTFILE: previewmaker.js
/**
   @fileoverview
   Defines the {@link Previewmaker} object, which generates short previews from wiki markup.
*/

/**
   Creates a new Previewmaker
   @constructor
   @class The Previewmaker class. Use an instance of this to generate short previews from Wikitext.
   @param {String} wikiText The Wikitext source of the page we wish to preview.
   @param {String} baseUrl The url we should prepend when creating relative urls.
   @param {Navpopup} owner The navpop associated to this preview generator
*/
function Previewmaker(wikiText, baseUrl, owner) {
	/** The wikitext which is manipulated to generate the preview. */
	this.originalData=wikiText;
	this.setData();
	this.baseUrl=baseUrl;
	this.owner=owner;
	this.maxCharacters=getValueOf('popupMaxPreviewCharacters');
	this.maxSentences=getValueOf('popupMaxPreviewSentences');
}
Previewmaker.prototype.setData=function() {
	var maxSize=max(10000, 2*this.maxCharacters);
	this.data=this.originalData.substring(0,maxSize);
};
/** Remove HTML comments
    @private
*/
Previewmaker.prototype.killComments = function () {
	// this also kills one trailing newline, eg [[diamyo]]
	this.data=this.data.replace(RegExp('&lt;!--[\\s\\S]*?--&gt;\\n?', 'g'), ''); 
};
/**
   @private
*/
Previewmaker.prototype.killDivs = function () {
	// say goodbye, divs (can be nested, so use * not *?)
	this.data=this.data.replace(RegExp('&lt; *div[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *div *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killGalleries = function () {
	this.data=this.data.replace(RegExp('&lt; *gallery[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *gallery *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.kill = function(opening, closing, subopening, subclosing, repl) {
	var oldk=this.data;
	var k=this.killStuff(this.data, opening, closing, subopening, subclosing, repl);
	while (k.length &lt; oldk.length) {
		oldk=k;
		k=this.killStuff(k, opening, closing, subopening, subclosing, repl);
	}
	this.data=k;
};
/**
   @private
*/
Previewmaker.prototype.killStuff = function (txt, opening, closing, subopening, subclosing, repl) {
	var op=this.makeRegexp(opening);
	var cl=this.makeRegexp(closing, '^');
	var sb=subopening ? this.makeRegexp(subopening, '^') : null;
	var sc=subclosing ? this.makeRegexp(subclosing, '^') : cl;
	if (!op || !cl) {
	    alert('Navigation Popups error: op or cl is null! something is wrong.');
	    return;
	}
	if (!op.test(txt)) { return txt; }
	var ret='';
	var opResult = op.exec(txt);
	ret = txt.substring(0,opResult.index);
	txt=txt.substring(opResult.index+opResult[0].length);
	var depth = 1;
	while (txt.length &gt; 0) {
		var removal=0;
		if (depth==1 &amp;&amp; cl.test(txt)) {
			depth--;
			removal=cl.exec(txt)[0].length;
		} else if (depth &gt; 1 &amp;&amp; sc.test(txt)) {
			depth--;
			removal=sc.exec(txt)[0].length;
		}else if (sb &amp;&amp; sb.test(txt)) {
			depth++;
			removal=sb.exec(txt)[0].length;
		}
		if ( !removal ) { removal = 1; }
		txt=txt.substring(removal);
		if (depth==0) { break; }
	}
	return ret + (repl || '') + txt;
};
/**
   @private
*/
Previewmaker.prototype.makeRegexp = function (x, prefix, suffix) {
	prefix = prefix || '';
	suffix = suffix || '';
	var reStr='';
	var flags='';
	if (isString(x)) {
		reStr=prefix + literalizeRegex(x) + suffix;
	} else if (isRegExp(x)) {
		var s=x.toString().substring(1);
		var sp=s.split('/');
		flags=sp[sp.length-1];
		sp[sp.length-1]='';
		s=sp.join('/');
		s=s.substring(0,s.length-1);
		reStr= prefix + s + suffix;
	} else {
		log ('makeRegexp failed');
	}

	log ('makeRegexp: got reStr=' + reStr + ', flags=' + flags);
	return RegExp(reStr, flags);
};
/**
   @private
*/
Previewmaker.prototype.killBoxTemplates = function () {

	// taxobox removal... in fact, there's a saudiprincebox_begin, so let's be more general
	// also, have float_begin, ... float_end
	this.kill(RegExp('[{][{][^{}\\s|]*?(float|box)[_ ](begin|start)', 'i'),	/[}][}]\s*/, '{{');

	// infoboxes etc
	// from [[User:Zyxw/popups.js]]: kill frames too
	this.kill(RegExp('[{][{][^{}\\s|]*?(infobox|elementbox|frame)[_ ]', 'i'), /[}][}]\s*/, '{{');

};
/**
   @private
*/
Previewmaker.prototype.killTemplates = function () {
	this.kill('{{', '}}', '{', '}', ' ');
};
/**
   @private
*/
Previewmaker.prototype.killTables = function () {
	// tables are bad, too
	// this can be slow, but it's an inprovement over a browser hang
	// torture test: [[Comparison_of_Intel_Central_Processing_Units]]
	this.kill('{|', /[|]}\s*/, '{|');
	this.kill(/&lt;table.*?&gt;/i, /&lt;\/table.*?&gt;/i, /&lt;table.*?&gt;/i);
	// remove lines starting with a pipe for the hell of it (?)
	this.data=this.data.replace(RegExp('^[|].*$', 'mg'), '');
};
/**
   @private
*/
Previewmaker.prototype.killImages = function () {
	var forbiddenNamespaceAliases = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=pg.nsImageId &amp;&amp; _namespaceId!=pg.nsCategoryId) return;
		forbiddenNamespaceAliases.push(_localizedNamespaceLc.split(' ').join('[ _]')); //todo: escape regexp fragments!
	});
	
	// images and categories are a nono
	this.kill(RegExp('[[][[]\\s*(' + forbiddenNamespaceAliases.join('|') + ')\\s*:', 'i'),
		  /\]\]\s*/, '[', ']');
};
/**
   @private
*/
Previewmaker.prototype.killHTML = function () {
	// kill &lt;ref ...&gt;...&lt;/ref&gt;
	this.kill(/&lt;ref\b[^/&gt;]*?&gt;/i, /&lt;\/ref&gt;/i);

	// let's also delete entire lines starting with &lt;. it's worth a try.
	this.data=this.data.replace(RegExp('(^|\\n) *&lt;.*', 'g'), '\n');

	// and those pesky html tags, but not &lt;nowiki&gt; or &lt;blockquote&gt;
	var splitted=this.data.parenSplit(/(&lt;.*?&gt;)/);
	var len=splitted.length;
	for (var i=1; i&lt;len; i=i+2) {
		switch (splitted[i]) {
		case '&lt;nowiki&gt;':
		case '&lt;/nowiki&gt;':
				// &lt;nowiki&gt;
			break;
		default:
			if (! /^&lt; *\/? *blockquote\b/i.test(splitted[i])) {
				splitted[i]='';
			}
		}
	}
	this.data=splitted.join('');
};
/**
   @private
*/
Previewmaker.prototype.killChunks = function() { // heuristics alert
	// chunks of italic text? you crazy, man?
	var italicChunkRegex=new RegExp
	(&quot;((^|\\n)\\s*:*\\s*''[^']([^']|'''|'[^']){20}(.|\\n[^\\n])*''[.!?\\s]*\\n)+&quot;, 'g');
	// keep stuff separated, though, so stick in \n (fixes [[Union Jack]]?
	this.data=this.data.replace(italicChunkRegex, '\n');
};
/**
   @private
*/
Previewmaker.prototype.mopup = function () {
	// we simply *can't* be doing with horizontal rules right now
	this.data=this.data.replace(RegExp('^-{4,}','mg'),'');

	// no indented lines
	this.data=this.data.replace(RegExp('(^|\\n) *:[^\\n]*','g'), '');

	// replace __TOC__, __NOTOC__ and whatever else there is
	// this'll probably do
	this.data=this.data.replace(RegExp('^__[A-Z_]*__ *$', 'gmi'),'');
};
/**
   @private
*/
Previewmaker.prototype.firstBit = function () {
	// dont't be givin' me no subsequent paragraphs, you hear me?
	/// first we &quot;normalize&quot; section headings, removing whitespace after, adding before
	var d=this.data;

	if (getValueOf('popupPreviewCutHeadings')) {
		this.data=this.data.replace(RegExp('\\s*(==+[^=]*==+)\\s*', 'g'), '\n\n$1 ');
		/// then we want to get rid of paragraph breaks whose text ends badly
		this.data=this.data.replace(RegExp('([:;]) *\\n{2,}', 'g'), '$1\n');

		this.data=this.data.replace(RegExp('^[\\s\\n]*'), '');
		stuff=(RegExp('^([^\\n]|\\n[^\\n\\s])*')).exec(this.data);
		if (stuff) { d = stuff[0]; }
		if (!getValueOf('popupPreviewFirstParOnly')) { d = this.data; }

		/// now put \n\n after sections so that bullets and numbered lists work
		d=d.replace(RegExp('(==+[^=]*==+)\\s*', 'g'), '$1\n\n');
	}


	// superfluous sentences are RIGHT OUT.
	// note: exactly 1 set of parens here needed to make the slice work
	d = d.parenSplit(RegExp('([!?.]+[&quot;'+&quot;'&quot;+']*\\s)','g'));
	// leading space is bad, mmkay?
	d[0]=d[0].replace(RegExp('^\\s*'), '');

	var notSentenceEnds=RegExp('([^.][a-z][.] *[a-z]|etc|sic|Dr|Mr|Mrs|Ms|St|no|op|cit|\\[[^\\]]*|\\s[A-Zvclm])$', 'i');
	d = this.fixSentenceEnds(d, notSentenceEnds);

	this.fullLength=d.join('').length;
	var maxChars=getValueOf('popupMaxPreviewCharacters') + this.extraCharacters;
	var n=this.maxSentences;
	var dd=this.firstSentences(d,n); 

	do {
		dd=this.firstSentences(d,n); --n;
	} while ( dd.length &gt; this.maxCharacters &amp;&amp; n != 0 );

	this.data = dd;
};
/**
   @private
*/
Previewmaker.prototype.fixSentenceEnds = function(strs, reg) {
	// take an array of strings, strs
	// join strs[i] to strs[i+1] &amp; strs[i+2] if strs[i] matches regex reg

	var abbrevRe=/\b[a-z][^a-z]*$/i;

	for (var i=0; i&lt;strs.length-2; ++i) {
		if (reg.test(strs[i])) {
			a=[];
			for (var j=0; j&lt;strs.length; ++j) {
				if (j&lt;i)   a[j]=strs[j];
				if (j==i)  a[i]=strs[i]+strs[i+1]+strs[i+2];
				if (j&gt;i+2) a[j-2]=strs[j];
			}
			return this.fixSentenceEnds(a,reg);
		}
		// BUGGY STUFF - trying to fix up [[S. C. Johnson &amp; Son]] preview
		if (false &amp;&amp; abbrevRe.test(strs[i])) {
			var j=i, buf='';
			do {
				buf=buf+strs[i]+strs[i+1];
				i=i+2;
			} while (i&lt;strs.length-2 &amp;&amp; abbrevRe.test(strs[i]));
			strs[i]=buf+strs[i];
			var a=(j?strs.slice(0,j-1):[]).concat(strs.slice(i));
			return this.fixSentenceEnds(a,reg);
		}
	}
	return strs;
};
/**
   @private
*/
Previewmaker.prototype.firstSentences = function(strs, howmany) {
	var t=strs.slice(0, 2*howmany);
	return t.join('');
};
/**
   @private
*/
Previewmaker.prototype.killBadWhitespace = function() {
	// also cleans up isolated '''', eg [[Suntory Sungoliath]]
	this.data=this.data.replace(RegExp('^ *\'+ *$', 'gm'), '');
};
/**
   Runs the various methods to generate the preview.
   The preview is stored in the &lt;code&gt;html&lt;/html&gt; field.
   @private
*/
Previewmaker.prototype.makePreview = function() {
	if (this.owner.article.namespaceId()!=pg.nsTemplateId &amp;&amp;
				this.owner.article.namespaceId()!=pg.nsImageId ) {
		this.killComments();
		this.killDivs();
		this.killGalleries();
		this.killBoxTemplates();

		if (getValueOf('popupPreviewKillTemplates')) {
			this.killTemplates();
		} else {
			this.killMultilineTemplates();
		}
		this.killTables();
		this.killImages();
		this.killHTML();
		this.killChunks();
		this.mopup();

		this.firstBit();
		this.killBadWhitespace();
	}
	else
	{
		this.killHTML();
	}
	this.html=wiki2html(this.data, this.baseUrl); // needs livepreview
	this.fixHTML();
	this.stripLongTemplates();
};
/**
   @private
*/
Previewmaker.prototype.esWiki2HtmlPart = function(data) {
  var reLinks = /(?:\[\[([^|\]]*)(?:\|([^|\]]*))*]]([a-z]*))/gi; //match a wikilink
  reLinks.lastIndex = 0; //reset regex

  var match;
  var result = &quot;&quot;;
  var postfixIndex = 0;
  while ((match = reLinks.exec(data)) != null) //match all wikilinks
  {
    //FIXME: the way that link is built here isn't perfect. It is clickable, but popups preview won't recognize it in some cases.
    result += mw.html.escape(data.substring(postfixIndex, match.index)) + 
              '&lt;a href=&quot;'+Insta.conf.paths.articles+mw.html.escape(match[1])+'&quot;&gt;'+mw.html.escape((match[2]?match[2]:match[1])+match[3])+&quot;&lt;/a&gt;&quot;;
    postfixIndex = reLinks.lastIndex;
  }
  //append the rest
  result += mw.html.escape(data.substring(postfixIndex));
  
  return result;
};
Previewmaker.prototype.editSummaryPreview=function() {
	var reAes   = /\/\* *(.*?) *\*\//g; //match the first section marker
	reAes.lastIndex = 0; //reset regex
	
	var match;
	
	match = reAes.exec(this.data);
	if (match)
	{
		//we have a section link. Split it, process it, combine it.
		var prefix = this.data.substring(0,match.index-1);
		var section = match[1];
		var postfix = this.data.substring(reAes.lastIndex);
		
		var start = &quot;&lt;span class='autocomment'&gt;&quot;;
		var end = &quot;&lt;/span&gt;&quot;;
		if (prefix.length&gt;0) start = this.esWiki2HtmlPart(prefix) + &quot; &quot; + start + &quot;- &quot;;
		if (postfix.length&gt;0) end = &quot;: &quot; + end + this.esWiki2HtmlPart(postfix);
		

		var t=new Title().fromURL(this.baseUrl);
		t.anchorFromUtf(section);
		var sectionLink = Insta.conf.paths.articles + mw.html.escape(t.toString(true)) + '#' + mw.html.escape(t.anchor);
		return start + '&lt;a href=&quot;'+sectionLink+'&quot;&gt;&amp;rarr;&lt;/a&gt; '+mw.html.escape(section) + end;
	}
	
	//else there's no section link, htmlify the whole thing.
	return this.esWiki2HtmlPart(this.data);
};

//&lt;NOLITE&gt;
/** Test function for debugging preview problems one step at a time.
 */
function previewSteps(txt) {
	try {
		txt=txt || document.editform.wpTextbox1.value;
	} catch (err) {
		if (pg.cache.pages.length &gt; 0) {
			txt=pg.cache.pages[pg.cache.pages.length-1].data;
		} else {
			alert('provide text or use an edit page');
		}
	}
	txt=txt.substring(0,10000);
	var base=pg.wiki.articlebase + Title.fromURL(document.location.href).urlString();
	var p=new Previewmaker(txt, base, pg.current.link.navpopup);
	if (this.owner.article.namespaceId() != pg.nsTemplateId) {
		p.killComments(); if (!confirm('done killComments(). Continue?\n---\n' + p.data)) { return; }
		p.killDivs(); if (!confirm('done killDivs(). Continue?\n---\n' + p.data)) { return; }
		p.killGalleries(); if (!confirm('done killGalleries(). Continue?\n---\n' + p.data)) { return; }
		p.killBoxTemplates(); if (!confirm('done killBoxTemplates(). Continue?\n---\n' + p.data)) { return; }

		if (getValueOf('popupPreviewKillTemplates')) {
			p.killTemplates(); if (!confirm('done killTemplates(). Continue?\n---\n' + p.data)) { return; }
		} else {
			p.killMultilineTemplates(); if (!confirm('done killMultilineTemplates(). Continue?\n---\n' + p.data)) { return; }
		}

		p.killTables(); if (!confirm('done killTables(). Continue?\n---\n' + p.data)) { return; }
		p.killImages(); if (!confirm('done killImages(). Continue?\n---\n' + p.data)) { return; }
		p.killHTML(); if (!confirm('done killHTML(). Continue?\n---\n' + p.data)) { return; }
		p.killChunks(); if (!confirm('done killChunks(). Continue?\n---\n' + p.data)) { return; }
		p.mopup(); if (!confirm('done mopup(). Continue?\n---\n' + p.data)) { return; }

		p.firstBit(); if (!confirm('done firstBit(). Continue?\n---\n' + p.data)) { return; }
		p.killBadWhitespace(); if (!confirm('done killBadWhitespace(). Continue?\n---\n' + p.data)) { return; }
	}

	p.html=wiki2html(p.data, base); // needs livepreview
	p.fixHTML(); if (!confirm('done fixHTML(). Continue?\n---\n' + p.html)) { return; }
	p.stripLongTemplates(); if (!confirm('done stripLongTemplates(). Continue?\n---\n' + p.html)) { return; }
	alert('finished preview - end result follows.\n---\n' + p.html);
}
//&lt;/NOLITE&gt;

/**
   Works around a quoting bug in livepreview.
   &lt;code&gt;wiki2html('[[Foo\'s &quot;bar&quot;]]')&lt;/code&gt; gives @literal{&lt;a href='Foo's &quot;bar&quot;'&gt;}
   which doesn't do very well. We change this into @literal{&lt;a href=&quot;Foo's %22bar%22&quot;&gt;}
   @private
*/
Previewmaker.prototype.fixHTML = function() {
	if(!this.html) return;
	// all links seem to have potential issues with quotation marks
	var splitted=this.html.parenSplit(/href='([^&gt;]*)'/g);
	var ret='';
	for (var i=0; i&lt;splitted.length; ++i) {
		if(i%2==0) { ret += splitted[i]; continue; }
		if(i%2==1) { ret += 'href=&quot;' + splitted[i].split('&quot;').join('%22') + '&quot;'; }
	}
	// fix question marks in wiki links
	// maybe this'll break some stuff :-(
	ret=ret.replace(RegExp('\(&lt;a href=&quot;' + pg.wiki.articlePath + '/[^&quot;]*\)[?]\(.*?&quot;\)', 'g'), '$1%3F$2');
	// FIXME fix up % too
	this.html=ret;
};
/**
   Generates the preview and displays it in the current popup.

   Does nothing if the generated preview is invalid or consists of whitespace only.
   Also activates wikilinks in the preview for subpopups if the popupSubpopups option is true.
*/
Previewmaker.prototype.showPreview = function () {
	this.makePreview();
	if (typeof this.html != typeof '') return;
	if (RegExp('^\\s*$').test(this.html)) return;
	setPopupHTML('&lt;hr&gt;', 'popupPrePreviewSep', this.owner.idNumber);
	setPopupTipsAndHTML(this.html, 'popupPreview', this.owner.idNumber, { owner: this.owner });
	var more = (this.fullLength &gt; this.data.length) ? this.moreLink() : '';
	setPopupHTML(more, 'popupPreviewMore', this.owner.idNumber);
};
/**
   @private
*/
Previewmaker.prototype.moreLink=function() {
	var a=document.createElement('a');
	a.className='popupMoreLink';
	a.innerHTML=popupString('more...');
	var savedThis=this;
	a.onclick=function() {
		savedThis.maxCharacters+=2000;
		savedThis.maxSentences+=20;
		savedThis.setData();
		savedThis.showPreview();
	}
	return a;
}

/**
   @private
*/
Previewmaker.prototype.stripLongTemplates = function() {
	// operates on the HTML!
	this.html=this.html.replace(RegExp('^.{0,1000}[{][{][^}]*?(&lt;(p|br)( /)?&gt;\\s*){2,}([^{}]*?[}][}])?', 'gi'), '');
	this.html=this.html.split('\n').join(' '); // workaround for &lt;pre&gt; templates
	this.html=this.html.replace(RegExp('[{][{][^}]*&lt;pre&gt;[^}]*[}][}]','gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killMultilineTemplates = function() {
	this.kill('{{{', '}}}');
	this.kill(RegExp('\\s*[{][{][^{}]*\\n'), '}}', '{{');
};
// ENDFILE: previewmaker.js
// STARTFILE: querypreview.js
function loadAPIPreview(queryType, article, navpop) {
	var art=new Title(article).urlString();
	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;';
	var htmlGenerator=function(a,d){alert('invalid html generator');};
	switch (queryType) {
	case 'history':
		url += 'meta=userinfo&amp;uiprop=options&amp;titles=' + art + '&amp;prop=revisions&amp;rvlimit=' +
			getValueOf('popupHistoryPreviewLimit');
		htmlGenerator=APIhistoryPreviewHTML;
		break;
	case 'category':
		url += 'list=categorymembers&amp;rawcontinue=&amp;cmtitle=' + art;
		htmlGenerator=APIcategoryPreviewHTML;
		break;
	case 'userinfo':
	  var username = new Title( article ).userName();
		var usernameart = encodeURIComponent( username );
		if (pg.re.ipUser.test(username)) {
			url += 'list=blocks&amp;bkprop=range&amp;bkip=' + usernameart;
		} else {
			url += 'list=users&amp;usprop=blockinfo|groups|editcount|registration&amp;ususers=' + usernameart + &quot;&amp;meta=globaluserinfo&amp;guiprop=groups|unattached&amp;guiuser=&quot;+ usernameart;
		}
		htmlGenerator=APIuserInfoPreviewHTML;
		break;
	case 'contribs':
		var usernameart = encodeURIComponent( new Title( article ).userName() );
		url += 'list=usercontribs&amp;meta=userinfo&amp;uiprop=options&amp;ucuser=' + usernameart +
			'&amp;uclimit=' + getValueOf('popupContribsPreviewLimit');
		htmlGenerator=APIcontribsPreviewHTML;
		break;
	case 'imagepagepreview':
		var trail='';
		if (getValueOf('popupImageLinks')) { trail = '&amp;list=imageusage&amp;iutitle=' + art; }
		url += 'titles=' + art + '&amp;prop=revisions|imageinfo&amp;rvprop=content' + trail;
		htmlGenerator=APIimagepagePreviewHTML;
		break;
	case 'backlinks':
		url += 'list=backlinks&amp;rawcontinue=&amp;bltitle=' + art;
		htmlGenerator=APIbacklinksPreviewHTML;
		break;
	}
	pendingNavpopTask(navpop);
	var callback=function(d){
	    log( &quot;callback of API functions was hit&quot; );
		showAPIPreview(queryType, htmlGenerator(article,d,navpop), navpop.idNumber, navpop, d);
	};
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_'+queryType+'_QUERY_DATA'); }
}

function linkList(list) {
	list.sort(function(x,y) { return (x==y ? 0 : (x&lt;y ? -1 : 1)); });
	var buf=[];
	for (var i=0; i&lt;list.length; ++i) {
		buf.push(wikiLink({article: new Title(list[i]),
				   text:    list[i].split(' ').join('&amp;nbsp;'),
				   action:  'view'}));
	}
	return buf.join(', ');
}

function getTimeOffset(tz) {
	if( tz ) {
		if( tz.indexOf('|') &gt; -1 ) {
			// New format
			return parseInt(tz.split('|')[1],10);
		} else if ( tz.indexOf(':') &gt; -1 ) {
			// Old format
			return( parseInt(tz,10)*60 + parseInt(tz.split(':')[1],10) );
		}
	}
	return 0;
}

function editPreviewTable(article, h, reallyContribs, timeOffset) {
	var html=['&lt;table&gt;'];
	var day=null;
	var curart=article;
	for (var i=0; i&lt;h.length; ++i) {
		if (reallyContribs) { 
		    var page=h[i]['title']; curart = new Title(page);
		}
		var minor=typeof h[i]['minor']=='undefined' ? '' : '&lt;b&gt;m &lt;/b&gt;';
		var editDate=adjustDate(getDateFromTimestamp(h[i].timestamp), timeOffset);
		var thisDay = dayFormat(editDate);
		var thisTime = timeFormat(editDate);
		if (thisDay==day) { thisDay=''; }
		else { day=thisDay; }
		if (thisDay) {
			html.push( '&lt;tr&gt;&lt;td colspan=3&gt;&lt;span class=&quot;popup_history_date&quot;&gt;' +
				  thisDay+'&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;' );
		}
		html.push('&lt;tr class=&quot;popup_history_row_' + ( (i%2) ? 'odd' : 'even') + '&quot;&gt;');
		html.push('&lt;td&gt;(&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;diff=prev&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + popupString('last') + '&lt;/a&gt;)&lt;/td&gt;');
		html.push('&lt;td&gt;' +
			'&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + thisTime + '&lt;/a&gt;&lt;/td&gt;');
		var col3url='', col3txt='';
		if (!reallyContribs) {
			var user=h[i]['user'];
			if( typeof h[i]['userhidden'] == &quot;undefined&quot; ) {
				if( pg.re.ipUser.test(user) ) {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId] + ':Contributions&amp;target=' + new Title(user).urlString();
				} else {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(user).urlString();
				}
				col3txt=mw.html.escape(user);
			} else {
				col3url=getValueOf('popupRevDelUrl');
				col3txt=mw.html.escape( popupString('revdel'));
			}
		} else {
			col3url=pg.wiki.titlebase + curart.urlString();
			col3txt=mw.html.escape(page);
		}
		html.push('&lt;td&gt;' + (reallyContribs ? minor : '') +
			'&lt;a href=&quot;' + col3url + '&quot;&gt;' + col3txt + '&lt;/a&gt;&lt;/td&gt;');
		var comment='';
		var c=h[i].comment || h[i]['*'];
		if (c) {
			comment=new Previewmaker(c, new Title(curart).toUrl()).editSummaryPreview();
		} else if (typeof h[i]['commenthidden'] != &quot;undefined&quot; ) {
			comment=popupString('revdel');
		}
		html.push('&lt;td&gt;' + (!reallyContribs ? minor : '') + comment + '&lt;/td&gt;');
		html.push('&lt;/tr&gt;');
		html=[html.join('')];
	}
	html.push('&lt;/table&gt;');
	return html.join('');
}

function getDateFromTimestamp(t) {
	var s=t.split(/[^0-9]/);
	switch(s.length) {
	case 0: return null;
	case 1: return new Date(s[0]);
	case 2: return new Date(s[0], s[1]-1);
	case 3: return new Date(s[0], s[1]-1, s[2]);
	case 4: return new Date(s[0], s[1]-1, s[2], s[3]);
	case 5: return new Date(s[0], s[1]-1, s[2], s[3], s[4]);
	case 6: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5]);
	default: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5], s[6]);
	}
}

function adjustDate(d, offset) {
	// offset is in minutes
	var o=offset * 60 * 1000;
	return new Date( +d + o);
}

function dayFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCFullYear(), editDate.getUTCMonth()+1, editDate.getUTCDate()]).join('-'); }
	return map(zeroFill, [editDate.getFullYear(), editDate.getMonth()+1, editDate.getDate()]).join('-');
}

function timeFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCHours(), editDate.getUTCMinutes(), editDate.getUTCSeconds()]).join(':'); }
	return map(zeroFill, [editDate.getHours(), editDate.getMinutes(), editDate.getSeconds()]).join(':');
}

function showAPIPreview(queryType, html, id, navpop, download) {
    // DJ: done
	var target='popupPreview';
	switch (queryType) {
	case 'imagelinks':
	case 'category':
	case 'userinfo':
		target='popupPostPreview'; break;
	}
	setPopupTipsAndHTML(html, target, id);
	completedNavpopTask(navpop);
}

function APIbacklinksPreviewHTML(article, download, navpop) {
    try {
	    var jsObj=getJsObj(download.data);
   	    var list=jsObj.query.backlinks;
	} catch (someError) { return 'backlinksPreviewHTML went wonky'; }
	var html=[];
	if (!list) { return popupString('No backlinks found'); }
	for ( var i=0; i &lt; list.length; i++ ) {
		var t=new Title(list[i]['title']);
		html.push('&lt;a href=&quot;' + pg.wiki.titlebase + t.urlString() + '&quot;&gt;' + t + '&lt;/a&gt;');
	}
	html=html.join(', ');
	if (jsObj['query-continue'] &amp;&amp; jsObj['query-continue'].backlinks &amp;&amp; jsObj['query-continue'].backlinks.blcontinue) {
		html += popupString(' and more');
	}
	return html;
}

function APIsharedImagePagePreviewHTML(obj) {
	log( &quot;APIsharedImagePagePreviewHTML&quot; );
	var popupid = obj['requestid'];
	if( obj['query'] &amp;&amp; obj['query']['pages'] )
	{
		var page=anyChild(obj['query']['pages']);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
		if( content ) 
		{
			/* Not entirely safe, but the best we can do */
			var p=new Previewmaker(content, pg.current.link.navpopup.article, pg.current.link.navpopup);
			p.makePreview();
			setPopupHTML( p.html, &quot;popupSecondPreview&quot;, popupid );
		}
	}
}

function APIimagepagePreviewHTML(article, download, navpop) {
	try {
	    var jsObj=getJsObj(download.data);
		var page=anyChild(jsObj.query.pages);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
	} catch (someError) {
		return 'API imagepage preview failed :(';
	}
	var ret='';
	var alt='';
	try{alt=navpop.parentAnchor.childNodes[0].alt;} catch(e){}
	if (alt) {
		ret = ret + '&lt;hr&gt;&lt;b&gt;' + popupString('Alt text:') + '&lt;/b&gt; ' + mw.html.escape(alt);
	}
	if (content) {
		var p=prepPreviewmaker(content, article, navpop);
		p.makePreview();
		if (p.html) { ret += '&lt;hr&gt;' + p.html; }
	}
	if (content!==null &amp;&amp; getValueOf('popupSummaryData')) {
		var info=getPageInfo(content, download);
		log(info);
		setPopupTrailer(info, navpop.idNumber);
	}
	if (page &amp;&amp; page.imagerepository == &quot;shared&quot; ) {
		var art=new Title(article);
		var encart = encodeURIComponent( &quot;File:&quot; + art.stripNamespace() );
		var shared_url =  pg.wiki.apicommonsbase + '?format=json&amp;callback=APIsharedImagePagePreviewHTML' +
							'&amp;requestid=' + navpop.idNumber +
							'&amp;action=query&amp;prop=revisions&amp;rvprop=content&amp;titles=' + encart;
		if (pg.flag.isIE) {
			shared_url = shared_url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
		}

		ret = ret +'&lt;hr&gt;' + popupString( 'Image from Commons') +
				': &lt;a href=&quot;' + pg.wiki.commonsbase + '?title=' + encart + '&quot;&gt;' +
				popupString( 'Description page') + '&lt;/a&gt;';
		mw.loader.load( shared_url );
	}
	showAPIPreview('imagelinks', APIimagelinksPreviewHTML(article,download), navpop.idNumber, download);
	return ret;
}

function APIimagelinksPreviewHTML(article, download) {
	try {
		var jsobj=getJsObj(download.data);
		var list=jsobj.query.imageusage;
		if (!list) { return popupString('No image links found'); }
	} catch(someError) { return 'Image links preview generation failed :('; }
	var ret=[];
	for (var i=0; i &lt; list.length; i++) {
		ret.push(list[i]['title']);
	}
	if (ret.length === 0) { return popupString('No image links found'); }
	return '&lt;h2&gt;' + popupString('File links') + '&lt;/h2&gt;' + linkList(ret);
}

function APIcategoryPreviewHTML(article, download) {
    try{
        var jsobj=getJsObj(download.data);
        var list=jsobj.query.categorymembers;
    } catch(someError) { return 'Category preview failed :('; }
	var ret=[];
	for (var p=0; p &lt; list.length; p++) { 
	   ret.push(list[p]['title']); 
	}
	if (ret.length === 0) { return popupString('Empty category'); }
	ret = '&lt;h2&gt;' + tprintf('Category members (%s shown)', [ret.length]) + '&lt;/h2&gt;' +linkList(ret);
	if (jsobj['query-continue'] &amp;&amp; jsobj['query-continue'].categorymembers &amp;&amp; jsobj['query-continue'].categorymembers.cmcontinue) {
		ret += popupString(' and more');
	}
	return ret;
}

function APIuserInfoPreviewHTML(article, download) {
	var ret=[];
	try{
		var queryobj=getJsObj(download.data).query;
	} catch(someError) { return 'Userinfo preview failed :('; }
	
	var user=anyChild(queryobj.users);
	if (user) {
		var globaluserinfo=queryobj.globaluserinfo;
		if (user.invalid == '') {
			ret.push( popupString( 'Invalid user') );
		} else if (user.missing == '') {
			ret.push( popupString( 'Not a registered username') );
		}
		if( user.blockedby )
			ret.push('&lt;b&gt;' + popupString('BLOCKED') + '&lt;/b&gt;');
		if( globaluserinfo &amp;&amp; (globaluserinfo.locked != null || globaluserinfo.hidden != null) ) {
			var lockedSulAccountIsAttachedToThis = true;
			for( var i=0; globaluserinfo.unattached &amp;&amp; i &lt; globaluserinfo.unattached.length; i++) {
				if (globaluserinfo.unattached[i].wiki===mw.config.get('wgDBname')) { lockedSulAccountIsAttachedToThis=false; break; }
			}
			if (lockedSulAccountIsAttachedToThis) {
				if (globaluserinfo.locked != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('LOCKED') + '&lt;/i&gt;&lt;/b&gt;');
				if (globaluserinfo.hidden != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('HIDDEN') + '&lt;/i&gt;&lt;/b&gt;');
			}
		}
		for( var i=0; (user.groups &amp;&amp; i &lt; user.groups.length); i++) {
			switch (user.groups[i]) {
				case '*':
				case 'user':
				case 'autoconfirmed':
					break;
				default:
					ret.push( mw.html.escape(user.groups[i]) );
			}
		}
		for( var i=0; (globaluserinfo &amp;&amp; globaluserinfo.groups &amp;&amp; i &lt; globaluserinfo.groups.length); i++) {
			ret.push( '&lt;i&gt;'+mw.html.escape(globaluserinfo.groups[i])+'&lt;/i&gt;' );
		}
		if( user.editcount || user.registration )
			ret.push( mw.html.escape((user.editcount?user.editcount:'') + popupString(' edits since: ') + (user.registration?dayFormat(getDateFromTimestamp(user.registration)):'')) );
	}
	
	if (queryobj.blocks) {
		ret.push( popupString( 'IP user') ); //we only request list=blocks for IPs
		for (var i=0; i&lt;queryobj.blocks.length; i++) {
			ret.push('&lt;b&gt;' + popupString(queryobj.blocks[i].rangestart===queryobj.blocks[i].rangeend ? 'BLOCKED' : 'RANGEBLOCKED') + '&lt;/b&gt;' );
		}
	}
	
	ret = '&lt;hr&gt;' + ret.join( ', ' );
	return ret;
}

function APIcontribsPreviewHTML(article, download, navpop) {
    return APIhistoryPreviewHTML(article, download, navpop, true);
}

function APIhistoryPreviewHTML(article, download, navpop, reallyContribs) {
    try {
		var jsobj=getJsObj(download.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
		if( reallyContribs )
		    var edits=jsobj.query.usercontribs;
		else 
		    var edits=anyChild(jsobj.query.pages)['revisions'];
	} catch (someError) {
		return 'History preview failed :-(';
	}
	var timeOffset = getTimeOffset(tz);
	Cookie.create('popTz', timeOffset, 1);

	var ret=editPreviewTable(article, edits, reallyContribs, timeOffset);
	return ret;
}


//&lt;/NOLITE&gt;
// ENDFILE: querypreview.js
// STARTFILE: debug.js
////////////////////////////////////////////////////////////////////
// Debugging functions
////////////////////////////////////////////////////////////////////

function log(){}; // dummy to stop errors
function setupDebugging() {
//&lt;NOLITE&gt;
	if (window.popupDebug) { // popupDebug is set from .version
		window.log=function(x) { //if(gMsg!='')gMsg += '\n'; gMsg+=time() + ' ' + x; };
			window.console.log(x);
		}
		window.errlog=function(x) {
			window.console.error(x);
		}
		log('Initializing logger');
	} else {
//&lt;/NOLITE&gt;
		window.log = function(x) {};
		window.errlog = function(x) {};
//&lt;NOLITE&gt;
	}
//&lt;/NOLITE&gt;
}
// ENDFILE: debug.js
// STARTFILE: images.js

// load image of type Title.
function loadImage(image, navpop) {
	if (typeof image.stripNamespace != 'function') { alert('loadImages bad'); }
    // API call to retrieve image info.

	if (!getValueOf('popupImages')) return;
	if (!isValidImageName(image)) return false;
	
	var art=image.urlString();

	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query';
	url += '&amp;prop=imageinfo&amp;iiprop=url|mime&amp;iiurlwidth=' + getValueOf('popupImageSizeLarge');;
	url += '&amp;titles=' + art;
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}

	pendingNavpopTask(navpop);
	var callback=function(d){
		popupsInsertImage(navpop.idNumber, navpop, d);
	};
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'after', 'DOWNLOAD_IMAGE_QUERY_DATA'); }

}

function popupsInsertImage(id, navpop, download) {
	log( &quot;popupsInsertImage&quot;);
	try {
		var jsObj=getJsObj(download.data);
		var imagepage=anyChild(jsObj.query.pages);
		if (typeof imagepage.imageinfo === 'undefined') return;
		var imageinfo = imagepage.imageinfo[0];
	} catch (someError) {
		log( &quot;popupsInsertImage failed :(&quot; );
		return;
	}

	var popupImage = document.getElementById(&quot;popupImg&quot;+id);
	if (!popupImage) {
		log( &quot;could not find insertion point for image&quot;);
		return;
	}

	popupImage.width=getValueOf('popupImageSize');
	popupImage.style.display='inline';

	// Set the source for the image.
	if( imageinfo.thumburl )
		popupImage.src=imageinfo.thumburl;
	else if( imageinfo.mime.indexOf(&quot;image&quot;) == 0 ){
		popupImage.src=imageinfo.url;
		log( &quot;a thumb could not be found, using original image&quot; );
	} else log( &quot;fullsize imagethumb, but not sure if it's an image&quot;);


	var a=document.getElementById(&quot;popupImageLink&quot;+id);
	if (a === null) { return null; }

    // Determine the action of the surrouding imagelink.
	switch (getValueOf('popupThumbAction')) {
	case 'imagepage':
		if (pg.current.article.namespaceId()!=pg.nsImageId) {
			a.href=imageinfo.descriptionurl;
			// FIXME: unreliable pg.idNumber
			popTipsSoonFn('popupImage' + id)();
			break;
		} // else fall through
	case 'sizetoggle':
		a.onclick=toggleSize;
		a.title=popupString('Toggle image size');
		return;
	case 'linkfull':
		a.href = imageinfo.url;
		a.title=popupString('Open full-size image');
		return;
	}

}

// Toggles the image between inline small and navpop fullwidth.
// It's the same image, no actual sizechange occurs, only display width.
function toggleSize() {
	var imgContainer=this;
	if (!imgContainer) { alert('imgContainer is null :/'); return;}
	img=imgContainer.firstChild;
	if (!img) { alert('img is null :/'); return;}
	if (!img.style.width || img.style.width=='') { img.style.width='100%'; }
	else { img.style.width=''; }
}

// Returns one title of an image from wikiText.
function getValidImageFromWikiText(wikiText) {
	// nb in pg.re.image we're interested in the second bracketed expression
	// this may change if the regex changes :-(
	//var match=pg.re.image.exec(wikiText);
	var matched=null;
	var match;
	// strip html comments, used by evil bots :-(
	var t = removeMatchesUnless(wikiText, RegExp('(&lt;!--[\\s\\S]*?--&gt;)'), 1,
				    RegExp('^&lt;!--[^[]*popup', 'i'));

	while ( match = pg.re.image.exec(t) ) {
		// now find a sane image name - exclude templates by seeking {
		var m = match[2] || match[6];
		if ( isValidImageName(m) ) {
			matched=m;
			break;
		}
	}
	pg.re.image.lastIndex=0;
	if (!matched) { return null; }
	return mw.config.get('wgFormattedNamespaces')[pg.nsImageId]+':'+upcaseFirst(matched);
}

function removeMatchesUnless(str, re1, parencount, re2) {
    var split=str.parenSplit(re1);
    var c=parencount + 1;
    for (var i=0; i&lt;split.length; ++i) {
	if ( i%c === 0 || re2.test(split[i]) ) { continue; }
	split[i]='';
    }
    return split.join('');
}

//&lt;/NOLITE&gt;
// ENDFILE: images.js
// STARTFILE: namespaces.js
// Set up namespaces and other non-strings.js localization
// (currently that means redirs too)


function namespaceListToRegex(list) {return RegExp('^('+list.join('|').split(' ').join('[ _]')+'):');};

function setNamespaces() {
	pg.nsSpecialId   = -1;
	pg.nsImageId     = 6;
	pg.nsUserId      = 2;
	pg.nsUsertalkId  = 3;
	pg.nsCategoryId  = 14;
	pg.nsTemplateId  = 10;
}


function setRedirs() {
	var r='redirect';
	var R='REDIRECT';
	var redirLists={
//&lt;NOLITE&gt;
		'ar':  [ R, 'تحويل' ],
		'be':  [ r, 'перанакіраваньне' ],
		'bg':  [ r, 'пренасочване', 'виж' ],
		'bs':  [ r, 'Preusmjeri', 'preusmjeri', 'PREUSMJERI' ],
		'cs':  [ R, 'PŘESMĚRUJ' ],
		'cy':  [ r, 'ail-cyfeirio' ],
		'de':  [ R, 'WEITERLEITUNG' ],
		'eo':  [ R, 'ALIDIREKTU', 'ALIDIREKTI' ],
		'es':  [ R, 'REDIRECCIÓN' ],
		'et':  [ r, 'suuna' ],
		'ga':  [ r, 'athsheoladh' ],
		'gl':  [ r, 'REDIRECCIÓN', 'REDIRECIONAMENTO'],
		'he':  [ R, 'הפניה' ],
		'hu':  [ R, 'ÁTIRÁNYÍTÁS' ],
		'is':  [ r, 'tilvísun', 'TILVÍSUN' ],
		'it':  [ R, 'RINVIA', 'Rinvia'],
		'mk':  [ r, 'пренасочување', 'види' ],
		'nds': [ r, 'wiederleiden' ],
		'nl':  [ R, 'DOORVERWIJZING' ],
		'nn':  [ r, 'omdiriger' ],
		'pl':  [ R, 'PATRZ', 'PRZEKIERUJ', 'TAM' ],
		'pt':  [ R, 'redir' ],
		'ru':  [ R, 'ПЕРЕНАПРАВЛЕНИЕ', 'ПЕРЕНАПР' ],
		'sk':  [ r, 'presmeruj' ],
		'sr':  [ r, 'Преусмери', 'преусмери', 'ПРЕУСМЕРИ', 'Preusmeri', 'preusmeri', 'PREUSMERI' ],
		'tt':  [ R, 'yünältü', 'перенаправление', 'перенапр' ],
		'uk': [ R, 'ПЕРЕНАПРАВЛЕННЯ', 'ПЕРЕНАПР' ],
		'vi':  [ r, 'đổi' ] // no comma
//&lt;/NOLITE&gt;
	};
	var redirList=redirLists[ pg.wiki.lang ] || [r, R];
	// Mediawiki is very tolerant about what comes after the #redirect at the start
	pg.re.redirect=RegExp('^\\s*[#](' + redirList.join('|') + ').*?\\[{2}([^\\|\\]]*)(|[^\\]]*)?\\]{2}\\s*(.*)', 'i');
}

function setInterwiki() {
	if (pg.wiki.wikimedia) {
		// From //meta.wikimedia.org/wiki/List_of_Wikipedias
		pg.wiki.interwiki='aa|ab|ace|af|ak|als|am|an|ang|ar|arc|arz|as|ast|av|ay|az|ba|bar|bat-smg|bcl|be|be-x-old|bg|bh|bi|bjn|bm|bn|bo|bpy|br|bs|bug|bxr|ca|cbk-zam|cdo|ce|ceb|ch|cho|chr|chy|ckb|co|cr|crh|cs|csb|cu|cv|cy|da|de|diq|dsb|dv|dz|ee|el|eml|en|eo|es|et|eu|ext|fa|ff|fi|fiu-vro|fj|fo|fr|frp|frr|fur|fy|ga|gag|gan|gd|gl|glk|gn|got|gu|gv|ha|hak|haw|he|hi|hif|ho|hr|hsb|ht|hu|hy|hz|ia|id|ie|ig|ii|ik|ilo|io|is|it|iu|ja|jbo|jv|ka|kaa|kab|kbd|kg|ki|kj|kk|kl|km|kn|ko|koi|kr|krc|ks|ksh|ku|kv|kw|ky|la|lad|lb|lbe|lg|li|lij|lmo|ln|lo|lt|ltg|lv|map-bms|mdf|mg|mh|mhr|mi|mk|ml|mn|mo|mr|mrj|ms|mt|mus|mwl|my|myv|mzn|na|nah|nap|nds|nds-nl|ne|new|ng|nl|nn|no|nov|nrm|nv|ny|oc|om|or|os|pa|pag|pam|pap|pcd|pdc|pfl|pi|pih|pl|pms|pnb|pnt|ps|pt|qu|rm|rmy|rn|ro|roa-rup|roa-tara|ru|rue|rw|sa|sah|sc|scn|sco|sd|se|sg|sh|si|simple|sk|sl|sm|sn|so|sq|sr|srn|ss|st|stq|su|sv|sw|szl|ta|te|tet|tg|th|ti|tk|tl|tn|to|tpi|tr|ts|tt|tum|tw|ty|udm|ug|uk|ur|uz|ve|vec|vi|vls|vo|wa|war|wo|wuu|xal|xh|yi|yo|za|zea|zh|zh-classical|zh-min-nan|zh-yue|zu';
		pg.re.interwiki=RegExp('^'+pg.wiki.interwiki+':');
	} else {
		pg.wiki.interwiki=null;
		pg.re.interwiki=RegExp('^$');
	}
}

// return a regexp pattern matching all variants to write the given namespace
function nsRe(namespaceId) {
	var imageNamespaceVariants = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=namespaceId) return;
		//todo: escape regexp fragments!
		_localizedNamespaceLc = upcaseFirst(_localizedNamespaceLc);
		imageNamespaceVariants.push(_localizedNamespaceLc.split(' ').join('[ _]'));
		imageNamespaceVariants.push(encodeURI(_localizedNamespaceLc));
	});

	return '(?:' + imageNamespaceVariants.join('|') + ')';
}

function nsReImage() {
	return nsRe(pg.nsImageId);
}

// ENDFILE: namespaces.js
// STARTFILE: selpop.js
//&lt;NOLITE&gt;
function getEditboxSelection() {
	// see http://www.webgurusforum.com/8/12/0
	try {
		var editbox=document.editform.wpTextbox1;
	} catch (dang) { return; }
	// IE, Opera
	if (document.selection) { return document.selection.createRange().text; }
	// Mozilla
	var selStart = editbox.selectionStart;
	var selEnd = editbox.selectionEnd;
	return (editbox.value).substring(selStart, selEnd);
}

function doSelectionPopup() {
	// popup if the selection looks like [[foo|anything afterwards at all
	// or [[foo|bar]]text without ']]'
	// or [[foo|bar]]
	var sel=getEditboxSelection();
	var open=sel.indexOf('[[');
	var pipe=sel.indexOf('|');
	var close=sel.indexOf(']]');
	if (open == -1 || ( pipe == -1 &amp;&amp; close == -1) ) { return; }
	if (pipe != -1 &amp;&amp; open &gt; pipe || close != -1 &amp;&amp; open &gt; close) { return; }
	if (getValueOf('popupOnEditSelection')=='boxpreview') {
		return doSeparateSelectionPopup(sel);
	}
	var article=new Title(sel.substring(open+2, (pipe &lt; 0) ? close : pipe)).urlString();
	if (close &gt; 0 &amp;&amp; sel.substring(close+2).indexOf('[[') &gt;= 0) { 
		return; 
	}
	var a=document.createElement('a');
	a.href=pg.wiki.titlebase + article;
	mouseOverWikiLink2(a);
	if (a.navpopup) {
		a.navpopup.addHook(function(){runStopPopupTimer(a.navpopup);}, 'unhide', 'after');
	}
}

function doSeparateSelectionPopup(str) {
	var div=document.getElementById('selectionPreview');
	if (!div) {
		div = document.createElement('div');
		div.id='selectionPreview';
		try { var box=document.editform.wpTextbox1; }
		catch (oopsie) { return; }
		box.parentNode.insertBefore(div, box);
	}
	div.innerHTML=wiki2html(str);
	div.ranSetupTooltipsAlready = false;
	popTipsSoonFn('selectionPreview')();
}
//&lt;/NOLITE&gt;
// ENDFILE: selpop.js
// STARTFILE: navpopup.js
/**
   @fileoverview  Defines two classes: {@link Navpopup} and {@link Mousetracker}.

   &lt;code&gt;Navpopup&lt;/code&gt; describes popups: when they appear, where, what
   they look like and so on.

   &lt;code&gt;Mousetracker&lt;/code&gt; &quot;captures&quot; the mouse using
   &lt;code&gt;document.onmousemove&lt;/code&gt;.
*/


/**
   Creates a new Mousetracker.
   @constructor
   @class The Mousetracker class. This monitors mouse movements and manages associated hooks.
*/
function Mousetracker() {
	/**
	   Interval to regularly run the hooks anyway, in milliseconds.
	   @type Integer
	*/
	this.loopDelay=400;

	/**
	   Timer for the loop.
	   @type Timer
	*/
	this.timer=null;

	/**
	   Flag - are we switched on?
	   @type Boolean
	*/
	this.active=false;
	/**
	   Flag - are we probably inaccurate, i.e. not reflecting the actual mouse position?
	*/
	this.dirty=true;
	/**
	   Array of hook functions.
	   @private
	   @type Array
	*/
	this.hooks=[];
}

/**
   Adds a hook, to be called when we get events.
   @param {Function} f A function which is called as
   &lt;code&gt;f(x,y)&lt;/code&gt;. It should return &lt;code&gt;true&lt;/code&gt; when it
   wants to be removed, and &lt;code&gt;false&lt;/code&gt; otherwise.
*/
Mousetracker.prototype.addHook = function (f) {
	this.hooks.push(f);
};

/**
   Runs hooks, passing them the x
   and y coords of the mouse.  Hook functions that return true are
   passed to {@link Mousetracker#removeHooks} for removal.
   @private
*/
Mousetracker.prototype.runHooks = function () {
	if (!this.hooks || !this.hooks.length) { return; }
	//log('Mousetracker.runHooks; we got some hooks to run');
	var remove=false;
	var removeObj={};
	// this method gets called a LOT -
	// pre-cache some variables
	var x=this.x, y=this.y, len = this.hooks.length;

	for (var i=0; i&lt;len; ++i) {
		//~ run the hook function, and remove it if it returns true
		if (this.hooks[i](x, y)===true) {
			remove=true;
			removeObj[i]=true;
		}
	}
	if (remove) { this.removeHooks(removeObj); }
};

/**
   Removes hooks.
   @private
   @param {Object} removeObj An object whose keys are the index
   numbers of functions for removal, with values that evaluate to true
*/
Mousetracker.prototype.removeHooks = function(removeObj) {
	var newHooks=[];
	var len = this.hooks.length;
	for (var i=0; i&lt;len; ++i) {
		if (! removeObj[i]) { newHooks.push(this.hooks[i]); }
	}
	this.hooks=newHooks;
};


/**
   Event handler for mouse wiggles.
   We simply grab the event, set x and y and run the hooks.
   This makes the cpu all hot and bothered :-(
   @private
   @param {Event} e Mousemove event
*/
Mousetracker.prototype.track=function (e) {
	//~ Apparently this is needed in IE.
	e = e || window.event;
	var x, y;
	if (e) {
		if (e.pageX) { x=e.pageX; y=e.pageY; }
		else if (typeof e.clientX!='undefined') {
			var left, top, docElt = window.document.documentElement;

			if (docElt) { left=docElt.scrollLeft; }
			left = left || window.document.body.scrollLeft || window.document.scrollLeft || 0;

			if (docElt) { top=docElt.scrollTop; }
			top = top || window.document.body.scrollTop || window.document.scrollTop || 0;

			x=e.clientX + left;
			y=e.clientY + top;
		} else { return; }
		this.setPosition(x,y);
	}
};

/**
   Sets the x and y coordinates stored and takes appropriate action,
   running hooks as appropriate.
   @param {Integer} x, y Screen coordinates to set
*/

Mousetracker.prototype.setPosition=function(x,y) {
	this.x = x;
	this.y = y;
	if (this.dirty || this.hooks.length === 0) { this.dirty=false; return; }
	if (typeof this.lastHook_x != 'number') { this.lastHook_x = -100; this.lastHook_y=-100; }
	var diff = (this.lastHook_x - x)*(this.lastHook_y - y);
	diff = (diff &gt;= 0) ? diff : -diff;
	if ( diff &gt; 1 ) {
		this.lastHook_x=x;
		this.lastHook_y=y;
		if (this.dirty) { this.dirty = false; }
		else { this.runHooks(); }
	}
}

/**
   Sets things in motion, unless they are already that is, registering an event handler on &lt;code&gt;document.onmousemove&lt;/code&gt;.
   A half-hearted attempt is made to preserve the old event handler if there is one.
*/
Mousetracker.prototype.enable = function () {
	if (this.active) { return; }
	this.active=true;
	//~ Save the current handler for mousemove events. This isn't too
	//~ robust, of course.
	this.savedHandler=document.onmousemove;
	//~ Gotta save @tt{this} again for the closure, and use apply for
	//~ the member function.
	var savedThis=this;
	document.onmousemove=function (e) {savedThis.track.apply(savedThis, [e]);};
	if (this.loopDelay) { this.timer = setInterval(function() { //log('loop delay in mousetracker is working');
								    savedThis.runHooks();}, this.loopDelay); }
};

/**
   Disables the tracker, removing the event handler.
*/
Mousetracker.prototype.disable = function () {
	if (!this.active) { return; }
	if (typeof this.savedHandler=='function') {
		document.onmousemove=this.savedHandler;
	} else { delete document.onmousemove; }
	if (this.timer) { clearInterval(this.timer); }
	this.active=false;
};

/**
   Creates a new Navpopup.
   Gets a UID for the popup and
   @param init Contructor object. If &lt;code&gt;init.draggable&lt;/code&gt; is true or absent, the popup becomes draggable.
   @constructor
   @class The Navpopup class. This generates popup hints, and does some management of them.
*/
function Navpopup(init) {
	//alert('new Navpopup(init)');
	/** UID for each Navpopup instance.
	    Read-only.
	    @type integer
	*/
	this.uid=Navpopup.uid++;
	/**
	   Read-only flag for current visibility of the popup.
	   @type boolean
	   @private
	*/
	this.visible=false;
	/** Flag to be set when we want to cancel a previous request to
	    show the popup in a little while.
	    @private
	    @type boolean
	*/
	this.noshow=false;
	/** Categorised list of hooks.
	    @see #runHooks
	    @see #addHook
	    @private
	    @type Object
	*/
	this.hooks={
		'create': [],
		'unhide': [],
		'hide': []
	};
	/** list of unique IDs of hook functions, to avoid duplicates
	    @private
	*/
	this.hookIds={};
	/** List of downloads associated with the popup.
	    @private
	    @type Array
	*/
	this.downloads=[];
	/** Number of uncompleted downloads.
	    @type integer
	*/
	this.pending=null;
	/** Tolerance in pixels when detecting whether the mouse has left the popup.
	    @type integer
	*/
	this.fuzz=5;
	/** Flag to toggle running {@link #limitHorizontalPosition} to regulate the popup's position.
	    @type boolean
	*/
	this.constrained=true;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.width=0;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.height=0;
	/** The main content DIV element.
	    @type HTMLDivElement
	*/
	this.mainDiv=null;
	this.createMainDiv();

//	if (!init || typeof init.popups_draggable=='undefined' || init.popups_draggable) {
//		this.makeDraggable(true);
//	}
}

/**
   A UID for each Navpopup. This constructor property is just a counter.
   @type integer
   @private
*/
Navpopup.uid=0;

/**
   Retrieves the {@link #visible} attribute, indicating whether the popup is currently visible.
   @type boolean
*/
Navpopup.prototype.isVisible=function() {
	return this.visible;
};

/**
   Repositions popup using CSS style.
   @private
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @param {boolean} noLimitHor Don't call {@link #limitHorizontalPosition}
*/
Navpopup.prototype.reposition= function (x,y, noLimitHor) {
	log ('reposition('+x+','+y+','+noLimitHor+')');
	if (typeof x != 'undefined' &amp;&amp; x!==null) { this.left=x; }
	if (typeof y != 'undefined' &amp;&amp; y!==null) { this.top=y; }
	if (typeof this.left != 'undefined' &amp;&amp; typeof this.top != 'undefined') {
		this.mainDiv.style.left=this.left + 'px';
		this.mainDiv.style.top=this.top + 'px';
	}
	if (!noLimitHor) { this.limitHorizontalPosition(); }
	//console.log('navpop'+this.uid+' - (left,top)=(' + this.left + ',' + this.top + '), css=('
	//+ this.mainDiv.style.left + ',' + this.mainDiv.style.top + ')');
};

/**
   Prevents popups from being in silly locations. Hopefully.
   Should not be run if {@link #constrained} is true.
   @private
*/
Navpopup.prototype.limitHorizontalPosition=function() {
	if (!this.constrained || this.tooWide) { return; }
	this.updateDimensions();
	var x=this.left;
	var w=this.width;
	var cWidth=document.body.clientWidth;


//	log('limitHorizontalPosition: x='+x+
//		    ', this.left=' + this.left +
//		    ', this.width=' + this.width +
//		    ', cWidth=' + cWidth);


	if ( (x+w) &gt;= cWidth ||
	     ( x &gt; 0 &amp;&amp; this.maxWidth &amp;&amp; this.width &lt; this.maxWidth &amp;&amp; this.height &gt; this.width
	       &amp;&amp; x &gt; cWidth - this.maxWidth ) ) {
		// This is a very nasty hack. There has to be a better way!
		// We find the &quot;natural&quot; width of the div by positioning it at the far left
		// then reset it so that it should be flush right (well, nearly)
		this.mainDiv.style.left='-10000px';
		this.mainDiv.style.width = this.maxWidth + 'px';
		var naturalWidth=parseInt(this.mainDiv.offsetWidth, 10);
		var newLeft=cWidth - naturalWidth - 1;
		if (newLeft &lt; 0) { newLeft = 0; this.tooWide=true; } // still unstable for really wide popups?
		log ('limitHorizontalPosition: moving to ('+newLeft + ','+ this.top+');' + ' naturalWidth=' + naturalWidth + ', clientWidth=' + cWidth);
		this.reposition(newLeft, null, true);
	}
};

/**
   Counter indicating the z-order of the &quot;highest&quot; popup.
   We start the z-index at 1000 so that popups are above everything
   else on the screen.
   @private
   @type integer
*/
Navpopup.highest=1000;

/**
   Brings popup to the top of the z-order.
   We increment the {@link #highest} property of the contructor here.
   @private
*/
Navpopup.prototype.raise = function () {
	this.mainDiv.style.zIndex=Navpopup.highest + 1;
	++Navpopup.highest;
};

/**
   Shows the popup provided {@link #noshow} is not true.
   Updates the position, brings the popup to the top of the z-order and unhides it.
*/
Navpopup.prototype.show = function () {
	//document.title+='s';
	if (this.noshow) { return; }
	//document.title+='t';
	this.reposition();
	this.raise();
	this.unhide();
};


/**
   Runs the {@link #show} method in a little while, unless we're
   already visible.
   @param {integer} time Delay in milliseconds
   @see #showSoonIfStable
*/
Navpopup.prototype.showSoon = function (time) {
	if (this.visible) { return; }
	this.noshow=false;
	//~ We have to save the value of @tt{this} so that the closure below
	//~ works.
	var savedThis=this;
	//this.start_x = Navpopup.tracker.x;
	//this.start_y = Navpopup.tracker.y;
	setTimeout(function () {
		if (Navpopup.tracker.active) {
			savedThis.reposition.apply(savedThis, [Navpopup.tracker.x + 2, Navpopup.tracker.y + 2]);
		}
		//~ Have to use apply to invoke his member function here
		savedThis.show.apply(savedThis, []);
	}, time);
};

/**
   Checks to see if the mouse pointer has
   stabilised (checking every &lt;code&gt;time&lt;/code&gt;/2 milliseconds) and runs the
   {@link #show} method if it has. This method makes {@link #showSoon} redundant.
   @param {integer} time The minimum time (ms) before the popup may be shown.
*/
Navpopup.prototype.showSoonIfStable = function (time) {
	log ('showSoonIfStable, time='+time);
	if (this.visible) { return; }
	this.noshow = false;

	//~ initialize these variables so that we never run @tt{show} after
	//~ just half the time
	this.stable_x = -10000; this.stable_y = -10000;

	var stableShow = function() {
		log('stableShow called');
		var new_x = Navpopup.tracker.x, new_y = Navpopup.tracker.y;
		var dx = savedThis.stable_x - new_x, dy = savedThis.stable_y - new_y;
		var fuzz2 = 0; // savedThis.fuzz * savedThis.fuzz;
		//document.title += '[' + [savedThis.stable_x,new_x, savedThis.stable_y,new_y, dx, dy, fuzz2].join(',') + '] ';
		if ( dx * dx &lt;= fuzz2 &amp;&amp; dy * dy &lt;= fuzz2 ) {
			log ('mouse is stable');
			clearInterval(savedThis.showSoonStableTimer);
			savedThis.reposition.apply(savedThis, [new_x + 2, new_y + 2]);
			savedThis.show.apply(savedThis, []);
			return;
		}
		savedThis.stable_x = new_x; savedThis.stable_y = new_y;
	};
	var savedThis = this;
	this.showSoonStableTimer = setInterval(stableShow, time/2);
};

/**
   Makes the popup unhidable until we call {@link #unstick}.
*/
Navpopup.prototype.stick=function() {
	this.noshow=false;
	this.sticky=true;
};

/**
   Allows the popup to be hidden.
*/
Navpopup.prototype.unstick=function() {
	this.sticky=false;
};

/**
   Sets the {@link #noshow} flag and hides the popup. This should be called
   when the mouse leaves the link before
   (or after) it's actually been displayed.
*/
Navpopup.prototype.banish = function () {
	log ('banish called');
	// hide and prevent showing with showSoon in the future
	this.noshow=true;
	if (this.showSoonStableTimer) {
		log('clearing showSoonStableTimer');
		clearInterval(this.showSoonStableTimer);
	}
	this.hide();
};

/**
   Runs hooks added with {@link #addHook}.
   @private
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
*/
Navpopup.prototype.runHooks = function (key, when) {
	if (!this.hooks[key]) { return; }
	var keyHooks=this.hooks[key];
	var len=keyHooks.length;
	for (var i=0; i&lt; len; ++i) {
		if (keyHooks[i] &amp;&amp; keyHooks[i].when == when) {
			if (keyHooks[i].hook.apply(this, [])) {
				// remove the hook
				if (keyHooks[i].hookId) {
					delete this.hookIds[keyHooks[i].hookId];
				}
				keyHooks[i]=null;
			}
		}
	}
};

/**
   Adds a hook to the popup. Hook functions are run with &lt;code&gt;this&lt;/code&gt; set to refer to the Navpopup instance, and no arguments.
   @param {Function} hook The hook function. Functions that return true are deleted.
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
   @param {String} uid A truthy string identifying the hook function; if it matches another hook in this position, it won't be added again.
*/
Navpopup.prototype.addHook = function ( hook, key, when, uid ) {
	when = when || 'after';
	if (!this.hooks[key]) { return; }
	// if uid is specified, don't add duplicates
	var hookId=null;
	if (uid) {
		hookId=[key,when,uid].join('|');
		if (this.hookIds[hookId]) {
			return;
		}
		this.hookIds[hookId]=true;
	}
	this.hooks[key].push( {hook: hook, when: when, hookId: hookId} );
};

/**
   Creates the main DIV element, which contains all the actual popup content.
   Runs hooks with key 'create'.
   @private
*/
Navpopup.prototype.createMainDiv = function () {
	if (this.mainDiv) { return; }
	this.runHooks('create', 'before');
	var mainDiv=document.createElement('div');

	var savedThis=this;
	mainDiv.onclick=function(e) {savedThis.onclickHandler(e);};
	mainDiv.className=(this.className) ? this.className : 'navpopup_maindiv';
	mainDiv.id=mainDiv.className + this.uid;

	mainDiv.style.position='absolute';
	mainDiv.style.display='none';
	mainDiv.className='navpopup';

	// easy access to javascript object through DOM functions
	mainDiv.navpopup=this;

	this.mainDiv=mainDiv;
	document.body.appendChild(mainDiv);
	this.runHooks('create', 'after');
};
/**
   Calls the {@link #raise} method.
   @private
*/
Navpopup.prototype.onclickHandler=function(e) {
	this.raise();
};
/**
   Makes the popup draggable, using a {@link Drag} object.
   @private
*/
Navpopup.prototype.makeDraggable=function(handleName) {
	if (!this.mainDiv) { this.createMainDiv(); }
	var drag=new Drag();
	if (!handleName) {
	    drag.startCondition=function(e) {
		try { if (!e.shiftKey) { return false; } } catch (err) { return false; }
		return true;
	    };
	}
	var dragHandle;
	if (handleName) dragHandle = document.getElementById(handleName);
	if (!dragHandle) dragHandle = this.mainDiv;
	var np=this;
	drag.endHook=function(x,y) {
		Navpopup.tracker.dirty=true;
		np.reposition(x,y);
	};
	drag.init(dragHandle,this.mainDiv);
};

/** Hides the popup using CSS. Runs hooks with key 'hide'.
    Sets {@link #visible} appropriately.     {@link #banish} should be called externally instead of this method.

    @private
*/
Navpopup.prototype.hide = function () {
	this.runHooks('hide', 'before');
	this.abortDownloads();
	if (this.sticky) { return; }
	if (typeof this.visible != 'undefined' &amp;&amp; this.visible) {
		this.mainDiv.style.display='none';
		this.visible=false;
	}
	this.runHooks('hide', 'after');
};

/** Shows the popup using CSS. Runs hooks with key 'unhide'.
    Sets {@link #visible} appropriately.   {@link #show} should be called externally instead of this method.
    @private
*/
Navpopup.prototype.unhide = function () {
	this.runHooks('unhide', 'before');
	if (typeof this.visible != 'undefined' &amp;&amp; !this.visible) {
		this.mainDiv.style.display='inline';
		this.visible=true;
	}
	this.runHooks('unhide', 'after');
};

/**
   Sets the &lt;code&gt;innerHTML&lt;/code&gt; attribute of the main div containing the popup content.
   @param {String} html The HTML to set.
*/
Navpopup.prototype.setInnerHTML = function (html) {
	this.mainDiv.innerHTML = html;
};

/**
   Updates the {@link #width} and {@link #height} attributes with the CSS properties.
   @private
*/
Navpopup.prototype.updateDimensions = function () {
	this.width=parseInt(this.mainDiv.offsetWidth, 10);
	this.height=parseInt(this.mainDiv.offsetHeight, 10);
};

/**
   Checks if the point (x,y) is within {@link #fuzz} of the
   {@link #mainDiv}.
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @type boolean
*/
Navpopup.prototype.isWithin = function(x,y) {
	//~ If we're not even visible, no point should be considered as
	//~ being within the popup.
	if (!this.visible) { return false; }
	this.updateDimensions();
	var fuzz=this.fuzz || 0;
	//~ Use a simple box metric here.
	return (x+fuzz &gt;= this.left &amp;&amp; x-fuzz &lt;= this.left + this.width &amp;&amp;
		y+fuzz &gt;= this.top  &amp;&amp; y-fuzz &lt;= this.top  + this.height);
};

/**
   Adds a download to {@link #downloads}.
   @param {Downloader} download
*/
Navpopup.prototype.addDownload=function(download) {
	if (!download) { return; }
	this.downloads.push(download);
};
/**
   Aborts the downloads listed in {@link #downloads}.
   @see Downloader#abort
*/
Navpopup.prototype.abortDownloads=function() {
	for(var i=0; i&lt;this.downloads.length; ++i) {
		var d=this.downloads[i];
		if (d &amp;&amp; d.abort) { d.abort(); }
	}
	this.downloads=[];
};


/**
   A {@link Mousetracker} instance which is a property of the constructor (pseudo-global).
*/
Navpopup.tracker=new Mousetracker();
// ENDFILE: navpopup.js
// STARTFILE: diff.js
//&lt;NOLITE&gt;
/*
 * Javascript Diff Algorithm
 *  By John Resig (http://ejohn.org/) and [[:en:User:Lupin]]
 *
 * More Info:
 *  http://ejohn.org/projects/javascript-diff-algorithm/
 */

function delFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;del class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/del&gt;&quot;;
}
function insFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;ins class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/ins&gt;&quot;;
}

function countCrossings(a, b, i, eject) {
	// count the crossings on the edge starting at b[i]
	if (!b[i].row &amp;&amp; b[i].row !== 0) { return -1; }
	var count=0;
	for (var j=0; j&lt;a.length; ++j) {
		if (!a[j].row &amp;&amp; a[j].row !== 0) { continue; }
		if ( (j-b[i].row)*(i-a[j].row) &gt; 0) {
			if(eject) { return true; }
			count++;
		}
	}
	return count;
}

function shortenDiffString(str, context) {
	var re=RegExp('(&lt;del[\\s\\S]*?&lt;/del&gt;|&lt;ins[\\s\\S]*?&lt;/ins&gt;)');
	var splitted=str.parenSplit(re);
	var ret=[''];
	for (var i=0; i&lt;splitted.length; i+=2) {
		if (splitted[i].length &lt; 2*context) {
			ret[ret.length-1] += splitted[i];
			if (i+1&lt;splitted.length) { ret[ret.length-1] += splitted[i+1]; }
			continue;
		}
		else {
			if (i &gt; 0) { ret[ret.length-1] += splitted[i].substring(0,context); }
			if (i+1 &lt; splitted.length) {
			    ret.push(splitted[i].substring(splitted[i].length-context) +
				     splitted[i+1]);
			}
		}
	}
	while (ret.length &gt; 0 &amp;&amp; !ret[0]) { ret = ret.slice(1); }
	return ret;
}


function diffString( o, n, simpleSplit ) {
	var splitRe=RegExp('([[]{2}|[\\]]{2}|[{]{2,3}|[}]{2,3}|[|]|=|&lt;|&gt;|[*:]+|\\s|\\b)');

	//  We need to split the strings o and n first, and entify() the parts
	//  individually, so that the HTML entities are never cut apart. (AxelBoldt)
	var out, i, oSplitted, nSplitted;
	if (simpleSplit) { 
		oSplitted=o.split(/\b/); 
		nSplitted=n.split(/\b/); 
	} else { 
		oSplitted=o.parenSplit(splitRe); 
		nSplitted=n.parenSplit(splitRe); 
	}
	for (i=0; i&lt;oSplitted.length; ++i) {oSplitted[i]=oSplitted[i].entify();}
	for (i=0; i&lt;nSplitted.length; ++i) {nSplitted[i]=nSplitted[i].entify();}
		
	out = diff (oSplitted, nSplitted);
	var str = &quot;&quot;;
	var acc=[]; // accumulator for prettier output

	// crossing pairings -- eg 'A B' vs 'B A' -- cause problems, so let's iron them out
	// this doesn't always do things optimally but it should be fast enough
	var maxOutputPair=0;
	for (i=0; i&lt;out.n.length; ++i) {
	    if ( out.n[i].paired ) {
		if( maxOutputPair &gt; out.n[i].row ) {
		    // tangle - delete pairing
		    out.o[ out.n[i].row ]=out.o[ out.n[i].row ].text;
		    out.n[i]=out.n[i].text;
		}
		if (maxOutputPair &lt; out.n[i].row) { maxOutputPair = out.n[i].row; }
	    }
	}

	// output the stuff preceding the first paired old line
	for (i=0; i&lt;out.o.length &amp;&amp; !out.o[i].paired; ++i) { acc.push( out.o[i] ); }
	str += delFmt(acc); acc=[];

	// main loop
	for ( i = 0; i &lt; out.n.length; ++i ) {
		// output unpaired new &quot;lines&quot;
		while ( i &lt; out.n.length &amp;&amp; !out.n[i].paired ) { acc.push( out.n[i++] ); }
		str += insFmt(acc); acc=[];
		if ( i &lt; out.n.length ) { // this new &quot;line&quot; is paired with the (out.n[i].row)th old &quot;line&quot;
			str += out.n[i].text;
			// output unpaired old rows starting after this new line's partner
			var m = out.n[i].row + 1;
			while ( m &lt; out.o.length &amp;&amp; !out.o[m].paired ) { acc.push ( out.o[m++] ); }
			str += delFmt(acc); acc=[];
		}
	}
	return str;
}

// see http://developer.mozilla.org/en/docs/Core_JavaScript_1.5_Reference:Global_Objects:Object
// FIXME: use obj.hasOwnProperty instead of this kludge!
window.jsReservedProperties=RegExp('^(constructor|prototype|__((define|lookup)[GS]etter)__' +
				   '|eval|hasOwnProperty|propertyIsEnumerable' +
				   '|to(Source|String|LocaleString)|(un)?watch|valueOf)$');
function diffBugAlert(word) {
	if (!diffBugAlert.list[word]) {
		diffBugAlert.list[word]=1;
		alert('Bad word: '+word+'\n\nPlease report this bug.');
	}
}
diffBugAlert.list={};

function makeDiffHashtable(src) {
	var ret={};
	for ( var i = 0; i &lt; src.length; i++ ) {
		if ( jsReservedProperties.test(src[i]) ) { src[i] += '&lt;!-- --&gt;'; }
		if ( !ret[ src[i] ] ) {	ret[ src[i] ] = []; }
		try { ret[ src[i] ].push( i ); } catch (err) { diffBugAlert(src[i]); }
	}
	return ret;
}

function diff( o, n ) {

	// pass 1: make hashtable ns with new rows as keys
	var ns = makeDiffHashtable(n);

	// pass 2: make hashtable os with old rows as keys
	var os = makeDiffHashtable(o);

	// pass 3: pair unique new rows and matching unique old rows
	var i;
	for ( i in ns ) {
		if ( ns[i].length == 1 &amp;&amp; os[i] &amp;&amp; os[i].length == 1 ) {
			n[ ns[i][0] ] = { text: n[ ns[i][0] ], row: os[i][0], paired: true };
			o[ os[i][0] ] = { text: o[ os[i][0] ], row: ns[i][0], paired: true };
		}
	}

	// pass 4: pair matching rows immediately following paired rows (not necessarily unique)
	for ( i = 0; i &lt; n.length - 1; i++ ) {
		if ( n[i].paired &amp;&amp; ! n[i+1].paired &amp;&amp; n[i].row + 1 &lt; o.length &amp;&amp; ! o[ n[i].row + 1 ].paired &amp;&amp;
		     n[i+1] == o[ n[i].row + 1 ] ) {
			n[i+1] = { text: n[i+1], row: n[i].row + 1, paired: true };
			o[n[i].row+1] = { text: o[n[i].row+1], row: i + 1, paired: true };
		}
	}

	// pass 5: pair matching rows immediately preceding paired rows (not necessarily unique)
	for ( i = n.length - 1; i &gt; 0; i-- ) {
		if ( n[i].paired &amp;&amp; ! n[i-1].paired &amp;&amp; n[i].row &gt; 0 &amp;&amp; ! o[ n[i].row - 1 ].paired &amp;&amp;
		     n[i-1] == o[ n[i].row - 1 ] ) {
			n[i-1] = { text: n[i-1], row: n[i].row - 1, paired: true };
			o[n[i].row-1] = { text: o[n[i].row-1], row: i - 1, paired: true };
		}
	}

	return { o: o, n: n };
}
//&lt;/NOLITE&gt;
// ENDFILE: diff.js
// STARTFILE: init.js
function setSiteInfo() {
	if (window.popupLocalDebug) {
		pg.wiki.hostname = 'en.wikiversity.org';
	} else {
		pg.wiki.hostname = location.hostname; // use in preference to location.hostname for flexibility (?)
	}
	pg.wiki.wikimedia=RegExp('(wiki([pm]edia|source|books|news|quote|versity)|wiktionary|mediawiki)[.]org').test(pg.wiki.hostname);
	pg.wiki.wikia=RegExp('[.]wikia[.]com$', 'i').test(pg.wiki.hostname);
	pg.wiki.isLocal=RegExp('^localhost').test(pg.wiki.hostname);
	pg.wiki.commons=( pg.wiki.wikimedia &amp;&amp; pg.wiki.hostname != 'commons.wikimedia.org') ? 'commons.wikimedia.org' : null;
	pg.wiki.lang = mw.config.get('wgContentLanguage');
	var port = location.port ? ':' + location.port : '';
	pg.wiki.sitebase = pg.wiki.hostname + port;
}

function setTitleBase() {
	var protocol = ( window.popupLocalDebug ? 'http:' : location.protocol );
	pg.wiki.articlePath = mw.config.get('wgArticlePath').replace(/\/\$1/, &quot;&quot;);   // as in http://some.thing.com/wiki/Article
	pg.wiki.botInterfacePath = mw.config.get('wgScript');
	pg.wiki.APIPath = wgScriptPath +&quot;/api.php&quot;;
	// default mediawiki setting is paths like http://some.thing.com/articlePath/index.php?title=foo

	var titletail = pg.wiki.botInterfacePath + '?title=';
	//var titletail2 = joinPath([pg.wiki.botInterfacePath, 'wiki.phtml?title=']);

	// other sites may need to add code here to set titletail depending on how their urls work

	pg.wiki.titlebase   = protocol + '//' + pg.wiki.sitebase + titletail;
	//pg.wiki.titlebase2  = protocol + '//' + joinPath([pg.wiki.sitebase, titletail2]);
	pg.wiki.wikibase    = protocol + '//' + pg.wiki.sitebase + pg.wiki.botInterfacePath;
	pg.wiki.apiwikibase = protocol + '//' + pg.wiki.sitebase + pg.wiki.APIPath;
	pg.wiki.articlebase = protocol + '//' + pg.wiki.sitebase + pg.wiki.articlePath;
	pg.wiki.commonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.botInterfacePath;
	pg.wiki.apicommonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.APIPath;
	pg.re.basenames = RegExp( '^(' +
				  map( literalizeRegex, [ pg.wiki.titlebase, //pg.wiki.titlebase2,
							  pg.wiki.articlebase ]).join('|') + ')' );
}


//////////////////////////////////////////////////
// Global regexps

function setMainRegex() {
	var reStart='[^:]*://';
	var preTitles = literalizeRegex(wgScriptPath) + '/(?:index[.]php|wiki[.]phtml)[?]title=';
	// slightly ugly hack when pg.wiki.articlePath is empty
	preTitles += '|' + literalizeRegex( ( pg.wiki.articlePath ? pg.wiki.articlePath + '/': ''));

	var reEnd='(' + preTitles + ')([^&amp;?#]*)[^#]*(?:#(.+))?';
	pg.re.main = RegExp(reStart + literalizeRegex(pg.wiki.sitebase) + reEnd);
}

function setRegexps() {
	setMainRegex();
	var sp=nsRe(pg.nsSpecialId);
	pg.re.urlNoPopup=RegExp('((title=|/)' + sp + '(?:%3A|:)|section=[0-9])') ;
	pg.re.contribs  =RegExp('(title=|/)'  + sp + '(?:%3A|:)Contributions' + '(&amp;target=|/|/' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)(.*)') ;
	pg.re.email     =RegExp('(title=|/)'  + sp + '(?:%3A|:)EmailUser'     + '(&amp;target=|/|/(?:' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)?)(.*)') ;
	pg.re.backlinks =RegExp('(title=|/)'  + sp + '(?:%3A|:)WhatLinksHere' + '(&amp;target=|/)([^&amp;]*)');

//&lt;NOLITE&gt;
	var im=nsReImage();
	// note: tries to get images in infobox templates too, e.g. movie pages, album pages etc
	//                      (^|\[\[)image: *([^|\]]*[^|\] ]) *
	//                      (^|\[\[)image: *([^|\]]*[^|\] ])([^0-9\]]*([0-9]+) *px)?
	//                                                        $4 = 120 as in 120px
	pg.re.image = RegExp('(^|\\[\\[)' + im + ': *([^|\\]]*[^|\\] ])' +
			     '([^0-9\\]]*([0-9]+) *px)?|(?:\\n *[|]?|[|]) *' +
			     '(' + getValueOf('popupImageVarsRegexp') + ')' +
			     ' *= *(?:\\[\\[ *)?(?:' + im + ':)?' +
			     '([^|]*?)(?:\\]\\])? *[|]? *\\n', 'img') ;
	pg.re.imageBracketCount = 6;

	pg.re.category = RegExp('\\[\\[' +nsRe(pg.nsCategoryId) +
				': *([^|\\]]*[^|\\] ]) *', 'i');
	pg.re.categoryBracketCount = 1;

	pg.re.ipUser=RegExp('('+nsRe(pg.nsUserId)+':)?' +
			    '((25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}' +
			    '(25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])');

	pg.re.stub= RegExp(getValueOf('popupStubRegexp'), 'im');
	pg.re.disambig=RegExp(getValueOf('popupDabRegexp'), 'im');

//&lt;/NOLITE&gt;
	// FIXME replace with general parameter parsing function, this is daft
	pg.re.oldid=RegExp('[?&amp;]oldid=([^&amp;]*)');
	pg.re.diff=RegExp('[?&amp;]diff=([^&amp;]*)');
}


//////////////////////////////////////////////////
// miscellany

function setupCache() {
	// page caching
	pg.cache.pages = [];
}

function setMisc() {
	pg.current.link=null;
	pg.current.links=[];
	pg.current.linksHash={};

	setupCache();

	pg.timer.checkPopupPosition=null;
	pg.counter.loop=0;

	// ids change with each popup: popupImage0, popupImage1 etc
	pg.idNumber=0;

	// for myDecodeURI
	pg.misc.decodeExtras = [
		{from: '%2C', to: ',' },
		{from: '_',   to: ' ' },
		{from: '%24', to: '$'},
		{from: '%26',   to: '&amp;' } // no ,
		];

}

function leadingInteger(s){
	var n=s.match(/^(\d*)/)[1];
	if (n) { return +n; }
	return null;
}

function setBrowserHacks() {
	var useOriginal=false;
	// browser-specific hacks
	if (typeof window.opera != 'undefined') {
		//if (leadingInteger(opera.version()) &lt; 9)
		{ useOriginal=true; } // v9 beta still seems to have buggy css
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
	} else if (navigator.appName=='Konqueror') {
		setDefault('popupNavLinkSeparator', ' &amp;bull; ');
		pg.flag.isKonq=true;
	} else if ( navigator.vendor &amp;&amp; navigator.vendor.toLowerCase().indexOf('apple computer')===0) {
		pg.flag.isSafari=true;
		var webkit=+navigator.userAgent.replace(RegExp('^.*AppleWebKit[/](\\d+).*', 'i'), '$1');
		if (webkit &lt; 420) { useOriginal=true; }
	} else if (navigator.appName.indexOf(&quot;Microsoft&quot;)!=-1) {
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
		var ver=+navigator.userAgent.replace(RegExp('^.*MSIE (\\d+).*'), '$1');
		pg.flag.isIE=true;
		pg.flag.IEVersion=ver;
	}
	if (pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 8) {
		useOriginal=true;
	}
	if ((pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 7) || pg.flag.isKonq || (pg.flag.isSafari &amp;&amp; webkit &lt; 420)) {
		pg.flag.linksLikeIE6=true;
	}
	if (useOriginal &amp;&amp; pg.structures.original) {
		setDefault('popupStructure','original');
	}
}

function setupPopups() {
	// NB translatable strings should be set up first (strings.js)
	// basics
	setupDebugging();
	setSiteInfo();
	setTitleBase();
	setOptions(); // see options.js

	// namespaces etc
	setNamespaces();
	setInterwiki();

	// regexps
	setRegexps();
	setRedirs();

	// other stuff
	setBrowserHacks();
	setMisc();
	setupLivePreview();

	// main deal here
	setupTooltips();
	Navpopup.tracker.enable();

	setupPopups.completed = true;
}
// ENDFILE: init.js
// STARTFILE: navlinks.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// navlinks... let the fun begin
//

function defaultNavlinkSpec() {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';
	if (getValueOf('popupLastEditLink')) {
		str += '*&lt;&lt;lastEdit|shortcut=/&gt;&gt;|&lt;&lt;lastContrib&gt;&gt;|&lt;&lt;sinceMe&gt;&gt;if(oldid){|&lt;&lt;oldEdit&gt;&gt;|&lt;&lt;diffCur&gt;&gt;}';
	}

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;*&lt;&lt;userlog|shortcut=L|log&gt;&gt;';
	str+='if(ipuser){*&lt;&lt;arin&gt;&gt;}if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;|&lt;&lt;blocklog|log&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{' + editstr + '}'
		var historystr='&lt;&lt;history|shortcut=h&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|&gt;&gt;}';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;*&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){&lt;br&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;*' +
		'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|&lt;&lt;deletelog|log&gt;&gt;}';
	return str;
}

function navLinksHTML (article, hint, params) { //oldid, rcid) {
	var str = '&lt;span class=&quot;popupNavLinks&quot;&gt;' + defaultNavlinkSpec() + '&lt;/span&gt;';
	// BAM
	return navlinkStringToHTML(str, article, params);
}

function expandConditionalNavlinkString(s,article,z,recursionCount) {
	var oldid=z.oldid, rcid=z.rcid, diff=z.diff;
	// nested conditionals (up to 10 deep) are ok, hopefully! (work from the inside out)
	if (typeof recursionCount!=typeof 0) { recursionCount=0; }
	var conditionalSplitRegex=RegExp(
		//(1     if    \\(    (2    2)    \\)      {(3    3)}  (4   else      {(5     5)}  4)1)
		'(;?\\s*if\\s*\\(\\s*([\\w]*)\\s*\\)\\s*\\{([^{}]*)\\}(\\s*else\\s*\\{([^{}]*?)\\}|))', 'i');
	var splitted=s.parenSplit(conditionalSplitRegex);
	// $1: whole conditional
	// $2: test condition
	// $3: true expansion
	// $4: else clause (possibly empty)
	// $5: false expansion (possibly null)
	var numParens=5;
	var ret = splitted[0];
	for (var i=1; i&lt;splitted.length; i=i+numParens+1) {

		var testString=splitted[i+2-1];
		var trueString=splitted[i+3-1];
		var falseString=splitted[i+5-1];
		if (typeof falseString=='undefined' || !falseString) { falseString=''; }
		var testResult=null;

		switch (testString) {
		case 'user':
			testResult=(article.userName())?true:false;
			break;
		case 'talk':
			testResult=(article.talkPage())?false:true; // talkPage converts _articles_ to talkPages
			break;
		case 'admin':
			testResult=getValueOf('popupAdminLinks')?true:false;
			break;
		case 'oldid':
			testResult=(typeof oldid != 'undefined' &amp;&amp; oldid)?true:false;
			break;
		case 'rcid':
			testResult=(typeof rcid != 'undefined' &amp;&amp; rcid)?true:false;
			break;
		case 'ipuser':
			testResult=(article.isIpUser())?true:false;
			break;
		case 'mainspace_en':
			testResult=isInMainNamespace(article) &amp;&amp;
				pg.wiki.hostname=='en.wikiversity.org';
			break;
		case 'wikimedia':
			testResult=(pg.wiki.wikimedia) ? true : false;
			break;
		case 'diff':
			testResult=(typeof diff != 'undefined' &amp;&amp; diff)?true:false;
			break;
		}

		switch(testResult) {
		case null: ret+=splitted[i];  break;
		case true: ret+=trueString;   break;
		case false: ret+=falseString; break;
		}

		// append non-conditional string
		ret += splitted[i+numParens];
	}
	if (conditionalSplitRegex.test(ret) &amp;&amp; recursionCount &lt; 10) {
		return expandConditionalNavlinkString(ret,article,z,recursionCount+1);
	}
	return ret;
}

function navlinkStringToArray(s, article, params) {
	s=expandConditionalNavlinkString(s,article,params);
	var splitted=s.parenSplit(RegExp('&lt;&lt;(.*?)&gt;&gt;'));
	var ret=[];
	for (var i=0; i&lt;splitted.length; ++i) {
		if (i%2) { // i odd, so s is a tag
			var t=new navlinkTag();
			var ss=splitted[i].split('|');
			t.id=ss[0];
			for (var j=1; j&lt;ss.length; ++j) {
				var sss=ss[j].split('=');
				if (sss.length&gt;1) {
					t[sss[0]]=sss[1];
				}
				else { // no assignment (no &quot;=&quot;), so treat this as a title (overwriting the last one)
					t.text=popupString(sss[0]);
				}
			}
			t.article=article;
			var oldid=params.oldid, rcid=params.rcid, diff=params.diff;
			if (typeof oldid != 'undefined' &amp;&amp; oldid != null) { t.oldid=oldid; }
			if (typeof rcid != 'undefined' &amp;&amp; rcid != null) { t.rcid=rcid; }
			if (typeof diff != 'undefined' &amp;&amp; diff != null) { t.diff=diff; }
			if (!t.text &amp;&amp; t.id != 'mainlink') { t.text=popupString(t.id); }
			ret.push(t);
		}
		else { // plain HTML
			ret.push(splitted[i]);
		}
	}
	return ret;
}


function navlinkSubstituteHTML(s) {
	return s.split('*').join(getValueOf('popupNavLinkSeparator'))
		.split('&lt;menurow&gt;').join('&lt;li class=&quot;popup_menu_row&quot;&gt;')
		.split('&lt;/menurow&gt;').join('&lt;/li&gt;')
		.split('&lt;menu&gt;').join('&lt;ul class=&quot;popup_menu&quot;&gt;')
		.split('&lt;/menu&gt;').join('&lt;/ul&gt;');

}

function navlinkDepth(magic,s) {
	return s.split('&lt;' + magic + '&gt;').length - s.split('&lt;/' + magic + '&gt;').length;
}


// navlinkString: * becomes the separator
//                &lt;&lt;foo|bar=baz|fubar&gt;&gt; becomes a foo-link with attribute bar='baz'
//                                      and visible text 'fubar'
//                if(test){...} and if(test){...}else{...} work too (nested ok)

function navlinkStringToHTML(s,article,params) {
	//limitAlert(navlinkStringToHTML, 5, 'navlinkStringToHTML\n' + article + '\n' + (typeof article));
	var p=navlinkStringToArray(s,article,params);
	var html='';
	var menudepth = 0; // nested menus not currently allowed, but doesn't do any harm to code for it
	var menurowdepth = 0;
	var wrapping = null;
	for (var i=0; i&lt;p.length; ++i) {
		if (typeof p[i] == typeof '') {
			html+=navlinkSubstituteHTML(p[i]);
			menudepth += navlinkDepth('menu', p[i]);
			menurowdepth += navlinkDepth('menurow', p[i]);
//			if (menudepth === 0) {
//				tagType='span';
//			} else if (menurowdepth === 0) {
//				tagType='li';
//			} else {
//				tagType = null;
//			}
		} else if (typeof p[i].type != 'undefined' &amp;&amp; p[i].type=='navlinkTag') {
			if (menudepth &gt; 0 &amp;&amp; menurowdepth === 0) {
				html += '&lt;li class=&quot;popup_menu_item&quot;&gt;' + p[i].html() + '&lt;/li&gt;';
			} else {
				html+=p[i].html();
			}
		}
	}
	return html;
}

function navlinkTag() {
	this.type='navlinkTag';
}

navlinkTag.prototype.html=function () {
	this.getNewWin();
	this.getPrintFunction();
	var html='';
	var opening, closing;
	var tagType='span';
	if (!tagType) {
		opening = ''; closing = '';
	} else {
		opening = '&lt;' + tagType + ' class=&quot;popup_' + this.id + '&quot;&gt;';
		closing = '&lt;/' + tagType + '&gt;';
	}
	if (typeof this.print!='function') {
		errlog ('Oh dear - invalid print function for a navlinkTag, id='+this.id);
	} else {
		html=this.print(this);
		if (typeof html != typeof '') {html='';}
		else if (typeof this.shortcut!='undefined') html=addPopupShortcut(html, this.shortcut);
	}
	return opening + html + closing;
};

navlinkTag.prototype.getNewWin=function() {
	getValueOf('popupLinksNewWindow');
	if (typeof pg.option.popupLinksNewWindow[this.id] === 'undefined') { this.newWin=null; }
	this.newWin=pg.option.popupLinksNewWindow[this.id];
}

navlinkTag.prototype.getPrintFunction=function() { //think about this some more
	// this.id and this.article should already be defined
	if (typeof this.id!=typeof '' || typeof this.article!=typeof {} ) { return; }
	var html='';
	var a,t;

	this.noPopup=1;
	switch (this.id) {
	case 'contribs': case 'history': case 'whatLinksHere':
	case 'userPage': case 'monobook': case 'userTalk':
	case 'talk': case 'article': case 'lastEdit':
		this.noPopup=null;
	}
	switch (this.id) {
	case 'email':     case 'contribs':  case 'block':     case 'unblock':
	case 'userlog':   case 'userSpace': case 'deletedContribs':
		this.article=this.article.userName();
	}

	switch (this.id) {
	case 'userTalk': case 'newUserTalk': case 'editUserTalk':
	case 'userPage': case 'monobook': case 'editMonobook': case 'blocklog':
		this.article=this.article.userName(true);
	// fall through; no break
	case 'pagelog': case 'deletelog': case 'protectlog':
	delete this.oldid;
	}

	if (this.id=='editMonobook' || this.id=='monobook') { this.article.append('/monobook.js'); }

	if (this.id != 'mainlink') {
		// FIXME anchor handling should be done differently with Title object
		this.article=this.article.removeAnchor();
		// if (typeof this.text=='undefined') this.text=popupString(this.id);
	}

	switch (this.id) {
	case 'undelete':       this.print=specialLink; this.specialpage='Undelete'; this.sep='/'; break;
	case 'whatLinksHere':  this.print=specialLink; this.specialpage='Whatlinkshere'; break;
	case 'relatedChanges': this.print=specialLink; this.specialpage='Recentchangeslinked'; break;
	case 'move':           this.print=specialLink; this.specialpage='Movepage'; break;
	case 'contribs':       this.print=specialLink; this.specialpage='Contributions'; break;
	case 'deletedContribs':this.print=specialLink; this.specialpage='Deletedcontributions'; break;
	case 'email':          this.print=specialLink; this.specialpage='EmailUser'; this.sep='/'; break;
	case 'block':          this.print=specialLink; this.specialpage='Blockip'; this.sep='&amp;ip='; break;
	case 'unblock':        this.print=specialLink; this.specialpage='Ipblocklist'; this.sep='&amp;action=unblock&amp;ip='; break;
	case 'userlog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;user='; break;
	case 'blocklog':       this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=block&amp;page='; break;
	case 'pagelog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;page='; break;
	case 'protectlog':     this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=protect&amp;page='; break;
	case 'deletelog':      this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=delete&amp;page='; break;
	case 'userSpace':      this.print=specialLink; this.specialpage='PrefixIndex'; this.sep='&amp;namespace=2&amp;prefix='; break;
	case 'search':         this.print=specialLink; this.specialpage='Search'; this.sep='&amp;fulltext=Search&amp;search='; break;
	case 'history': case 'historyfeed': case 'unwatch': case 'watch':
	case 'unprotect': case 'protect':
	this.print=wikiLink; this.action=this.id; break;

	case 'delete':
	this.print=wikiLink; this.action='delete';
	if (this.article.namespaceId()==pg.nsImageId) {
	    var img=this.article.stripNamespace();
	    this.action+='&amp;image='+img;
	}
	break;

	case 'markpatrolled':
	case 'edit': // editOld should keep the oldid, but edit should not.
	delete this.oldid; // fall through
	case 'view': case 'purge': case 'render':
	this.print=wikiLink;
	this.action=this.id; break;
	case 'raw':
	this.print=wikiLink; this.action='raw&amp;ctype=text/css'; break;
	case 'new':
	this.print=wikiLink; this.action='edit&amp;section=new'; break;
	case 'mainlink':
	if (typeof this.text=='undefined') { this.text=this.article.toString().entify(); }
	if (getValueOf('popupSimplifyMainLink') &amp;&amp; isInStrippableNamespace(this.article)) {
	    var s=this.text.split('/'); this.text=s[s.length-1];
	    if (this.text=='' &amp;&amp; s.length &gt; 1) { this.text=s[s.length-2]; }
	}
	this.print=titledWikiLink;
	if (typeof this.title=='undefined' &amp;&amp; pg.current.link &amp;&amp; typeof pg.current.link.href != 'undefined') {
	    this.title=safeDecodeURI((pg.current.link.originalTitle)?pg.current.link.originalTitle:this.article);
	    if (typeof this.oldid != 'undefined' &amp;&amp; this.oldid) {
		this.title=tprintf('Revision %s of %s', [this.oldid, this.title]);
	    }
	}
	this.action='view'; break;
	case 'userPage':
	case 'article':
	case 'monobook':
	case 'editMonobook':
	case 'editArticle':
	delete this.oldid;
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.article=this.article.articleFromTalkOrArticle();
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.print=wikiLink;
	if (this.id.indexOf('edit')==0) {
	    this.action='edit';
	} else { this.action='view';}
	break;
	case 'userTalk':
	case 'talk':
	this.article=this.article.talkPage();
	delete this.oldid;
	this.print=wikiLink;
	this.action='view'; break;
	case 'arin':
	this.print=arinLink; break;
	case 'count':
	this.print=editCounterLink; break;
	case 'google':
	this.print=googleLink; break;
	case 'editors':
	this.print=editorListLink; break;
	case 'globalsearch':
	this.print=globalSearchLink; break;
	case 'lastEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the last edit');
	this.from='prev'; this.to='cur'; break;
	case 'oldEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the edit made to get revision') + ' ' + this.oldid;
	this.from='prev'; this.to=this.oldid; break;
	case 'editOld':
	this.print=wikiLink; this.action='edit'; break;
	case 'undo':
	this.print=wikiLink; this.action='edit&amp;undo='; break;
	case 'markpatrolled':
	this.print=wikiLink; this.action='markpatrolled';
	case 'revert':
	this.print=wikiLink; this.action='revert'; break;
	case 'nullEdit':
	this.print=wikiLink; this.action='nullEdit'; break;
	case 'diffCur':
	this.print=titledDiffLink;
	this.title=tprintf('Show changes since revision %s', [this.oldid]);
	this.from=this.oldid; this.to='cur'; break;
	case 'editUserTalk':
	case 'editTalk':
	delete this.oldid;
	this.article=this.article.talkPage();
	this.action='edit'; this.print=wikiLink; break;
	case 'newUserTalk':
	case 'newTalk':
	this.article=this.article.talkPage();
	this.action='edit&amp;section=new'; this.print=wikiLink; break;
	case 'lastContrib':
	case 'sinceMe':
	this.print=magicHistoryLink;
	break;
	case 'togglePreviews':
	this.text=popupString(pg.option.simplePopups ? 'enable previews' : 'disable previews');
	case 'disablePopups': case 'purgePopups':
	this.print=popupMenuLink;
	break;
	default:
	this.print=function () {return 'Unknown navlink type: '+this.id+''};
	}
};
//
//  end navlinks
//////////////////////////////////////////////////
//&lt;/NOLITE&gt;
// ENDFILE: navlinks.js
// STARTFILE: shortcutkeys.js
//&lt;NOLITE&gt;
function popupHandleKeypress(evt) {
	var keyCode = window.event ? window.event.keyCode : ( evt.keyCode ? evt.keyCode : evt.which);
	if (!keyCode || !pg.current.link || !pg.current.link.navpopup) { return; }
	if (keyCode==27) { // escape
		killPopup();
		return false; // swallow keypress
	}

	var letter=String.fromCharCode(keyCode);
	var links=pg.current.link.navpopup.mainDiv.getElementsByTagName('A');
	var startLink=0;
	var i,j;

	if (popupHandleKeypress.lastPopupLinkSelected) {
		for (i=0; i&lt;links.length; ++i) {
			if (links[i]==popupHandleKeypress.lastPopupLinkSelected) { startLink=i; }
		}
	}
	for (j=0; j&lt;links.length; ++j) {
		i=(startLink + j + 1) % links.length;
		if (links[i].getAttribute('popupkey')==letter) {
			if (evt &amp;&amp; evt.preventDefault) evt.preventDefault();
			links[i].focus();
			popupHandleKeypress.lastPopupLinkSelected=links[i];
			return false; // swallow keypress
		}
	}

	// pass keypress on
	if (document.oldPopupOnkeypress) { return document.oldPopupOnkeypress(evt); }
	return true;
}

function addPopupShortcuts() {
	if (document.onkeypress!=popupHandleKeypress) {
		document.oldPopupOnkeypress=document.onkeypress;
	}
	document.onkeypress=popupHandleKeypress;
}

function rmPopupShortcuts() {
	popupHandleKeypress.lastPopupLinkSelected=null;
	try {
		if (document.oldPopupOnkeypress &amp;&amp; document.oldPopupOnkeypress==popupHandleKeypress) {
			// panic
			document.onkeypress=null; //function () {};
			return;
		}
		document.onkeypress=document.oldPopupOnkeypress;
	} catch (nasties) { /* IE goes here */ }
}


function addLinkProperty(html, property) {
	// take &quot;&lt;a href=...&gt;...&lt;/a&gt; and add a property
	// not sophisticated at all, easily broken
	var i=html.indexOf('&gt;');
	if (i&lt;0) { return html; }
	return html.substring(0,i) + ' ' + property + html.substring(i);
}

function addPopupShortcut(html, key) {
	if (!getValueOf('popupShortcutKeys')) { return html; }
	var ret= addLinkProperty(html, 'popupkey=&quot;'+key+'&quot;');
	if (key==' ') { key=popupString('spacebar'); }
	return ret.replace(RegExp('^(.*?)(title=&quot;)(.*?)(&quot;.*)$', 'i'),'$1$2$3 ['+key+']$4');
}
//&lt;/NOLITE&gt;
// ENDFILE: shortcutkeys.js
// STARTFILE: diffpreview.js
//&lt;NOLITE&gt;
function loadDiff(article, oldid, diff, navpop) {
	navpop.diffData={};
	var oldRev, newRev;
	switch (diff) {
	case 'cur':
		switch ( oldid ) {
		case null:
		case '':
		case 'prev':
			// eg newmessages diff link
			oldRev='0&amp;direction=prev';
			newRev=0;
			break;
		default:
			oldRev = oldid;
			newRev = 0;
		}
		break;
	case 'prev':
		oldRev = ( oldid || 0 ) + '&amp;direction=prev'; newRev = oldid; break;
	case 'next':
		oldRev = oldid; newRev = oldid + '&amp;direction=next';
		break;
	default:
		oldRev = oldid || 0; newRev = diff || 0; break;
	}
	oldRev = oldRev || 0;
	newRev = newRev || 0;

	var go = function() {
		pendingNavpopTask(navpop);
		getWiki(article, doneDiffNew, newRev, navpop);

		pendingNavpopTask(navpop);
		getWiki(article, doneDiffOld, oldRev, navpop);

		var tz = Cookie.read('popTz');
		if (getValueOf('popupAdjustDiffDates') &amp;&amp; tz===null) {
		    pendingNavpopTask(navpop);
		    getPageWithCaching(pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;meta=userinfo&amp;uiprop=options',
				       function(d) {
					       completedNavpopTask(navpop);
					       setTimecorrectionCookie(d);
					       if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
				       },  navpop);
		}
		return true; // remove hook once run
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_DIFFS'); }
}

function setTimecorrectionCookie(d) {
	try {
		var jsobj=getJsObj(d.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
	} catch (someError) {
		logerr( 'setTimecorretion failed' );
		return;
	}
    Cookie.create( 'popTz', getTimeOffset(tz), 1);
}

function doneDiff(download, isOld) {
	if (!download.owner || !download.owner.diffData) { return; }
	var navpop=download.owner;
	var label= (isOld) ? 'Old' : 'New';
	var otherLabel=(isOld) ? 'New' : 'Old';
	navpop.diffData[label]=download;
	completedNavpopTask(download.owner);
	if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
}

function diffDownloadsComplete(navpop) {
	if ( Cookie.read('popTz')===null) { return false; }
	return navpop.diffData.Old &amp;&amp; navpop.diffData.New;
}

function doneDiffNew(download) { doneDiff(download, false); }
function doneDiffOld(download) { doneDiff(download, true);  }

function rmBoringLines(a,b,context) {

	if (typeof context == 'undefined') { context=2; }
	// this is fairly slow... i think it's quicker than doing a word-based diff from the off, though
	var aa=[], aaa=[];
	var bb=[], bbb=[];
	var i, j;

	// first, gather all disconnected nodes in a and all crossing nodes in a and b
	for (i=0; i&lt;a.length; ++i ) {
		if(!a[i].paired) { aa[i]=1; }
		else if (countCrossings(b,a,i, true)) {
			aa[i]=1;
			bb[ a[i].row ] = 1;
		}
	}

	// pick up remaining disconnected nodes in b
	for (i=0; i&lt;b.length; ++i ) {
		if (bb[i]==1) { continue; }
		if(!b[i].paired) { bb[i]=1; }
	}

	// another pass to gather context: we want the neighbours of included nodes which are not yet included
	// we have to add in partners of these nodes, but we don't want to add context for *those* nodes in the next pass
	for (i=0; i&lt;b.length; ++i) {
		if ( bb[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(b.length, i+context); ++j) {
				if ( !bb[j] ) { bb[j] = 1; aa[ b[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;a.length; ++i) {
		if ( aa[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(a.length, i+context); ++j) {
				if ( !aa[j] ) { aa[j] = 1; bb[ a[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;bb.length; ++i) {
		if (bb[i] &gt; 0) { // it's a row we need
			if (b[i].paired) { bbb.push(b[i].text); } // joined; partner should be in aa
			else {
				bbb.push(b[i]);
			}
		}
	}
	for (i=0; i&lt;aa.length; ++i) {
		if (aa[i] &gt; 0) { // it's a row we need
			if (a[i].paired) { aaa.push(a[i].text); } // joined; partner should be in aa
			else {
				aaa.push(a[i]);
			}
		}
	}

	return { a: aaa, b: bbb};
}

function stripOuterCommonLines(a,b,context) {
	var i=0;
	while (i&lt;a.length &amp;&amp; i &lt; b.length &amp;&amp; a[i]==b[i]) { ++i; }
	var j=a.length-1; var k=b.length-1;
	while ( j&gt;=0 &amp;&amp; k&gt;=0 &amp;&amp; a[j]==b[k] ) { --j; --k; }

	return { a: a.slice(max(0,i - 1 - context), min(a.length+1, j + context+1)),
			    b: b.slice(max(0,i - 1 - context), min(b.length+1, k + context+1)) };
}

function insertDiff(navpop) {
	// for speed reasons, we first do a line-based diff, discard stuff that seems boring, then do a word-based diff
	// FIXME: sometimes this gives misleading diffs as distant chunks are squashed together
	var oldlines=navpop.diffData.Old.data.split('\n');
	var newlines=navpop.diffData.New.data.split('\n');
	var inner=stripOuterCommonLines(oldlines,newlines,getValueOf('popupDiffContextLines'));
	oldlines=inner.a; newlines=inner.b;
	var truncated=false;
	getValueOf('popupDiffMaxLines');
	if (oldlines.length &gt; pg.option.popupDiffMaxLines || newlines.length &gt; pg.option.popupDiffMaxLines) {
		// truncate
		truncated=true;
		inner=stripOuterCommonLines(oldlines.slice(0,pg.option.popupDiffMaxLines),
					    newlines.slice(0,pg.option.popupDiffMaxLines),
					    pg.option.popupDiffContextLines);
		oldlines=inner.a; newlines=inner.b;
	}

	var lineDiff=diff(oldlines, newlines);
	var lines2=rmBoringLines(lineDiff.o, lineDiff.n);
	var oldlines2=lines2.a; var newlines2=lines2.b;

	var simpleSplit = !String.prototype.parenSplit.isNative;
	var html='&lt;hr&gt;';
	if (getValueOf('popupDiffDates')) {
		html += diffDatesTable(navpop.diffData.Old, navpop.diffData.New);
		html += '&lt;hr&gt;';
	}
	html += shortenDiffString(
		diffString(oldlines2.join('\n'), newlines2.join('\n'), simpleSplit),
		getValueOf('popupDiffContextCharacters') ).join('&lt;hr&gt;');
	setPopupTipsAndHTML(html.split('\n').join('&lt;br&gt;') +
		     (truncated ? '&lt;hr&gt;&lt;b&gt;'+popupString('Diff truncated for performance reasons')+'&lt;/b&gt;' : '') ,
			    'popupPreview', navpop.idNumber);
}

function diffDatesTable( oldDl, newDl ) {
	var html='&lt;table class=&quot;popup_diff_dates&quot;&gt;';
	html += diffDatesTableRow( newDl, tprintf('New revision'));
	html += diffDatesTableRow( oldDl, tprintf('Old revision'));
	html += '&lt;/table&gt;';
	return html;
}
function diffDatesTableRow( dl, label ) {
	var txt='';
	if (!dl) {
		txt=popupString('Something went wrong :-(');
	} else if (!dl.lastModified) {
		txt= (/^\s*$/.test(dl.data)) ?
			popupString('Empty revision, maybe non-existent') : popupString('Unknown date');
	} else {
		var datePrint=getValueOf('popupDiffDatePrinter');
		if (typeof dl.lastModified[datePrint] == 'function') {
			if (getValueOf('popupAdjustDiffDates')) {
				var off;
				if (off=Cookie.read('popTz')) {
					var d2=adjustDate(dl.lastModified, off);
					txt = dayFormat(d2, true) + ' ' + timeFormat(d2, true);
				}
			} else {
				txt = dl.lastModified[datePrint]();
			}
		} else {
			txt = tprintf('Invalid %s %s', ['popupDiffDatePrinter', datePrint]);
		}
	}
	var revlink = generalLink({url: dl.url.replace(/&amp;.*?(oldid=[0-9]+(?:&amp;direction=[^&amp;]*)?).*/, '&amp;$1'),
				   text: label, title: label});
	return simplePrintf('&lt;tr&gt;&lt;td&gt;%s&lt;/td&gt;&lt;td&gt;%s&lt;/td&gt;&lt;/tr&gt;', [ revlink, txt ]);
}
//&lt;/NOLITE&gt;
// ENDFILE: diffpreview.js
// STARTFILE: links.js
//&lt;NOLITE&gt;
/////////////////////
// LINK GENERATION //
/////////////////////

// titledDiffLink --&gt; titledWikiLink --&gt; generalLink
// wikiLink       --&gt; titledWikiLink --&gt; generalLink
// editCounterLink --&gt; generalLink

function titledDiffLink(l) { // article, text, title, from, to) {
	return titledWikiLink({article: l.article, action: l.to + '&amp;oldid=' + l.from,
				newWin: l.newWin,
				noPopup: l.noPopup,
				text: l.text, title: l.title,
				/* hack: no oldid here */
				actionName: 'diff'});
}


function wikiLink(l) {
	//{article:article, action:action, text:text, oldid, newid}) {
	if (! (typeof l.article == typeof {}
	       &amp;&amp; typeof l.action == typeof '' &amp;&amp; typeof l.text==typeof '')) return null;
	if (typeof l.oldid == 'undefined') { l.oldid=null; }
	var savedOldid = l.oldid;
	if (!/^(edit|view|revert|render)$|^raw/.test(l.action)) { l.oldid=null; }
	var hint=popupString(l.action + 'Hint'); // revertHint etc etc etc
	var oldidData=[l.oldid, safeDecodeURI(l.article)];
	var revisionString = tprintf('revision %s of %s', oldidData);
	log('revisionString='+revisionString);
	switch (l.action) {
	case 'edit&amp;section=new': hint = popupString('newSectionHint');  break;
	case 'edit&amp;undo=':
		if (l.diff &amp;&amp; l.diff != 'prev' &amp;&amp; savedOldid ) {
		  l.action += l.diff + '&amp;undoafter=' + savedOldid;
		} else if (savedOldid) {
		  l.action += savedOldid;
		}
		hint = popupString('undoHint');
		break;
	case 'raw&amp;ctype=text/css': hint=popupString('rawHint'); break;
	case 'revert':
		var p=parseParams(pg.current.link.href);
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=' + revertSummary(l.oldid, p.diff);
		if (p.diff=='prev') {
			l.action += '&amp;direction=prev';
			revisionString = tprintf('the revision prior to revision %s of %s', oldidData);
		}
		if (getValueOf('popupRevertSummaryPrompt')) { l.action += '&amp;autosummaryprompt=true'; }
		if (getValueOf('popupMinorReverts')) { l.action += '&amp;autominor=true'; }
		log('revisionString is now '+revisionString);
		break;
	case 'nullEdit':
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=null';
		break;
	case 'historyfeed':
		l.action='history&amp;feed=rss';
		break;
	case 'markpatrolled':
		l.action='markpatrolled&amp;rcid='+l.rcid;
	}

	if (hint) {
		if (l.oldid) {
			hint = simplePrintf(hint, [revisionString]);
		}
		else {
			hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
		}
	}
	else {
		hint = safeDecodeURI(l.article + '&amp;action=' + l.action) + (l.oldid) ? '&amp;oldid='+l.oldid : '';
	}

	return titledWikiLink({article: l.article, action: l.action, text: l.text, newWin:l.newWin,
				title: hint, oldid: l.oldid, noPopup: l.noPopup});
}

function revertSummary(oldid, diff) {
	var ret='';
	if (diff == 'prev') {
		ret=getValueOf('popupQueriedRevertToPreviousSummary');
	} else { ret = getValueOf('popupQueriedRevertSummary'); }
	return ret + '&amp;autorv=' + oldid;
}

function titledWikiLink(l) {
	// possible properties of argument:
	// article, action, text, title, oldid, actionName, className, noPopup
	// oldid = null is fine here

	// article and action are mandatory args

	if (typeof l.article == 'undefined' || typeof l.action=='undefined') {
		errlog('got undefined article or action in titledWikiLink');
		return null;
	}

	var base = pg.wiki.titlebase +  l.article.urlString();
	var url=base;

	if (typeof l.actionName=='undefined' || !l.actionName) { l.actionName='action'; }

	// no need to add &amp;action=view, and this confuses anchors
	if (l.action != 'view') { url = base + '&amp;' + l.actionName + '=' + l.action; }

	if (typeof l.oldid!='undefined' &amp;&amp; l.oldid) { url+='&amp;oldid='+l.oldid; }

	var cssClass=pg.misc.defaultNavlinkClassname;
	if (typeof l.className!='undefined' &amp;&amp; l.className) { cssClass=l.className; }

	return generalNavLink({url: url, newWin: l.newWin,
				title: (typeof l.title != 'undefined') ? l.title : null,
				text: (typeof l.text!='undefined')?l.text:null,
				className: cssClass, noPopup:l.noPopup});
}

function getLastContrib(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processLastContribInfo(x,{page: wikipage, newWin: newWin})});
}
function processLastContribInfo(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: an odd thing happened. Please retry.'); return; }
	if(!info.firstNewEditor) {
		alert(tprintf('Only found one editor: %s made %s edits', [info.edits[0].editor,info.edits.length]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+info.firstNewEditor.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function getDiffSinceMyEdit(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processDiffSinceMyEdit(x,{page: wikipage, newWin: newWin})});
}
function processDiffSinceMyEdit(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: something fishy happened. Please try again.'); return; }
	var friendlyName=stuff.page.split('_').join(' ');
	if(!info.myLastEdit) {
		alert(tprintf('Couldn\'t find an edit by %s\nin the last %s edits to\n%s',
			      [info.userName, getValueOf('popupHistoryLimit'), friendlyName]));
		return;
	}
	if(info.myLastEdit.index==0) {
		alert(tprintf(&quot;%s seems to be the last editor to the page %s&quot;, [info.userName, friendlyName]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+ info.myLastEdit.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function displayUrl(url, newWin){
	if(newWin) { window.open(url); }
	else { document.location=url; }
}

function purgePopups() {
	processAllPopups(true);
	setupCache(); // deletes all cached items (not browser cached, though...)
	pg.option={};
	abortAllDownloads();
}

function processAllPopups(nullify, banish) {
	for (var i=0; i&lt;pg.current.links.length; ++i) {
		if (!pg.current.links[i].navpopup) { continue; }
		(nullify || banish) &amp;&amp; pg.current.links[i].navpopup.banish();
		pg.current.links[i].simpleNoMore=false;
		nullify &amp;&amp; (pg.current.links[i].navpopup=null);
	}
}

function disablePopups(){
	processAllPopups(false, true);
	setupTooltips(null, true);
}

function togglePreviews() {
	processAllPopups(true, true);
	pg.option.simplePopups=!pg.option.simplePopups;
	abortAllDownloads();
}

function magicHistoryLink(l) {
	// FIXME use onclick change href trick to sort this out instead of window.open

	var jsUrl='', title='';
	switch(l.id) {
	case 'lastContrib':
		jsUrl=simplePrintf('javascript:getLastContrib(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('lastContribHint');
		break;
	case 'sinceMe':
		jsUrl=simplePrintf('javascript:getDiffSinceMyEdit(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('sinceMeHint');
		break;
	}

	return generalNavLink({url: jsUrl, newWin: false, // can't have new windows with JS links, I think
				title: title, text: l.text, noPopup: l.noPopup});
}

function popupMenuLink(l) {
	var jsUrl=simplePrintf('javascript:%s()', [l.id]);
	var title=popupString(simplePrintf('%sHint', [l.id]));
	return generalNavLink({url: jsUrl, newWin:false, title:title, text:l.text, noPopup:l.noPopup});
}

function specialLink(l) {
	// properties: article, specialpage, text, sep
	if (typeof l.specialpage=='undefined'||!l.specialpage) return null;
	var base = pg.wiki.titlebase +  mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId]+':'+l.specialpage;
	if (typeof l.sep == 'undefined' || l.sep===null) l.sep='&amp;target=';
	var article=l.article.urlString({keepSpaces: l.specialpage=='Search'});
	var hint=popupString(l.specialpage+'Hint');
	switch (l.specialpage) {
	case 'Log':
	    switch (l.sep) {
	    case '&amp;user=': hint=popupString('userLogHint'); break;
	    case '&amp;type=block&amp;page=': hint=popupString('blockLogHint'); break;
	    case '&amp;page=': hint=popupString('pageLogHint'); break;
	    case '&amp;type=protect&amp;page=': hint=popupString('protectLogHint'); break;
	    case '&amp;type=delete&amp;page=': hint=popupString('deleteLogHint'); break;
	    default: log('Unknown log type, sep=' + l.sep); hint='Missing hint (FIXME)';
	    }
	    break;
	case 'PrefixIndex': article += '/'; break;
	}
	if (hint) hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
	else hint = safeDecodeURI(l.specialpage+':'+l.article) ;

	var url = base + l.sep + article;
	return generalNavLink({url: url, title: hint, text: l.text, newWin:l.newWin, noPopup:l.noPopup});
}

function generalLink(l) {
	// l.url, l.text, l.title, l.newWin, l.className, l.noPopup
	if (typeof l.url=='undefined') return null;

	// only quotation marks in the url can screw us up now... I think
	var url=l.url.split('&quot;').join('%22');

	var ret='&lt;a href=&quot;' + url + '&quot;';
	if (typeof l.title!='undefined' &amp;&amp; l.title) { ret += ' title=&quot;' + mw.html.escape(l.title) + '&quot;'; }
	if (l.noPopup) { ret += ' noPopup=1'; }
	var newWin;
	if (typeof l.newWin=='undefined' || l.newWin===null) { newWin=getValueOf('popupNewWindows'); }
	else { newWin=l.newWin; }
	if (newWin) { ret += ' target=&quot;_blank&quot;'; }
	if (typeof l.className!='undefined'&amp;&amp;l.className) { ret+=' class=&quot;'+l.className+'&quot;'; }
	ret += '&gt;';
	if (typeof l.text==typeof '') { ret+= l.text; }
	ret +='&lt;/a&gt;';
	return ret;
}

function appendParamsToLink(linkstr, params) {
	var sp=linkstr.parenSplit(RegExp('(href=&quot;[^&quot;]+?)&quot;', 'i'));
	if (sp.length&lt;2) return null;
	var ret=sp.shift() + sp.shift();
	ret += '&amp;' + params + '&quot;';
	ret += sp.join('');
	return ret;
}

function changeLinkTargetLink(x) { // newTarget, text, hint, summary, clickButton, minor, title (optional) {
	if (x.newTarget) {
		log ('changeLinkTargetLink: newTarget=' + x.newTarget);
	}
	// optional: oldTarget (in wikitext)
	// if x.newTarget omitted or null, remove the link

	x.clickButton=encodeURI(x.clickButton);

	// FIXME: first character of page title as well as namespace should be case insensitive
	// eg [[category:foo]] and [[Category:Foo]] are equivalent
	// this'll break if charAt(0) is nasty
	var cA=literalizeRegex(x.oldTarget);
	var chs=cA[0].toUpperCase();
	chs='['+chs + chs.toLowerCase()+']';
	var currentArticleRegexBit=encodeURIComponent(chs+cA.substring(1));
	currentArticleRegexBit=currentArticleRegexBit
		.split(RegExp('[_ ]+', 'g')).join('[_ ]+')
		.split( &quot;%20&quot; ).join('[_ ]+')
		.split('\\(').join('(?:%2528|\\()')
		.split('\\)').join('(?:%2529|\\))');
	// leading and trailing space should be ignored, and anchor bits optional:
	currentArticleRegexBit = '\\s*(' + currentArticleRegexBit + '(?:#[^\\[\\|]*)?)\\s*';
	// e.g. Computer (archaic) -&gt; \s*([Cc]omputer[_ ](?:%2528|\()archaic(?:%2528|\)))\s*

	// autoedit=s~\[\[([Cc]ad)\]\]~[[Computer-aided%20design|$1]]~g;s~\[\[([Cc]AD)[|]~[[Computer-aided%20design|~g

	var title=x.title || mw.config.get('wgPageName').split('_').join(' ');
	var lk=titledWikiLink({article: new Title(title), newWin:x.newWin,
						action:  'edit',
						text:    x.text,
						title:   x.hint,
						className: 'popup_change_title_link'
						});
	var cmd='';
	if (x.newTarget) {
		// escape '&amp;' and other nasties
		var t=encodeURIComponent(x.newTarget);
		var s=encodeURIComponent(literalizeRegex(x.newTarget));
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~[['+t+'|$1]]~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|]~[['+t+'|~g;';
		cmd += 's~\\[\\['+s + '\\|' + s + '\\]\\]~[[' + t + ']]~g';
	} else {
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~$1~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|](.*?)\\]\\]~$2~g';
	}
	cmd += '&amp;autoclick='+x.clickButton + '&amp;actoken=' + autoClickToken();
	cmd += ( x.minor == null ) ? '' : '&amp;autominor='+x.minor;
	cmd += ( x.watch == null ) ? '' : '&amp;autowatch='+x.watch;
	cmd += '&amp;autosummary='+encodeURIComponent(x.summary);
	return appendParamsToLink(lk, 'autoedit='+cmd);
}


function redirLink(redirMatch, article) {
	// NB redirMatch is in wikiText
	var ret='';

	if (getValueOf('popupAppendRedirNavLinks') &amp;&amp; getValueOf('popupNavLinks')) {
		ret += '&lt;hr&gt;';
		if (getValueOf('popupFixRedirs') &amp;&amp; typeof autoEdit != 'undefined' &amp;&amp; autoEdit) {
			log('redirLink: newTarget=' + redirMatch);
			ret += addPopupShortcut(
				changeLinkTargetLink(
				{newTarget: redirMatch, text: popupString('Redirects'),
					hint: popupString('Fix this redirect'),
						summary: simplePrintf(getValueOf('popupFixRedirsSummary'),
								      [article.toString(), redirMatch ]),
						oldTarget: article.toString(),
						clickButton: getValueOf('popupRedirAutoClick'), minor: true,
						watch: getValueOf('popupWatchRedirredPages')})
				, 'R');
			ret += popupString(' to ');
		}
		else ret += popupString('Redirects') + popupString(' to ');
		return ret;
	}

	else return '&lt;br&gt; ' + popupString('Redirects') + popupString(' to ') +
		     titledWikiLink({article: new Title().fromWikiText(redirMatch), action: 'view',  /* FIXME: newWin */
						      text: safeDecodeURI(redirMatch), title: popupString('Bypass redirect')});
}

function arinLink(l) {
	if (!saneLinkCheck(l)) { return null; }
	if ( ! l.article.isIpUser() || ! pg.wiki.wikimedia) return null;

	var uN=l.article.userName();

	return generalNavLink({url:'http://ws.arin.net/cgi-bin/whois.pl?queryinput=' + encodeURIComponent(uN), newWin:l.newWin,
				title: tprintf('Look up %s in ARIN whois database', [uN]),
				text: l.text, noPopup:1});
}

function toolDbName(cookieStyle) {
	var ret = mw.config.get('wgDBname');
	if (!cookieStyle) { ret+= '_p'; }
	return ret;
}

function saneLinkCheck(l) {
	if (typeof l.article != typeof {} || typeof l.text != typeof '') { return false; }
	return true;
}
function editCounterLink(l) {
	if(!saneLinkCheck(l)) return null;
	if (! pg.wiki.wikimedia) return null;
	var uN=l.article.userName();
	var tool=getValueOf('popupEditCounterTool');
	var url;
	var soxredToolUrl='http://toolserver.org/~soxred93/count/index.php?name=$1&amp;lang=$2&amp;wiki=$3';
	var kateToolUrl='http://toolserver.org/~$3/cgi-bin/Tool1/wannabe_kate?username=$1&amp;site=en.wikiversity.org&amp;$2';

	switch(tool) {
	case 'custom':
		url=simplePrintf(getValueOf('popupEditCounterUrl'), [ encodeURIComponent(uN), toolDbName() ]);
		break;
	case 'kate':
	case 'interiot':
		url=simplePrintf(kateToolUrl, [ encodeURIComponent(uN), toolDbName(), tool ]);
		break;
	default:
	    var theWiki=pg.wiki.hostname.split('.');
		url=simplePrintf(soxredToolUrl, [ encodeURIComponent(uN), theWiki[0], theWiki[1] ]);
	}
	return generalNavLink({url:url, title: tprintf('editCounterLinkHint', [uN]),
				newWin:l.newWin, text: l.text, noPopup:1});
}


function globalSearchLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://vs.aka-online.de/cgi-bin/globalwpsearch.pl?timeout=120&amp;search=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + article, newWin:l.newWin,
				title: tprintf('globalSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function googleLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://www.google.com/search?q=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + '%22' + article + '%22', newWin:l.newWin,
				title: tprintf('googleSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function editorListLink(l) {
	if(!saneLinkCheck(l)) return null;
	var article= l.article.articleFromTalkPage() || l.article;
        var theWiki=pg.wiki.hostname.split('.');
        var base='http://toolserver.org/~soxred93/articleinfo/index.php?&amp;uselang=' + wgUserLanguage +
            'lang=' + theWiki[0] + '&amp;wiki=' + theWiki[1] + '&amp;begin=&amp;end=&amp;article='
	return generalNavLink({url:base+article.urlString(),
				title: tprintf('editorListHint', [article]),
				newWin:l.newWin, text: l.text, noPopup:1});
}

function generalNavLink(l) {
	l.className = (l.className==null) ? 'popupNavLink' : l.className;
	return generalLink(l);
}

//////////////////////////////////////////////////
// magic history links
//

function getHistoryInfo(wikipage, whatNext) {
	log('getHistoryInfo');
	getHistory(wikipage, whatNext ? function(d){whatNext(processHistory(d));} : processHistory);
}

// FIXME eliminate pg.idNumber ... how? :-(

function getHistory(wikipage, onComplete) {
	log('getHistory');
	var url = pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;prop=revisions&amp;titles=' +
			new Title(wikipage).urlString() + '&amp;rvlimit=' + getValueOf('popupHistoryLimit');
	log('getHistory: url='+url);
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	return startDownload(url, pg.idNumber+'history', onComplete);
}

function processHistory(download) {
	var jsobj = getJsObj(download.data);
	try {
		window.x=jsobj;
		var p=jsobj['query']['pages']
		for (var pageid in p) {
			var revisions=p[pageid]['revisions'];
			// we only get the first one
			break;
		}
	} catch (someError) {
		log('Something went wrong with JSON business');
		return finishProcessHistory([]);
	}
	var edits=[];
	for (var i=0; i&lt;revisions.length; ++i) {
		edits.push({ oldid: revisions[i]['revid'], editor: revisions[i]['user'] });
	}
	log('processed ' + edits.length + ' edits');
	return finishProcessHistory(edits, mw.config.get('wgUserName'));
}


function finishProcessHistory(edits, userName) {
	var histInfo={};

	histInfo.edits=edits;
	histInfo.userName=userName;

	for (var i=0; i&lt;edits.length; ++i) {
		if (typeof histInfo.myLastEdit == 'undefined' &amp;&amp; userName &amp;&amp; edits[i].editor==userName) {
			histInfo.myLastEdit={index: i, oldid: edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
		if (typeof histInfo.firstNewEditor == 'undefined' &amp;&amp; edits[i].editor != edits[0].editor) {
			histInfo.firstNewEditor={index:i, oldid:edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
	}
	//pg.misc.historyInfo=histInfo;
	return histInfo;
}
//&lt;/NOLITE&gt;
// ENDFILE: links.js
// STARTFILE: options.js
//////////////////////////////////////////////////
// options

// check for cookies and existing value, else use default
function defaultize(x) {
	var val=null;
	if (x!='popupCookies') {
		defaultize('popupCookies');
		if (pg.option.popupCookies &amp;&amp; (val=Cookie.read(x))) {
			pg.option[x]=val;
			return;
		}
	}
	if (pg.option[x]===null || typeof pg.option[x]=='undefined') {
		if (typeof window[x] != 'undefined' ) pg.option[x]=window[x];
		else pg.option[x]=pg.optionDefault[x];
	}
}

function newOption(x, def) {
	pg.optionDefault[x]=def;
}

function setDefault(x, def) {
	return newOption(x, def);
}

function getValueOf(varName) {
	defaultize(varName);
	return pg.option[varName];
}

function useDefaultOptions() { // for testing
	for (var p in pg.optionDefault) {
		pg.option[p]=pg.optionDefault[p];
		if (typeof window[p]!='undefined') { delete window[p]; }
	}
}

function setOptions() {
	// user-settable parameters and defaults
	var userIsSysop = false;
	if ( mw.config.get('wgUserGroups') ) {
		for ( var g = 0; g &lt; mw.config.get('wgUserGroups').length; ++g ) {
			if ( mw.config.get('wgUserGroups')[g] == &quot;sysop&quot; )
				userIsSysop = true
		}
	}

	// Basic options
	newOption('popupDelay',               0.5);
	newOption('popupHideDelay',           0.5);
	newOption('simplePopups',             false);
	newOption('popupStructure',           'shortmenus');   // see later - default for popupStructure is 'original' if simplePopups is true
	newOption('popupActionsMenu',         true);
	newOption('popupSetupMenu',           true);
	newOption('popupAdminLinks',          userIsSysop);
	newOption('popupShortcutKeys',        false);
	newOption('popupHistoricalLinks',     true);
	newOption('popupOnlyArticleLinks',    true);
	newOption('removeTitles',             true);
	newOption('popupMaxWidth',            350);
	newOption('popupInitialWidth',        false); // integer or false
	newOption('popupSimplifyMainLink',    true);
	newOption('popupAppendRedirNavLinks', true);
	newOption('popupTocLinks',            false);
	newOption('popupSubpopups',           true);
	newOption('popupDragHandle',          false /* 'popupTopLinks'*/);
	newOption('popupLazyPreviews',        true);
	newOption('popupLazyDownloads',       true);
	newOption('popupAllDabsStubs',        false);
	newOption('popupDebugging',           false);
	newOption('popupAdjustDiffDates',     true);
	newOption('popupActiveNavlinks',      true);
	newOption('popupModifier',            false); // ctrl, shift, alt or meta
	newOption('popupModifierAction',      'enable'); // or 'disable'
	newOption('popupDraggable',           true);

//&lt;NOLITE&gt;
	// images
	newOption('popupImages',                 true);
	newOption('imagePopupsForImages',        true);
	newOption('popupNeverGetThumbs',         false);
	//newOption('popupImagesToggleSize',       true);
	newOption('popupThumbAction',            'imagepage'); //'sizetoggle');
	newOption('popupImageSize',              60);
	newOption('popupImageSizeLarge',         200);

	// redirs, dabs, reversion
	newOption('popupFixRedirs',             false);
	newOption('popupRedirAutoClick',        'wpDiff');
	newOption('popupFixDabs',               false);
	newOption('popupRevertSummaryPrompt',   false);
	newOption('popupMinorReverts',          false);
	newOption('popupRedlinkRemoval',        false);
	newOption('popupWatchDisambiggedPages', null);
	newOption('popupWatchRedirredPages',    null);
	newOption('popupDabWiktionary',         'last');

	// navlinks
	newOption('popupNavLinks',          true);
	newOption('popupNavLinkSeparator',  ' &amp;sdot; ');
	newOption('popupLastEditLink',      true);
	newOption('popupEditCounterTool',   'soxred');
	newOption('popupEditCounterUrl',    '');
	newOption('popupExtraUserMenu',     '');
//&lt;/NOLITE&gt;

	// previews etc
	newOption('popupPreviews',             true);
	newOption('popupSummaryData',          true);
	newOption('popupMaxPreviewSentences',  5);
	newOption('popupMaxPreviewCharacters', 600);
	newOption('popupLastModified',         true);
	newOption('popupPreviewKillTemplates', true);
	newOption('popupPreviewRawTemplates',  true);
	newOption('popupPreviewFirstParOnly',  true);
	newOption('popupPreviewCutHeadings',   true);
	newOption('popupPreviewButton',        false);
	newOption('popupPreviewButtonEvent',   'click');

//&lt;NOLITE&gt;
	// diffs
	newOption('popupPreviewDiffs',          true);
	newOption('popupDiffMaxLines',          100);
	newOption('popupDiffContextLines',      2);
	newOption('popupDiffContextCharacters', 40);
	newOption('popupDiffDates',             true);
	newOption('popupDiffDatePrinter',       'toLocaleString');

	// edit summaries. God, these are ugly.
	newOption('popupFixDabsSummary',           popupString('defaultpopupFixDabsSummary') );
	newOption('popupExtendedRevertSummary',    popupString('defaultpopupExtendedRevertSummary') );
	newOption('popupTimeOffset',               null);
	newOption('popupRevertSummary',            popupString('defaultpopupRevertSummary') );
	newOption('popupRevertToPreviousSummary',  popupString('defaultpopupRevertToPreviousSummary') );
	newOption('popupQueriedRevertSummary',            popupString('defaultpopupQueriedRevertSummary') );
	newOption('popupQueriedRevertToPreviousSummary',  popupString('defaultpopupQueriedRevertToPreviousSummary') );
	newOption('popupFixRedirsSummary',         popupString('defaultpopupFixRedirsSummary') );
	newOption('popupRedlinkSummary',           popupString('defaultpopupRedlinkSummary') );
	newOption('popupRmDabLinkSummary',         popupString('defaultpopupRmDabLinkSummary') );
//&lt;/NOLITE&gt;
	// misc
	newOption('popupCookies',             false);
	newOption('popupHistoryLimit',        50);
//&lt;NOLITE&gt;
	newOption('popupFilters',             [popupFilterStubDetect,     popupFilterDisambigDetect,
					       popupFilterPageSize,       popupFilterCountLinks,
					       popupFilterCountImages,    popupFilterCountCategories,
					       popupFilterLastModified]);
	newOption('extraPopupFilters',        []);
	newOption('popupOnEditSelection', 'cursor');
	newOption('popupPreviewHistory',      true);
	newOption('popupImageLinks',          true);
	newOption('popupCategoryMembers',     true);
	newOption('popupUserInfo',            true);
	newOption('popupHistoryPreviewLimit', 25);
	newOption('popupContribsPreviewLimit',25);
	newOption('popupRevDelUrl',          '//en.wikiversity.org/wiki/Wikiversity:Revision_deletion');
//&lt;/NOLITE&gt;

	// new windows
	newOption('popupNewWindows',     false);
	newOption('popupLinksNewWindow', {'lastContrib': true, 'sinceMe': true});

	// regexps
	newOption('popupDabRegexp', '([{][{]\\s*disambig|disambig\\s*[}][}]|disamb\\s*[}][}]|dab\\s*[}][}])|[{][{]\\s*(((geo|hn|road?|school|number)dis)|[234][lc][acw]|shipindex)(\\s*[|][^}]*)?\\s*[}][}]|is a .*disambiguation.*page');
	newOption('popupAnchorRegexp', 'anchors?'); //how to identify an anchors template
	newOption('popupStubRegexp', '(sect)?stub[}][}]|This .*-related article is a .*stub');
	newOption('popupImageVarsRegexp', 'image|image_(?:file|skyline|name|flag|seal)|cover|badge|logo');
}
// ENDFILE: options.js
// STARTFILE: strings.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Translatable strings
//////////////////////////////////////////////////
//
// See instructions at
// //en.wikipedia.org/wiki/Wikipedia:Tools/Navigation_popups/Translation

pg.string = {
	/////////////////////////////////////
	// summary data, searching etc.
	/////////////////////////////////////
	'article': 'article',
	'category': 'category',
	'categories': 'categories',
	'image': 'image',
	'images': 'images',
	'stub': 'stub',
	'section stub': 'section stub',
	'Empty page': 'Empty page',
	'kB': 'kB',
	'bytes': 'bytes',
	'day': 'day',
	'days': 'days',
	'hour': 'hour',
	'hours': 'hours',
	'minute': 'minute',
	'minutes': 'minutes',
	'second': 'second',
	'seconds': 'seconds',
	'week': 'week',
	'weeks': 'weeks',
	'search': 'search',
	'SearchHint': 'Find English Wikiversity resources containing %s',
	'web': 'web',
	'global': 'global',
	'globalSearchHint': 'Search across Wikiversity in different languages for %s',
	'googleSearchHint': 'Google for %s',
	/////////////////////////////////////
	// article-related actions and info
	// (some actions also apply to user pages)
	/////////////////////////////////////
	'actions': 'actions',         ///// view articles and view talk
	'popupsMenu': 'popups',
	'togglePreviewsHint': 'Toggle preview generation in popups on this page',
	'enable previews': 'enable previews',
	'disable previews': 'disable previews',
	'toggle previews': 'toggle previews',
	'show preview': 'show preview',
	'reset': 'reset',
	'more...': 'more...',
	'disable': 'disable popups',
	'disablePopupsHint': 'Disable popups on this page. Reload page to re-enable.',
	'historyfeedHint': 'RSS feed of recent changes to this page',
	'purgePopupsHint': 'Reset popups, clearing all cached popup data.',
	'PopupsHint': 'Reset popups, clearing all cached popup data.',
	'spacebar': 'space',
	'view': 'view',
	'view article': 'view article',
	'viewHint': 'Go to %s',
	'talk': 'talk',
	'talk page': 'talk page',
	'this&amp;nbsp;revision': 'this&amp;nbsp;revision',
	'revision %s of %s': 'revision %s of %s',
	'Revision %s of %s': 'Revision %s of %s',
	'the revision prior to revision %s of %s': 'the revision prior to revision %s of %s',
	'Toggle image size': 'Click to toggle image size',
	'del': 'del',                 ///// delete, protect, move
	'delete': 'delete',
	'deleteHint': 'Delete %s',
	'undeleteShort': 'un',
	'UndeleteHint': 'Show the deletion history for %s',
	'protect': 'protect',
	'protectHint': 'Restrict editing rights to %s',
	'unprotectShort': 'un',
	'unprotectHint': 'Allow %s to be edited by anyone again',
	'move': 'move',
	'move page': 'move page',
	'MovepageHint': 'Change the title of %s',
	'edit': 'edit',               ///// edit articles and talk
	'edit article': 'edit article',
	'editHint': 'Change the content of %s',
	'edit talk': 'edit talk',
	'new': 'new',
	'new topic': 'new topic',
	'newSectionHint': 'Start a new section on %s',
	'null edit': 'null edit',
	'nullEditHint': 'Submit an edit to %s, making no changes ',
	'hist': 'hist',               ///// history, diffs, editors, related
	'history': 'history',
	'historyHint': 'List the changes made to %s',
	'last': 'last',
	'lastEdit': 'lastEdit',
	'mark patrolled': 'mark patrolled',
	'markpatrolledHint': 'Mark this edit as patrolled',
	'show last edit': 'most recent edit',
	'Show the last edit': 'Show the effects of the most recent change',
	'lastContrib': 'lastContrib',
	'last set of edits': 'latest edits',
	'lastContribHint': 'Show the net effect of changes made by the last editor',
	'cur': 'cur',
	'diffCur': 'diffCur',
	'Show changes since revision %s': 'Show changes since revision %s',
	'%s old': '%s old', // as in 4 weeks old
	'oldEdit': 'oldEdit',
	'purge': 'purge',
	'purgeHint': 'Demand a fresh copy of %s',
	'raw': 'source',
	'rawHint': 'Download the source of %s',
	'render': 'simple',
	'renderHint': 'Show a plain HTML version of %s',
	'Show the edit made to get revision': 'Show the edit made to get revision',
	'sinceMe': 'sinceMe',
	'changes since mine': 'diff my edit',
	'sinceMeHint': 'Show changes since my last edit',
	'Couldn\'t find an edit by %s\nin the last %s edits to\n%s': 'Couldn\'t find an edit by %s\nin the last %s edits to\n%s',
	'eds': 'eds',
	'editors': 'editors',
	'editorListHint': 'List the users who have edited %s',
	'related': 'related',
	'relatedChanges': 'relatedChanges',
	'related changes': 'related changes',
	'RecentchangeslinkedHint': 'Show changes in articles related to %s',
	'editOld': 'editOld',          ///// edit old version, or revert
	'rv': 'rv',
	'revert': 'revert',
	'revertHint': 'Revert to %s',
	'defaultpopupRedlinkSummary': 'Removing link to empty page [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupFixDabsSummary': 'Disambiguate [[%s]] to [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupFixRedirsSummary': 'Redirect bypass from [[%s]] to [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupExtendedRevertSummary': 'Revert to revision dated %s by %s, oldid %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRevertToPreviousSummary': 'Revert to the revision prior to revision %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRevertSummary': 'Revert to revision %s using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupQueriedRevertToPreviousSummary': 'Revert to the revision prior to revision $1 dated $2 by $3 using [[:en:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupQueriedRevertSummary': 'Revert to revision $1 dated $2 by $3 using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'defaultpopupRmDabLinkSummary': 'Remove link to dab page [[%s]] using [[:w:Wikipedia:Tools/Navigation_popups|popups]]',
	'Redirects': 'Redirects', // as in Redirects to ...
	' to ': ' to ',           // as in Redirects to ...
	'Bypass redirect': 'Bypass redirect',
	'Fix this redirect': 'Fix this redirect',
	'disambig': 'disambig',          ///// add or remove dab etc.
	'disambigHint': 'Disambiguate this link to [[%s]]',
	'Click to disambiguate this link to:': 'Click to disambiguate this link to:',
	'remove this link': 'remove this link',
	'remove all links to this page from this article': 'remove all links to this page from this article',
	'remove all links to this disambig page from this article': 'remove all links to this disambig page from this article',
	'mainlink': 'mainlink',          ///// links, watch, unwatch
	'wikiLink': 'wikiLink',
	'wikiLinks': 'wikiLinks',
	'links here': 'links here',
	'whatLinksHere': 'whatLinksHere',
	'what links here': 'what links here',
	'WhatlinkshereHint': 'List the pages that are hyperlinked to %s',
	'unwatchShort': 'un',
	'watchThingy': 'watch',  // called watchThingy because {}.watch is a function
	'watchHint': 'Add %s to my watchlist',
	'unwatchHint': 'Remove %s from my watchlist',
	'Only found one editor: %s made %s edits': 'Only found one editor: %s made %s edits',
	'%s seems to be the last editor to the page %s': '%s seems to be the last editor to the page %s',
	'rss': 'rss',
	/////////////////////////////////////
	// diff previews
	/////////////////////////////////////
	'Diff truncated for performance reasons': 'Diff truncated for performance reasons',
	'Old revision': 'Old revision',
	'New revision': 'New revision',
	'Something went wrong :-(': 'Something went wrong :-(',
	'Empty revision, maybe non-existent': 'Empty revision, maybe non-existent',
	'Unknown date': 'Unknown date',
	/////////////////////////////////////
	// other special previews
	/////////////////////////////////////
	'Empty category': 'Empty category',
	'Category members (%s shown)': 'Category members (%s shown)',
	'No image links found': 'No image links found',
	'File links': 'File links',
	'No image found': 'No image found',
	'Image from Commons': 'Image from Commons',
	'Description page': 'Description page',
	'Alt text:': 'Alt text:',
	'revdel':'Hidden revision',
	/////////////////////////////////////
	// user-related actions and info
	/////////////////////////////////////
	'user': 'user',               ///// user page, talk, email, space
	'user&amp;nbsp;page': 'user&amp;nbsp;page',
	'user talk': 'user talk',
	'edit user talk': 'edit user talk',
	'leave comment': 'leave comment',
	'email': 'email',
	'email user': 'email user',
	'EmailuserHint': 'Send an email to %s',
	'space': 'space', // short form for userSpace link
	'PrefixIndexHint': 'Show pages in the userspace of %s',
	'count': 'count',             ///// contributions, log
	'edit counter': 'edit counter',
	'editCounterLinkHint': 'Count the contributions made by %s',
	'contribs': 'contribs',
	'contributions': 'contributions',
	'deletedContribs': 'deleted contributions',
	'DeletedcontributionsHint': 'List deleted edits made by %s',
	'ContributionsHint': 'List the contributions made by %s',
	'log': 'log',
	'user log': 'user log',
	'userLogHint': 'Show %s\'s user log',
	'arin': 'ARIN lookup',             ///// ARIN lookup, block user or IP
	'Look up %s in ARIN whois database': 'Look up %s in the ARIN whois database',
	'unblockShort': 'un',
	'block': 'block',
	'block user': 'block user',
	'IpblocklistHint': 'Unblock %s',
	'BlockipHint': 'Prevent %s from editing',
	'block log': 'block log',
	'blockLogHint': 'Show the block log for %s',
	'protectLogHint': 'Show the protection log for %s',
	'pageLogHint': 'Show the page log for %s',
	'deleteLogHint': 'Show the deletion log for %s',
	'Invalid %s %s': 'The option %s is invalid: %s',
	'No backlinks found': 'No backlinks found',
	' and more': ' and more',
	'undo': 'undo',
	'undoHint': 'undo this edit',
	'Download preview data': 'Download preview data',
	'Invalid or IP user': 'Invalid or IP user',
	'Not a registered username': 'Not a registered username',
	'BLOCKED': 'BLOCKED',
	' edits since: ': ' edits since: ',
	/////////////////////////////////////
	// Autoediting
	/////////////////////////////////////
	'Enter a non-empty edit summary or press cancel to abort': 'Enter a non-empty edit summary or press cancel to abort',
	'Failed to get revision information, please edit manually.\n\n': 'Failed to get revision information, please edit manually.\n\n',
	'The %s button has been automatically clicked. Please wait for the next page to load.': 'The %s button has been automatically clicked. Please wait for the next page to load.',
	'Could not find button %s. Please check the settings in your javascript file.': 'Could not find button %s. Please check the settings in your javascript file.',
	/////////////////////////////////////
	// Popups setup
	/////////////////////////////////////
	'Open full-size image': 'Open full-size image',
	'zxy': 'zxy'
};


function popupString(str) {
	if (typeof popupStrings != 'undefined' &amp;&amp; popupStrings &amp;&amp; popupStrings[str]) { return popupStrings[str]; }
	if (pg.string[str]) { return pg.string[str]; }
	return str;
}


function tprintf(str,subs) {
	if (typeof subs != typeof []) { subs = [subs]; }
	return simplePrintf(popupString(str), subs);
}

//&lt;/NOLITE&gt;
// ENDFILE: strings.js


////////////////////////////////////////////////////////////////////
// Run things
////////////////////////////////////////////////////////////////////

hookEvent('load', setupPopups);
$(autoEdit);

//support for MediaWiki's live preview
$( function() {
   	if(typeof doLivePreview != &quot;function&quot; || typeof $ != &quot;function&quot;) return;
	$(&quot;#wpPreview&quot;).click(function(){
		var i = setInterval(function(){
			var p = document.getElementById(&quot;wikiPreview&quot;);
			if(p.previousSibling.className == &quot;mw-ajax-loader&quot;) return;

			p.ranSetupTooltipsAlready = false;
			setupTooltips(p);
			clearInterval(i);
		}, 500);
	});
});
// &lt;/nowiki&gt;</text>
      <sha1>dvlz067wiphlvragdziqjzs3956an5h</sha1>
    </revision>
    <revision>
      <id>2810151</id>
      <parentid>2810147</parentid>
      <timestamp>2026-05-18T19:16:47Z</timestamp>
      <contributor>
        <username>WikiBayer</username>
        <id>2181512</id>
      </contributor>
      <comment>Undid revision [[Special:Diff/2810145|2810145]] by [[Special:Contributions/WikiBayer|WikiBayer]] ([[User talk:WikiBayer|talk]])</comment>
      <origin>2810151</origin>
      <model>javascript</model>
      <format>text/javascript</format>
      <text bytes="246554" sha1="7fsesesihhzunjaobyicdhzai986jqu" xml:space="preserve">// STARTFILE: main.js
// **********************************************************************
// **                                                                  **
// **             changes to this file affect many users.              **
// **           please discuss on the talk page before editing         **
// **                                                                  **
// **********************************************************************
// **                                                                  **
// ** if you do edit this file, be sure that your editor recognizes it **
// ** as utf8, or the weird and wonderful characters in the namespaces **
// **   below will be completely broken. You can check with the show   **
// **            changes button before submitting the edit.            **
// **                      test: مدیا מיוחד Мэдыя                      **
// **                                                                  **
// **********************************************************************

//////////////////////////////////////////////////
// Globals
//

// Trying to shove as many of these as possible into the pg (popup globals) object
function pg(){}; // dummy to stop errors
window.pg = {
	re: {},               // regexps
	ns: {},               // namespaces
	string: {},           // translatable strings
	wiki: {},             // local site info
	misc: {},             // YUCK PHOOEY
	option: {},           // options, see newOption etc
	optionDefault: {},    // default option values
	flag: {},             // misc flags
	cache: {},            // page and image cache
	structures: {},       // navlink structures
	timer: {},            // all sorts of timers (too damn many)
	counter: {},          // .. and all sorts of counters
	current: {},          // state info
	endoflist: null
};
window.pop = {          // wrap various functions in here
	init: {},
	util: {},
	endoflist: null
};
function popupsReady() {
	if (!window.pg) { return false; }
	if (!pg.flag) { return false; }
	if (!pg.flag.finishedLoading) { return false; }
	return true;
}

/// Local Variables: ///
/// mode:c ///
/// End: ///
// ENDFILE: main.js
// STARTFILE: actions.js
function setupTooltips(container, remove, force, popData) {
	log('setupTooltips, container='+container+', remove='+remove);
	if (!container) {
//&lt;NOLITE&gt;
		// the main initial call
		if (getValueOf('popupOnEditSelection') &amp;&amp; window.doSelectionPopup &amp;&amp; document &amp;&amp; document.editform &amp;&amp; document.editform.wpTextbox1) {
			document.editform.wpTextbox1.onmouseup=doSelectionPopup;
		}
//&lt;/NOLITE&gt;
		// article/content is a structure-dependent thing
		container = defaultPopupsContainer();
	}

	if (!remove &amp;&amp; !force &amp;&amp; container.ranSetupTooltipsAlready) { return; }
	container.ranSetupTooltipsAlready = !remove;

	var anchors;
	anchors=container.getElementsByTagName('A');
	setupTooltipsLoop(anchors, 0, 250, 100, remove, popData);
}

function defaultPopupsContainer() {
    if (getValueOf('popupOnlyArticleLinks')) {
	    return document.getElementById('mw_content') || 
		    document.getElementById('content') ||
		    document.getElementById('article') || document;
    }
    return  document;
}

function setupTooltipsLoop(anchors,begin,howmany,sleep, remove, popData) {
	log(simplePrintf('setupTooltipsLoop(%s,%s,%s,%s,%s)', arguments));
	var finish=begin+howmany;
	var loopend = min(finish, anchors.length);
	var j=loopend - begin;
	log ('setupTooltips: anchors.length=' + anchors.length + ', begin=' + begin +
	     ', howmany=' + howmany + ', loopend=' + loopend + ', remove=' + remove);
	var doTooltip= remove ? removeTooltip : addTooltip;
	// try a faster (?) loop construct
	if (j &gt; 0) {
		do {
			var a=anchors[loopend - j];
			if (typeof a=='undefined' || !a || !a.href) {
				log('got null anchor at index ' + loopend - j);
				continue;
			}
			doTooltip(a, popData);
		} while (--j);
	}
	if (finish &lt; anchors.length) {
		setTimeout(function() {
				setupTooltipsLoop(anchors,finish,howmany,sleep,remove,popData);},
			sleep);
	} else {
		if ( !remove &amp;&amp; ! getValueOf('popupTocLinks')) { rmTocTooltips(); }
		pg.flag.finishedLoading=true;
	}
}

// eliminate popups from the TOC
// This also kills any onclick stuff that used to be going on in the toc
function rmTocTooltips() {
	var toc=document.getElementById('toc');
	if (toc) {
		var tocLinks=toc.getElementsByTagName('A');
		var tocLen = tocLinks.length;
		for (j=0; j&lt;tocLen; ++j) {
			removeTooltip(tocLinks[j], true);
		}
	}
}

function addTooltip(a, popData) {
	if ( !isPopupLink(a) ) { return; }
	a.onmouseover=mouseOverWikiLink;
	a.onmouseout= mouseOutWikiLink;
	a.onmousedown = killPopup;
	a.hasPopup = true;
	a.popData = popData;
}

function removeTooltip(a) {
	if ( !a.hasPopup ) { return; }
	a.onmouseover = null;
	a.onmouseout = null;
	if (a.originalTitle) { a.title = a.originalTitle; }
	a.hasPopup=false;
}

function removeTitle(a) {
	a.title='';
	if (a.originalTitle) { return; }
	a.originalTitle=a.title;
}

function restoreTitle(a) {
	if ( a.title || !a.originalTitle ) { return; }
	a.title = a.originalTitle;
}

function registerHooks(np) {
	var popupMaxWidth=getValueOf('popupMaxWidth');

	if (typeof popupMaxWidth == 'number') {
		var setMaxWidth = function () {
			np.mainDiv.style.maxWidth = popupMaxWidth + 'px';
			np.maxWidth = popupMaxWidth;

            try {
				// hack for IE
				// see http://www.svendtofte.com/code/max_width_in_ie/
				// use setExpression as documented here on msdn: http://tinyurl dot com/dqljn
	
				if (np.mainDiv.style.setExpression) {
					np.mainDiv.style.setExpression(
						'width', 'document.body.clientWidth &gt; ' +
						popupMaxWidth + ' ? &quot;' +popupMaxWidth + 'px&quot;: &quot;auto&quot;');
				}
            }
            catch (errors) {
            	errlog( &quot;Running on IE8 are we not?: &quot; + errors );
            }
		};
		np.addHook(setMaxWidth, 'unhide', 'before');
	}
//&lt;NOLITE&gt;
	if (window.addPopupShortcuts &amp;&amp; window.rmPopupShortcuts) {
	    np.addHook(addPopupShortcuts, 'unhide', 'after');
	    np.addHook(rmPopupShortcuts, 'hide', 'before');
	}
//&lt;/NOLITE&gt;
}


function mouseOverWikiLink(evt) {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	if (!evt &amp;&amp; window.event) {evt=window.event}
	return mouseOverWikiLink2(this, evt);
}

function footnoteTarget(a) {
	var aTitle=Title.fromAnchor(a);
	// We want &quot;.3A&quot; rather than &quot;%3A&quot; or &quot;?&quot; here, so use the anchor property directly
	var anch = aTitle.anchor;
	if ( ! /^(cite_note-|_note-|endnote)/.test(anch) ) { return false;	}

	var lTitle=Title.fromURL(location.href);
	if ( lTitle.toString(true) != aTitle.toString(true) ) {	return false; }

	var el=document.getElementById(anch);
	while ( el &amp;&amp; typeof el.nodeName == 'string') {
		var nt = el.nodeName.toLowerCase();
		if ( nt == 'li' ) { return el; }
		else if ( nt == 'body' ) { return false; }
		else if ( el.parentNode ) { el=el.parentNode; }
		else { return false; }
	}
	return false;
}

function footnotePreview(x, navpop) {
	setPopupHTML('&lt;hr&gt;' + x.innerHTML, 'popupPreview',  navpop.idNumber,
		     getValueOf('popupSubpopups') ? function() {
		setupTooltips(document.getElementById('popupPreview' + navpop.idNumber));
	} : null);
}

// var modid=0;
// if(!window.opera) { window.opera={postError: console.log}; }

function modifierKeyHandler(a) {
	return function(evt) {
		//		opera.postError('modifierKeyHandler called' + (++modid));
		//		opera.postError(''+evt + modid);
		//		for (var i in evt) {
		//			opera.postError('' + modid + ' ' + i + ' ' + evt[i]);
		//		}
		//		opera.postError(''+evt.ctrlKey + modid);
		var mod=getValueOf('popupModifier');
		if (!mod) { return true; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
		//		opera.postError('And now....'+modid);
		//		opera.postError(''+evt+modid);
		//		opera.postError(''+evt.ctrlKey+modid);

		var modPressed = modifierPressed(evt);
		var action = getValueOf('popupModifierAction');

		// FIXME: probable bug - modifierPressed should be modPressed below?
		if ( action == 'disable' &amp;&amp; modifierPressed ) { return true; }
		if ( action == 'enable' &amp;&amp; !modifierPressed ) { return true; }

		mouseOverWikiLink2(a, evt);
	};
}

function modifierPressed(evt) {
		var mod=getValueOf('popupModifier');
		if (!mod) { return false; }

		if (!evt &amp;&amp; window.event) {evt=window.event};
//		opera.postError('And now....'+modid);
//		opera.postError(''+evt+modid);
//		opera.postError(''+evt.ctrlKey+modid);

		return ( evt &amp;&amp; mod &amp;&amp; evt[mod.toLowerCase() + 'Key'] );

}

function dealWithModifier(a,evt) {
	if (!getValueOf('popupModifier')) { return false; }
	var action = getValueOf('popupModifierAction');
	if ( action == 'enable' &amp;&amp; !modifierPressed(evt) ||
	     action == 'disable' &amp;&amp; modifierPressed(evt) ) {
		// if the modifier is needed and not pressed, listen for it until
		// we mouseout of this link.
		restoreTitle(a);
		var addHandler='addEventListener';
		var rmHandler='removeEventListener';
		var on='';
		if (!document.addEventListener) {
			addHandler='attachEvent';
			rmHandler='detachEvent';
			on='on';
		}
		if (!document[addHandler]) { // forget it
			return;
		}

		a.modifierKeyHandler=modifierKeyHandler(a);

		switch (action) {
		case 'enable':
			document[addHandler](on+'keydown', a.modifierKeyHandler, false);
			a[addHandler](on+'mouseout', function() {
					document[rmHandler](on+'keydown',
							    a.modifierKeyHandler, false);
				}, true);
			break;
		case 'disable':
			document[addHandler](on+'keyup', a.modifierKeyHandler, false);
		}

		return true;
	}
	return false;
}

function mouseOverWikiLink2(a, evt) {
	if (dealWithModifier(a,evt)) { return; }
	if ( getValueOf('removeTitles') ) { removeTitle(a); }
	if ( a==pg.current.link &amp;&amp; a.navpopup &amp;&amp; a.navpopup.isVisible() ) { return; }
	pg.current.link=a;

	if (getValueOf('simplePopups') &amp;&amp; pg.option.popupStructure===null) {
		// reset *default value* of popupStructure
		setDefault('popupStructure', 'original');
	}

	var article=(new Title()).fromAnchor(a);
	// set global variable (ugh) to hold article (wikipage)
	pg.current.article = article;

	if (!a.navpopup) {
		// FIXME: this doesn't behave well if you mouse out of a popup
		// directly into a link with the same href
		if (pg.current.linksHash[a.href] &amp;&amp; false) {
			a.navpopup = pg.current.linksHash[a.href];
		}
		else {
			a.navpopup=newNavpopup(a, article);
			pg.current.linksHash[a.href] = a.navpopup;
			pg.current.links.push(a);
		}
	}
	if (a.navpopup.pending===null || a.navpopup.pending!==0) {
		// either fresh popups or those with unfinshed business are redone from scratch
		simplePopupContent(a, article);
	}
	a.navpopup.showSoonIfStable(a.navpopup.delay);

	getValueOf('popupInitialWidth');

	clearInterval(pg.timer.checkPopupPosition);
	pg.timer.checkPopupPosition=setInterval(checkPopupPosition, 600);

	if(getValueOf('simplePopups')) {
		if (getValueOf('popupPreviewButton') &amp;&amp; !a.simpleNoMore) {
			var d=document.createElement('div');
			d.className='popupPreviewButtonDiv';
			var s=document.createElement('span');
			d.appendChild(s);
			s.className='popupPreviewButton';
			s['on' + getValueOf('popupPreviewButtonEvent')] = function() {
				a.simpleNoMore=true;
				nonsimplePopupContent(a,article);
			}
			s.innerHTML=popupString('show preview');
			setPopupHTML(d, 'popupPreview', a.navpopup.idNumber);
		}
		return;
	}

	if (a.navpopup.pending!==0 ) {
	    nonsimplePopupContent(a, article);
	}
}

// simplePopupContent: the content that is shown even when simplePopups is true
function simplePopupContent(a, article) {
	/* FIXME hack */ a.navpopup.hasPopupMenu=false;
	a.navpopup.setInnerHTML(popupHTML(a));
	fillEmptySpans({navpopup:a.navpopup});

	if (getValueOf('popupDraggable'))
	{
		var dragHandle = getValueOf('popupDragHandle') || null;
		if (dragHandle &amp;&amp; dragHandle != 'all') {
			dragHandle += a.navpopup.idNumber;
		}
		setTimeout(function(){a.navpopup.makeDraggable(dragHandle);}, 150);
	}

//&lt;NOLITE&gt;
	if (getValueOf('popupRedlinkRemoval') &amp;&amp; a.className=='new') {
		setPopupHTML('&lt;br&gt;'+popupRedlinkHTML(article), 'popupRedlink', a.navpopup.idNumber);
	}
//&lt;/NOLITE&gt;
}

function debugData(navpopup) {
	if(getValueOf('popupDebugging') &amp;&amp; navpopup.idNumber) {
		setPopupHTML('idNumber='+navpopup.idNumber + ', pending=' + navpopup.pending,
			     'popupError', navpopup.idNumber);
	}
}

function newNavpopup(a, article) {
	var navpopup = new Navpopup();
	navpopup.fuzz=5;
	navpopup.delay=getValueOf('popupDelay')*1000;
	// increment global counter now
	navpopup.idNumber = ++pg.idNumber;
	navpopup.parentAnchor = a;
	navpopup.parentPopup = (a.popData &amp;&amp; a.popData.owner);
	navpopup.article = article;
	registerHooks(navpopup);
	return navpopup;
}


function nonsimplePopupContent(a, article) {
	var diff=null, history=null;
	var params=parseParams(a.href);
	var oldid=(typeof params.oldid=='undefined' ? null : params.oldid);
//&lt;NOLITE&gt;
	if(getValueOf('popupPreviewDiffs') &amp;&amp; window.loadDiff) {
		diff=params.diff;
	}
	if(getValueOf('popupPreviewHistory')) {
		history=(params.action=='history');
	}
//&lt;/NOLITE&gt;
	a.navpopup.pending=0;
	var x;
	
	if (x=footnoteTarget(a)) {
		footnotePreview(x, a.navpopup);
//&lt;NOLITE&gt;
	} else if ( diff || diff === 0 ) {
		loadDiff(article, oldid, diff, a.navpopup);
	} else if ( history ) {
		loadAPIPreview('history', article, a.navpopup);
	} else if ( pg.re.contribs.test(a.href) ) {
		loadAPIPreview('contribs', article, a.navpopup);
	} else if ( pg.re.backlinks.test(a.href) ) {
		loadAPIPreview('backlinks', article, a.navpopup);
    } else if ( // FIXME should be able to get all preview combinations with options
		article.namespaceId()==pg.nsImageId &amp;&amp;
		( getValueOf('imagePopupsForImages') || ! anchorContainsImage(a) )
		) {
		loadAPIPreview('imagepagepreview', article, a.navpopup);
		loadImage(article, a.navpopup);
//&lt;/NOLITE&gt;
	} else {
		if (article.namespaceId() == pg.nsCategoryId &amp;&amp;
				getValueOf('popupCategoryMembers')) {
			loadAPIPreview('category', article, a.navpopup);
		} else if ((article.namespaceId() == pg.nsUserId || article.namespaceId() == pg.nsUsertalkId) &amp;&amp;
				getValueOf('popupUserInfo')) {
			loadAPIPreview('userinfo', article, a.navpopup);
		}
		startArticlePreview(article, oldid, a.navpopup);
	}
}

function pendingNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending===null) { navpop.pending=0; }
	++navpop.pending;
	debugData(navpop);
}

function completedNavpopTask(navpop) {
	if (navpop &amp;&amp; navpop.pending) { --navpop.pending; }
	debugData(navpop);
}

function startArticlePreview(article, oldid, navpop) {
	navpop.redir=0;
	loadPreview(article, oldid, navpop);
}

function loadPreview(article, oldid, navpop) {
	pendingNavpopTask(navpop);
	if (!navpop.redir) { navpop.originalArticle=article; }
	if (!navpop.visible &amp;&amp; getValueOf('popupLazyDownloads')) {
		var id=(navpop.redir) ? 'DOWNLOAD_PREVIEW_REDIR_HOOK' : 'DOWNLOAD_PREVIEW_HOOK';
		navpop.addHook(function() {
				getWiki(article, insertPreview, oldid, navpop);
				return true; }, 'unhide', 'before', id);
	} else {
		getWiki(article, insertPreview, oldid, navpop);
	}
}

function loadPreviewFromRedir(redirMatch, navpop) {
	// redirMatch is a regex match
	var target = new Title().fromWikiText(redirMatch[2]);
	// overwrite (or add) anchor from original target
	// mediawiki does overwrite; eg [[User:Lupin/foo3#Done]]
	if ( navpop.article.anchor ) { target.anchor = navpop.article.anchor; }
	var trailingRubbish=redirMatch[4];
	navpop.redir++;
	navpop.redirTarget=target;
//&lt;NOLITE&gt;
	if (window.redirLink) {
		var warnRedir = redirLink(target, navpop.article);
		setPopupHTML(warnRedir, 'popupWarnRedir', navpop.idNumber);
	}
//&lt;/NOLITE&gt;
	navpop.article=target;
	fillEmptySpans({redir: true, redirTarget: target, navpopup:navpop});
	return loadPreview(target, null,  navpop);
}

function insertPreview(download) {
	if (!download.owner) { return; }

	var redirMatch = pg.re.redirect.exec(download.data);
	if (download.owner.redir===0 &amp;&amp; redirMatch) {
		completedNavpopTask(download.owner);
		loadPreviewFromRedir(redirMatch, download.owner);
		return;
	}

	if (download.owner.visible || !getValueOf('popupLazyPreviews')) {
	    insertPreviewNow(download);
	} else {
		var id=(download.owner.redir) ? 'PREVIEW_REDIR_HOOK' : 'PREVIEW_HOOK';
		download.owner.addHook( function(){insertPreviewNow(download); return true;},
					'unhide', 'after', id );
	}
}

function insertPreviewNow(download) {
	if (!download.owner) { return; }
	var wikiText=download.data;
	var navpop=download.owner;
	completedNavpopTask(navpop);
	var art=navpop.redirTarget || navpop.originalArticle;

//&lt;NOLITE&gt;
	makeFixDabs(wikiText, navpop);
	if (getValueOf('popupSummaryData') &amp;&amp; window.getPageInfo) {
		var info=getPageInfo(wikiText, download);
		setPopupTrailer(getPageInfo(wikiText, download), navpop.idNumber);
	}

	var imagePage='';
	if (art.namespaceId()==pg.nsImageId) { imagePage=art.toString(); }
	else { imagePage=getValidImageFromWikiText(wikiText); }
	if(imagePage) { loadImage(Title.fromWikiText(imagePage), navpop); }
//&lt;/NOLITE&gt;

	if (getValueOf('popupPreviews')) { insertArticlePreview(download, art, navpop); }

}

function insertArticlePreview(download, art, navpop) {
	if (download &amp;&amp; typeof download.data == typeof ''){
		if (art.namespaceId()==pg.nsTemplateId &amp;&amp; getValueOf('popupPreviewRawTemplates')) {
			// FIXME compare/consolidate with diff escaping code for wikitext
			var h='&lt;hr&gt;&lt;tt&gt;' + download.data.entify().split('\\n').join('&lt;br&gt;\\n') + '&lt;/tt&gt;';
			setPopupHTML(h, 'popupPreview', navpop.idNumber);
		}
		else {
			var p=prepPreviewmaker(download.data, art, navpop);
			p.showPreview();
		}
	}
}

function prepPreviewmaker(data, article, navpop) {
	// deal with tricksy anchors
	var d=anchorize(data, article.anchorString());
	var urlBase=joinPath([pg.wiki.articlebase, article.urlString()]);
	var p=new Previewmaker(d, urlBase, navpop);
	return p;
}


// Try to imitate the way mediawiki generates HTML anchors from section titles
function anchorize(d, anch) {
	if (!anch) { return d; }
	var anchRe=RegExp('(?:=+\\s*' + literalizeRegex(anch).replace(/[_ ]/g, '[_ ]') + '\\s*=+|\\{\\{\\s*'+getValueOf('popupAnchorRegexp')+'\\s*(?:\\|[^|}]*)*?\\s*'+literalizeRegex(anch)+'\\s*(?:\\|[^}]*)?\}\})');
	var match=d.match(anchRe);
	if(match &amp;&amp; match.length &gt; 0 &amp;&amp; match[0]) { return d.substring(d.indexOf(match[0])); }

	// now try to deal with == foo [[bar|baz]] boom == -&gt; #foo_baz_boom
	var lines=d.split('\n');
	for (var i=0; i&lt;lines.length; ++i) {
		lines[i]=lines[i].replace(RegExp('[[]{2}([^|\\]]*?[|])?(.*?)[\\]]{2}', 'g'), '$2')
			.replace(/'''([^'])/g, '$1').replace(RegExp(&quot;''([^'])&quot;, 'g'), '$1');
		if (lines[i].match(anchRe)) {
			return d.split('\n').slice(i).join('\n').replace(RegExp('^[^=]*'), '');
		}
	}
	return d;
}

function killPopup() {
	if (getValueOf('popupShortcutKeys') &amp;&amp; window.rmPopupShortcuts) { rmPopupShortcuts(); }
	if (!pg) { return; }
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp; pg.current.link.navpopup.banish();
	pg.current.link=null;
	abortAllDownloads();
	if (pg.timer.checkPopupPosition !== null) {
		clearInterval(pg.timer.checkPopupPosition);
		pg.timer.checkPopupPosition=null;
	}
	return true; // preserve default action
}
// ENDFILE: actions.js
// STARTFILE: domdrag.js
/**
   @fileoverview
   The {@link Drag} object, which enables objects to be dragged around.

   &lt;pre&gt;
   *************************************************
   dom-drag.js
   09.25.2001
   www.youngpup.net
   **************************************************
   10.28.2001 - fixed minor bug where events
   sometimes fired off the handle, not the root.
   *************************************************
   Pared down, some hooks added by [[User:Lupin]]

   Copyright Aaron Boodman.
   Saying stupid things daily since March 2001.
   &lt;/pre&gt;
*/

/**
   Creates a new Drag object. This is used to make various DOM elements draggable.
   @constructor
*/
function Drag () {
	/**
	   Condition to determine whether or not to drag. This function should take one parameter, an Event.
	   To disable this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.startCondition = null;
	/**
	   Hook to be run when the drag finishes. This is passed the final coordinates of
	   the dragged object (two integers, x and y). To disables this, set it to &lt;code&gt;null&lt;/code&gt;.
	   @type Function
	*/
	this.endHook = null;
}

/**
   Gets an event in a cross-browser manner.
   @param {Event} e
   @private
*/
Drag.prototype.fixE = function(e) {
	if (typeof e == 'undefined') { e = window.event; }
	if (typeof e.layerX == 'undefined') { e.layerX = e.offsetX; }
	if (typeof e.layerY == 'undefined') { e.layerY = e.offsetY; }
	return e;
};
/**
   Initialises the Drag instance by telling it which object you want to be draggable, and what you want to drag it by.
   @param {DOMElement} o The &quot;handle&quot; by which &lt;code&gt;oRoot&lt;/code&gt; is dragged.
   @param {DOMElement} oRoot The object which moves when &lt;code&gt;o&lt;/code&gt; is dragged, or &lt;code&gt;o&lt;/code&gt; if omitted.
*/
Drag.prototype.init = function(o, oRoot) {
	var dragObj      = this;
	this.obj = o;
	o.onmousedown    = function(e) { dragObj.start.apply( dragObj, [e]); };
	o.dragging       = false;
	o.popups_draggable      = true;
	o.hmode          = true;
	o.vmode          = true;

	o.root = oRoot &amp;&amp; oRoot !== null ? oRoot : o ;

	if (isNaN(parseInt(o.root.style.left, 10))) { o.root.style.left   = &quot;0px&quot;; }
	if (isNaN(parseInt(o.root.style.top,  10))) { o.root.style.top    = &quot;0px&quot;; }

	o.root.onthisStart  = function(){};
	o.root.onthisEnd    = function(){};
	o.root.onthis       = function(){};
};

/**
   Starts the drag.
   @private
   @param {Event} e
*/
Drag.prototype.start = function(e) {
	var o = this.obj; // = this;
	e = this.fixE(e);
	if (this.startCondition &amp;&amp; !this.startCondition(e)) { return; }
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10);
	o.root.onthisStart(x, y);

	o.lastMouseX    = e.clientX;
	o.lastMouseY    = e.clientY;

	var dragObj      = this;
	o.onmousemoveDefault    = document.onmousemove;
	o.dragging              = true;
	document.onmousemove    = function(e) { dragObj.drag.apply( dragObj, [e] ); };
	document.onmouseup      = function(e) { dragObj.end.apply( dragObj, [e] ); };
	return false;
};
/**
   Does the drag.
   @param {Event} e
   @private
*/
Drag.prototype.drag = function(e) {
	e = this.fixE(e);
	var o = this.obj;

	var ey    = e.clientY;
	var ex    = e.clientX;
	var y = parseInt(o.vmode ? o.root.style.top  : o.root.style.bottom, 10);
	var x = parseInt(o.hmode ? o.root.style.left : o.root.style.right,  10 );
	var nx, ny;

	nx = x + ((ex - o.lastMouseX) * (o.hmode ? 1 : -1));
	ny = y + ((ey - o.lastMouseY) * (o.vmode ? 1 : -1));

	this.obj.root.style[o.hmode ? &quot;left&quot; : &quot;right&quot;] = nx + &quot;px&quot;;
	this.obj.root.style[o.vmode ? &quot;top&quot; : &quot;bottom&quot;] = ny + &quot;px&quot;;
	this.obj.lastMouseX    = ex;
	this.obj.lastMouseY    = ey;

	this.obj.root.onthis(nx, ny);
	return false;
};

/**
   Ends the drag.
   @private
*/
Drag.prototype.end = function()  {
	document.onmousemove=this.obj.onmousemoveDefault;
	document.onmouseup   = null;
	this.obj.dragging    = false;
	if (this.endHook) {
		this.endHook( parseInt(this.obj.root.style[this.obj.hmode ? &quot;left&quot; : &quot;right&quot;], 10),
			      parseInt(this.obj.root.style[this.obj.vmode ? &quot;top&quot; : &quot;bottom&quot;], 10));
	}
};
// ENDFILE: domdrag.js
// STARTFILE: structures.js
//&lt;NOLITE&gt;
pg.structures.original={};
pg.structures.original.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle',
		'popupData', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks',
			       'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
pg.structures.original.popupRedirSpans=function () {
	return ['popupRedir', 'popupWarnRedir', 'popupRedirTopLinks',
		'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'];
};
pg.structures.original.popupTitle=function (x) {
	log ('defaultstructure.popupTitle');
	if (!getValueOf('popupNavLinks')) {
		return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	}
	return '';
};
pg.structures.original.popupTopLinks=function (x) {
	log ('defaultstructure.popupTopLinks');
	if (getValueOf('popupNavLinks')) { return navLinksHTML(x.article, x.hint, x.params); }
	return '';
};
pg.structures.original.popupImage=function(x) {
	log ('original.popupImage, x.article='+x.article+', x.navpop.idNumber='+x.navpop.idNumber);
	return imageHTML(x.article, x.navpop.idNumber);
};
pg.structures.original.popupRedirTitle=pg.structures.original.popupTitle;
pg.structures.original.popupRedirTopLinks=pg.structures.original.popupTopLinks;


function copyStructure(oldStructure, newStructure) {
	pg.structures[newStructure]={};
	for (var prop in pg.structures[oldStructure]) {
		pg.structures[newStructure][prop]=pg.structures[oldStructure][prop];
	}
}

copyStructure('original', 'nostalgia');
pg.structures.nostalgia.popupTopLinks=function(x)  {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;';
	str+='if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{'
	+ editstr + '}'
	var historystr='&lt;&lt;history|shortcut=h&gt;&gt;';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;';
	str += 'if(admin){&lt;br&gt;}else{*}&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){*&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*' +
	'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;}';
	return navlinkStringToHTML(str, x.article, x.params);
};
pg.structures.nostalgia.popupRedirTopLinks=pg.structures.nostalgia.popupTopLinks;

/** -- fancy -- **/
copyStructure('original', 'fancy');
pg.structures.fancy.popupTitle=function (x) {
	return navlinkStringToHTML('&lt;font size=+0&gt;&lt;&lt;mainlink&gt;&gt;&lt;/font&gt;',x.article,x.params);
};
pg.structures.fancy.popupTopLinks=function(x) {
	var hist='&lt;&lt;history|shortcut=h|hist&gt;&gt;|&lt;&lt;lastEdit|shortcut=/|last&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|eds&gt;&gt;}';
	var watch='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';
	var move='&lt;&lt;move|shortcut=m|move&gt;&gt;';
	return navlinkStringToHTML('if(talk){' +
				   '&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;new|shortcut=+|+&gt;&gt;*' + hist + '*' +
				   '&lt;&lt;article|shortcut=a&gt;&gt;|&lt;&lt;editArticle|edit&gt;&gt;' + '*' + watch + '*' + move +
				   '}else{&lt;&lt;edit|shortcut=e&gt;&gt;*' + hist +
				   '*&lt;&lt;talk|shortcut=t|&gt;&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;' +
				   '*' + watch + '*' + move+'}&lt;br&gt;', x.article, x.params);
};
pg.structures.fancy.popupOtherLinks=function(x) {
	var admin='&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;*&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d|del&gt;&gt;';
	var user='&lt;&lt;contribs|shortcut=c&gt;&gt;if(wikimedia){|&lt;&lt;count|shortcut=#|#&gt;&gt;}';
	user+='if(ipuser){|&lt;&lt;arin&gt;&gt;}else{*&lt;&lt;email|shortcut=E|'+
	popupString('email')+'&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;}';

	var normal='&lt;&lt;whatLinksHere|shortcut=l|links here&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r|related&gt;&gt;';
	return navlinkStringToHTML('&lt;br&gt;if(user){' + user + '*}if(admin){'+admin+'if(user){&lt;br&gt;}else{*}}' + normal,
				   x.article, x.params);
};
pg.structures.fancy.popupRedirTitle=pg.structures.fancy.popupTitle;
pg.structures.fancy.popupRedirTopLinks=pg.structures.fancy.popupTopLinks;
pg.structures.fancy.popupRedirOtherLinks=pg.structures.fancy.popupOtherLinks;


/** -- fancy2 -- **/
// hack for [[User:MacGyverMagic]]
copyStructure('fancy', 'fancy2');
pg.structures.fancy2.popupTopLinks=function(x) { // hack out the &lt;br&gt; at the end and put one at the beginning
	return '&lt;br&gt;'+pg.structures.fancy.popupTopLinks(x).replace(RegExp('&lt;br&gt;$','i'),'');
};
pg.structures.fancy2.popupLayout=function () { // move toplinks to after the title
	return ['popupError', 'popupImage', 'popupTitle', 'popupData', 'popupTopLinks', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};

/** -- menus -- **/
copyStructure('original', 'menus');
pg.structures.menus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'],
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview', 'popupFixDab'];
};
function toggleSticky(uid) {
	var popDiv=document.getElementById('navpopup_maindiv'+uid);
	if (!popDiv) { return; }
	if (!popDiv.navpopup.sticky) { popDiv.navpopup.stick(); }
	else {
		popDiv.navpopup.unstick();
		popDiv.navpopup.hide();
	}
}
pg.structures.menus.popupTopLinks = function (x, shorter) {
	// FIXME maybe this stuff should be cached
	var s=[];
	var dropdiv='&lt;div class=&quot;popup_drop&quot;&gt;';
	var enddiv='&lt;/div&gt;';
	var endspan='&lt;/span&gt;';
	var hist='&lt;&lt;history|shortcut=h&gt;&gt;';
	if (!shorter) { hist = '&lt;menurow&gt;' + hist +
			'|&lt;&lt;historyfeed|rss&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E&gt;&gt;}&lt;/menurow&gt;'; }
	var lastedit='&lt;&lt;lastEdit|shortcut=/|show last edit&gt;&gt;';
	var jsHistory='&lt;&lt;lastContrib|last set of edits&gt;&gt;&lt;&lt;sinceMe|changes since mine&gt;&gt;';
	var linkshere='&lt;&lt;whatLinksHere|shortcut=l|what links here&gt;&gt;';
	var related='&lt;&lt;relatedChanges|shortcut=r|related changes&gt;&gt;';
	var search='&lt;menurow&gt;&lt;&lt;search|shortcut=s&gt;&gt;if(wikimedia){|&lt;&lt;globalsearch|shortcut=g|global&gt;&gt;}' +
	'|&lt;&lt;google|shortcut=G|web&gt;&gt;&lt;/menurow&gt;';
	var watch='&lt;menurow&gt;&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;&lt;/menurow&gt;';
	var protect='&lt;menurow&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|' +
	'&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;&lt;/menurow&gt;';
	var del='&lt;menurow&gt;&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|' +
	'&lt;&lt;deletelog|log&gt;&gt;&lt;/menurow&gt;';
	var move='&lt;&lt;move|shortcut=m|move page&gt;&gt;';
	var nullPurge='&lt;menurow&gt;&lt;&lt;nullEdit|shortcut=n|null edit&gt;&gt;|&lt;&lt;purge|shortcut=P&gt;&gt;&lt;/menurow&gt;';
	var viewOptions='&lt;menurow&gt;&lt;&lt;view|shortcut=v&gt;&gt;|&lt;&lt;render|shortcut=S&gt;&gt;|&lt;&lt;raw&gt;&gt;&lt;/menurow&gt;';
	var editRow='if(oldid){' +
	'&lt;menurow&gt;&lt;&lt;edit|shortcut=e&gt;&gt;|&lt;&lt;editOld|shortcut=e|this&amp;nbsp;revision&gt;&gt;&lt;/menurow&gt;' +
	'&lt;menurow&gt;&lt;&lt;revert|shortcut=v&gt;&gt;|&lt;&lt;undo&gt;&gt;&lt;/menurow&gt;' + '}else{&lt;&lt;edit|shortcut=e&gt;&gt;}';
	var markPatrolled='if(rcid){&lt;&lt;markpatrolled|mark patrolled&gt;&gt;}';
	var newTopic='if(talk){&lt;&lt;new|shortcut=+|new topic&gt;&gt;}';
	var protectDelete='if(admin){' + protect + del + '}';

	if (getValueOf('popupActionsMenu')) {
		s.push( '&lt;&lt;mainlink&gt;&gt;*' + dropdiv + menuTitle('actions'));
	} else {
		s.push( dropdiv + '&lt;&lt;mainlink&gt;&gt;');
	}
	s.push( '&lt;menu&gt;')
	s.push( editRow + markPatrolled + newTopic + hist + lastedit )
	if (!shorter) { s.push(jsHistory); }
	s.push( move + linkshere + related)
	if (!shorter) { s.push(nullPurge + search); }
	if (!shorter) { s.push(viewOptions); }
	s.push('&lt;hr&gt;' + watch + protectDelete);
	s.push('&lt;hr&gt;' +
	       'if(talk){&lt;&lt;article|shortcut=a|view article&gt;&gt;&lt;&lt;editArticle|edit article&gt;&gt;}' +
	       'else{&lt;&lt;talk|shortcut=t|talk page&gt;&gt;&lt;&lt;editTalk|edit talk&gt;&gt;' +
	       '&lt;&lt;newTalk|shortcut=+|new topic&gt;&gt;}&lt;/menu&gt;' + enddiv);

	// user menu starts here
	var email='&lt;&lt;email|shortcut=E|email user&gt;&gt;';
	var contribs=	'if(wikimedia){&lt;menurow&gt;}&lt;&lt;contribs|shortcut=c|contributions&gt;&gt;if(wikimedia){&lt;/menurow&gt;}' +
	'if(admin){&lt;menurow&gt;&lt;&lt;deletedContribs&gt;&gt;&lt;/menurow&gt;}';


	s.push('if(user){*' + dropdiv + menuTitle('user'));
	s.push('&lt;menu&gt;'); +
	s.push('&lt;menurow&gt;&lt;&lt;userPage|shortcut=u|user&amp;nbsp;page&gt;&gt;|&lt;&lt;userSpace|space&gt;&gt;&lt;/menurow&gt;');
	s.push('&lt;&lt;userTalk|shortcut=t|user talk&gt;&gt;&lt;&lt;editUserTalk|edit user talk&gt;&gt;' +
	       '&lt;&lt;newUserTalk|shortcut=+|leave comment&gt;&gt;');
	if(!shorter) { s.push( 'if(ipuser){&lt;&lt;arin&gt;&gt;}else{' + email + '}') }
	else { s.push( 'if(ipuser){}else{' + email + '}') }
	s.push('&lt;hr&gt;' + contribs + '&lt;&lt;userlog|shortcut=L|user log&gt;&gt;');
	s.push('if(wikimedia){&lt;&lt;count|shortcut=#|edit counter&gt;&gt;}');
	s.push('if(admin){&lt;menurow&gt;&lt;&lt;unblock|unblockShort&gt;&gt;|&lt;&lt;block|shortcut=b|block user&gt;&gt;&lt;/menurow&gt;}');
	s.push('&lt;&lt;blocklog|shortcut=B|block log&gt;&gt;' + getValueOf('popupExtraUserMenu'));
	s.push('&lt;/menu&gt;'  + enddiv + '}');

	// popups menu starts here
	if (getValueOf('popupSetupMenu') &amp;&amp; !x.navpop.hasPopupMenu /* FIXME: hack */) {
		x.navpop.hasPopupMenu=true;
		s.push('*' + dropdiv + menuTitle('popupsMenu') + '&lt;menu&gt;');
		s.push('&lt;&lt;togglePreviews|toggle previews&gt;&gt;');
		s.push('&lt;&lt;purgePopups|reset&gt;&gt;');
		s.push('&lt;&lt;disablePopups|disable&gt;&gt;');
		s.push('&lt;/menu&gt;'+enddiv);
	}
	return navlinkStringToHTML(s.join(''), x.article, x.params);
};

function menuTitle(s) {
	return '&lt;a href=&quot;#&quot; noPopup=1&gt;' + popupString(s) + '&lt;/a&gt;';
}

pg.structures.menus.popupRedirTitle=pg.structures.menus.popupTitle;
pg.structures.menus.popupRedirTopLinks=pg.structures.menus.popupTopLinks;

copyStructure('menus', 'shortmenus');
pg.structures.shortmenus.popupTopLinks=function(x) {
	return pg.structures.menus.popupTopLinks(x,true);
};
pg.structures.shortmenus.popupRedirTopLinks=pg.structures.shortmenus.popupTopLinks;

copyStructure('shortmenus', 'dabshortmenus');
pg.structures.dabshortmenus.popupLayout=function () {
	return ['popupError', 'popupImage', 'popupTopLinks', 'popupTitle', 'popupOtherLinks',
		'popupRedir', ['popupWarnRedir', 'popupRedirTopLinks', 'popupRedirTitle', 'popupRedirData', 'popupRedirOtherLinks'],
		'popupData', 'popupMiscTools', ['popupRedlink'], 'popupFixDab',
		'popupPrePreviewSep', 'popupPreview', 'popupSecondPreview', 'popupPreviewMore', 'popupPostPreview'];
};

copyStructure('menus', 'dabmenus');
pg.structures.dabmenus.popupLayout=pg.structures.dabshortmenus.popupLayout;


//&lt;/NOLITE&gt;
pg.structures.lite={};
pg.structures.lite.popupLayout=function () {
	return ['popupTitle', 'popupPreview' ];
};
pg.structures.lite.popupTitle=function (x) {
	log (x.article + ': structures.lite.popupTitle');
	//return navlinkStringToHTML('&lt;b&gt;&lt;&lt;mainlink&gt;&gt;&lt;/b&gt;',x.article,x.params);
	return '&lt;div&gt;&lt;span class=&quot;popup_mainlink&quot;&gt;&lt;b&gt;' + x.article.toString() + '&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;';
};
// ENDFILE: structures.js
// STARTFILE: autoedit.js
//&lt;NOLITE&gt;
function getParamValue(paramName, h) {
	if (typeof h == 'undefined' ) { h = document.location.href; }
	var cmdRe=RegExp('[&amp;?]'+paramName+'=([^&amp;]*)');
	var m=cmdRe.exec(h);
	if (m) {
		try {
			return decodeURIComponent(m[1]);
		} catch (someError) {}
	}
	return null;
}

function substitute(data,cmdBody) {
	// alert('sub\nfrom: '+cmdBody.from+'\nto: '+cmdBody.to+'\nflags: '+cmdBody.flags);
	var fromRe=RegExp(cmdBody.from, cmdBody.flags);
	return data.replace(fromRe, cmdBody.to);
}

function execCmds(data, cmdList) {
	for (var i=0; i&lt;cmdList.length; ++i) {
		data=cmdList[i].action(data, cmdList[i]);
	}
	return data;
}

function parseCmd(str) {
	// returns a list of commands
	if (!str.length) { return []; }
	var p=false;
	switch (str[0]) {
	case 's':
		p=parseSubstitute(str);
		break;
	default:
		return false;
	}
	if (p) { return [p].concat(parseCmd(p.remainder)); }
	return false;
}

function unEscape(str, sep) {
	return str.split('\\\\').join('\\').split('\\'+sep).join(sep).split('\\n').join('\n');
}


function parseSubstitute(str) {
	// takes a string like s/a/b/flags;othercmds and parses it

	var from,to,flags,tmp;

	if (str.length&lt;4) { return false; }
	var sep=str.charAt(1);
	str=str.substring(2);

	tmp=skipOver(str,sep);
	if (tmp) { from=tmp.segment; str=tmp.remainder; }
	else { return false; }

	tmp=skipOver(str,sep);
	if (tmp) { to=tmp.segment; str=tmp.remainder; }
	else { return false; }

	flags='';
	if (str.length) {
		tmp=skipOver(str,';') || skipToEnd(str, ';');
		if (tmp) {flags=tmp.segment; str=tmp.remainder; }
	}

	return {action: substitute, from: from, to: to, flags: flags, remainder: str};

}

function skipOver(str,sep) {
	var endSegment=findNext(str,sep);
	if (endSegment&lt;0) { return false; }
	var segment=unEscape(str.substring(0,endSegment), sep);
	return {segment: segment, remainder: str.substring(endSegment+1)};
}

function skipToEnd(str,sep) {
	return {segment: str, remainder: ''};
}

function findNext(str, ch) {
	for (var i=0; i&lt;str.length; ++i) {
		if (str.charAt(i)=='\\') { i+=2; }
		if (str.charAt(i)==ch) { return i; }
	}
	return -1;
}

function setCheckbox(param, box) {
	var val=getParamValue(param);
	if (val!==null) {
		switch (val) {
		case '1': case 'yes': case 'true':
			box.checked=true;
			break;
		case '0': case 'no':  case 'false':
			box.checked=false;
		}
	}
}

function autoEdit() {
	if (!setupPopups.completed) { setupPopups(); }
	if (!document.editform) { return false; }
	if (window.autoEdit.alreadyRan) { return false; }
	window.autoEdit.alreadyRan=true;
	var cmdString=getParamValue('autoedit');
	if (cmdString) {
		try {
			var editbox=document.editform.wpTextbox1;
		} catch (dang) { return; }
		var cmdList=parseCmd(cmdString);
		var input=editbox.value;
		var output=execCmds(input, cmdList);
		editbox.value=output;
		// wikEd user script compatibility
		if (typeof(wikEdUseWikEd) != 'undefined') {
			if (wikEdUseWikEd == true) {
				WikEdUpdateFrame();
			}
		}
	}
	setCheckbox('autominor', document.editform.wpMinoredit);
	setCheckbox('autowatch', document.editform.wpWatchthis);

	var rvid = getParamValue('autorv');
	if (rvid) {
		var url=pg.wiki.apiwikibase + '?action=query&amp;format=json&amp;prop=revisions&amp;revids='+rvid;
		startDownload(url, null, autoEdit2);
	} else { autoEdit2(); }
}

function autoEdit2(d) {
	var summary=getParamValue('autosummary');
	var summaryprompt=getParamValue('autosummaryprompt');
	var summarynotice='';
	if (d &amp;&amp; d.data &amp;&amp; getParamValue('autorv')) {
		var s = getRvSummary(summary, d.data);
		if (s===false) {
			summaryprompt=true;
			summarynotice=popupString('Failed to get revision information, please edit manually.\n\n');
			summary = simplePrintf(summary, [getParamValue('autorv'), '(unknown)', '(unknown)']);
		} else { summary = s; }
	}
	if (summaryprompt) {
		var txt= summarynotice +
			popupString('Enter a non-empty edit summary or press cancel to abort');
		var response=prompt(txt, summary);
		if (response) { summary=response; }
		else { return; }
	}
	if (summary) { document.editform.wpSummary.value=summary; }
	// Attempt to avoid possible premature clicking of the save button
	// (maybe delays in updates to the DOM are to blame?? or a red herring)
	setTimeout(autoEdit3, 100);
}

function autoClickToken() {
    return mw.user.sessionId();
}

function autoEdit3() {
    if( getParamValue('actoken') != autoClickToken()) return;

	var btn=getParamValue('autoclick');
	if (btn) {
		if (document.editform &amp;&amp; document.editform[btn]) {
			var button=document.editform[btn];
			var msg=tprintf('The %s button has been automatically clicked. Please wait for the next page to load.',
					[ button.value ]);
			bannerMessage(msg);
			document.title='('+document.title+')';
			button.click();
		} else {
			alert(tprintf('Could not find button %s. Please check the settings in your javascript file.',
				      [ btn ]));
		}
	}
}

function bannerMessage(s) {
	var headings=document.getElementsByTagName('h1');
	if (headings) {
		var div=document.createElement('div');
		div.innerHTML='&lt;font size=+1&gt;&lt;b&gt;' + s + '&lt;/b&gt;&lt;/font&gt;';
		headings[0].parentNode.insertBefore(div, headings[0]);
	}
}

function getRvSummary(template, json) {
	try {
	    var o=getJsObj(json);
	    var edit = anyChild(o.query.pages).revisions[0];
	} catch (badness) {return false;}
	var timestamp = edit.timestamp.split(/[A-Z]/g).join(' ').replace(/^ *| *$/g, '');
	return simplePrintf(template, [edit.revid, timestamp, edit.userhidden === undefined ? edit.user : '(hidden)']);
}

//&lt;/NOLITE&gt;
// ENDFILE: autoedit.js
// STARTFILE: downloader.js
/**
   @fileoverview
   {@link Downloader}, a xmlhttprequest wrapper, and helper functions.
*/

/**
   Creates a new Downloader
   @constructor
   @class The Downloader class. Create a new instance of this class to download stuff.
   @param {String} url The url to download. This can be omitted and supplied later.
*/
function Downloader(url) {
	// Source: http://jibbering.com/2002/4/httprequest.html
	/** xmlhttprequest object which we're wrapping */
	this.http = false;

	/*@cc_on @*/
	/*@if (@_jscript_version &gt;= 5)
	// JScript gives us Conditional compilation,
	// we can cope with old IE versions.
	// and security blocked creation of the objects.
	try {
	this.http = new ActiveXObject(&quot;Msxml2.XMLHTTP&quot;);
	} catch (e) {
	try {
	this.http = new ActiveXObject(&quot;Microsoft.XMLHTTP&quot;);
	} catch (E) {
	// this.http = false;
	}
	}
	@end @*/

	if (! this.http &amp;&amp; typeof XMLHttpRequest!='undefined') { this.http = new XMLHttpRequest(); }
	/**
	    The url to download
	    @type String
	*/
	this.url = url;
	/**
	    A universally unique ID number
	    @type integer
	*/
	this.id=null;
	/**
	    Modification date, to be culled from the incoming headers
	    @type Date
	    @private
	*/
	this.lastModified = null;
	/**
	    What to do when the download completes successfully
	    @type Function
	    @private
	*/
	this.callbackFunction = null;
	/**
	    What to do on failure
	    @type Function
	    @private
	*/
	this.onFailure = null;
	/**
	    Flag set on &lt;code&gt;abort&lt;/code&gt;
	    @type boolean
	*/
	this.aborted = false;
	/**
	   HTTP method. See http://www.w3.org/Protocols/rfc2616/rfc2616-sec9.html for possibilities.
	   @type String
	*/
	this.method='GET';
	/**
	    Async flag.
	    @type boolean
	*/
	this.async=true;
}

new Downloader();

/** Submits the http request. */
Downloader.prototype.send = function (x) {
	if (!this.http) { return null; }
	return this.http.send(x);
};
/** Aborts the download, setting the &lt;code&gt;aborted&lt;/code&gt; field to true.  */
Downloader.prototype.abort = function () {
	if (!this.http) { return null; }
	this.aborted=true;
	return this.http.abort();
};
/** Returns the downloaded data. */
Downloader.prototype.getData = function () {if (!this.http) { return null; } return this.http.responseText;};
/** Prepares the download. */
Downloader.prototype.setTarget = function () {
	if (!this.http) { return null; }
	this.http.open(this.method, this.url, this.async);
};
/** Gets the state of the download. */
Downloader.prototype.getReadyState=function () {if (!this.http) { return null; } return this.http.readyState;};

pg.misc.downloadsInProgress = { };

/** Starts the download.
    Note that setTarget {@link Downloader#setTarget} must be run first
*/
Downloader.prototype.start=function () {
	if (!this.http) { return; }
	pg.misc.downloadsInProgress[this.id] = this;
	this.http.send(null);
};

/** Gets the 'Last-Modified' date from the download headers.
    Should be run after the download completes.
    Returns &lt;code&gt;null&lt;/code&gt; on failure.
    @return {Date}
*/
Downloader.prototype.getLastModifiedDate=function () {
	if(!this.http) { return null; }
	var lastmod=null;
	try {
		lastmod=this.http.getResponseHeader('Last-Modified');
	} catch (err) {}
	if (lastmod) { return new Date(lastmod); }
	return null;
};

/** Sets the callback function.
    @param {Function} f callback function, called as &lt;code&gt;f(this)&lt;/code&gt; on success
*/
Downloader.prototype.setCallback = function (f) {
	if(!this.http) { return; }
	this.http.onreadystatechange = f;
};

Downloader.prototype.getStatus = function() { if (!this.http) { return null; } return this.http.status; };

//////////////////////////////////////////////////
// helper functions

/** Creates a new {@link Downloader} and prepares it for action.
    @param {String} url The url to download
    @param {integer} id The ID of the {@link Downloader} object
    @param {Function} callback The callback function invoked on success
    @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function newDownload(url, id, callback, onfailure) {
	var d=new Downloader(url);
	if (!d.http) { return 'ohdear'; }
	d.id=id;
	d.setTarget();
	if (!onfailure) {
		onfailure=2;
	}
	var f = function () {
		if (d.getReadyState() == 4) {
			delete pg.misc.downloadsInProgress[this.id];
			try {
				if ( d.getStatus() == 200 ) {
					d.data=d.getData();
					d.lastModified=d.getLastModifiedDate();
					callback(d);
				} else if (typeof onfailure == typeof 1) {
					if (onfailure &gt; 0) {
						// retry
						newDownload(url, id, callback, onfailure - 1);
					}
				} else if (typeof onfailure == 'function') {
					onfailure(d,url,id,callback);
				}
			} catch (somerr) { /* ignore it */ }
		}
	};
	d.setCallback(f);
	return d;
}
/** Simulates a download from cached data.
    The supplied data is put into a {@link Downloader} as if it had downloaded it.
    @param {String} url The url.
    @param {integer} id The ID.
    @param {Function} callback The callback, which is invoked immediately as &lt;code&gt;callback(d)&lt;/code&gt;,
    where &lt;code&gt;d&lt;/code&gt; is the new {@link Downloader}.
    @param {String} data The (cached) data.
    @param {Date} lastModified The (cached) last modified date.
*/
function fakeDownload(url, id, callback, data, lastModified, owner) {
	var d=newDownload(url,callback);
	d.owner=owner;
	d.id=id; d.data=data;
	d.lastModified=lastModified;
	return callback(d);
}

/**
   Starts a download.
   @param {String} url The url to download
   @param {integer} id The ID of the {@link Downloader} object
   @param {Function} callback The callback function invoked on success
   @return {String/Downloader} the {@link Downloader} object created, or 'ohdear' if an unsupported browser
*/
function startDownload(url, id, callback) {
	var d=newDownload(url, id, callback);
	if (typeof d == typeof '' ) { return d; }
	d.start();
	return d;
}

/**
   Aborts all downloads which have been started.
*/
function abortAllDownloads() {
	for ( var x in pg.misc.downloadsInProgress ) {
		try {
			pg.misc.downloadsInProgress[x].aborted=true;
			pg.misc.downloadsInProgress[x].abort();
			delete pg.misc.downloadsInProgress[x];
		} catch (e) { }
	}
}
// ENDFILE: downloader.js
// STARTFILE: livepreview.js
// TODO: location is often not correct (eg relative links in previews)

/**
 * InstaView - a Mediawiki to HTML converter in JavaScript
 * Version 0.6.1
 * Copyright (C) Pedro Fayolle 2005-2006
 * //en.wikipedia.org/wiki/User:Pilaf
 * Distributed under the BSD license
 *
 * Changelog:
 *
 * 0.6.1
 * - Fixed problem caused by \r characters
 * - Improved inline formatting parser
 *
 * 0.6
 * - Changed name to InstaView
 * - Some major code reorganizations and factored out some common functions
 * - Handled conversion of relative links (i.e. [[/foo]])
 * - Fixed misrendering of adjacent definition list items
 * - Fixed bug in table headings handling
 * - Changed date format in signatures to reflect Mediawiki's
 * - Fixed handling of [[:Image:...]]
 * - Updated MD5 function (hopefully it will work with UTF-8)
 * - Fixed bug in handling of links inside images
 *
 * To do:
 * - Better support for &lt;math&gt;
 * - Full support for &lt;nowiki&gt;
 * - Parser-based (as opposed to RegExp-based) inline wikicode handling (make it one-pass and bullet-proof)
 * - Support for templates (through AJAX)
 * - Support for coloured links (AJAX)
 */


var Insta = {}

function setupLivePreview() {

    // options
    Insta.conf =
	{
	    baseUrl: '',

	    user: {},

	    wiki: {
		lang: pg.wiki.lang,
		interwiki: pg.wiki.interwiki,
		default_thumb_width: 180
	    },

	    paths: {
		articles: pg.wiki.articlePath + '/',
		// Only used for Insta previews with images. (not in popups)
		math: '/math/',
		images: '//upload.wikimedia.org/wikiversity/en/', // FIXME ( window.getImageUrlStart ? getImageUrlStart(pg.wiki.hostname) : ''),
		images_fallback: '//upload.wikimedia.org/wikipedia/commons/',
		magnify_icon: 'skins/common/images/magnify-clip.png'
	    },

	    locale: {
		user: mw.config.get('wgFormattedNamespaces')[pg.nsUserId],
		image: mw.config.get('wgFormattedNamespaces')[pg.nsImageId],
		category: mw.config.get('wgFormattedNamespaces')[pg.nsCategoryId],
		// shouldn't be used in popup previews, i think
		months: ['Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec']
	    }
	}

    // options with default values or backreferences
    with (Insta.conf) {
	user.name = user.name || 'Wikiversity participant'
	user.signature = '[['+locale.user+':'+user.name+'|'+user.name+']]'
    }

    // define constants
    Insta.BLOCK_IMAGE = new RegExp('^\\[\\[(?:File|Image|'+Insta.conf.locale.image+
				       '):.*?\\|.*?(?:frame|thumbnail|thumb|none|right|left|center)', 'i');

}


Insta.dump = function(from, to)
{
	if (typeof from == 'string') from = document.getElementById(from)
	if (typeof to == 'string') to = document.getElementById(to)
	to.innerHTML = this.convert(from.value)
}

Insta.convert = function(wiki)
{
	var	ll = (typeof wiki == 'string')? wiki.replace(/\r/g,'').split(/\n/): wiki, // lines of wikicode
		o='',	// output
		p=0,	// para flag
		$r	// result of passing a regexp to $()

	// some shorthands
	function remain() { return ll.length }
	function sh() { return ll.shift() } // shift
	function ps(s) { o+=s } // push

	function f() // similar to C's printf, uses ? as placeholders, ?? to escape question marks
	{
		var i=1,a=arguments,f=a[0],o='',c,p
		for (;i&lt;a.length; i++) if ((p=f.indexOf('?'))+1) {
			// allow character escaping
			i -= c=f.charAt(p+1)=='?'?1:0
			o += f.substring(0,p)+(c?'?':a[i])
			f=f.substr(p+1+c)
		} else break;
		return o+f
	}

	function html_entities(s) { return s.replace(/&amp;/g,&quot;&amp;amp;&quot;).replace(/&lt;/g,&quot;&amp;lt;&quot;).replace(/&gt;/g,&quot;&amp;gt;&quot;) }

	function max(a,b) { return (a&gt;b)?a:b }
	function min(a,b) { return (a&lt;b)?a:b }

	// return the first non matching character position between two strings
	function str_imatch(a, b)
	{
		for (var i=0, l=min(a.length, b.length); i&lt;l; i++) if (a.charAt(i)!=b.charAt(i)) break
		return i
	}

	// compare current line against a string or regexp
	// if passed a string it will compare only the first string.length characters
	// if passed a regexp the result is stored in $r
	function $(c) { return (typeof c == 'string') ? (ll[0].substr(0,c.length)==c) : ($r = ll[0].match(c)) }

	function $$(c) { return ll[0]==c } // compare current line against a string
	function _(p) { return ll[0].charAt(p) } // return char at pos p

	function endl(s) { ps(s); sh() }

	function parse_list()
	{
		var prev='';

		while (remain() &amp;&amp; $(/^([*#:;]+)(.*)$/)) {

			var l_match = $r

			sh()

			var ipos = str_imatch(prev, l_match[1])

			// close uncontinued lists
			for (var i=prev.length-1; i &gt;= ipos; i--) {

				var pi = prev.charAt(i)

				if (pi=='*') ps('&lt;/ul&gt;')
				else if (pi=='#') ps('&lt;/ol&gt;')
				// close a dl only if the new item is not a dl item (:, ; or empty)
				else switch (l_match[1].charAt(i)) { case'':case'*':case'#': ps('&lt;/dl&gt;') }
			}

			// open new lists
			for (var i=ipos; i&lt;l_match[1].length; i++) {

				var li = l_match[1].charAt(i)

				if (li=='*') ps('&lt;ul&gt;')
				else if (li=='#') ps('&lt;ol&gt;')
				// open a new dl only if the prev item is not a dl item (:, ; or empty)
				else switch(prev.charAt(i)) { case'':case'*':case'#': ps('&lt;dl&gt;') }
			}

			switch (l_match[1].charAt(l_match[1].length-1)) {

				case '*': case '#':
					ps('&lt;li&gt;' + parse_inline_nowiki(l_match[2])); break

				case ';':
					ps('&lt;dt&gt;')

					var dt_match

					// handle ;dt :dd format
					if (dt_match = l_match[2].match(/(.*?)(:.*?)$/)) {

						ps(parse_inline_nowiki(dt_match[1]))
						ll.unshift(dt_match[2])

					} else ps(parse_inline_nowiki(l_match[2]))

					break

				case ':':
					ps('&lt;dd&gt;' + parse_inline_nowiki(l_match[2]))
			}

			prev=l_match[1]
		}

		// close remaining lists
		for (var i=prev.length-1; i&gt;=0; i--)
			ps(f('&lt;/?&gt;', (prev.charAt(i)=='*')? 'ul': ((prev.charAt(i)=='#')? 'ol': 'dl')))
	}

	function parse_table()
	{
		endl(f('&lt;table?&gt;', $(/^\{\|( .*)$/)? $r[1]: ''))

		for (;remain();) if ($('|')) switch (_(1)) {
			case '}': endl('&lt;/table&gt;'); return
			case '-': endl(f('&lt;tr ?&gt;', $(/\|-*(.*)/)[1])); break
			default: parse_table_data()
		}
		else if ($('!')) parse_table_data()
		else sh()
	}

	function parse_table_data()
	{
		var td_line, match_i

		// 1: &quot;|+&quot;, '|' or '+'
		// 2: ??
		// 3: attributes ??
		// TODO: finish commenting this regexp
		var td_match = sh().match(/^(\|\+|\||!)((?:([^[|]*?)\|(?!\|))?(.*))$/)

		if (td_match[1] == '|+') ps('&lt;caption');
		else ps('&lt;t' + ((td_match[1]=='|')?'d':'h'))

		if (typeof td_match[3] != 'undefined') {

			ps(' ' + td_match[3])
			match_i = 4

		} else match_i = 2

		ps('&gt;')

		if (td_match[1] != '|+') {

			// use || or !! as a cell separator depending on context
			// NOTE: when split() is passed a regexp make sure to use non-capturing brackets
			td_line = td_match[match_i].split((td_match[1] == '|')? '||': /(?:\|\||!!)/)

			ps(parse_inline_nowiki(td_line.shift()))

			while (td_line.length) ll.unshift(td_match[1] + td_line.pop())

		} else ps(td_match[match_i])

		var tc = 0, td = []

		for (;remain(); td.push(sh()))
		if ($('|')) {
			if (!tc) break // we're at the outer-most level (no nested tables), skip to td parse
			else if (_(1)=='}') tc--
		}
		else if (!tc &amp;&amp; $('!')) break
		else if ($('{|')) tc++

		if (td.length) ps(Insta.convert(td))
	}

	function parse_pre()
	{
		ps('&lt;pre&gt;')
		do endl(parse_inline_nowiki(ll[0].substring(1)) + &quot;\n&quot;); while (remain() &amp;&amp; $(' '))
		ps('&lt;/pre&gt;')
	}

	function parse_block_image()
	{
		ps(parse_image(sh()))
	}

	function parse_image(str)
	{
//&lt;NOLITE&gt;
		// get what's in between &quot;[[Image:&quot; and &quot;]]&quot;
		var tag = str.substring(str.indexOf(':') + 1, str.length - 2);

		var width;
		var attr = [], filename, caption = '';
		var thumb=0, frame=0, center=0;
		var align='';

		if (tag.match(/\|/)) {
			// manage nested links
			var nesting = 0;
			var last_attr;
			for (var i = tag.length-1; i &gt; 0; i--) {
				if (tag.charAt(i) == '|' &amp;&amp; !nesting) {
					last_attr = tag.substr(i+1);
					tag = tag.substring(0, i);
					break;
				} else switch (tag.substr(i-1, 2)) {
					case ']]':
						nesting++;
						i--;
						break;
					case '[[':
						nesting--;
						i--;
				}
			}

			attr = tag.split(/\s*\|\s*/);
			attr.push(last_attr);
			filename = attr.shift();

			var w_match;

			for (;attr.length; attr.shift())
			if (w_match = attr[0].match(/^(\d*)(?:[px]*\d*)?px$/)) width = w_match[1]
			else switch(attr[0]) {
				case 'thumb':
				case 'thumbnail':
					thumb=true;
				case 'frame':
					frame=true;
					break;
				case 'none':
				case 'right':
				case 'left':
					center=false;
					align=attr[0];
					break;
				case 'center':
					center=true;
					align='none';
					break;
				default:
					if (attr.length == 1) caption = attr[0];
			}

		} else filename = tag;


		var o='';

		if (frame) {

			if (align=='') align = 'right';

			o += f(&quot;&lt;div class='thumb t?'&gt;&quot;, align);

			if (thumb) {
				if (!width) width = Insta.conf.wiki.default_thumb_width;

				o += f(&quot;&lt;div style='width:?px;'&gt;?&quot;, 2+width*1, make_image(filename, caption, width)) +
					f(&quot;&lt;div class='thumbcaption'&gt;&lt;div class='magnify' style='float:right'&gt;&lt;a href='?' class='internal' title='Enlarge'&gt;&lt;img src='?'&gt;&lt;/a&gt;&lt;/div&gt;?&lt;/div&gt;&quot;,
						Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename,
						Insta.conf.paths.magnify_icon,
						parse_inline_nowiki(caption)
					)
			} else {
				o += '&lt;div&gt;' + make_image(filename, caption) + f(&quot;&lt;div class='thumbcaption'&gt;?&lt;/div&gt;&quot;, parse_inline_nowiki(caption))
			}

			o += '&lt;/div&gt;&lt;/div&gt;';

		} else if (align != '') {
			o += f(&quot;&lt;div class='float?'&gt;&lt;span&gt;?&lt;/span&gt;&lt;/div&gt;&quot;, align, make_image(filename, caption, width));
		} else {
			return make_image(filename, caption, width);
		}

		return center? f(&quot;&lt;div class='center'&gt;?&lt;/div&gt;&quot;, o): o;
//&lt;/NOLITE&gt;
	}

	function parse_inline_nowiki(str)
	{
		var start, lastend=0
		var substart=0, nestlev=0, open, close, subloop;
		var html='';

		while (-1 != (start = str.indexOf('&lt;nowiki&gt;', substart))) {
			html += parse_inline_wiki(str.substring(lastend, start));
			start += 8;
			substart = start;
			subloop = true;
			do {
				open = str.indexOf('&lt;nowiki&gt;', substart);
				close = str.indexOf('&lt;/nowiki&gt;', substart);
				// &lt;/nowiki&gt;
				if (close&lt;=open || open==-1) {
					if (close==-1) {
						return html + html_entities(str.substr(start));
					}
					substart = close+9;
					if (nestlev) {
						nestlev--;
					} else {
						lastend = substart;
						html += html_entities(str.substring(start, lastend-9));
						subloop = false;
					}
				} else {
					substart = open+8;
					nestlev++;
				}
			} while (subloop)
		}

		return html + parse_inline_wiki(str.substr(lastend));
	}

	function make_image(filename, caption, width)
	{
//&lt;NOLITE&gt;
		// uppercase first letter in file name
		filename = filename[0].toUpperCase() + filename.substr(1);
		// replace spaces with underscores
		filename = filename.replace(/ /g, '_');

		caption = strip_inline_wiki(caption);

		var md5 = hex_md5(filename);

		var source = md5[0] + '/' + md5.substr(0,2) + '/' + filename;

		if (width) width = &quot;width='&quot; + width + &quot;px'&quot;;

		var img = f(&quot;&lt;img onerror=\&quot;this.onerror=null;this.src='?'\&quot; src='?' ? ?&gt;&quot;, Insta.conf.paths.images_fallback + source, Insta.conf.paths.images + source, (caption!='')? &quot;alt='&quot; + caption + &quot;'&quot; : '', width);

		return f(&quot;&lt;a class='image' ? href='?'&gt;?&lt;/a&gt;&quot;, (caption!='')? &quot;title='&quot; + caption + &quot;'&quot; : '', Insta.conf.paths.articles + Insta.conf.locale.image + ':' + filename, img);
//&lt;/NOLITE&gt;
	}

	function parse_inline_images(str)
	{
//&lt;NOLITE&gt;
		var start, substart=0, nestlev=0;
		var loop, close, open, wiki, html;

		while (-1 != (start=str.indexOf('[[', substart))) {
			if(str.substr(start+2).match(RegExp('^(Image|File|' + Insta.conf.locale.image + '):','i'))) {
				loop=true;
				substart=start;
				do {
					substart+=2;
					close=str.indexOf(']]',substart);
					open=str.indexOf('[[',substart);
					if (close&lt;=open||open==-1) {
						if (close==-1) return str;
						substart=close;
						if (nestlev) {
							nestlev--;
						} else {
							wiki=str.substring(start,close+2);
							html=parse_image(wiki);
							str=str.replace(wiki,html);
							substart=start+html.length;
							loop=false;
						}
					} else {
						substart=open;
						nestlev++;
					}
				} while (loop)

			} else break;
		}

//&lt;/NOLITE&gt;
		return str;
	}

	// the output of this function doesn't respect the FILO structure of HTML
	// but since most browsers can handle it I'll save myself the hassle
	function parse_inline_formatting(str)
	{
		var em,st,i,li,o='';
		while ((i=str.indexOf(&quot;''&quot;,li))+1) {
			o += str.substring(li,i);
			li=i+2;
			if (str.charAt(i+2)==&quot;'&quot;) {
				li++;
				st=!st;
				o+=st?'&lt;strong&gt;':'&lt;/strong&gt;';
			} else {
				em=!em;
				o+=em?'&lt;em&gt;':'&lt;/em&gt;';
			}
		}
		return o+str.substr(li);
	}

	function parse_inline_wiki(str)
	{
		var aux_match;

		str = parse_inline_images(str);
		str = parse_inline_formatting(str);

		// math
		while (aux_match = str.match(/&lt;(?:)math&gt;(.*?)&lt;\/math&gt;/i)) {
			var math_md5 = hex_md5(aux_match[1]);
			str = str.replace(aux_match[0], f(&quot;&lt;img src='?.png'&gt;&quot;, Insta.conf.paths.math+math_md5));
		}

		// Build a Mediawiki-formatted date string
		var date = new Date;
		var minutes = date.getUTCMinutes();
		if (minutes &lt; 10) minutes = '0' + minutes;
		var date = f(&quot;?:?, ? ? ? (UTC)&quot;, date.getUTCHours(), minutes, date.getUTCDate(), Insta.conf.locale.months[date.getUTCMonth()], date.getUTCFullYear());

		// text formatting
		return str.
			// signatures
			replace(/~{5}(?!~)/g, date).
			replace(/~{4}(?!~)/g, Insta.conf.user.name+' '+date).
			replace(/~{3}(?!~)/g, Insta.conf.user.name).

			// [[:Category:...]], [[:Image:...]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):[^|]*?)\\]\\](\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$1$2&lt;/a&gt;&quot;).
			// remove straight category and interwiki tags
			replace(RegExp('\\[\\[(?:'+Insta.conf.locale.category+'|'+Insta.conf.wiki.interwiki+'):.*?\\]\\]','gi'),'').

			// [[:Category:...|Links]], [[:Image:...|Links]], etc...
			replace(RegExp('\\[\\[:((?:'+Insta.conf.locale.category+'|Image|File|'+Insta.conf.locale.image+'|'+Insta.conf.wiki.interwiki+'):.*?)\\|([^\\]]+?)\\]\\](\\w*)','gi'), &quot;&lt;a href='&quot;+Insta.conf.paths.articles+&quot;$1'&gt;$2$3&lt;/a&gt;&quot;).

			// [[/Relative links]]
			replace(/\[\[(\/[^|]*?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$1&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[/Replaced|Relative links]]
			replace(/\[\[(\/.*?)\|(.+?)\]\]/g, f(&quot;&lt;a href='?$1'&gt;$2&lt;/a&gt;&quot;, Insta.conf.baseUrl)).

			// [[Common links]]
			replace(/\[\[([^|]*?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$1$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Replaced|Links]]
			replace(/\[\[(.*?)\|([^\]]+?)\]\](\w*)/g, f(&quot;&lt;a href='?$1'&gt;$2$3&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// [[Stripped:Namespace|Namespace]]
			replace(/\[\[([^\]]*?:)?(.*?)( *\(.*?\))?\|\]\]/g, f(&quot;&lt;a href='?$1$2$3'&gt;$2&lt;/a&gt;&quot;, Insta.conf.paths.articles)).

			// External links
			replace(/\[(https?|news|ftp|mailto|gopher|irc):(\/*)([^\]]*?) (.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$4&lt;/a&gt;&quot;).
			replace(/\[http:\/\/(.*?)\]/g, &quot;&lt;a class='external' href='http://$1'&gt;[#]&lt;/a&gt;&quot;).
			replace(/\[(news|ftp|mailto|gopher|irc):(\/*)(.*?)\]/g, &quot;&lt;a class='external' href='$1:$2$3'&gt;$1:$2$3&lt;/a&gt;&quot;).
			replace(/(^| )(https?|news|ftp|mailto|gopher|irc):(\/*)([^ $]*[^.,!?;: $])/g, &quot;$1&lt;a class='external' href='$2:$3$4'&gt;$2:$3$4&lt;/a&gt;&quot;).

			replace('__NOTOC__','').
			replace('__NOEDITSECTION__','');
	}
/*
*/
	function strip_inline_wiki(str)
	{
		return str
			.replace(/\[\[[^\]]*\|(.*?)\]\]/g,'$1')
			.replace(/\[\[(.*?)\]\]/g,'$1')
			.replace(/''(.*?)''/g,'$1');
	}

	// begin parsing
	for (;remain();) if ($(/^(={1,6})(.*)\1(.*)$/)) {
		p=0
		endl(f('&lt;h?&gt;?&lt;/h?&gt;?', $r[1].length, parse_inline_nowiki($r[2]), $r[1].length, $r[3]))

	} else if ($(/^[*#:;]/)) {
		p=0
		parse_list()

	} else if ($(' ')) {
		p=0
		parse_pre()

	} else if ($('{|')) {
		p=0
		parse_table()

	} else if ($(/^----+$/)) {
		p=0
		endl('&lt;hr&gt;')

	} else if ($(Insta.BLOCK_IMAGE)) {
		p=0
		parse_block_image()

	} else {

		// handle paragraphs
		if ($$('')) {
			if (p = (remain()&gt;1 &amp;&amp; ll[1]==(''))) endl('&lt;p&gt;&lt;br&gt;')
		} else {
			if(!p) {
				ps('&lt;p&gt;')
				p=1
			}
			ps(parse_inline_nowiki(ll[0]) + ' ')
		}

		sh();
	}

	return o
};

window.wiki2html=function(txt,baseurl) {
    Insta.conf.baseUrl=baseurl;
    return Insta.convert(txt);
};
// ENDFILE: livepreview.js
// STARTFILE: pageinfo.js
//&lt;NOLITE&gt;
function popupFilterPageSize(data) {
	return formatBytes(data.length);
}

function popupFilterCountLinks(data) {
	var num=countLinks(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('wikiLinks'):popupString('wikiLink'));
}

function popupFilterCountImages(data) {
	var num=countImages(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('images'):popupString('image'));
}

function popupFilterCountCategories(data) {
	var num=countCategories(data);
	return String(num) + '&amp;nbsp;' + ((num!=1)?popupString('categories'):popupString('category'));
}


function popupFilterLastModified(data,download) {
	var lastmod=download.lastModified;
	var now=new Date();
	var age=now-lastmod;
	if (lastmod &amp;&amp; getValueOf('popupLastModified')) {
		return (tprintf('%s old', [formatAge(age)])).replace(RegExp(' ','g'), '&amp;nbsp;');
	}
	return '';
}

function formatAge(age) {
	// coerce into a number
	var a=0+age, aa=a;

	var seclen  = 1000;
	var minlen  = 60*seclen;
	var hourlen = 60*minlen;
	var daylen  = 24*hourlen;
	var weeklen = 7*daylen;

	var numweeks = (a-a%weeklen)/weeklen; a = a-numweeks*weeklen; var sweeks = addunit(numweeks, 'week');
	var numdays  = (a-a%daylen)/daylen;   a = a-numdays*daylen;   var sdays  = addunit(numdays, 'day');
	var numhours = (a-a%hourlen)/hourlen; a = a-numhours*hourlen; var shours = addunit(numhours,'hour');
	var nummins  = (a-a%minlen)/minlen;   a = a-nummins*minlen;   var smins  = addunit(nummins, 'minute');
	var numsecs  = (a-a%seclen)/seclen;   a = a-numsecs*seclen;   var ssecs  = addunit(numsecs, 'second');

	if (aa &gt; 4*weeklen) { return sweeks; }
	if (aa &gt; weeklen)   { return sweeks + ' ' + sdays; }
	if (aa &gt; daylen)    { return sdays  + ' ' + shours; }
	if (aa &gt; 6*hourlen) { return shours; }
	if (aa &gt; hourlen)   { return shours + ' ' + smins; }
	if (aa &gt; 10*minlen) { return smins; }
	if (aa &gt; minlen)    { return smins  + ' ' + ssecs; }
	return ssecs;
}

function addunit(num,str) { return '' + num + ' ' + ((num!=1) ? popupString(str+'s') : popupString(str)) ;}

function runPopupFilters(list, data, download) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i] &amp;&amp; typeof list[i] == 'function') {
			var s=list[i](data, download, download.owner.article);
			if (s) { ret.push(s); }
		}
	}
	return ret;
}

function getPageInfo(data, download) {
	if (!data || data.length === 0) { return popupString('Empty page'); }

	var popupFilters=getValueOf('popupFilters') || [];
	var extraPopupFilters = getValueOf('extraPopupFilters') || [];
	var pageInfoArray = runPopupFilters(popupFilters.concat(extraPopupFilters), data, download);

	var pageInfo=pageInfoArray.join(', ');
	if (pageInfo !== '' ) { pageInfo = upcaseFirst(pageInfo); }
	return pageInfo;
}


// this could be improved!
function countLinks(wikiText) { return wikiText.split('[[').length - 1; }

// if N = # matches, n = # brackets, then
// String.parenSplit(regex) intersperses the N+1 split elements
// with Nn other elements. So total length is
// L= N+1 + Nn = N(n+1)+1. So N=(L-1)/(n+1).

function countImages(wikiText) {
	return (wikiText.parenSplit(pg.re.image).length - 1) / (pg.re.imageBracketCount + 1);
}

function countCategories(wikiText) {
	return (wikiText.parenSplit(pg.re.category).length - 1) / (pg.re.categoryBracketCount + 1);
}

function popupFilterStubDetect(data, download, article)     {
	var counts=stubCount(data, article);
	if (counts.real) { return popupString('stub'); }
	if (counts.sect) { return popupString('section stub'); }
	return '';
}

function popupFilterDisambigDetect(data, download, article) {
	if (getValueOf('popupOnlyArticleDabStub') &amp;&amp; article.namespace()) { return ''; }
	return (isDisambig(data, article)) ? popupString('disambig') : '';
}

function formatBytes(num) {
	return (num &gt; 949) ? (Math.round(num/100)/10+popupString('kB')) : (num +'&amp;nbsp;' + popupString('bytes')) ;
}
//&lt;/NOLITE&gt;
// ENDFILE: pageinfo.js
// STARTFILE: titles.js
/**
   @fileoverview Defines the {@link Title} class, and associated crufty functions.

   &lt;code&gt;Title&lt;/code&gt; deals with article titles and their various
   forms.  {@link Stringwrapper} is the parent class of
   &lt;code&gt;Title&lt;/code&gt;, which exists simply to make things a little
   neater.

*/

/**
   Creates a new Stringwrapper.
   @constructor

   @class the Stringwrapper class. This base class is not really
   useful on its own; it just wraps various common string operations.
*/
function Stringwrapper() {
	/**
	   Wrapper for this.toString().indexOf()
	   @param {String} x
	   @type integer
	*/
	this.indexOf=function(x){return this.toString().indexOf(x);};
	/**
	   Returns this.value.
	   @type String
	*/
	this.toString=function(){return this.value;};
	/**
	   Wrapper for {@link String#parenSplit} applied to this.toString()
	   @param {RegExp} x
	   @type Array
	*/
	this.parenSplit=function(x){return this.toString().parenSplit(x);};
	/**
	   Wrapper for this.toString().substring()
	   @param {String} x
	   @param {String} y (optional)
	   @type String
	*/
	this.substring=function(x,y){
		if (typeof y=='undefined') { return this.toString().substring(x); }
		return this.toString().substring(x,y);
	};
	/**
	   Wrapper for this.toString().split()
	   @param {String} x
	   @type Array
	*/
	this.split=function(x){return this.toString().split(x);};
	/**
	   Wrapper for this.toString().replace()
	   @param {String} x
	   @param {String} y
	   @type String
	*/
	this.replace=function(x,y){ return this.toString().replace(x,y); };
}


/**
   Creates a new &lt;code&gt;Title&lt;/code&gt;.
   @constructor

   @class The Title class. Holds article titles and converts them into
   various forms. Also deals with anchors, by which we mean the bits
   of the article URL after a # character, representing locations
   within an article.

   @param {String} value The initial value to assign to the
   article. This must be the canonical title (see {@link
   Title#value}. Omit this in the constructor and use another function
   to set the title if this is unavailable.
*/
function Title(val) {
	/**
	   The canonical article title. This must be in UTF-8 with no
	   entities, escaping or nasties. Also, underscores should be
	   replaced with spaces.
	   @type String
	   @private
	*/
	this.value=null;
	/**
	   The canonical form of the anchor. This should be exactly as
	   it appears in the URL, i.e. with the .C3.0A bits in.
	   @type String
	*/
	this.anchor='';

	this.setUtf(val);
}
Title.prototype=new Stringwrapper();
/**
   Returns the canonical representation of the article title, optionally without anchor.
   @param {boolean} omitAnchor
   @fixme Decide specs for anchor
   @return String The article title and the anchor.
*/
Title.prototype.toString=function(omitAnchor) {
	return this.value + ( (!omitAnchor &amp;&amp; this.anchor) ? '#' + this.anchorString() : '' );
};
Title.prototype.anchorString=function() {
	if (!this.anchor) { return ''; }
	var split=this.anchor.parenSplit(/((?:[.][0-9A-F]{2})+)/);
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		// FIXME s/decodeURI/decodeURIComponent/g ?
		split[j]=decodeURIComponent(split[j].split('.').join('%')).split('_').join(' ');
	}
	return split.join('');
};
Title.prototype.urlAnchor=function() {
	var split=this.anchor.parenSplit('/((?:[%][0-9A-F]{2})+)/');
	var len=split.length;
	for (var j=1; j&lt;len; j+=2) {
		split[j]=split[j].split('%').join('.');
	}
	return split.join('');
};
Title.prototype.anchorFromUtf=function(str) {
	this.anchor=encodeURIComponent(str.split(' ').join('_'))
	.split('%3A').join(':').split(&quot;'&quot;).join('%27').split('%').join('.');
};
Title.fromURL=function(h) {
	return new Title().fromURL(h);
};
Title.prototype.fromURL=function(h) {
	if (typeof h != 'string') {
		this.value=null;
		return this;
	}

	// NOTE : playing with decodeURI, encodeURI, escape, unescape,
	// we seem to be able to replicate the IE borked encoding

	// IE doesn't do this new-fangled utf-8 thing.
	// and it's worse than that.
	// IE seems to treat the query string differently to the rest of the url
	// the query is treated as bona-fide utf8, but the first bit of the url is pissed around with

	// we fix up &amp; for all browsers, just in case.
	var splitted=h.split('?');
	splitted[0]=splitted[0].split('&amp;').join('%26');

	if (pg.flag.linksLikeIE6) {
		splitted[0]=encodeURI(decode_utf8(splitted[0]));
	}

	h=splitted.join('?');

	var contribs=pg.re.contribs.exec(h);
	if (contribs !== null) {
		if (contribs[1]=='title=') { contribs[3]=contribs[3].split('+').join(' '); }
		var u=new Title(contribs[3]);
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + u.stripNamespace()));
		return this;
	}

	var email=pg.re.email.exec(h);
	if (email !== null) {
		this.setUtf(this.decodeNasties(mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(email[3]).stripNamespace()));
		return this;
	}

	var backlinks=pg.re.backlinks.exec(h);
	if (backlinks) {
		this.setUtf(this.decodeNasties(new Title(backlinks[3])));
		return this;
	}

	// no more special cases to check --
	// hopefully it's not a disguised user-related or specially treated special page
	var m=pg.re.main.exec(h);
	if(m===null) { this.value=null; }
	else {
        var fromBotInterface = /[?](.+[&amp;])?title=/.test(h);
        if (fromBotInterface) {
            m[2]=m[2].split('+').join('_');
        }
        var extracted = m[2] + (m[3] ? '#' + m[3] : '');
        if (pg.flag.isSafari &amp;&amp; /%25[0-9A-Fa-f]{2}/.test(extracted)) {
            // Fix Safari issue
            // Safari sometimes encodes % as %25 in UTF-8 encoded strings like %E5%A3 -&gt; %25E5%25A3.
            this.setUtf(decodeURIComponent(unescape(extracted)));
        } else {
            this.setUtf(this.decodeNasties(extracted));
        }
    }
	return this;
};
Title.prototype.decodeNasties=function(txt) {
	var ret= this.decodeEscapes(decodeURI(txt));
	ret = ret.replace(/[_ ]*$/, '');
	return ret;
};
Title.prototype.decodeEscapes=function(txt) {
	var split=txt.parenSplit(/((?:[%][0-9A-Fa-f]{2})+)/);
	var len=split.length;
	for (var i=1; i&lt;len; i=i+2) {
		// FIXME is decodeURIComponent better?
		split[i]=unescape(split[i]);
	}
	return split.join('');
};
Title.fromAnchor=function(a) {
	return new Title().fromAnchor(a);
};
Title.prototype.fromAnchor=function(a) {
	if (!a) { this.value=null; return this; }
	return this.fromURL(a.href);
};
Title.fromWikiText=function(txt) {
	return new Title().fromWikiText(txt);
};
Title.prototype.fromWikiText=function(txt) {
	// FIXME - testing needed
	if (!pg.flag.linksLikeIE6) { txt=myDecodeURI(txt); }
	this.setUtf(txt);
	return this;
};
Title.prototype.hintValue=function(){
	if(!this.value) { return ''; }
	return safeDecodeURI(this.value);
};
//&lt;NOLITE&gt;
Title.prototype.toUserName=function(withNs) {
	if (this.namespaceId() != pg.nsUserId &amp;&amp; this.namespaceId() != pg.nsUsertalkId) {
		this.value=null;
		return;
	}
	this.value = (withNs ? mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' : '') + this.stripNamespace().split('/')[0];
};
Title.prototype.userName=function(withNs) {
	var t=(new Title(this.value));
	t.toUserName(withNs);
	if (t.value) { return t; }
	return null;
};
Title.prototype.toTalkPage=function() {
	// convert article to a talk page, or if we can't, return null
	// In other words: return null if this ALREADY IS a talk page
	// and return the corresponding talk page otherwise
	//
	// Per //www.mediawiki.org/wiki/Manual:Namespace#Subject_and_talk_namespaces
	// * All discussion namespaces have odd-integer indices
	// * The discussion namespace index for a specific namespace with index n is n + 1
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 0) //non-special and subject namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId+1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
//&lt;/NOLITE&gt;
// Return canonical, localized namespace
Title.prototype.namespace=function() {
	return mw.config.get('wgFormattedNamespaces')[this.namespaceId()];
};
Title.prototype.namespaceId=function() {
	var n=this.value.indexOf(':');
	if (n&lt;0) { return 0; } //mainspace
	var namespaceId = mw.config.get('wgNamespaceIds')[this.value.substring(0,n).split(' ').join('_').toLowerCase()];
	if (typeof namespaceId=='undefined') return 0; //mainspace
	return namespaceId;
};
//&lt;NOLITE&gt;
Title.prototype.talkPage=function() {
	var t=new Title(this.value);
	t.toTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.isTalkPage=function() {
	if (this.talkPage()===null) { return true; }
	return false;
};
Title.prototype.toArticleFromTalkPage=function() {
	//largely copy/paste from toTalkPage above.
	if (this.value===null) { return null; }
	
	var namespaceId = this.namespaceId();
	if (namespaceId&gt;=0 &amp;&amp; namespaceId % 2 == 1) //non-special and talk namespace
	{
		var localizedNamespace = mw.config.get('wgFormattedNamespaces')[namespaceId-1];
		if (typeof localizedNamespace!=='undefined')
		{
			if (localizedNamespace==='') return this.value = this.stripNamespace();
			this.value = localizedNamespace.split(' ').join('_') + ':' + this.stripNamespace();
			return this.value;
		}
	}

	this.value=null;
	return null;
};
Title.prototype.articleFromTalkPage=function() {
	var t=new Title(this.value);
	t.toArticleFromTalkPage();
	if (t.value) { return t; }
	return null;
};
Title.prototype.articleFromTalkOrArticle=function() {
	var t=new Title(this.value);
	if ( t.toArticleFromTalkPage() ) { return t; }
	return this;
};
Title.prototype.isIpUser=function() {
	return pg.re.ipUser.test(this.userName());
};
//&lt;/NOLITE&gt;
Title.prototype.stripNamespace=function(){ // returns a string, not a Title
	var n=this.value.indexOf(':');
	if (n&lt;0) { return this.value; }
	var namespaceId = this.namespaceId();
	if (typeof namespaceId==='undefined') return this.value;
	return this.value.substring(n+1);
};
Title.prototype.setUtf=function(value){
	if (!value) { this.value=''; return; }
	var anch=value.indexOf('#');
	if(anch &lt; 0) { this.value=value.split('_').join(' '); this.anchor=''; return; }
	this.value=value.substring(0,anch).split('_').join(' ');
	this.anchor=value.substring(anch+1);
	this.ns=null; // wait until namespace() is called
};
Title.prototype.setUrl=function(urlfrag) {
	var anch=urlfrag.indexOf('#');
	this.value=safeDecodeURI(urlfrag.substring(0,anch));
	this.anchor=value.substring(anch+1);
};
Title.prototype.append=function(x){
	this.setUtf(this.value + x);
};
Title.prototype.urlString=function(x) {
	x || ( x={} );
	var v=this.toString(true);
	if (!x.omitAnchor &amp;&amp; this.anchor) { v+= '#' + this.urlAnchor(); }
	if (!x.keepSpaces) { v=v.split(' ').join('_'); }
	return encodeURI(v).split('&amp;').join('%26').split('?').join('%3F').split('+').join('%2B');
};
Title.prototype.removeAnchor=function() {
	return new Title(this.toString(true));
};
Title.prototype.toUrl=function() {
	return pg.wiki.titlebase + this.urlString();
};


function paramValue(param, url) {
	var s=url.parenSplit(RegExp('[?&amp;]' + literalizeRegex(param) + '=([^?&amp;]*)'));
	if (!url) { return null; }
	return s[1] || null;
}

function parseParams(url) {
	var ret={};
	if (url.indexOf('?')==-1) { return ret; }
	var s=url.split('?').slice(1).join();
	var t=s.split('&amp;');
	for (var i=0; i&lt;t.length; ++i) {
		var z=t[i].split('=');
		z.push(null);
		ret[z[0]]=z[1];
	}
	return ret;
}

// all sorts of stuff here
// FIXME almost everything needs to be rewritten

function oldidFromAnchor(a) { return paramValue('oldid', a.href); }
//function diffFromAnchor(a) { return paramValue('diff', a.href); }


function wikiMarkupToAddressFragment (str) { // for images
	var ret = safeDecodeURI(str);
	ret = ret.split(' ').join('_');
	ret = encodeURI(ret);
	return ret;
}

// (a) myDecodeURI (first standard decodeURI, then pg.re.urlNoPopup)
// (b) change spaces to underscores
// (c) encodeURI (just the straight one, no pg.re.urlNoPopup)

function myDecodeURI (str) {
	var ret;
	// FIXME decodeURIComponent??
	try { ret=decodeURI(str.toString()); }
	catch (summat) { return str; }
	for (var i=0; i&lt;pg.misc.decodeExtras.length; ++i) {
		var from=pg.misc.decodeExtras[i].from;
		var to=pg.misc.decodeExtras[i].to;
		ret=ret.split(from).join(to);
	}
	return ret;
}

function safeDecodeURI(str) { var ret=myDecodeURI(str); return ret || str; }

///////////
// TESTS //
///////////

//&lt;NOLITE&gt;
function isIpUser(user) {return pg.re.ipUser.test(user);}

function isDisambig(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	return ! article.isTalkPage() &amp;&amp; pg.re.disambig.test(data);
}

function stubCount(data, article) {
	if (!getValueOf('popupAllDabsStubs') &amp;&amp; article.namespace()) { return false; }
	var sectStub=0;
	var realStub=0;
	if (pg.re.stub.test(data)) {
		var s=data.parenSplit(pg.re.stub);
		for (var i=1; i&lt;s.length; i=i+2) {
			if (s[i]) { ++sectStub; }
			else { ++realStub; }
		}
	}
	return { real: realStub, sect: sectStub };
}

function isValidImageName(str){ // extend as needed...
	return ( str.indexOf('{') == -1 );
}

function isInStrippableNamespace(article) {
	//I believe that this method means to return whether the given article is in a namspace without subpages. Meaning, it's broken.
	return ( article.namespace() !== '' );
}

function isInMainNamespace(article) { return !isInStrippableNamespace(article); }

function anchorContainsImage(a) {
	// iterate over children of anchor a
	// see if any are images
	if (a===null) { return false; }
	kids=a.childNodes;
	for (var i=0; i&lt;kids.length; ++i) { if (kids[i].nodeName=='IMG') { return true; } }
	return false;
}
//&lt;/NOLITE&gt;
function isPopupLink(a) {
	// NB for performance reasons, TOC links generally return true
	// they should be stripped out later

	if (!markNopopupSpanLinks.done) { markNopopupSpanLinks(); }
	if (a.inNopopupSpan || a.className=='sortheader') { return false; }

	// FIXME is this faster inline?
	if (a.onmousedown || a.getAttribute('nopopup')) { return false; }
	var h=a.href;
	if (!pg.re.basenames.test(h)) { return false; }
	if ( !pg.re.urlNoPopup.test(h) ) { return true;	}
	return (
		(pg.re.email.test(h) || pg.re.contribs.test(h) || pg.re.backlinks.test(h)) &amp;&amp;
		h.indexOf('&amp;limit=') == -1 );
}

function markNopopupSpanLinks() {
	if( !getValueOf('popupOnlyArticleLinks'))
		fixVectorMenuPopups();

	var s=getElementsByClassName(document, '*', &quot;nopopups&quot;)
	for (var i=0; i&lt;s.length; ++i) {
		var as=s[i].getElementsByTagName('a');
		for (var j=0; j&lt;as.length; ++j) {
			as[j].inNopopupSpan=true;
		}
	}
	
	markNopopupSpanLinks.done=true;
}

function fixVectorMenuPopups() {
	var vmenus = getElementsByClassName( document, 'div', 'vectorMenu');
	for( i= 0; vmenus &amp;&amp; i&lt; vmenus.length; i++ ) {
		var h5 = vmenus[i].getElementsByTagName('h5')[0];
		if( h5) var a = h5.getElementsByTagName('a')[0];
		if( a ) a.inNopopupSpan=true;
	}
}
// ENDFILE: titles.js
// STARTFILE: cookies.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Cookie handling
// from http://www.quirksmode.org/js/cookies.html

var Cookie= {
	create: function(name,value,days)
	{
		var expires;
		if (days)
		{
			var date = new Date();
			date.setTime(date.getTime()+(days*24*60*60*1000));
			expires = &quot;; expires=&quot;+date.toGMTString();
		}
		else { expires = &quot;&quot;; }
		document.cookie = name+&quot;=&quot;+value+expires+&quot;; path=/&quot;;
	},

	read: function(name)
	{
		var nameEQ = name + &quot;=&quot;;
		var ca = document.cookie.split(';');
		for(var i=0;i &lt; ca.length;i++)
		{
			var c = ca[i];
			while (c[0]==' ') { c = c.substring(1,c.length); }
			if (c.indexOf(nameEQ) === 0) { return c.substring(nameEQ.length,c.length); }
		}
		return null;
	},

	erase: function(name)
	{
		Cookie.create(name,&quot;&quot;,-1);
	}
};
//&lt;/NOLITE&gt;
// ENDFILE: cookies.js
// STARTFILE: getpage.js
//////////////////////////////////////////////////
// Wiki-specific downloading
//

// Schematic for a getWiki call
//
//   getWiki-&gt;-getPageWithCaching
//                    |
//       false        |          true
// getPage&lt;-[findPictureInCache]-&gt;-onComplete(a fake download)
//   \.
//     (async)-&gt;addPageToCache(download)-&gt;-onComplete(download)


/** @todo {document}
    @param {Title} article
    @param {Function} onComplete
    @param {integer} oldid
    @param {Navapopup} owner
*/
function getWiki(article, onComplete, oldid, owner) {
	// set ctype=text/css to get around opera gzip bug
	var url = pg.wiki.titlebase + article.removeAnchor().urlString() +
	    '&amp;action=raw&amp;ctype=text/css';
	if (oldid || oldid===0 || oldid==='0') { url += '&amp;oldid='+oldid; }
	url += '';

	getPageWithCaching(url, onComplete, owner);
}

// check cache to see if page exists

function getPageWithCaching(url, onComplete, owner) {
	log('getPageWithCaching, url='+url);
	var i=findInPageCache(url);
	if (i &gt; -1) {
		var d=fakeDownload(url, owner.idNumber, onComplete,
				   pg.cache.pages[i].data, pg.cache.pages[i].lastModified,
				   owner);
	} else {
		var d=getPage(url, onComplete, owner);
		if (d &amp;&amp; owner &amp;&amp; owner.addDownload) {
			owner.addDownload(d);
			d.owner=owner;
		}
	}
}

function getPage(url, onComplete, owner) {
	log('getPage');
	var callback= function (d) { if (!d.aborted) {addPageToCache(d); onComplete(d);} };
	return startDownload(url, owner.idNumber, callback);
}

function findInPageCache(url) {
	for (var i=0; i&lt;pg.cache.pages.length; ++i) {
		if (url==pg.cache.pages[i].url) { return i; }
	}
	return -1;
}

function addPageToCache(download) {
	log('addPageToCache '+download.url);
	var page = {url: download.url, data: download.data, lastModified: download.lastModified};
	return pg.cache.pages.push(page);
}
// ENDFILE: getpage.js
// STARTFILE: md5-2.2alpha.js
//&lt;NOLITE&gt;
/*
 * A JavaScript implementation of the RSA Data Security, Inc. MD5 Message
 * Digest Algorithm, as defined in {{RFC|1321}}.
 * Version 2.2-alpha Copyright (C) Paul Johnston 1999 - 2005
 * Other contributors: Greg Holt, Andrew Kepert, Ydnar, Lostinet
 * Distributed under the BSD License
 * See http://pajhome.org.uk/crypt/md5 for more info.
 */

/*
 * Configurable variables. You may need to tweak these to be compatible with
 * the server-side, but the defaults work in most cases.
 */
var hexcase = 0;   /* hex output format. 0 - lowercase; 1 - uppercase	     */
var b64pad  = &quot;&quot;; /* base-64 pad character. &quot;=&quot; for strict RFC compliance   */

/*
 * These are the functions you'll usually want to call
 * They take string arguments and return either hex or base-64 encoded strings
 */
function hex_md5(s)    { return rstr2hex(rstr_md5(str2rstr_utf8(s))); }
function b64_md5(s)    { return rstr2b64(rstr_md5(str2rstr_utf8(s))); }
function any_md5(s, e) { return rstr2any(rstr_md5(str2rstr_utf8(s)), e); }
function hex_hmac_md5(k, d)
  { return rstr2hex(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function b64_hmac_md5(k, d)
  { return rstr2b64(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d))); }
function any_hmac_md5(k, d, e)
  { return rstr2any(rstr_hmac_md5(str2rstr_utf8(k), str2rstr_utf8(d)), e); }

/*
 * Perform a simple self-test to see if the VM is working
 */
function md5_vm_test()
{
  return hex_md5(&quot;abc&quot;) == &quot;900150983cd24fb0d6963f7d28e17f72&quot;;
}

/*
 * Calculate the MD5 of a raw string
 */
function rstr_md5(s)
{
  return binl2rstr(binl_md5(rstr2binl(s), s.length * 8));
}

/*
 * Calculate the HMAC-MD5, of a key and some data (raw strings)
 */
function rstr_hmac_md5(key, data)
{
  var bkey = rstr2binl(key);
  if(bkey.length &gt; 16) bkey = binl_md5(bkey, key.length * 8);

  var ipad = Array(16), opad = Array(16);
  for(var i = 0; i &lt; 16; i++)
  {
    ipad[i] = bkey[i] ^ 0x36363636;
    opad[i] = bkey[i] ^ 0x5C5C5C5C;
  }

  var hash = binl_md5(ipad.concat(rstr2binl(data)), 512 + data.length * 8);
  return binl2rstr(binl_md5(opad.concat(hash), 512 + 128));
}

/*
 * Convert a raw string to a hex string
 */
function rstr2hex(input)
{
  var hex_tab = hexcase ? &quot;0123456789ABCDEF&quot; : &quot;0123456789abcdef&quot;;
  var output = &quot;&quot;;
  var x;
  for(var i = 0; i &lt; input.length; i++)
  {
    x = input.charCodeAt(i);
    output += hex_tab.charAt((x &gt;&gt;&gt; 4) &amp; 0x0F)
	   +  hex_tab.charAt( x	       &amp; 0x0F);
  }
  return output;
}

/*
 * Convert a raw string to a base-64 string
 */
function rstr2b64(input)
{
  var tab = &quot;ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/&quot;;
  var output = &quot;&quot;;
  var len = input.length;
  for(var i = 0; i &lt; len; i += 3)
  {
    var triplet = (input.charCodeAt(i) &lt;&lt; 16)
		| (i + 1 &lt; len ? input.charCodeAt(i+1) &lt;&lt; 8 : 0)
		| (i + 2 &lt; len ? input.charCodeAt(i+2)	    : 0);
    for(var j = 0; j &lt; 4; j++)
    {
      if(i * 8 + j * 6 &gt; input.length * 8) output += b64pad;
      else output += tab.charAt((triplet &gt;&gt;&gt; 6*(3-j)) &amp; 0x3F);
    }
  }
  return output;
}

/*
 * Convert a raw string to an arbitrary string encoding
 */
function rstr2any(input, encoding)
{
  var divisor = encoding.length;
  var remainders = Array();
  var i, q, x, quotient;

  /* Convert to an array of 16-bit big-endian values, forming the dividend */
  var dividend = Array(input.length / 2);
  for(i = 0; i &lt; dividend.length; i++)
  {
    dividend[i] = (input.charCodeAt(i * 2) &lt;&lt; 8) | input.charCodeAt(i * 2 + 1);
  }

  /*
   * Repeatedly perform a long division. The binary array forms the dividend,
   * the length of the encoding is the divisor. Once computed, the quotient
   * forms the dividend for the next step. We stop when the dividend is zero.
   * All remainders are stored for later use.
   */
  while(dividend.length &gt; 0)
  {
    quotient = Array();
    x = 0;
    for(i = 0; i &lt; dividend.length; i++)
    {
      x = (x &lt;&lt; 16) + dividend[i];
      q = Math.floor(x / divisor);
      x -= q * divisor;
      if(quotient.length &gt; 0 || q &gt; 0)
	quotient[quotient.length] = q;
    }
    remainders[remainders.length] = x;
    dividend = quotient;
  }

  /* Convert the remainders to the output string */
  var output = &quot;&quot;;
  for(i = remainders.length - 1; i &gt;= 0; i--)
    output += encoding.charAt(remainders[i]);

  return output;
}

/*
 * Encode a string as utf-8.
 * For efficiency, this assumes the input is valid utf-16.
 */
function str2rstr_utf8(input)
{
  var output = &quot;&quot;;
  var i = -1;
  var x, y;

  while(++i &lt; input.length)
  {
    /* Decode utf-16 surrogate pairs */
    x = input.charCodeAt(i);
    y = i + 1 &lt; input.length ? input.charCodeAt(i + 1) : 0;
    if(0xD800 &lt;= x &amp;&amp; x &lt;= 0xDBFF &amp;&amp; 0xDC00 &lt;= y &amp;&amp; y &lt;= 0xDFFF)
    {
      x = 0x10000 + ((x &amp; 0x03FF) &lt;&lt; 10) + (y &amp; 0x03FF);
      i++;
    }

    /* Encode output as utf-8 */
    if(x &lt;= 0x7F)
      output += String.fromCharCode(x);
    else if(x &lt;= 0x7FF)
      output += String.fromCharCode(0xC0 | ((x &gt;&gt;&gt; 6 ) &amp; 0x1F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0xFFFF)
      output += String.fromCharCode(0xE0 | ((x &gt;&gt;&gt; 12) &amp; 0x0F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
    else if(x &lt;= 0x1FFFFF)
      output += String.fromCharCode(0xF0 | ((x &gt;&gt;&gt; 18) &amp; 0x07),
				    0x80 | ((x &gt;&gt;&gt; 12) &amp; 0x3F),
				    0x80 | ((x &gt;&gt;&gt; 6 ) &amp; 0x3F),
				    0x80 | ( x	       &amp; 0x3F));
  }
  return output;
}

/*
 * Encode a string as utf-16
 */
function str2rstr_utf16le(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode( input.charCodeAt(i)	      &amp; 0xFF,
				  (input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF);
  return output;
}

function str2rstr_utf16be(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length; i++)
    output += String.fromCharCode((input.charCodeAt(i) &gt;&gt;&gt; 8) &amp; 0xFF,
				   input.charCodeAt(i)	      &amp; 0xFF);
  return output;
}

/*
 * Convert a raw string to an array of little-endian words
 * Characters &gt;255 have their high-byte silently ignored.
 */
function rstr2binl(input)
{
  var output = Array(input.length &gt;&gt; 2);
  for(var i = 0; i &lt; output.length; i++)
    output[i] = 0;
  for(var i = 0; i &lt; input.length * 8; i += 8)
    output[i&gt;&gt;5] |= (input.charCodeAt(i / 8) &amp; 0xFF) &lt;&lt; (i%32);
  return output;
}

/*
 * Convert an array of little-endian words to a string
 */
function binl2rstr(input)
{
  var output = &quot;&quot;;
  for(var i = 0; i &lt; input.length * 32; i += 8)
    output += String.fromCharCode((input[i&gt;&gt;5] &gt;&gt;&gt; (i % 32)) &amp; 0xFF);
  return output;
}

/*
 * Calculate the MD5 of an array of little-endian words, and a bit length.
 */
function binl_md5(x, len)
{
  /* append padding */
  x[len &gt;&gt; 5] |= 0x80 &lt;&lt; ((len) % 32);
  x[(((len + 64) &gt;&gt;&gt; 9) &lt;&lt; 4) + 14] = len;

  var a =  1732584193;
  var b = -271733879;
  var c = -1732584194;
  var d =  271733878;

  for(var i = 0; i &lt; x.length; i += 16)
  {
    var olda = a;
    var oldb = b;
    var oldc = c;
    var oldd = d;

    a = md5_ff(a, b, c, d, x[i+ 0], 7 , -680876936);
    d = md5_ff(d, a, b, c, x[i+ 1], 12, -389564586);
    c = md5_ff(c, d, a, b, x[i+ 2], 17,	 606105819);
    b = md5_ff(b, c, d, a, x[i+ 3], 22, -1044525330);
    a = md5_ff(a, b, c, d, x[i+ 4], 7 , -176418897);
    d = md5_ff(d, a, b, c, x[i+ 5], 12,	 1200080426);
    c = md5_ff(c, d, a, b, x[i+ 6], 17, -1473231341);
    b = md5_ff(b, c, d, a, x[i+ 7], 22, -45705983);
    a = md5_ff(a, b, c, d, x[i+ 8], 7 ,	 1770035416);
    d = md5_ff(d, a, b, c, x[i+ 9], 12, -1958414417);
    c = md5_ff(c, d, a, b, x[i+10], 17, -42063);
    b = md5_ff(b, c, d, a, x[i+11], 22, -1990404162);
    a = md5_ff(a, b, c, d, x[i+12], 7 ,	 1804603682);
    d = md5_ff(d, a, b, c, x[i+13], 12, -40341101);
    c = md5_ff(c, d, a, b, x[i+14], 17, -1502002290);
    b = md5_ff(b, c, d, a, x[i+15], 22,	 1236535329);

    a = md5_gg(a, b, c, d, x[i+ 1], 5 , -165796510);
    d = md5_gg(d, a, b, c, x[i+ 6], 9 , -1069501632);
    c = md5_gg(c, d, a, b, x[i+11], 14,	 643717713);
    b = md5_gg(b, c, d, a, x[i+ 0], 20, -373897302);
    a = md5_gg(a, b, c, d, x[i+ 5], 5 , -701558691);
    d = md5_gg(d, a, b, c, x[i+10], 9 ,	 38016083);
    c = md5_gg(c, d, a, b, x[i+15], 14, -660478335);
    b = md5_gg(b, c, d, a, x[i+ 4], 20, -405537848);
    a = md5_gg(a, b, c, d, x[i+ 9], 5 ,	 568446438);
    d = md5_gg(d, a, b, c, x[i+14], 9 , -1019803690);
    c = md5_gg(c, d, a, b, x[i+ 3], 14, -187363961);
    b = md5_gg(b, c, d, a, x[i+ 8], 20,	 1163531501);
    a = md5_gg(a, b, c, d, x[i+13], 5 , -1444681467);
    d = md5_gg(d, a, b, c, x[i+ 2], 9 , -51403784);
    c = md5_gg(c, d, a, b, x[i+ 7], 14,	 1735328473);
    b = md5_gg(b, c, d, a, x[i+12], 20, -1926607734);

    a = md5_hh(a, b, c, d, x[i+ 5], 4 , -378558);
    d = md5_hh(d, a, b, c, x[i+ 8], 11, -2022574463);
    c = md5_hh(c, d, a, b, x[i+11], 16,	 1839030562);
    b = md5_hh(b, c, d, a, x[i+14], 23, -35309556);
    a = md5_hh(a, b, c, d, x[i+ 1], 4 , -1530992060);
    d = md5_hh(d, a, b, c, x[i+ 4], 11,	 1272893353);
    c = md5_hh(c, d, a, b, x[i+ 7], 16, -155497632);
    b = md5_hh(b, c, d, a, x[i+10], 23, -1094730640);
    a = md5_hh(a, b, c, d, x[i+13], 4 ,	 681279174);
    d = md5_hh(d, a, b, c, x[i+ 0], 11, -358537222);
    c = md5_hh(c, d, a, b, x[i+ 3], 16, -722521979);
    b = md5_hh(b, c, d, a, x[i+ 6], 23,	 76029189);
    a = md5_hh(a, b, c, d, x[i+ 9], 4 , -640364487);
    d = md5_hh(d, a, b, c, x[i+12], 11, -421815835);
    c = md5_hh(c, d, a, b, x[i+15], 16,	 530742520);
    b = md5_hh(b, c, d, a, x[i+ 2], 23, -995338651);

    a = md5_ii(a, b, c, d, x[i+ 0], 6 , -198630844);
    d = md5_ii(d, a, b, c, x[i+ 7], 10,	 1126891415);
    c = md5_ii(c, d, a, b, x[i+14], 15, -1416354905);
    b = md5_ii(b, c, d, a, x[i+ 5], 21, -57434055);
    a = md5_ii(a, b, c, d, x[i+12], 6 ,	 1700485571);
    d = md5_ii(d, a, b, c, x[i+ 3], 10, -1894986606);
    c = md5_ii(c, d, a, b, x[i+10], 15, -1051523);
    b = md5_ii(b, c, d, a, x[i+ 1], 21, -2054922799);
    a = md5_ii(a, b, c, d, x[i+ 8], 6 ,	 1873313359);
    d = md5_ii(d, a, b, c, x[i+15], 10, -30611744);
    c = md5_ii(c, d, a, b, x[i+ 6], 15, -1560198380);
    b = md5_ii(b, c, d, a, x[i+13], 21,	 1309151649);
    a = md5_ii(a, b, c, d, x[i+ 4], 6 , -145523070);
    d = md5_ii(d, a, b, c, x[i+11], 10, -1120210379);
    c = md5_ii(c, d, a, b, x[i+ 2], 15,	 718787259);
    b = md5_ii(b, c, d, a, x[i+ 9], 21, -343485551);

    a = safe_add(a, olda);
    b = safe_add(b, oldb);
    c = safe_add(c, oldc);
    d = safe_add(d, oldd);
  }
  return Array(a, b, c, d);
}

/*
 * These functions implement the four basic operations the algorithm uses.
 */
function md5_cmn(q, a, b, x, s, t)
{
  return safe_add(bit_rol(safe_add(safe_add(a, q), safe_add(x, t)), s),b);
}
function md5_ff(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; c) | ((~b) &amp; d), a, b, x, s, t);
}
function md5_gg(a, b, c, d, x, s, t)
{
  return md5_cmn((b &amp; d) | (c &amp; (~d)), a, b, x, s, t);
}
function md5_hh(a, b, c, d, x, s, t)
{
  return md5_cmn(b ^ c ^ d, a, b, x, s, t);
}
function md5_ii(a, b, c, d, x, s, t)
{
  return md5_cmn(c ^ (b | (~d)), a, b, x, s, t);
}

/*
 * Add integers, wrapping at 2^32. This uses 16-bit operations internally
 * to work around bugs in some JS interpreters.
 */
function safe_add(x, y)
{
  var lsw = (x &amp; 0xFFFF) + (y &amp; 0xFFFF);
  var msw = (x &gt;&gt; 16) + (y &gt;&gt; 16) + (lsw &gt;&gt; 16);
  return (msw &lt;&lt; 16) | (lsw &amp; 0xFFFF);
}

/*
 * Bitwise rotate a 32-bit number to the left.
 */
function bit_rol(num, cnt)
{
  return (num &lt;&lt; cnt) | (num &gt;&gt;&gt; (32 - cnt));
}
//&lt;/NOLITE&gt;
// ENDFILE: md5-2.2alpha.js
// STARTFILE: parensplit.js
//////////////////////////////////////////////////
// parenSplit

// String.prototype.parenSplit should do what ECMAscript says
// String.prototype.split does, interspersing paren matches between
// the split elements

if (String('abc'.split(/(b)/))!='a,b,c') {
	// broken String.split, e.g. konq, IE
	String.prototype.parenSplit=function (re) {
		re=nonGlobalRegex(re);
		var s=this;
		var m=re.exec(s);
		var ret=[];
		while (m &amp;&amp; s) {
			// without the following loop, we have
			// 'ab'.parenSplit(/a|(b)/) != 'ab'.split(/a|(b)/)
			for(var i=0; i&lt;m.length; ++i) {
				if (typeof m[i]=='undefined') m[i]='';
			}
			ret.push(s.substring(0,m.index));
			ret = ret.concat(m.slice(1));
			s=s.substring(m.index + m[0].length);
			m=re.exec(s);
		}
		ret.push(s);
		return ret;
	};
} else {
	String.prototype.parenSplit=function (re) { return this.split(re); };
	String.prototype.parenSplit.isNative=true;
}

function nonGlobalRegex(re) {
	var s=re.toString();
	flags='';
	for (var j=s.length; s.charAt(j) != '/'; --j) {
		if (s.charAt(j) != 'g') { flags += s.charAt(j); }
	}
	var t=s.substring(1,j);
	return RegExp(t,flags);
}
// ENDFILE: parensplit.js
// STARTFILE: tools.js
// IE madness with encoding
// ========================
//
// suppose throughout that the page is in utf8, like wikipedia
//
// if a is an anchor DOM element and a.href should consist of
//
// http://host.name.here/wiki/foo?bar=baz
//
// then IE gives foo as &quot;latin1-encoded&quot; utf8; we have foo = decode_utf8(decodeURI(foo_ie))
// but IE gives bar=baz correctly as plain utf8
//
// ---------------------------------
//
// IE's xmlhttp doesn't understand utf8 urls. Have to use encodeURI here.
//
// ---------------------------------
//
// summat else

// Source: http://aktuell.de.selfhtml.org/artikel/javascript/utf8b64/utf8.htm

//&lt;NOLITE&gt;
function encode_utf8(rohtext) {
	// dient der Normalisierung des Zeilenumbruchs
	rohtext = rohtext.replace(/\r\n/g,&quot;\n&quot;);
	var utftext = &quot;&quot;;
	for(var n=0; n&lt;rohtext.length; n++)
	{
		// ermitteln des Unicodes des  aktuellen Zeichens
		var c=rohtext.charCodeAt(n);
		// alle Zeichen von 0-127 =&gt; 1byte
		if (c&lt;128)
			utftext += String.fromCharCode(c);
		// alle Zeichen von 127 bis 2047 =&gt; 2byte
		else if((c&gt;127) &amp;&amp; (c&lt;2048)) {
			utftext += String.fromCharCode((c&gt;&gt;6)|192);
			utftext += String.fromCharCode((c&amp;63)|128);}
		// alle Zeichen von 2048 bis 66536 =&gt; 3byte
		else {
			utftext += String.fromCharCode((c&gt;&gt;12)|224);
			utftext += String.fromCharCode(((c&gt;&gt;6)&amp;63)|128);
			utftext += String.fromCharCode((c&amp;63)|128);}
	}
	return utftext;
}

function getJsObj(json) {
	try {
		var json_ret = eval('(' + json + ')');
	} catch (someError) {
		errlog('Something went wrong with getJsobj, json='+json);
		return 1;
	}
	if( json_ret['warnings'] ) {
		for( var w=0; w &lt; json_ret['warnings'].length; w++ ) {
			log( json_ret['warnings'][w]['*'] );
		}
	} else if ( json_ret['error'] ) {
		errlog( json_ret['error'].code + ': ' + json_ret['error'].info );
	}
	return json_ret;
}

function anyChild(obj) {
	for (var p in obj) {
		return obj[p];
	}
	return null;
}

//&lt;/NOLITE&gt;

function decode_utf8(utftext) {
	var plaintext = &quot;&quot;; var i=0, c=0, c1=0, c2=0;
	// while-Schleife, weil einige Zeichen uebersprungen werden
	while(i&lt;utftext.length)
	{
		c = utftext.charCodeAt(i);
		if (c&lt;128) {
			plaintext += String.fromCharCode(c);
			i++;}
		else if((c&gt;191) &amp;&amp; (c&lt;224)) {
			c2 = utftext.charCodeAt(i+1);
			plaintext += String.fromCharCode(((c&amp;31)&lt;&lt;6) | (c2&amp;63));
			i+=2;}
		else {
			c2 = utftext.charCodeAt(i+1); c3 = utftext.charCodeAt(i+2);
			plaintext += String.fromCharCode(((c&amp;15)&lt;&lt;12) | ((c2&amp;63)&lt;&lt;6) | (c3&amp;63));
			i+=3;}
	}
	return plaintext;
}


function upcaseFirst(str) {
	if (typeof str != typeof '' || str=='') return '';
	return str[0].toUpperCase() + str.substring(1);
}


function findInArray(arr, foo) {
	if (!arr || !arr.length) { return -1; }
	var len=arr.length;
	for (var i=0; i&lt;len; ++i) { if (arr[i]==foo) { return i; } }
	return -1;
}

function nextOne (array, value) {
	// NB if the array has two consecutive entries equal
	//    then this will loop on successive calls
	var i=findInArray(array, value);
	if (i&lt;0) { return null; }
	return array[i+1];
}

function literalizeRegex(str){
	return str.replace(RegExp('([-.|()\\\\+?*^${}\\[\\]])', 'g'), '\\$1');
}

String.prototype.entify=function() {
	//var shy='&amp;shy;';
	return this.split('&amp;').join('&amp;amp;').split('&lt;').join('&amp;lt;').split('&gt;').join('&amp;gt;'/*+shy*/).split('&quot;').join('&amp;quot;');
};

function findThis(array, value) {
	if (typeof array.length == 'undefined') { return null; }
	for (var i=0; i&lt;array.length; ++i) {
		if (array[i]==value) { return i; }
	}
	return null;
}

function removeNulls(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (list[i]) {
			ret.push(list[i]);
		}
	}
	return ret;
}
function joinPath(list) {
	return removeNulls(list).join('/');
}


function simplePrintf(str, subs) {
	if (!str || !subs) { return str; }
	var ret=[];
	var s=str.parenSplit(/(%s|\$[0-9]+)/);
	var i=0;
	do {
		ret.push(s.shift());
		if ( !s.length ) { break; }
		var cmd=s.shift();
		if (cmd == '%s') {
			if ( i &lt; subs.length ) { ret.push(subs[i]); } else { ret.push(cmd); }
			++i;
		} else {
			var j=parseInt( cmd.replace('$', ''), 10 ) - 1;
			if ( j &gt; -1 &amp;&amp; j &lt; subs.length ) { ret.push(subs[j]); } else { ret.push(cmd); }
		}
	} while (s.length &gt; 0);
	return ret.join('');
}

function max(a,b){return a&lt;b ? b : a;}
function min(a,b){return a&gt;b ? b : a;}

function isString(x) { return (typeof x === 'string' || x instanceof String); }
//function isNumber(x) { return (typeof x === 'number' || x instanceof Number); }
function isRegExp(x) { return x instanceof RegExp; }
function isArray (x) { return x instanceof Array; }
function isObject(x) { return x instanceof Object; }
function isFunction(x) {
    return !isRegExp(x) &amp;&amp; (typeof x === 'function' || x instanceof Function);
}

function repeatString(s,mult) {
	var ret='';
	for (var i=0; i&lt;mult; ++i) { ret += s; }
	return ret;
}

function zeroFill(s, min) {
	min = min || 2;
	var t=s.toString();
	return repeatString('0', min - t.length) + t;
}

function map(f, o) {
	if (isArray(o)) { return map_array(f,o); }
	return map_object(f,o);
}
function map_array(f,o) {
	var ret=[];
	for (var i=0; i&lt;o.length; ++i) {
		ret.push(f(o[i]));
	}
	return ret;
}
function map_object(f,o) {
	var ret={};
	for (var i in o) { ret[o]=f(o[i]); }
	return ret;
}
// ENDFILE: tools.js
// STARTFILE: dab.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Dab-fixing code
//


function retargetDab(newTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) {
	log('retargetDab: newTarget='+newTarget + ' oldTarget=' + oldTarget);
	return changeLinkTargetLink(
	{newTarget: newTarget,
			text: newTarget.split(' ').join('&amp;nbsp;'),
			hint: tprintf('disambigHint', [newTarget]),
			summary: simplePrintf(
				    getValueOf('popupFixDabsSummary'), [friendlyCurrentArticleName, newTarget ]),
			clickButton: 'wpDiff', minor: true, oldTarget: oldTarget,
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit});
}

function listLinks(wikitext, oldTarget, titleToEdit) {
	// mediawiki strips trailing spaces, so we do the same
	// testcase: //en.wikipedia.org/w/index.php?title=Radial&amp;oldid=97365633
	var reg=RegExp('\\[\\[([^|]*?) *(\\||\\]\\])', 'gi');
	var ret=[];
	var splitted=wikitext.parenSplit(reg);
	// ^[a-z]+ should match interwiki links, hopefully (case-insensitive)
	// and ^[a-z]* should match those and [[:Category...]] style links too
	var omitRegex=RegExp('^[a-z]*:|^[Ss]pecial:|^[Ii]mage|^[Cc]ategory');
	var friendlyCurrentArticleName= oldTarget.toString();
	var wikPos = getValueOf('popupDabWiktionary');

	for (var i=1; i&lt;splitted.length; i=i+3) {
		if (typeof splitted[i] == typeof 'string' &amp;&amp; splitted[i].length&gt;0 &amp;&amp; !omitRegex.test(splitted[i])) {
			ret.push( retargetDab(splitted[i], oldTarget, friendlyCurrentArticleName, titleToEdit) );
		} /* if */
	} /* for loop */

	ret = rmDupesFromSortedList(ret.sort());

	if (wikPos) {
		var wikTarget='wiktionary:' +
			friendlyCurrentArticleName.replace( RegExp('^(.+)\\s+[(][^)]+[)]\\s*$'), '$1' );

		var meth;
		if (wikPos.toLowerCase() == 'first') { meth = 'unshift'; }
		else { meth = 'push'; }

		ret[meth]( retargetDab(wikTarget, oldTarget, friendlyCurrentArticleName, titleToEdit) );
	}

	ret.push(changeLinkTargetLink(
	{ newTarget: null,
			text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this disambig page from this article&quot;),
			clickButton: &quot;wpDiff&quot;, oldTarget: oldTarget,
			summary: simplePrintf(getValueOf('popupRmDabLinkSummary'), [friendlyCurrentArticleName]),
			watch: getValueOf('popupWatchDisambiggedPages'),
			title: titleToEdit
			}));
	return ret;
}

function rmDupesFromSortedList(list) {
	var ret=[];
	for (var i=0; i&lt;list.length; ++i) {
		if (ret.length===0 || list[i]!=ret[ret.length-1]) { ret.push(list[i]); }
	}
	return ret;
}

function makeFixDab(data, navpop) {
	// grab title from parent popup if there is one; default exists in changeLinkTargetLink
	var titleToEdit=(navpop.parentPopup &amp;&amp; navpop.parentPopup.article.toString());
	var list=listLinks(data, navpop.originalArticle, titleToEdit);
	if (list.length===0) { log('listLinks returned empty list'); return null; }
	var html='&lt;hr&gt;' + popupString('Click to disambiguate this link to:') + '&lt;br&gt;';
	html+=list.join(', ');
	return html;
}


function makeFixDabs(wikiText, navpop) {
	if (getValueOf('popupFixDabs') &amp;&amp; isDisambig(wikiText, navpop.article) &amp;&amp;
	    Title.fromURL(location.href).namespaceId() != pg.nsSpecialId &amp;&amp;
	    navpop.article.talkPage() ) {
		setPopupHTML(makeFixDab(wikiText, navpop), 'popupFixDab', navpop.idNumber);
	}
}

function popupRedlinkHTML(article) {
	return changeLinkTargetLink(
		{ newTarget: null, text: popupString('remove this link').split(' ').join('&amp;nbsp;'),
			hint: popupString(&quot;remove all links to this page from this article&quot;),
			clickButton: &quot;wpDiff&quot;,
			oldTarget: article.toString(),
			summary: simplePrintf(getValueOf('popupRedlinkSummary'), [article.toString()])});
}
//&lt;/NOLITE&gt;
// ENDFILE: dab.js
// STARTFILE: htmloutput.js

function appendPopupContent(obj, elementId, popupId, onSuccess) {
	return setPopupHTML(obj, elementId, popupId, onSuccess, true);
}

// this has to use a timer loop as we don't know if the DOM element exists when we want to set the text
function setPopupHTML (str, elementId, popupId, onSuccess, append) {
	if (elementId=='popupPreview') {
	}
	if (typeof popupId === 'undefined') {
		//console.error('popupId is not defined in setPopupHTML, html='+str.substring(0,100));
		popupId = pg.idNumber;
	}

	var popupElement=document.getElementById(elementId+popupId);
	if (popupElement) {
		if (!append) { popupElement.innerHTML=''; }
		if (isString(str)) {
			popupElement.innerHTML+=str;
		} else {
			popupElement.appendChild(str);
		}
		if (onSuccess) { onSuccess(); }
		setTimeout(checkPopupPosition, 100);
		return true;
	} else {
		// call this function again in a little while...
		setTimeout(function(){
				setPopupHTML(str,elementId,popupId,onSuccess);
			}, 600);
	}
	return null;
}

//&lt;NOLITE&gt;
function setPopupTrailer(str,id) {return setPopupHTML(str, 'popupData', id);}
//&lt;/NOLITE&gt;


function fillEmptySpans(args) { return fillEmptySpans2(args); }

// args.navpopup is mandatory
// optional: args.redir, args.redirTarget
// FIXME: ye gods, this is ugly stuff
function fillEmptySpans2(args) { // if redir is present and true then redirTarget is mandatory
	var redir=true;
	if (typeof args != 'object' || typeof args.redir == 'undefined' || !args.redir) { redir=false; }
	var a=args.navpopup.parentAnchor;

	var article, hint=null, oldid=null, params={};
	if (redir &amp;&amp; typeof args.redirTarget == typeof {}) {
		article=args.redirTarget;
		//hint=article.hintValue();
	} else {
		article=(new Title()).fromAnchor(a);
		hint=a.originalTitle || article.hintValue();
		params=parseParams(a.href);
		oldid=(getValueOf('popupHistoricalLinks')) ? params.oldid : null;
		rcid=params.rcid;
	}
	var x={ article:article, hint: hint, oldid: oldid, rcid: rcid, navpop:args.navpopup, params:params };

	var structure=pg.structures[getValueOf('popupStructure')];
	if (typeof structure != 'object') {
		setPopupHTML('popupError', 'Unknown structure (this should never happen): '+
			     pg.option.popupStructure, args.navpopup.idNumber);
		return;
	}
	var spans=flatten(pg.misc.layout);
	var numspans = spans.length;
	var redirs=pg.misc.redirSpans;

	for (var i=0; i&lt;numspans; ++i) {
		var f=findThis(redirs, spans[i]);
		//log('redir='+redir+', f='+f+', spans[i]='+spans[i]);
		if ( (f!==null &amp;&amp; !redir) || (f===null &amp;&amp; redir) ) {
			//log('skipping this set of the loop');
			continue;
		}
		var structurefn=structure[spans[i]];
		var setfn = setPopupHTML;
		if (getValueOf('popupActiveNavlinks') &amp;&amp; 
		    (spans[i].indexOf('popupTopLinks')==0 || spans[i].indexOf('popupRedirTopLinks')==0)
			    ) {
			setfn = setPopupTipsAndHTML;
		}
		switch (typeof structurefn) {
		case 'function':
			//log('running '+spans[i]+'({article:'+x.article+', hint:'+x.hint+', oldid: '+x.oldid+'})');
			setfn(structurefn(x), spans[i], args.navpopup.idNumber);
			break;
		case 'string':
			setfn(structurefn, spans[i], args.navpopup.idNumber);
			break;
		default:
			errlog('unknown thing with label '+spans[i]);
			break;
		}
	}
}

// flatten an array
function flatten(list, start) {
	var ret=[];
	if (typeof start == 'undefined') { start=0; }
	for (var i=start; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof []) {
			return ret.concat(flatten(list[i])).concat(flatten(list, i+1));
		}
		else { ret.push(list[i]); }
	}
	return ret;
}

// Generate html for whole popup
function popupHTML (a) {
	getValueOf('popupStructure');
	var structure=pg.structures[pg.option.popupStructure];
	if (typeof structure != 'object') {
		//return 'Unknown structure: '+pg.option.popupStructure;
		// override user choice
		pg.option.popupStructure=pg.optionDefault.popupStructure;
		return popupHTML(a);
	}
	if (typeof structure.popupLayout != 'function') { return 'Bad layout'; }
	pg.misc.layout=structure.popupLayout();
	if (typeof structure.popupRedirSpans == 'function') { pg.misc.redirSpans=structure.popupRedirSpans(); }
	else { pg.misc.redirSpans=[]; }
	return makeEmptySpans(pg.misc.layout, a.navpopup);
}

function makeEmptySpans (list, navpop) {
	var ret='';
	for (var i=0; i&lt;list.length; ++i) {
		if (typeof list[i] == typeof '') {
		    ret += emptySpanHTML(list[i], navpop.idNumber, 'div');
		} else if (typeof list[i] == typeof [] &amp;&amp; list[i].length &gt; 0 ) {
			ret = ret.parenSplit(RegExp('(&lt;/[^&gt;]*?&gt;$)')).join(makeEmptySpans(list[i], navpop));
		} else if (typeof list[i] == typeof {} &amp;&amp; list[i].nodeType ) {
			ret += emptySpanHTML(list[i].name, navpop.idNumber, list[i].nodeType);
		}
	}
	return ret;
}


function emptySpanHTML(name, id, tag, classname) {
	tag = tag || 'span';
	if (!classname) { classname = emptySpanHTML.classAliases[name]; }
	classname = classname || name;
	if (name == getValueOf('popupDragHandle')) { classname += ' popupDragHandle'; }
	return simplePrintf('&lt;%s id=&quot;%s&quot; class=&quot;%s&quot;&gt;&lt;/%s&gt;', [tag, name + id, classname, tag]);
}
emptySpanHTML.classAliases={ 'popupSecondPreview': 'popupPreview' };

// generate html for popup image
// &lt;a id=&quot;popupImageLinkn&quot;&gt;&lt;img id=&quot;popupImagen&quot;&gt;
// where n=idNumber
function imageHTML(article, idNumber) {
	return simplePrintf('&lt;a id=&quot;popupImageLink$1&quot;&gt;' +
			    '&lt;img align=&quot;right&quot; valign=&quot;top&quot; id=&quot;popupImg$1&quot; style=&quot;display: none;&quot;&gt;&lt;/img&gt;' +
			    '&lt;/a&gt;', [ idNumber ]);
}

function popTipsSoonFn(id, when, popData) {
	when || ( when=250 );
	var popTips=function(){ setupTooltips(document.getElementById(id), false, true, popData); };
	return function() { setTimeout( popTips, when, popData ); };
}

function setPopupTipsAndHTML(html, divname, idnumber, popData) {
	setPopupHTML(html, divname, idnumber,
		     getValueOf('popupSubpopups') ? 
		     popTipsSoonFn(divname + idnumber, null, popData) : 
		     null);
}
// ENDFILE: htmloutput.js
// STARTFILE: mouseout.js
//////////////////////////////////////////////////
// fuzzy checks

function fuzzyCursorOffMenus(x,y, fuzz, parent) {
	if (!parent) { return null; }
	var uls=parent.getElementsByTagName('ul');
	for (var i=0; i&lt;uls.length; ++i) {
		if (uls[i].className=='popup_menu') {
			if (uls[i].offsetWidth &gt; 0) return false;
		} // else {document.title+='.';}
	}
	return true;
}

function checkPopupPosition () { // stop the popup running off the right of the screen
	// FIXME avoid pg.current.link
	pg.current.link &amp;&amp; pg.current.link.navpopup &amp;&amp;
	    pg.current.link.navpopup.limitHorizontalPosition();
}

function mouseOutWikiLink () {
	if (!window.popupsReady || !window.popupsReady()) { return; }
	//console ('mouseOutWikiLink');
	var a=this;
	if (a.navpopup==null) return;
	if ( ! a.navpopup.isVisible() ) {
		a.navpopup.banish();
		return;
	}
        restoreTitle(a);
	Navpopup.tracker.addHook(posCheckerHook(a.navpopup));
}

function posCheckerHook(navpop) {
	return function() {
		if (!navpop.isVisible()) { return true; /* remove this hook */ }
		if (Navpopup.tracker.dirty) {
		    return false;
		}
		var x=Navpopup.tracker.x, y=Navpopup.tracker.y;
		var mouseOverNavpop = navpop.isWithin(x,y,navpop.fuzz, navpop.mainDiv) ||
		    !fuzzyCursorOffMenus(x,y,navpop.fuzz, navpop.mainDiv);

		// FIXME it'd be prettier to do this internal to the Navpopup objects
		var t=getValueOf('popupHideDelay');
		if (t) { t = t * 1000; }
		if (!t) {
			if(!mouseOverNavpop) {
			    navpop.banish();
			    return true; /* remove this hook */
			}
			return false;
		}
		// we have a hide delay set
		var d=+(new Date());
		if ( !navpop.mouseLeavingTime ) {
			navpop.mouseLeavingTime = d;
			return false;
		}
		if ( mouseOverNavpop ) {
			navpop.mouseLeavingTime=null;
			return false;
		}
		if (d - navpop.mouseLeavingTime &gt; t) {
			navpop.mouseLeavingTime=null;
			navpop.banish(); return true; /* remove this hook */
		}
		return false;
	};
}

function runStopPopupTimer(navpop) {
	// at this point, we should have left the link but remain within the popup
	// so we call this function again until we leave the popup.
	if (!navpop.stopPopupTimer) {
		navpop.stopPopupTimer=setInterval(posCheckerHook(navpop), 500);
		navpop.addHook(function(){clearInterval(navpop.stopPopupTimer);},
			       'hide', 'before');
	}
}
// ENDFILE: mouseout.js
// STARTFILE: previewmaker.js
/**
   @fileoverview
   Defines the {@link Previewmaker} object, which generates short previews from wiki markup.
*/

/**
   Creates a new Previewmaker
   @constructor
   @class The Previewmaker class. Use an instance of this to generate short previews from Wikitext.
   @param {String} wikiText The Wikitext source of the page we wish to preview.
   @param {String} baseUrl The url we should prepend when creating relative urls.
   @param {Navpopup} owner The navpop associated to this preview generator
*/
function Previewmaker(wikiText, baseUrl, owner) {
	/** The wikitext which is manipulated to generate the preview. */
	this.originalData=wikiText;
	this.setData();
	this.baseUrl=baseUrl;
	this.owner=owner;
	this.maxCharacters=getValueOf('popupMaxPreviewCharacters');
	this.maxSentences=getValueOf('popupMaxPreviewSentences');
}
Previewmaker.prototype.setData=function() {
	var maxSize=max(10000, 2*this.maxCharacters);
	this.data=this.originalData.substring(0,maxSize);
};
/** Remove HTML comments
    @private
*/
Previewmaker.prototype.killComments = function () {
	// this also kills one trailing newline, eg [[diamyo]]
	this.data=this.data.replace(RegExp('&lt;!--[\\s\\S]*?--&gt;\\n?', 'g'), ''); 
};
/**
   @private
*/
Previewmaker.prototype.killDivs = function () {
	// say goodbye, divs (can be nested, so use * not *?)
	this.data=this.data.replace(RegExp('&lt; *div[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *div *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killGalleries = function () {
	this.data=this.data.replace(RegExp('&lt; *gallery[^&gt;]* *&gt;[\\s\\S]*?&lt; */ *gallery *&gt;',
					   'gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.kill = function(opening, closing, subopening, subclosing, repl) {
	var oldk=this.data;
	var k=this.killStuff(this.data, opening, closing, subopening, subclosing, repl);
	while (k.length &lt; oldk.length) {
		oldk=k;
		k=this.killStuff(k, opening, closing, subopening, subclosing, repl);
	}
	this.data=k;
};
/**
   @private
*/
Previewmaker.prototype.killStuff = function (txt, opening, closing, subopening, subclosing, repl) {
	var op=this.makeRegexp(opening);
	var cl=this.makeRegexp(closing, '^');
	var sb=subopening ? this.makeRegexp(subopening, '^') : null;
	var sc=subclosing ? this.makeRegexp(subclosing, '^') : cl;
	if (!op || !cl) {
	    alert('Navigation Popups error: op or cl is null! something is wrong.');
	    return;
	}
	if (!op.test(txt)) { return txt; }
	var ret='';
	var opResult = op.exec(txt);
	ret = txt.substring(0,opResult.index);
	txt=txt.substring(opResult.index+opResult[0].length);
	var depth = 1;
	while (txt.length &gt; 0) {
		var removal=0;
		if (depth==1 &amp;&amp; cl.test(txt)) {
			depth--;
			removal=cl.exec(txt)[0].length;
		} else if (depth &gt; 1 &amp;&amp; sc.test(txt)) {
			depth--;
			removal=sc.exec(txt)[0].length;
		}else if (sb &amp;&amp; sb.test(txt)) {
			depth++;
			removal=sb.exec(txt)[0].length;
		}
		if ( !removal ) { removal = 1; }
		txt=txt.substring(removal);
		if (depth==0) { break; }
	}
	return ret + (repl || '') + txt;
};
/**
   @private
*/
Previewmaker.prototype.makeRegexp = function (x, prefix, suffix) {
	prefix = prefix || '';
	suffix = suffix || '';
	var reStr='';
	var flags='';
	if (isString(x)) {
		reStr=prefix + literalizeRegex(x) + suffix;
	} else if (isRegExp(x)) {
		var s=x.toString().substring(1);
		var sp=s.split('/');
		flags=sp[sp.length-1];
		sp[sp.length-1]='';
		s=sp.join('/');
		s=s.substring(0,s.length-1);
		reStr= prefix + s + suffix;
	} else {
		log ('makeRegexp failed');
	}

	log ('makeRegexp: got reStr=' + reStr + ', flags=' + flags);
	return RegExp(reStr, flags);
};
/**
   @private
*/
Previewmaker.prototype.killBoxTemplates = function () {

	// taxobox removal... in fact, there's a saudiprincebox_begin, so let's be more general
	// also, have float_begin, ... float_end
	this.kill(RegExp('[{][{][^{}\\s|]*?(float|box)[_ ](begin|start)', 'i'),	/[}][}]\s*/, '{{');

	// infoboxes etc
	// from [[User:Zyxw/popups.js]]: kill frames too
	this.kill(RegExp('[{][{][^{}\\s|]*?(infobox|elementbox|frame)[_ ]', 'i'), /[}][}]\s*/, '{{');

};
/**
   @private
*/
Previewmaker.prototype.killTemplates = function () {
	this.kill('{{', '}}', '{', '}', ' ');
};
/**
   @private
*/
Previewmaker.prototype.killTables = function () {
	// tables are bad, too
	// this can be slow, but it's an inprovement over a browser hang
	// torture test: [[Comparison_of_Intel_Central_Processing_Units]]
	this.kill('{|', /[|]}\s*/, '{|');
	this.kill(/&lt;table.*?&gt;/i, /&lt;\/table.*?&gt;/i, /&lt;table.*?&gt;/i);
	// remove lines starting with a pipe for the hell of it (?)
	this.data=this.data.replace(RegExp('^[|].*$', 'mg'), '');
};
/**
   @private
*/
Previewmaker.prototype.killImages = function () {
	var forbiddenNamespaceAliases = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=pg.nsImageId &amp;&amp; _namespaceId!=pg.nsCategoryId) return;
		forbiddenNamespaceAliases.push(_localizedNamespaceLc.split(' ').join('[ _]')); //todo: escape regexp fragments!
	});
	
	// images and categories are a nono
	this.kill(RegExp('[[][[]\\s*(' + forbiddenNamespaceAliases.join('|') + ')\\s*:', 'i'),
		  /\]\]\s*/, '[', ']');
};
/**
   @private
*/
Previewmaker.prototype.killHTML = function () {
	// kill &lt;ref ...&gt;...&lt;/ref&gt;
	this.kill(/&lt;ref\b[^/&gt;]*?&gt;/i, /&lt;\/ref&gt;/i);

	// let's also delete entire lines starting with &lt;. it's worth a try.
	this.data=this.data.replace(RegExp('(^|\\n) *&lt;.*', 'g'), '\n');

	// and those pesky html tags, but not &lt;nowiki&gt; or &lt;blockquote&gt;
	var splitted=this.data.parenSplit(/(&lt;.*?&gt;)/);
	var len=splitted.length;
	for (var i=1; i&lt;len; i=i+2) {
		switch (splitted[i]) {
		case '&lt;nowiki&gt;':
		case '&lt;/nowiki&gt;':
				// &lt;nowiki&gt;
			break;
		default:
			if (! /^&lt; *\/? *blockquote\b/i.test(splitted[i])) {
				splitted[i]='';
			}
		}
	}
	this.data=splitted.join('');
};
/**
   @private
*/
Previewmaker.prototype.killChunks = function() { // heuristics alert
	// chunks of italic text? you crazy, man?
	var italicChunkRegex=new RegExp
	(&quot;((^|\\n)\\s*:*\\s*''[^']([^']|'''|'[^']){20}(.|\\n[^\\n])*''[.!?\\s]*\\n)+&quot;, 'g');
	// keep stuff separated, though, so stick in \n (fixes [[Union Jack]]?
	this.data=this.data.replace(italicChunkRegex, '\n');
};
/**
   @private
*/
Previewmaker.prototype.mopup = function () {
	// we simply *can't* be doing with horizontal rules right now
	this.data=this.data.replace(RegExp('^-{4,}','mg'),'');

	// no indented lines
	this.data=this.data.replace(RegExp('(^|\\n) *:[^\\n]*','g'), '');

	// replace __TOC__, __NOTOC__ and whatever else there is
	// this'll probably do
	this.data=this.data.replace(RegExp('^__[A-Z_]*__ *$', 'gmi'),'');
};
/**
   @private
*/
Previewmaker.prototype.firstBit = function () {
	// dont't be givin' me no subsequent paragraphs, you hear me?
	/// first we &quot;normalize&quot; section headings, removing whitespace after, adding before
	var d=this.data;

	if (getValueOf('popupPreviewCutHeadings')) {
		this.data=this.data.replace(RegExp('\\s*(==+[^=]*==+)\\s*', 'g'), '\n\n$1 ');
		/// then we want to get rid of paragraph breaks whose text ends badly
		this.data=this.data.replace(RegExp('([:;]) *\\n{2,}', 'g'), '$1\n');

		this.data=this.data.replace(RegExp('^[\\s\\n]*'), '');
		stuff=(RegExp('^([^\\n]|\\n[^\\n\\s])*')).exec(this.data);
		if (stuff) { d = stuff[0]; }
		if (!getValueOf('popupPreviewFirstParOnly')) { d = this.data; }

		/// now put \n\n after sections so that bullets and numbered lists work
		d=d.replace(RegExp('(==+[^=]*==+)\\s*', 'g'), '$1\n\n');
	}


	// superfluous sentences are RIGHT OUT.
	// note: exactly 1 set of parens here needed to make the slice work
	d = d.parenSplit(RegExp('([!?.]+[&quot;'+&quot;'&quot;+']*\\s)','g'));
	// leading space is bad, mmkay?
	d[0]=d[0].replace(RegExp('^\\s*'), '');

	var notSentenceEnds=RegExp('([^.][a-z][.] *[a-z]|etc|sic|Dr|Mr|Mrs|Ms|St|no|op|cit|\\[[^\\]]*|\\s[A-Zvclm])$', 'i');
	d = this.fixSentenceEnds(d, notSentenceEnds);

	this.fullLength=d.join('').length;
	var maxChars=getValueOf('popupMaxPreviewCharacters') + this.extraCharacters;
	var n=this.maxSentences;
	var dd=this.firstSentences(d,n); 

	do {
		dd=this.firstSentences(d,n); --n;
	} while ( dd.length &gt; this.maxCharacters &amp;&amp; n != 0 );

	this.data = dd;
};
/**
   @private
*/
Previewmaker.prototype.fixSentenceEnds = function(strs, reg) {
	// take an array of strings, strs
	// join strs[i] to strs[i+1] &amp; strs[i+2] if strs[i] matches regex reg

	var abbrevRe=/\b[a-z][^a-z]*$/i;

	for (var i=0; i&lt;strs.length-2; ++i) {
		if (reg.test(strs[i])) {
			a=[];
			for (var j=0; j&lt;strs.length; ++j) {
				if (j&lt;i)   a[j]=strs[j];
				if (j==i)  a[i]=strs[i]+strs[i+1]+strs[i+2];
				if (j&gt;i+2) a[j-2]=strs[j];
			}
			return this.fixSentenceEnds(a,reg);
		}
		// BUGGY STUFF - trying to fix up [[S. C. Johnson &amp; Son]] preview
		if (false &amp;&amp; abbrevRe.test(strs[i])) {
			var j=i, buf='';
			do {
				buf=buf+strs[i]+strs[i+1];
				i=i+2;
			} while (i&lt;strs.length-2 &amp;&amp; abbrevRe.test(strs[i]));
			strs[i]=buf+strs[i];
			var a=(j?strs.slice(0,j-1):[]).concat(strs.slice(i));
			return this.fixSentenceEnds(a,reg);
		}
	}
	return strs;
};
/**
   @private
*/
Previewmaker.prototype.firstSentences = function(strs, howmany) {
	var t=strs.slice(0, 2*howmany);
	return t.join('');
};
/**
   @private
*/
Previewmaker.prototype.killBadWhitespace = function() {
	// also cleans up isolated '''', eg [[Suntory Sungoliath]]
	this.data=this.data.replace(RegExp('^ *\'+ *$', 'gm'), '');
};
/**
   Runs the various methods to generate the preview.
   The preview is stored in the &lt;code&gt;html&lt;/html&gt; field.
   @private
*/
Previewmaker.prototype.makePreview = function() {
	if (this.owner.article.namespaceId()!=pg.nsTemplateId &amp;&amp;
				this.owner.article.namespaceId()!=pg.nsImageId ) {
		this.killComments();
		this.killDivs();
		this.killGalleries();
		this.killBoxTemplates();

		if (getValueOf('popupPreviewKillTemplates')) {
			this.killTemplates();
		} else {
			this.killMultilineTemplates();
		}
		this.killTables();
		this.killImages();
		this.killHTML();
		this.killChunks();
		this.mopup();

		this.firstBit();
		this.killBadWhitespace();
	}
	else
	{
		this.killHTML();
	}
	this.html=wiki2html(this.data, this.baseUrl); // needs livepreview
	this.fixHTML();
	this.stripLongTemplates();
};
/**
   @private
*/
Previewmaker.prototype.esWiki2HtmlPart = function(data) {
  var reLinks = /(?:\[\[([^|\]]*)(?:\|([^|\]]*))*]]([a-z]*))/gi; //match a wikilink
  reLinks.lastIndex = 0; //reset regex

  var match;
  var result = &quot;&quot;;
  var postfixIndex = 0;
  while ((match = reLinks.exec(data)) != null) //match all wikilinks
  {
    //FIXME: the way that link is built here isn't perfect. It is clickable, but popups preview won't recognize it in some cases.
    result += mw.html.escape(data.substring(postfixIndex, match.index)) + 
              '&lt;a href=&quot;'+Insta.conf.paths.articles+mw.html.escape(match[1])+'&quot;&gt;'+mw.html.escape((match[2]?match[2]:match[1])+match[3])+&quot;&lt;/a&gt;&quot;;
    postfixIndex = reLinks.lastIndex;
  }
  //append the rest
  result += mw.html.escape(data.substring(postfixIndex));
  
  return result;
};
Previewmaker.prototype.editSummaryPreview=function() {
	var reAes   = /\/\* *(.*?) *\*\//g; //match the first section marker
	reAes.lastIndex = 0; //reset regex
	
	var match;
	
	match = reAes.exec(this.data);
	if (match)
	{
		//we have a section link. Split it, process it, combine it.
		var prefix = this.data.substring(0,match.index-1);
		var section = match[1];
		var postfix = this.data.substring(reAes.lastIndex);
		
		var start = &quot;&lt;span class='autocomment'&gt;&quot;;
		var end = &quot;&lt;/span&gt;&quot;;
		if (prefix.length&gt;0) start = this.esWiki2HtmlPart(prefix) + &quot; &quot; + start + &quot;- &quot;;
		if (postfix.length&gt;0) end = &quot;: &quot; + end + this.esWiki2HtmlPart(postfix);
		

		var t=new Title().fromURL(this.baseUrl);
		t.anchorFromUtf(section);
		var sectionLink = Insta.conf.paths.articles + mw.html.escape(t.toString(true)) + '#' + mw.html.escape(t.anchor);
		return start + '&lt;a href=&quot;'+sectionLink+'&quot;&gt;&amp;rarr;&lt;/a&gt; '+mw.html.escape(section) + end;
	}
	
	//else there's no section link, htmlify the whole thing.
	return this.esWiki2HtmlPart(this.data);
};

//&lt;NOLITE&gt;
/** Test function for debugging preview problems one step at a time.
 */
function previewSteps(txt) {
	try {
		txt=txt || document.editform.wpTextbox1.value;
	} catch (err) {
		if (pg.cache.pages.length &gt; 0) {
			txt=pg.cache.pages[pg.cache.pages.length-1].data;
		} else {
			alert('provide text or use an edit page');
		}
	}
	txt=txt.substring(0,10000);
	var base=pg.wiki.articlebase + Title.fromURL(document.location.href).urlString();
	var p=new Previewmaker(txt, base, pg.current.link.navpopup);
	if (this.owner.article.namespaceId() != pg.nsTemplateId) {
		p.killComments(); if (!confirm('done killComments(). Continue?\n---\n' + p.data)) { return; }
		p.killDivs(); if (!confirm('done killDivs(). Continue?\n---\n' + p.data)) { return; }
		p.killGalleries(); if (!confirm('done killGalleries(). Continue?\n---\n' + p.data)) { return; }
		p.killBoxTemplates(); if (!confirm('done killBoxTemplates(). Continue?\n---\n' + p.data)) { return; }

		if (getValueOf('popupPreviewKillTemplates')) {
			p.killTemplates(); if (!confirm('done killTemplates(). Continue?\n---\n' + p.data)) { return; }
		} else {
			p.killMultilineTemplates(); if (!confirm('done killMultilineTemplates(). Continue?\n---\n' + p.data)) { return; }
		}

		p.killTables(); if (!confirm('done killTables(). Continue?\n---\n' + p.data)) { return; }
		p.killImages(); if (!confirm('done killImages(). Continue?\n---\n' + p.data)) { return; }
		p.killHTML(); if (!confirm('done killHTML(). Continue?\n---\n' + p.data)) { return; }
		p.killChunks(); if (!confirm('done killChunks(). Continue?\n---\n' + p.data)) { return; }
		p.mopup(); if (!confirm('done mopup(). Continue?\n---\n' + p.data)) { return; }

		p.firstBit(); if (!confirm('done firstBit(). Continue?\n---\n' + p.data)) { return; }
		p.killBadWhitespace(); if (!confirm('done killBadWhitespace(). Continue?\n---\n' + p.data)) { return; }
	}

	p.html=wiki2html(p.data, base); // needs livepreview
	p.fixHTML(); if (!confirm('done fixHTML(). Continue?\n---\n' + p.html)) { return; }
	p.stripLongTemplates(); if (!confirm('done stripLongTemplates(). Continue?\n---\n' + p.html)) { return; }
	alert('finished preview - end result follows.\n---\n' + p.html);
}
//&lt;/NOLITE&gt;

/**
   Works around a quoting bug in livepreview.
   &lt;code&gt;wiki2html('[[Foo\'s &quot;bar&quot;]]')&lt;/code&gt; gives @literal{&lt;a href='Foo's &quot;bar&quot;'&gt;}
   which doesn't do very well. We change this into @literal{&lt;a href=&quot;Foo's %22bar%22&quot;&gt;}
   @private
*/
Previewmaker.prototype.fixHTML = function() {
	if(!this.html) return;
	// all links seem to have potential issues with quotation marks
	var splitted=this.html.parenSplit(/href='([^&gt;]*)'/g);
	var ret='';
	for (var i=0; i&lt;splitted.length; ++i) {
		if(i%2==0) { ret += splitted[i]; continue; }
		if(i%2==1) { ret += 'href=&quot;' + splitted[i].split('&quot;').join('%22') + '&quot;'; }
	}
	// fix question marks in wiki links
	// maybe this'll break some stuff :-(
	ret=ret.replace(RegExp('\(&lt;a href=&quot;' + pg.wiki.articlePath + '/[^&quot;]*\)[?]\(.*?&quot;\)', 'g'), '$1%3F$2');
	// FIXME fix up % too
	this.html=ret;
};
/**
   Generates the preview and displays it in the current popup.

   Does nothing if the generated preview is invalid or consists of whitespace only.
   Also activates wikilinks in the preview for subpopups if the popupSubpopups option is true.
*/
Previewmaker.prototype.showPreview = function () {
	this.makePreview();
	if (typeof this.html != typeof '') return;
	if (RegExp('^\\s*$').test(this.html)) return;
	setPopupHTML('&lt;hr&gt;', 'popupPrePreviewSep', this.owner.idNumber);
	setPopupTipsAndHTML(this.html, 'popupPreview', this.owner.idNumber, { owner: this.owner });
	var more = (this.fullLength &gt; this.data.length) ? this.moreLink() : '';
	setPopupHTML(more, 'popupPreviewMore', this.owner.idNumber);
};
/**
   @private
*/
Previewmaker.prototype.moreLink=function() {
	var a=document.createElement('a');
	a.className='popupMoreLink';
	a.innerHTML=popupString('more...');
	var savedThis=this;
	a.onclick=function() {
		savedThis.maxCharacters+=2000;
		savedThis.maxSentences+=20;
		savedThis.setData();
		savedThis.showPreview();
	}
	return a;
}

/**
   @private
*/
Previewmaker.prototype.stripLongTemplates = function() {
	// operates on the HTML!
	this.html=this.html.replace(RegExp('^.{0,1000}[{][{][^}]*?(&lt;(p|br)( /)?&gt;\\s*){2,}([^{}]*?[}][}])?', 'gi'), '');
	this.html=this.html.split('\n').join(' '); // workaround for &lt;pre&gt; templates
	this.html=this.html.replace(RegExp('[{][{][^}]*&lt;pre&gt;[^}]*[}][}]','gi'), '');
};
/**
   @private
*/
Previewmaker.prototype.killMultilineTemplates = function() {
	this.kill('{{{', '}}}');
	this.kill(RegExp('\\s*[{][{][^{}]*\\n'), '}}', '{{');
};
// ENDFILE: previewmaker.js
// STARTFILE: querypreview.js
function loadAPIPreview(queryType, article, navpop) {
	var art=new Title(article).urlString();
	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;';
	var htmlGenerator=function(a,d){alert('invalid html generator');};
	switch (queryType) {
	case 'history':
		url += 'meta=userinfo&amp;uiprop=options&amp;titles=' + art + '&amp;prop=revisions&amp;rvlimit=' +
			getValueOf('popupHistoryPreviewLimit');
		htmlGenerator=APIhistoryPreviewHTML;
		break;
	case 'category':
		url += 'list=categorymembers&amp;rawcontinue=&amp;cmtitle=' + art;
		htmlGenerator=APIcategoryPreviewHTML;
		break;
	case 'userinfo':
	  var username = new Title( article ).userName();
		var usernameart = encodeURIComponent( username );
		if (pg.re.ipUser.test(username)) {
			url += 'list=blocks&amp;bkprop=range&amp;bkip=' + usernameart;
		} else {
			url += 'list=users&amp;usprop=blockinfo|groups|editcount|registration&amp;ususers=' + usernameart + &quot;&amp;meta=globaluserinfo&amp;guiprop=groups|unattached&amp;guiuser=&quot;+ usernameart;
		}
		htmlGenerator=APIuserInfoPreviewHTML;
		break;
	case 'contribs':
		var usernameart = encodeURIComponent( new Title( article ).userName() );
		url += 'list=usercontribs&amp;meta=userinfo&amp;uiprop=options&amp;ucuser=' + usernameart +
			'&amp;uclimit=' + getValueOf('popupContribsPreviewLimit');
		htmlGenerator=APIcontribsPreviewHTML;
		break;
	case 'imagepagepreview':
		var trail='';
		if (getValueOf('popupImageLinks')) { trail = '&amp;list=imageusage&amp;iutitle=' + art; }
		url += 'titles=' + art + '&amp;prop=revisions|imageinfo&amp;rvprop=content' + trail;
		htmlGenerator=APIimagepagePreviewHTML;
		break;
	case 'backlinks':
		url += 'list=backlinks&amp;rawcontinue=&amp;bltitle=' + art;
		htmlGenerator=APIbacklinksPreviewHTML;
		break;
	}
	pendingNavpopTask(navpop);
	var callback=function(d){
	    log( &quot;callback of API functions was hit&quot; );
		showAPIPreview(queryType, htmlGenerator(article,d,navpop), navpop.idNumber, navpop, d);
	};
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_'+queryType+'_QUERY_DATA'); }
}

function linkList(list) {
	list.sort(function(x,y) { return (x==y ? 0 : (x&lt;y ? -1 : 1)); });
	var buf=[];
	for (var i=0; i&lt;list.length; ++i) {
		buf.push(wikiLink({article: new Title(list[i]),
				   text:    list[i].split(' ').join('&amp;nbsp;'),
				   action:  'view'}));
	}
	return buf.join(', ');
}

function getTimeOffset(tz) {
	if( tz ) {
		if( tz.indexOf('|') &gt; -1 ) {
			// New format
			return parseInt(tz.split('|')[1],10);
		} else if ( tz.indexOf(':') &gt; -1 ) {
			// Old format
			return( parseInt(tz,10)*60 + parseInt(tz.split(':')[1],10) );
		}
	}
	return 0;
}

function editPreviewTable(article, h, reallyContribs, timeOffset) {
	var html=['&lt;table&gt;'];
	var day=null;
	var curart=article;
	for (var i=0; i&lt;h.length; ++i) {
		if (reallyContribs) { 
		    var page=h[i]['title']; curart = new Title(page);
		}
		var minor=typeof h[i]['minor']=='undefined' ? '' : '&lt;b&gt;m &lt;/b&gt;';
		var editDate=adjustDate(getDateFromTimestamp(h[i].timestamp), timeOffset);
		var thisDay = dayFormat(editDate);
		var thisTime = timeFormat(editDate);
		if (thisDay==day) { thisDay=''; }
		else { day=thisDay; }
		if (thisDay) {
			html.push( '&lt;tr&gt;&lt;td colspan=3&gt;&lt;span class=&quot;popup_history_date&quot;&gt;' +
				  thisDay+'&lt;/span&gt;&lt;/td&gt;&lt;/tr&gt;' );
		}
		html.push('&lt;tr class=&quot;popup_history_row_' + ( (i%2) ? 'odd' : 'even') + '&quot;&gt;');
		html.push('&lt;td&gt;(&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;diff=prev&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + popupString('last') + '&lt;/a&gt;)&lt;/td&gt;');
		html.push('&lt;td&gt;' +
			'&lt;a href=&quot;' + pg.wiki.titlebase + new Title(curart).urlString() +
			'&amp;oldid=' + h[i]['revid'] + '&quot;&gt;' + thisTime + '&lt;/a&gt;&lt;/td&gt;');
		var col3url='', col3txt='';
		if (!reallyContribs) {
			var user=h[i]['user'];
			if( typeof h[i]['userhidden'] == &quot;undefined&quot; ) {
				if( pg.re.ipUser.test(user) ) {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId] + ':Contributions&amp;target=' + new Title(user).urlString();
				} else {
					col3url=pg.wiki.titlebase + mw.config.get('wgFormattedNamespaces')[pg.nsUserId] + ':' + new Title(user).urlString();
				}
				col3txt=mw.html.escape(user);
			} else {
				col3url=getValueOf('popupRevDelUrl');
				col3txt=mw.html.escape( popupString('revdel'));
			}
		} else {
			col3url=pg.wiki.titlebase + curart.urlString();
			col3txt=mw.html.escape(page);
		}
		html.push('&lt;td&gt;' + (reallyContribs ? minor : '') +
			'&lt;a href=&quot;' + col3url + '&quot;&gt;' + col3txt + '&lt;/a&gt;&lt;/td&gt;');
		var comment='';
		var c=h[i].comment || h[i]['*'];
		if (c) {
			comment=new Previewmaker(c, new Title(curart).toUrl()).editSummaryPreview();
		} else if (typeof h[i]['commenthidden'] != &quot;undefined&quot; ) {
			comment=popupString('revdel');
		}
		html.push('&lt;td&gt;' + (!reallyContribs ? minor : '') + comment + '&lt;/td&gt;');
		html.push('&lt;/tr&gt;');
		html=[html.join('')];
	}
	html.push('&lt;/table&gt;');
	return html.join('');
}

function getDateFromTimestamp(t) {
	var s=t.split(/[^0-9]/);
	switch(s.length) {
	case 0: return null;
	case 1: return new Date(s[0]);
	case 2: return new Date(s[0], s[1]-1);
	case 3: return new Date(s[0], s[1]-1, s[2]);
	case 4: return new Date(s[0], s[1]-1, s[2], s[3]);
	case 5: return new Date(s[0], s[1]-1, s[2], s[3], s[4]);
	case 6: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5]);
	default: return new Date(s[0], s[1]-1, s[2], s[3], s[4], s[5], s[6]);
	}
}

function adjustDate(d, offset) {
	// offset is in minutes
	var o=offset * 60 * 1000;
	return new Date( +d + o);
}

function dayFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCFullYear(), editDate.getUTCMonth()+1, editDate.getUTCDate()]).join('-'); }
	return map(zeroFill, [editDate.getFullYear(), editDate.getMonth()+1, editDate.getDate()]).join('-');
}

function timeFormat(editDate, utc) {
	if (utc) { return map(zeroFill, [editDate.getUTCHours(), editDate.getUTCMinutes(), editDate.getUTCSeconds()]).join(':'); }
	return map(zeroFill, [editDate.getHours(), editDate.getMinutes(), editDate.getSeconds()]).join(':');
}

function showAPIPreview(queryType, html, id, navpop, download) {
    // DJ: done
	var target='popupPreview';
	switch (queryType) {
	case 'imagelinks':
	case 'category':
	case 'userinfo':
		target='popupPostPreview'; break;
	}
	setPopupTipsAndHTML(html, target, id);
	completedNavpopTask(navpop);
}

function APIbacklinksPreviewHTML(article, download, navpop) {
    try {
	    var jsObj=getJsObj(download.data);
   	    var list=jsObj.query.backlinks;
	} catch (someError) { return 'backlinksPreviewHTML went wonky'; }
	var html=[];
	if (!list) { return popupString('No backlinks found'); }
	for ( var i=0; i &lt; list.length; i++ ) {
		var t=new Title(list[i]['title']);
		html.push('&lt;a href=&quot;' + pg.wiki.titlebase + t.urlString() + '&quot;&gt;' + t + '&lt;/a&gt;');
	}
	html=html.join(', ');
	if (jsObj['query-continue'] &amp;&amp; jsObj['query-continue'].backlinks &amp;&amp; jsObj['query-continue'].backlinks.blcontinue) {
		html += popupString(' and more');
	}
	return html;
}

function APIsharedImagePagePreviewHTML(obj) {
	log( &quot;APIsharedImagePagePreviewHTML&quot; );
	var popupid = obj['requestid'];
	if( obj['query'] &amp;&amp; obj['query']['pages'] )
	{
		var page=anyChild(obj['query']['pages']);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
		if( content ) 
		{
			/* Not entirely safe, but the best we can do */
			var p=new Previewmaker(content, pg.current.link.navpopup.article, pg.current.link.navpopup);
			p.makePreview();
			setPopupHTML( p.html, &quot;popupSecondPreview&quot;, popupid );
		}
	}
}

function APIimagepagePreviewHTML(article, download, navpop) {
	try {
	    var jsObj=getJsObj(download.data);
		var page=anyChild(jsObj.query.pages);
		var content=(page &amp;&amp; page.revisions ) ? page.revisions[0]['*'] : null;
	} catch (someError) {
		return 'API imagepage preview failed :(';
	}
	var ret='';
	var alt='';
	try{alt=navpop.parentAnchor.childNodes[0].alt;} catch(e){}
	if (alt) {
		ret = ret + '&lt;hr&gt;&lt;b&gt;' + popupString('Alt text:') + '&lt;/b&gt; ' + mw.html.escape(alt);
	}
	if (content) {
		var p=prepPreviewmaker(content, article, navpop);
		p.makePreview();
		if (p.html) { ret += '&lt;hr&gt;' + p.html; }
	}
	if (content!==null &amp;&amp; getValueOf('popupSummaryData')) {
		var info=getPageInfo(content, download);
		log(info);
		setPopupTrailer(info, navpop.idNumber);
	}
	if (page &amp;&amp; page.imagerepository == &quot;shared&quot; ) {
		var art=new Title(article);
		var encart = encodeURIComponent( &quot;File:&quot; + art.stripNamespace() );
		var shared_url =  pg.wiki.apicommonsbase + '?format=json&amp;callback=APIsharedImagePagePreviewHTML' +
							'&amp;requestid=' + navpop.idNumber +
							'&amp;action=query&amp;prop=revisions&amp;rvprop=content&amp;titles=' + encart;
		if (pg.flag.isIE) {
			shared_url = shared_url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
		}

		ret = ret +'&lt;hr&gt;' + popupString( 'Image from Commons') +
				': &lt;a href=&quot;' + pg.wiki.commonsbase + '?title=' + encart + '&quot;&gt;' +
				popupString( 'Description page') + '&lt;/a&gt;';
		mw.loader.load( shared_url );
	}
	showAPIPreview('imagelinks', APIimagelinksPreviewHTML(article,download), navpop.idNumber, download);
	return ret;
}

function APIimagelinksPreviewHTML(article, download) {
	try {
		var jsobj=getJsObj(download.data);
		var list=jsobj.query.imageusage;
		if (!list) { return popupString('No image links found'); }
	} catch(someError) { return 'Image links preview generation failed :('; }
	var ret=[];
	for (var i=0; i &lt; list.length; i++) {
		ret.push(list[i]['title']);
	}
	if (ret.length === 0) { return popupString('No image links found'); }
	return '&lt;h2&gt;' + popupString('File links') + '&lt;/h2&gt;' + linkList(ret);
}

function APIcategoryPreviewHTML(article, download) {
    try{
        var jsobj=getJsObj(download.data);
        var list=jsobj.query.categorymembers;
    } catch(someError) { return 'Category preview failed :('; }
	var ret=[];
	for (var p=0; p &lt; list.length; p++) { 
	   ret.push(list[p]['title']); 
	}
	if (ret.length === 0) { return popupString('Empty category'); }
	ret = '&lt;h2&gt;' + tprintf('Category members (%s shown)', [ret.length]) + '&lt;/h2&gt;' +linkList(ret);
	if (jsobj['query-continue'] &amp;&amp; jsobj['query-continue'].categorymembers &amp;&amp; jsobj['query-continue'].categorymembers.cmcontinue) {
		ret += popupString(' and more');
	}
	return ret;
}

function APIuserInfoPreviewHTML(article, download) {
	var ret=[];
	try{
		var queryobj=getJsObj(download.data).query;
	} catch(someError) { return 'Userinfo preview failed :('; }
	
	var user=anyChild(queryobj.users);
	if (user) {
		var globaluserinfo=queryobj.globaluserinfo;
		if (user.invalid == '') {
			ret.push( popupString( 'Invalid user') );
		} else if (user.missing == '') {
			ret.push( popupString( 'Not a registered username') );
		}
		if( user.blockedby )
			ret.push('&lt;b&gt;' + popupString('BLOCKED') + '&lt;/b&gt;');
		if( globaluserinfo &amp;&amp; (globaluserinfo.locked != null || globaluserinfo.hidden != null) ) {
			var lockedSulAccountIsAttachedToThis = true;
			for( var i=0; globaluserinfo.unattached &amp;&amp; i &lt; globaluserinfo.unattached.length; i++) {
				if (globaluserinfo.unattached[i].wiki===mw.config.get('wgDBname')) { lockedSulAccountIsAttachedToThis=false; break; }
			}
			if (lockedSulAccountIsAttachedToThis) {
				if (globaluserinfo.locked != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('LOCKED') + '&lt;/i&gt;&lt;/b&gt;');
				if (globaluserinfo.hidden != null) ret.push('&lt;b&gt;&lt;i&gt;' + popupString('HIDDEN') + '&lt;/i&gt;&lt;/b&gt;');
			}
		}
		for( var i=0; (user.groups &amp;&amp; i &lt; user.groups.length); i++) {
			switch (user.groups[i]) {
				case '*':
				case 'user':
				case 'autoconfirmed':
					break;
				default:
					ret.push( mw.html.escape(user.groups[i]) );
			}
		}
		for( var i=0; (globaluserinfo &amp;&amp; globaluserinfo.groups &amp;&amp; i &lt; globaluserinfo.groups.length); i++) {
			ret.push( '&lt;i&gt;'+mw.html.escape(globaluserinfo.groups[i])+'&lt;/i&gt;' );
		}
		if( user.editcount || user.registration )
			ret.push( mw.html.escape((user.editcount?user.editcount:'') + popupString(' edits since: ') + (user.registration?dayFormat(getDateFromTimestamp(user.registration)):'')) );
	}
	
	if (queryobj.blocks) {
		ret.push( popupString( 'IP user') ); //we only request list=blocks for IPs
		for (var i=0; i&lt;queryobj.blocks.length; i++) {
			ret.push('&lt;b&gt;' + popupString(queryobj.blocks[i].rangestart===queryobj.blocks[i].rangeend ? 'BLOCKED' : 'RANGEBLOCKED') + '&lt;/b&gt;' );
		}
	}
	
	ret = '&lt;hr&gt;' + ret.join( ', ' );
	return ret;
}

function APIcontribsPreviewHTML(article, download, navpop) {
    return APIhistoryPreviewHTML(article, download, navpop, true);
}

function APIhistoryPreviewHTML(article, download, navpop, reallyContribs) {
    try {
		var jsobj=getJsObj(download.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
		if( reallyContribs )
		    var edits=jsobj.query.usercontribs;
		else 
		    var edits=anyChild(jsobj.query.pages)['revisions'];
	} catch (someError) {
		return 'History preview failed :-(';
	}
	var timeOffset = getTimeOffset(tz);
	Cookie.create('popTz', timeOffset, 1);

	var ret=editPreviewTable(article, edits, reallyContribs, timeOffset);
	return ret;
}


//&lt;/NOLITE&gt;
// ENDFILE: querypreview.js
// STARTFILE: debug.js
////////////////////////////////////////////////////////////////////
// Debugging functions
////////////////////////////////////////////////////////////////////

function log(){}; // dummy to stop errors
function setupDebugging() {
//&lt;NOLITE&gt;
	if (window.popupDebug) { // popupDebug is set from .version
		window.log=function(x) { //if(gMsg!='')gMsg += '\n'; gMsg+=time() + ' ' + x; };
			window.console.log(x);
		}
		window.errlog=function(x) {
			window.console.error(x);
		}
		log('Initializing logger');
	} else {
//&lt;/NOLITE&gt;
		window.log = function(x) {};
		window.errlog = function(x) {};
//&lt;NOLITE&gt;
	}
//&lt;/NOLITE&gt;
}
// ENDFILE: debug.js
// STARTFILE: images.js

// load image of type Title.
function loadImage(image, navpop) {
	if (typeof image.stripNamespace != 'function') { alert('loadImages bad'); }
    // API call to retrieve image info.

	if (!getValueOf('popupImages')) return;
	if (!isValidImageName(image)) return false;
	
	var art=image.urlString();

	var url=pg.wiki.apiwikibase + '?format=json&amp;action=query';
	url += '&amp;prop=imageinfo&amp;iiprop=url|mime&amp;iiurlwidth=' + getValueOf('popupImageSizeLarge');;
	url += '&amp;titles=' + art;
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}

	pendingNavpopTask(navpop);
	var callback=function(d){
		popupsInsertImage(navpop.idNumber, navpop, d);
	};
	var go = function(){
	    getPageWithCaching(url, callback, navpop);
		return true;
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'after', 'DOWNLOAD_IMAGE_QUERY_DATA'); }

}

function popupsInsertImage(id, navpop, download) {
	log( &quot;popupsInsertImage&quot;);
	try {
		var jsObj=getJsObj(download.data);
		var imagepage=anyChild(jsObj.query.pages);
		if (typeof imagepage.imageinfo === 'undefined') return;
		var imageinfo = imagepage.imageinfo[0];
	} catch (someError) {
		log( &quot;popupsInsertImage failed :(&quot; );
		return;
	}

	var popupImage = document.getElementById(&quot;popupImg&quot;+id);
	if (!popupImage) {
		log( &quot;could not find insertion point for image&quot;);
		return;
	}

	popupImage.width=getValueOf('popupImageSize');
	popupImage.style.display='inline';

	// Set the source for the image.
	if( imageinfo.thumburl )
		popupImage.src=imageinfo.thumburl;
	else if( imageinfo.mime.indexOf(&quot;image&quot;) == 0 ){
		popupImage.src=imageinfo.url;
		log( &quot;a thumb could not be found, using original image&quot; );
	} else log( &quot;fullsize imagethumb, but not sure if it's an image&quot;);


	var a=document.getElementById(&quot;popupImageLink&quot;+id);
	if (a === null) { return null; }

    // Determine the action of the surrouding imagelink.
	switch (getValueOf('popupThumbAction')) {
	case 'imagepage':
		if (pg.current.article.namespaceId()!=pg.nsImageId) {
			a.href=imageinfo.descriptionurl;
			// FIXME: unreliable pg.idNumber
			popTipsSoonFn('popupImage' + id)();
			break;
		} // else fall through
	case 'sizetoggle':
		a.onclick=toggleSize;
		a.title=popupString('Toggle image size');
		return;
	case 'linkfull':
		a.href = imageinfo.url;
		a.title=popupString('Open full-size image');
		return;
	}

}

// Toggles the image between inline small and navpop fullwidth.
// It's the same image, no actual sizechange occurs, only display width.
function toggleSize() {
	var imgContainer=this;
	if (!imgContainer) { alert('imgContainer is null :/'); return;}
	img=imgContainer.firstChild;
	if (!img) { alert('img is null :/'); return;}
	if (!img.style.width || img.style.width=='') { img.style.width='100%'; }
	else { img.style.width=''; }
}

// Returns one title of an image from wikiText.
function getValidImageFromWikiText(wikiText) {
	// nb in pg.re.image we're interested in the second bracketed expression
	// this may change if the regex changes :-(
	//var match=pg.re.image.exec(wikiText);
	var matched=null;
	var match;
	// strip html comments, used by evil bots :-(
	var t = removeMatchesUnless(wikiText, RegExp('(&lt;!--[\\s\\S]*?--&gt;)'), 1,
				    RegExp('^&lt;!--[^[]*popup', 'i'));

	while ( match = pg.re.image.exec(t) ) {
		// now find a sane image name - exclude templates by seeking {
		var m = match[2] || match[6];
		if ( isValidImageName(m) ) {
			matched=m;
			break;
		}
	}
	pg.re.image.lastIndex=0;
	if (!matched) { return null; }
	return mw.config.get('wgFormattedNamespaces')[pg.nsImageId]+':'+upcaseFirst(matched);
}

function removeMatchesUnless(str, re1, parencount, re2) {
    var split=str.parenSplit(re1);
    var c=parencount + 1;
    for (var i=0; i&lt;split.length; ++i) {
	if ( i%c === 0 || re2.test(split[i]) ) { continue; }
	split[i]='';
    }
    return split.join('');
}

//&lt;/NOLITE&gt;
// ENDFILE: images.js
// STARTFILE: namespaces.js
// Set up namespaces and other non-strings.js localization
// (currently that means redirs too)


function namespaceListToRegex(list) {return RegExp('^('+list.join('|').split(' ').join('[ _]')+'):');};

function setNamespaces() {
	pg.nsSpecialId   = -1;
	pg.nsImageId     = 6;
	pg.nsUserId      = 2;
	pg.nsUsertalkId  = 3;
	pg.nsCategoryId  = 14;
	pg.nsTemplateId  = 10;
}


function setRedirs() {
	var r='redirect';
	var R='REDIRECT';
	var redirLists={
//&lt;NOLITE&gt;
		'ar':  [ R, 'تحويل' ],
		'be':  [ r, 'перанакіраваньне' ],
		'bg':  [ r, 'пренасочване', 'виж' ],
		'bs':  [ r, 'Preusmjeri', 'preusmjeri', 'PREUSMJERI' ],
		'cs':  [ R, 'PŘESMĚRUJ' ],
		'cy':  [ r, 'ail-cyfeirio' ],
		'de':  [ R, 'WEITERLEITUNG' ],
		'eo':  [ R, 'ALIDIREKTU', 'ALIDIREKTI' ],
		'es':  [ R, 'REDIRECCIÓN' ],
		'et':  [ r, 'suuna' ],
		'ga':  [ r, 'athsheoladh' ],
		'gl':  [ r, 'REDIRECCIÓN', 'REDIRECIONAMENTO'],
		'he':  [ R, 'הפניה' ],
		'hu':  [ R, 'ÁTIRÁNYÍTÁS' ],
		'is':  [ r, 'tilvísun', 'TILVÍSUN' ],
		'it':  [ R, 'RINVIA', 'Rinvia'],
		'mk':  [ r, 'пренасочување', 'види' ],
		'nds': [ r, 'wiederleiden' ],
		'nl':  [ R, 'DOORVERWIJZING' ],
		'nn':  [ r, 'omdiriger' ],
		'pl':  [ R, 'PATRZ', 'PRZEKIERUJ', 'TAM' ],
		'pt':  [ R, 'redir' ],
		'ru':  [ R, 'ПЕРЕНАПРАВЛЕНИЕ', 'ПЕРЕНАПР' ],
		'sk':  [ r, 'presmeruj' ],
		'sr':  [ r, 'Преусмери', 'преусмери', 'ПРЕУСМЕРИ', 'Preusmeri', 'preusmeri', 'PREUSMERI' ],
		'tt':  [ R, 'yünältü', 'перенаправление', 'перенапр' ],
		'uk': [ R, 'ПЕРЕНАПРАВЛЕННЯ', 'ПЕРЕНАПР' ],
		'vi':  [ r, 'đổi' ] // no comma
//&lt;/NOLITE&gt;
	};
	var redirList=redirLists[ pg.wiki.lang ] || [r, R];
	// Mediawiki is very tolerant about what comes after the #redirect at the start
	pg.re.redirect=RegExp('^\\s*[#](' + redirList.join('|') + ').*?\\[{2}([^\\|\\]]*)(|[^\\]]*)?\\]{2}\\s*(.*)', 'i');
}

function setInterwiki() {
	if (pg.wiki.wikimedia) {
		// From //meta.wikimedia.org/wiki/List_of_Wikipedias
		pg.wiki.interwiki='aa|ab|ace|af|ak|als|am|an|ang|ar|arc|arz|as|ast|av|ay|az|ba|bar|bat-smg|bcl|be|be-x-old|bg|bh|bi|bjn|bm|bn|bo|bpy|br|bs|bug|bxr|ca|cbk-zam|cdo|ce|ceb|ch|cho|chr|chy|ckb|co|cr|crh|cs|csb|cu|cv|cy|da|de|diq|dsb|dv|dz|ee|el|eml|en|eo|es|et|eu|ext|fa|ff|fi|fiu-vro|fj|fo|fr|frp|frr|fur|fy|ga|gag|gan|gd|gl|glk|gn|got|gu|gv|ha|hak|haw|he|hi|hif|ho|hr|hsb|ht|hu|hy|hz|ia|id|ie|ig|ii|ik|ilo|io|is|it|iu|ja|jbo|jv|ka|kaa|kab|kbd|kg|ki|kj|kk|kl|km|kn|ko|koi|kr|krc|ks|ksh|ku|kv|kw|ky|la|lad|lb|lbe|lg|li|lij|lmo|ln|lo|lt|ltg|lv|map-bms|mdf|mg|mh|mhr|mi|mk|ml|mn|mo|mr|mrj|ms|mt|mus|mwl|my|myv|mzn|na|nah|nap|nds|nds-nl|ne|new|ng|nl|nn|no|nov|nrm|nv|ny|oc|om|or|os|pa|pag|pam|pap|pcd|pdc|pfl|pi|pih|pl|pms|pnb|pnt|ps|pt|qu|rm|rmy|rn|ro|roa-rup|roa-tara|ru|rue|rw|sa|sah|sc|scn|sco|sd|se|sg|sh|si|simple|sk|sl|sm|sn|so|sq|sr|srn|ss|st|stq|su|sv|sw|szl|ta|te|tet|tg|th|ti|tk|tl|tn|to|tpi|tr|ts|tt|tum|tw|ty|udm|ug|uk|ur|uz|ve|vec|vi|vls|vo|wa|war|wo|wuu|xal|xh|yi|yo|za|zea|zh|zh-classical|zh-min-nan|zh-yue|zu';
		pg.re.interwiki=RegExp('^'+pg.wiki.interwiki+':');
	} else {
		pg.wiki.interwiki=null;
		pg.re.interwiki=RegExp('^$');
	}
}

// return a regexp pattern matching all variants to write the given namespace
function nsRe(namespaceId) {
	var imageNamespaceVariants = [];
	jQuery.each(mw.config.get('wgNamespaceIds'), function(_localizedNamespaceLc, _namespaceId) {
		if (_namespaceId!=namespaceId) return;
		//todo: escape regexp fragments!
		_localizedNamespaceLc = upcaseFirst(_localizedNamespaceLc);
		imageNamespaceVariants.push(_localizedNamespaceLc.split(' ').join('[ _]'));
		imageNamespaceVariants.push(encodeURI(_localizedNamespaceLc));
	});

	return '(?:' + imageNamespaceVariants.join('|') + ')';
}

function nsReImage() {
	return nsRe(pg.nsImageId);
}

// ENDFILE: namespaces.js
// STARTFILE: selpop.js
//&lt;NOLITE&gt;
function getEditboxSelection() {
	// see http://www.webgurusforum.com/8/12/0
	try {
		var editbox=document.editform.wpTextbox1;
	} catch (dang) { return; }
	// IE, Opera
	if (document.selection) { return document.selection.createRange().text; }
	// Mozilla
	var selStart = editbox.selectionStart;
	var selEnd = editbox.selectionEnd;
	return (editbox.value).substring(selStart, selEnd);
}

function doSelectionPopup() {
	// popup if the selection looks like [[foo|anything afterwards at all
	// or [[foo|bar]]text without ']]'
	// or [[foo|bar]]
	var sel=getEditboxSelection();
	var open=sel.indexOf('[[');
	var pipe=sel.indexOf('|');
	var close=sel.indexOf(']]');
	if (open == -1 || ( pipe == -1 &amp;&amp; close == -1) ) { return; }
	if (pipe != -1 &amp;&amp; open &gt; pipe || close != -1 &amp;&amp; open &gt; close) { return; }
	if (getValueOf('popupOnEditSelection')=='boxpreview') {
		return doSeparateSelectionPopup(sel);
	}
	var article=new Title(sel.substring(open+2, (pipe &lt; 0) ? close : pipe)).urlString();
	if (close &gt; 0 &amp;&amp; sel.substring(close+2).indexOf('[[') &gt;= 0) { 
		return; 
	}
	var a=document.createElement('a');
	a.href=pg.wiki.titlebase + article;
	mouseOverWikiLink2(a);
	if (a.navpopup) {
		a.navpopup.addHook(function(){runStopPopupTimer(a.navpopup);}, 'unhide', 'after');
	}
}

function doSeparateSelectionPopup(str) {
	var div=document.getElementById('selectionPreview');
	if (!div) {
		div = document.createElement('div');
		div.id='selectionPreview';
		try { var box=document.editform.wpTextbox1; }
		catch (oopsie) { return; }
		box.parentNode.insertBefore(div, box);
	}
	div.innerHTML=wiki2html(str);
	div.ranSetupTooltipsAlready = false;
	popTipsSoonFn('selectionPreview')();
}
//&lt;/NOLITE&gt;
// ENDFILE: selpop.js
// STARTFILE: navpopup.js
/**
   @fileoverview  Defines two classes: {@link Navpopup} and {@link Mousetracker}.

   &lt;code&gt;Navpopup&lt;/code&gt; describes popups: when they appear, where, what
   they look like and so on.

   &lt;code&gt;Mousetracker&lt;/code&gt; &quot;captures&quot; the mouse using
   &lt;code&gt;document.onmousemove&lt;/code&gt;.
*/


/**
   Creates a new Mousetracker.
   @constructor
   @class The Mousetracker class. This monitors mouse movements and manages associated hooks.
*/
function Mousetracker() {
	/**
	   Interval to regularly run the hooks anyway, in milliseconds.
	   @type Integer
	*/
	this.loopDelay=400;

	/**
	   Timer for the loop.
	   @type Timer
	*/
	this.timer=null;

	/**
	   Flag - are we switched on?
	   @type Boolean
	*/
	this.active=false;
	/**
	   Flag - are we probably inaccurate, i.e. not reflecting the actual mouse position?
	*/
	this.dirty=true;
	/**
	   Array of hook functions.
	   @private
	   @type Array
	*/
	this.hooks=[];
}

/**
   Adds a hook, to be called when we get events.
   @param {Function} f A function which is called as
   &lt;code&gt;f(x,y)&lt;/code&gt;. It should return &lt;code&gt;true&lt;/code&gt; when it
   wants to be removed, and &lt;code&gt;false&lt;/code&gt; otherwise.
*/
Mousetracker.prototype.addHook = function (f) {
	this.hooks.push(f);
};

/**
   Runs hooks, passing them the x
   and y coords of the mouse.  Hook functions that return true are
   passed to {@link Mousetracker#removeHooks} for removal.
   @private
*/
Mousetracker.prototype.runHooks = function () {
	if (!this.hooks || !this.hooks.length) { return; }
	//log('Mousetracker.runHooks; we got some hooks to run');
	var remove=false;
	var removeObj={};
	// this method gets called a LOT -
	// pre-cache some variables
	var x=this.x, y=this.y, len = this.hooks.length;

	for (var i=0; i&lt;len; ++i) {
		//~ run the hook function, and remove it if it returns true
		if (this.hooks[i](x, y)===true) {
			remove=true;
			removeObj[i]=true;
		}
	}
	if (remove) { this.removeHooks(removeObj); }
};

/**
   Removes hooks.
   @private
   @param {Object} removeObj An object whose keys are the index
   numbers of functions for removal, with values that evaluate to true
*/
Mousetracker.prototype.removeHooks = function(removeObj) {
	var newHooks=[];
	var len = this.hooks.length;
	for (var i=0; i&lt;len; ++i) {
		if (! removeObj[i]) { newHooks.push(this.hooks[i]); }
	}
	this.hooks=newHooks;
};


/**
   Event handler for mouse wiggles.
   We simply grab the event, set x and y and run the hooks.
   This makes the cpu all hot and bothered :-(
   @private
   @param {Event} e Mousemove event
*/
Mousetracker.prototype.track=function (e) {
	//~ Apparently this is needed in IE.
	e = e || window.event;
	var x, y;
	if (e) {
		if (e.pageX) { x=e.pageX; y=e.pageY; }
		else if (typeof e.clientX!='undefined') {
			var left, top, docElt = window.document.documentElement;

			if (docElt) { left=docElt.scrollLeft; }
			left = left || window.document.body.scrollLeft || window.document.scrollLeft || 0;

			if (docElt) { top=docElt.scrollTop; }
			top = top || window.document.body.scrollTop || window.document.scrollTop || 0;

			x=e.clientX + left;
			y=e.clientY + top;
		} else { return; }
		this.setPosition(x,y);
	}
};

/**
   Sets the x and y coordinates stored and takes appropriate action,
   running hooks as appropriate.
   @param {Integer} x, y Screen coordinates to set
*/

Mousetracker.prototype.setPosition=function(x,y) {
	this.x = x;
	this.y = y;
	if (this.dirty || this.hooks.length === 0) { this.dirty=false; return; }
	if (typeof this.lastHook_x != 'number') { this.lastHook_x = -100; this.lastHook_y=-100; }
	var diff = (this.lastHook_x - x)*(this.lastHook_y - y);
	diff = (diff &gt;= 0) ? diff : -diff;
	if ( diff &gt; 1 ) {
		this.lastHook_x=x;
		this.lastHook_y=y;
		if (this.dirty) { this.dirty = false; }
		else { this.runHooks(); }
	}
}

/**
   Sets things in motion, unless they are already that is, registering an event handler on &lt;code&gt;document.onmousemove&lt;/code&gt;.
   A half-hearted attempt is made to preserve the old event handler if there is one.
*/
Mousetracker.prototype.enable = function () {
	if (this.active) { return; }
	this.active=true;
	//~ Save the current handler for mousemove events. This isn't too
	//~ robust, of course.
	this.savedHandler=document.onmousemove;
	//~ Gotta save @tt{this} again for the closure, and use apply for
	//~ the member function.
	var savedThis=this;
	document.onmousemove=function (e) {savedThis.track.apply(savedThis, [e]);};
	if (this.loopDelay) { this.timer = setInterval(function() { //log('loop delay in mousetracker is working');
								    savedThis.runHooks();}, this.loopDelay); }
};

/**
   Disables the tracker, removing the event handler.
*/
Mousetracker.prototype.disable = function () {
	if (!this.active) { return; }
	if (typeof this.savedHandler=='function') {
		document.onmousemove=this.savedHandler;
	} else { delete document.onmousemove; }
	if (this.timer) { clearInterval(this.timer); }
	this.active=false;
};

/**
   Creates a new Navpopup.
   Gets a UID for the popup and
   @param init Contructor object. If &lt;code&gt;init.draggable&lt;/code&gt; is true or absent, the popup becomes draggable.
   @constructor
   @class The Navpopup class. This generates popup hints, and does some management of them.
*/
function Navpopup(init) {
	//alert('new Navpopup(init)');
	/** UID for each Navpopup instance.
	    Read-only.
	    @type integer
	*/
	this.uid=Navpopup.uid++;
	/**
	   Read-only flag for current visibility of the popup.
	   @type boolean
	   @private
	*/
	this.visible=false;
	/** Flag to be set when we want to cancel a previous request to
	    show the popup in a little while.
	    @private
	    @type boolean
	*/
	this.noshow=false;
	/** Categorised list of hooks.
	    @see #runHooks
	    @see #addHook
	    @private
	    @type Object
	*/
	this.hooks={
		'create': [],
		'unhide': [],
		'hide': []
	};
	/** list of unique IDs of hook functions, to avoid duplicates
	    @private
	*/
	this.hookIds={};
	/** List of downloads associated with the popup.
	    @private
	    @type Array
	*/
	this.downloads=[];
	/** Number of uncompleted downloads.
	    @type integer
	*/
	this.pending=null;
	/** Tolerance in pixels when detecting whether the mouse has left the popup.
	    @type integer
	*/
	this.fuzz=5;
	/** Flag to toggle running {@link #limitHorizontalPosition} to regulate the popup's position.
	    @type boolean
	*/
	this.constrained=true;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.width=0;
	/** The popup width in pixels.
	    @private
	    @type integer
	*/
	this.height=0;
	/** The main content DIV element.
	    @type HTMLDivElement
	*/
	this.mainDiv=null;
	this.createMainDiv();

//	if (!init || typeof init.popups_draggable=='undefined' || init.popups_draggable) {
//		this.makeDraggable(true);
//	}
}

/**
   A UID for each Navpopup. This constructor property is just a counter.
   @type integer
   @private
*/
Navpopup.uid=0;

/**
   Retrieves the {@link #visible} attribute, indicating whether the popup is currently visible.
   @type boolean
*/
Navpopup.prototype.isVisible=function() {
	return this.visible;
};

/**
   Repositions popup using CSS style.
   @private
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @param {boolean} noLimitHor Don't call {@link #limitHorizontalPosition}
*/
Navpopup.prototype.reposition= function (x,y, noLimitHor) {
	log ('reposition('+x+','+y+','+noLimitHor+')');
	if (typeof x != 'undefined' &amp;&amp; x!==null) { this.left=x; }
	if (typeof y != 'undefined' &amp;&amp; y!==null) { this.top=y; }
	if (typeof this.left != 'undefined' &amp;&amp; typeof this.top != 'undefined') {
		this.mainDiv.style.left=this.left + 'px';
		this.mainDiv.style.top=this.top + 'px';
	}
	if (!noLimitHor) { this.limitHorizontalPosition(); }
	//console.log('navpop'+this.uid+' - (left,top)=(' + this.left + ',' + this.top + '), css=('
	//+ this.mainDiv.style.left + ',' + this.mainDiv.style.top + ')');
};

/**
   Prevents popups from being in silly locations. Hopefully.
   Should not be run if {@link #constrained} is true.
   @private
*/
Navpopup.prototype.limitHorizontalPosition=function() {
	if (!this.constrained || this.tooWide) { return; }
	this.updateDimensions();
	var x=this.left;
	var w=this.width;
	var cWidth=document.body.clientWidth;


//	log('limitHorizontalPosition: x='+x+
//		    ', this.left=' + this.left +
//		    ', this.width=' + this.width +
//		    ', cWidth=' + cWidth);


	if ( (x+w) &gt;= cWidth ||
	     ( x &gt; 0 &amp;&amp; this.maxWidth &amp;&amp; this.width &lt; this.maxWidth &amp;&amp; this.height &gt; this.width
	       &amp;&amp; x &gt; cWidth - this.maxWidth ) ) {
		// This is a very nasty hack. There has to be a better way!
		// We find the &quot;natural&quot; width of the div by positioning it at the far left
		// then reset it so that it should be flush right (well, nearly)
		this.mainDiv.style.left='-10000px';
		this.mainDiv.style.width = this.maxWidth + 'px';
		var naturalWidth=parseInt(this.mainDiv.offsetWidth, 10);
		var newLeft=cWidth - naturalWidth - 1;
		if (newLeft &lt; 0) { newLeft = 0; this.tooWide=true; } // still unstable for really wide popups?
		log ('limitHorizontalPosition: moving to ('+newLeft + ','+ this.top+');' + ' naturalWidth=' + naturalWidth + ', clientWidth=' + cWidth);
		this.reposition(newLeft, null, true);
	}
};

/**
   Counter indicating the z-order of the &quot;highest&quot; popup.
   We start the z-index at 1000 so that popups are above everything
   else on the screen.
   @private
   @type integer
*/
Navpopup.highest=1000;

/**
   Brings popup to the top of the z-order.
   We increment the {@link #highest} property of the contructor here.
   @private
*/
Navpopup.prototype.raise = function () {
	this.mainDiv.style.zIndex=Navpopup.highest + 1;
	++Navpopup.highest;
};

/**
   Shows the popup provided {@link #noshow} is not true.
   Updates the position, brings the popup to the top of the z-order and unhides it.
*/
Navpopup.prototype.show = function () {
	//document.title+='s';
	if (this.noshow) { return; }
	//document.title+='t';
	this.reposition();
	this.raise();
	this.unhide();
};


/**
   Runs the {@link #show} method in a little while, unless we're
   already visible.
   @param {integer} time Delay in milliseconds
   @see #showSoonIfStable
*/
Navpopup.prototype.showSoon = function (time) {
	if (this.visible) { return; }
	this.noshow=false;
	//~ We have to save the value of @tt{this} so that the closure below
	//~ works.
	var savedThis=this;
	//this.start_x = Navpopup.tracker.x;
	//this.start_y = Navpopup.tracker.y;
	setTimeout(function () {
		if (Navpopup.tracker.active) {
			savedThis.reposition.apply(savedThis, [Navpopup.tracker.x + 2, Navpopup.tracker.y + 2]);
		}
		//~ Have to use apply to invoke his member function here
		savedThis.show.apply(savedThis, []);
	}, time);
};

/**
   Checks to see if the mouse pointer has
   stabilised (checking every &lt;code&gt;time&lt;/code&gt;/2 milliseconds) and runs the
   {@link #show} method if it has. This method makes {@link #showSoon} redundant.
   @param {integer} time The minimum time (ms) before the popup may be shown.
*/
Navpopup.prototype.showSoonIfStable = function (time) {
	log ('showSoonIfStable, time='+time);
	if (this.visible) { return; }
	this.noshow = false;

	//~ initialize these variables so that we never run @tt{show} after
	//~ just half the time
	this.stable_x = -10000; this.stable_y = -10000;

	var stableShow = function() {
		log('stableShow called');
		var new_x = Navpopup.tracker.x, new_y = Navpopup.tracker.y;
		var dx = savedThis.stable_x - new_x, dy = savedThis.stable_y - new_y;
		var fuzz2 = 0; // savedThis.fuzz * savedThis.fuzz;
		//document.title += '[' + [savedThis.stable_x,new_x, savedThis.stable_y,new_y, dx, dy, fuzz2].join(',') + '] ';
		if ( dx * dx &lt;= fuzz2 &amp;&amp; dy * dy &lt;= fuzz2 ) {
			log ('mouse is stable');
			clearInterval(savedThis.showSoonStableTimer);
			savedThis.reposition.apply(savedThis, [new_x + 2, new_y + 2]);
			savedThis.show.apply(savedThis, []);
			return;
		}
		savedThis.stable_x = new_x; savedThis.stable_y = new_y;
	};
	var savedThis = this;
	this.showSoonStableTimer = setInterval(stableShow, time/2);
};

/**
   Makes the popup unhidable until we call {@link #unstick}.
*/
Navpopup.prototype.stick=function() {
	this.noshow=false;
	this.sticky=true;
};

/**
   Allows the popup to be hidden.
*/
Navpopup.prototype.unstick=function() {
	this.sticky=false;
};

/**
   Sets the {@link #noshow} flag and hides the popup. This should be called
   when the mouse leaves the link before
   (or after) it's actually been displayed.
*/
Navpopup.prototype.banish = function () {
	log ('banish called');
	// hide and prevent showing with showSoon in the future
	this.noshow=true;
	if (this.showSoonStableTimer) {
		log('clearing showSoonStableTimer');
		clearInterval(this.showSoonStableTimer);
	}
	this.hide();
};

/**
   Runs hooks added with {@link #addHook}.
   @private
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
*/
Navpopup.prototype.runHooks = function (key, when) {
	if (!this.hooks[key]) { return; }
	var keyHooks=this.hooks[key];
	var len=keyHooks.length;
	for (var i=0; i&lt; len; ++i) {
		if (keyHooks[i] &amp;&amp; keyHooks[i].when == when) {
			if (keyHooks[i].hook.apply(this, [])) {
				// remove the hook
				if (keyHooks[i].hookId) {
					delete this.hookIds[keyHooks[i].hookId];
				}
				keyHooks[i]=null;
			}
		}
	}
};

/**
   Adds a hook to the popup. Hook functions are run with &lt;code&gt;this&lt;/code&gt; set to refer to the Navpopup instance, and no arguments.
   @param {Function} hook The hook function. Functions that return true are deleted.
   @param {String} key Key name of the {@link #hooks} array - one of 'create', 'unhide', 'hide'
   @param {String} when Controls exactly when the hook is run: either 'before' or 'after'
   @param {String} uid A truthy string identifying the hook function; if it matches another hook in this position, it won't be added again.
*/
Navpopup.prototype.addHook = function ( hook, key, when, uid ) {
	when = when || 'after';
	if (!this.hooks[key]) { return; }
	// if uid is specified, don't add duplicates
	var hookId=null;
	if (uid) {
		hookId=[key,when,uid].join('|');
		if (this.hookIds[hookId]) {
			return;
		}
		this.hookIds[hookId]=true;
	}
	this.hooks[key].push( {hook: hook, when: when, hookId: hookId} );
};

/**
   Creates the main DIV element, which contains all the actual popup content.
   Runs hooks with key 'create'.
   @private
*/
Navpopup.prototype.createMainDiv = function () {
	if (this.mainDiv) { return; }
	this.runHooks('create', 'before');
	var mainDiv=document.createElement('div');

	var savedThis=this;
	mainDiv.onclick=function(e) {savedThis.onclickHandler(e);};
	mainDiv.className=(this.className) ? this.className : 'navpopup_maindiv';
	mainDiv.id=mainDiv.className + this.uid;

	mainDiv.style.position='absolute';
	mainDiv.style.display='none';
	mainDiv.className='navpopup';

	// easy access to javascript object through DOM functions
	mainDiv.navpopup=this;

	this.mainDiv=mainDiv;
	document.body.appendChild(mainDiv);
	this.runHooks('create', 'after');
};
/**
   Calls the {@link #raise} method.
   @private
*/
Navpopup.prototype.onclickHandler=function(e) {
	this.raise();
};
/**
   Makes the popup draggable, using a {@link Drag} object.
   @private
*/
Navpopup.prototype.makeDraggable=function(handleName) {
	if (!this.mainDiv) { this.createMainDiv(); }
	var drag=new Drag();
	if (!handleName) {
	    drag.startCondition=function(e) {
		try { if (!e.shiftKey) { return false; } } catch (err) { return false; }
		return true;
	    };
	}
	var dragHandle;
	if (handleName) dragHandle = document.getElementById(handleName);
	if (!dragHandle) dragHandle = this.mainDiv;
	var np=this;
	drag.endHook=function(x,y) {
		Navpopup.tracker.dirty=true;
		np.reposition(x,y);
	};
	drag.init(dragHandle,this.mainDiv);
};

/** Hides the popup using CSS. Runs hooks with key 'hide'.
    Sets {@link #visible} appropriately.     {@link #banish} should be called externally instead of this method.

    @private
*/
Navpopup.prototype.hide = function () {
	this.runHooks('hide', 'before');
	this.abortDownloads();
	if (this.sticky) { return; }
	if (typeof this.visible != 'undefined' &amp;&amp; this.visible) {
		this.mainDiv.style.display='none';
		this.visible=false;
	}
	this.runHooks('hide', 'after');
};

/** Shows the popup using CSS. Runs hooks with key 'unhide'.
    Sets {@link #visible} appropriately.   {@link #show} should be called externally instead of this method.
    @private
*/
Navpopup.prototype.unhide = function () {
	this.runHooks('unhide', 'before');
	if (typeof this.visible != 'undefined' &amp;&amp; !this.visible) {
		this.mainDiv.style.display='inline';
		this.visible=true;
	}
	this.runHooks('unhide', 'after');
};

/**
   Sets the &lt;code&gt;innerHTML&lt;/code&gt; attribute of the main div containing the popup content.
   @param {String} html The HTML to set.
*/
Navpopup.prototype.setInnerHTML = function (html) {
	this.mainDiv.innerHTML = html;
};

/**
   Updates the {@link #width} and {@link #height} attributes with the CSS properties.
   @private
*/
Navpopup.prototype.updateDimensions = function () {
	this.width=parseInt(this.mainDiv.offsetWidth, 10);
	this.height=parseInt(this.mainDiv.offsetHeight, 10);
};

/**
   Checks if the point (x,y) is within {@link #fuzz} of the
   {@link #mainDiv}.
   @param {integer} x x-coordinate (px)
   @param {integer} y y-coordinate (px)
   @type boolean
*/
Navpopup.prototype.isWithin = function(x,y) {
	//~ If we're not even visible, no point should be considered as
	//~ being within the popup.
	if (!this.visible) { return false; }
	this.updateDimensions();
	var fuzz=this.fuzz || 0;
	//~ Use a simple box metric here.
	return (x+fuzz &gt;= this.left &amp;&amp; x-fuzz &lt;= this.left + this.width &amp;&amp;
		y+fuzz &gt;= this.top  &amp;&amp; y-fuzz &lt;= this.top  + this.height);
};

/**
   Adds a download to {@link #downloads}.
   @param {Downloader} download
*/
Navpopup.prototype.addDownload=function(download) {
	if (!download) { return; }
	this.downloads.push(download);
};
/**
   Aborts the downloads listed in {@link #downloads}.
   @see Downloader#abort
*/
Navpopup.prototype.abortDownloads=function() {
	for(var i=0; i&lt;this.downloads.length; ++i) {
		var d=this.downloads[i];
		if (d &amp;&amp; d.abort) { d.abort(); }
	}
	this.downloads=[];
};


/**
   A {@link Mousetracker} instance which is a property of the constructor (pseudo-global).
*/
Navpopup.tracker=new Mousetracker();
// ENDFILE: navpopup.js
// STARTFILE: diff.js
//&lt;NOLITE&gt;
/*
 * Javascript Diff Algorithm
 *  By John Resig (http://ejohn.org/) and [[:en:User:Lupin]]
 *
 * More Info:
 *  http://ejohn.org/projects/javascript-diff-algorithm/
 */

function delFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;del class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/del&gt;&quot;;
}
function insFmt(x) {
	if (!x.length) { return ''; }
	return &quot;&lt;ins class='popupDiff'&gt;&quot; + x.join('') +&quot;&lt;/ins&gt;&quot;;
}

function countCrossings(a, b, i, eject) {
	// count the crossings on the edge starting at b[i]
	if (!b[i].row &amp;&amp; b[i].row !== 0) { return -1; }
	var count=0;
	for (var j=0; j&lt;a.length; ++j) {
		if (!a[j].row &amp;&amp; a[j].row !== 0) { continue; }
		if ( (j-b[i].row)*(i-a[j].row) &gt; 0) {
			if(eject) { return true; }
			count++;
		}
	}
	return count;
}

function shortenDiffString(str, context) {
	var re=RegExp('(&lt;del[\\s\\S]*?&lt;/del&gt;|&lt;ins[\\s\\S]*?&lt;/ins&gt;)');
	var splitted=str.parenSplit(re);
	var ret=[''];
	for (var i=0; i&lt;splitted.length; i+=2) {
		if (splitted[i].length &lt; 2*context) {
			ret[ret.length-1] += splitted[i];
			if (i+1&lt;splitted.length) { ret[ret.length-1] += splitted[i+1]; }
			continue;
		}
		else {
			if (i &gt; 0) { ret[ret.length-1] += splitted[i].substring(0,context); }
			if (i+1 &lt; splitted.length) {
			    ret.push(splitted[i].substring(splitted[i].length-context) +
				     splitted[i+1]);
			}
		}
	}
	while (ret.length &gt; 0 &amp;&amp; !ret[0]) { ret = ret.slice(1); }
	return ret;
}


function diffString( o, n, simpleSplit ) {
	var splitRe=RegExp('([[]{2}|[\\]]{2}|[{]{2,3}|[}]{2,3}|[|]|=|&lt;|&gt;|[*:]+|\\s|\\b)');

	//  We need to split the strings o and n first, and entify() the parts
	//  individually, so that the HTML entities are never cut apart. (AxelBoldt)
	var out, i, oSplitted, nSplitted;
	if (simpleSplit) { 
		oSplitted=o.split(/\b/); 
		nSplitted=n.split(/\b/); 
	} else { 
		oSplitted=o.parenSplit(splitRe); 
		nSplitted=n.parenSplit(splitRe); 
	}
	for (i=0; i&lt;oSplitted.length; ++i) {oSplitted[i]=oSplitted[i].entify();}
	for (i=0; i&lt;nSplitted.length; ++i) {nSplitted[i]=nSplitted[i].entify();}
		
	out = diff (oSplitted, nSplitted);
	var str = &quot;&quot;;
	var acc=[]; // accumulator for prettier output

	// crossing pairings -- eg 'A B' vs 'B A' -- cause problems, so let's iron them out
	// this doesn't always do things optimally but it should be fast enough
	var maxOutputPair=0;
	for (i=0; i&lt;out.n.length; ++i) {
	    if ( out.n[i].paired ) {
		if( maxOutputPair &gt; out.n[i].row ) {
		    // tangle - delete pairing
		    out.o[ out.n[i].row ]=out.o[ out.n[i].row ].text;
		    out.n[i]=out.n[i].text;
		}
		if (maxOutputPair &lt; out.n[i].row) { maxOutputPair = out.n[i].row; }
	    }
	}

	// output the stuff preceding the first paired old line
	for (i=0; i&lt;out.o.length &amp;&amp; !out.o[i].paired; ++i) { acc.push( out.o[i] ); }
	str += delFmt(acc); acc=[];

	// main loop
	for ( i = 0; i &lt; out.n.length; ++i ) {
		// output unpaired new &quot;lines&quot;
		while ( i &lt; out.n.length &amp;&amp; !out.n[i].paired ) { acc.push( out.n[i++] ); }
		str += insFmt(acc); acc=[];
		if ( i &lt; out.n.length ) { // this new &quot;line&quot; is paired with the (out.n[i].row)th old &quot;line&quot;
			str += out.n[i].text;
			// output unpaired old rows starting after this new line's partner
			var m = out.n[i].row + 1;
			while ( m &lt; out.o.length &amp;&amp; !out.o[m].paired ) { acc.push ( out.o[m++] ); }
			str += delFmt(acc); acc=[];
		}
	}
	return str;
}

// see http://developer.mozilla.org/en/docs/Core_JavaScript_1.5_Reference:Global_Objects:Object
// FIXME: use obj.hasOwnProperty instead of this kludge!
window.jsReservedProperties=RegExp('^(constructor|prototype|__((define|lookup)[GS]etter)__' +
				   '|eval|hasOwnProperty|propertyIsEnumerable' +
				   '|to(Source|String|LocaleString)|(un)?watch|valueOf)$');
function diffBugAlert(word) {
	if (!diffBugAlert.list[word]) {
		diffBugAlert.list[word]=1;
		alert('Bad word: '+word+'\n\nPlease report this bug.');
	}
}
diffBugAlert.list={};

function makeDiffHashtable(src) {
	var ret={};
	for ( var i = 0; i &lt; src.length; i++ ) {
		if ( jsReservedProperties.test(src[i]) ) { src[i] += '&lt;!-- --&gt;'; }
		if ( !ret[ src[i] ] ) {	ret[ src[i] ] = []; }
		try { ret[ src[i] ].push( i ); } catch (err) { diffBugAlert(src[i]); }
	}
	return ret;
}

function diff( o, n ) {

	// pass 1: make hashtable ns with new rows as keys
	var ns = makeDiffHashtable(n);

	// pass 2: make hashtable os with old rows as keys
	var os = makeDiffHashtable(o);

	// pass 3: pair unique new rows and matching unique old rows
	var i;
	for ( i in ns ) {
		if ( ns[i].length == 1 &amp;&amp; os[i] &amp;&amp; os[i].length == 1 ) {
			n[ ns[i][0] ] = { text: n[ ns[i][0] ], row: os[i][0], paired: true };
			o[ os[i][0] ] = { text: o[ os[i][0] ], row: ns[i][0], paired: true };
		}
	}

	// pass 4: pair matching rows immediately following paired rows (not necessarily unique)
	for ( i = 0; i &lt; n.length - 1; i++ ) {
		if ( n[i].paired &amp;&amp; ! n[i+1].paired &amp;&amp; n[i].row + 1 &lt; o.length &amp;&amp; ! o[ n[i].row + 1 ].paired &amp;&amp;
		     n[i+1] == o[ n[i].row + 1 ] ) {
			n[i+1] = { text: n[i+1], row: n[i].row + 1, paired: true };
			o[n[i].row+1] = { text: o[n[i].row+1], row: i + 1, paired: true };
		}
	}

	// pass 5: pair matching rows immediately preceding paired rows (not necessarily unique)
	for ( i = n.length - 1; i &gt; 0; i-- ) {
		if ( n[i].paired &amp;&amp; ! n[i-1].paired &amp;&amp; n[i].row &gt; 0 &amp;&amp; ! o[ n[i].row - 1 ].paired &amp;&amp;
		     n[i-1] == o[ n[i].row - 1 ] ) {
			n[i-1] = { text: n[i-1], row: n[i].row - 1, paired: true };
			o[n[i].row-1] = { text: o[n[i].row-1], row: i - 1, paired: true };
		}
	}

	return { o: o, n: n };
}
//&lt;/NOLITE&gt;
// ENDFILE: diff.js
// STARTFILE: init.js
function setSiteInfo() {
	if (window.popupLocalDebug) {
		pg.wiki.hostname = 'en.wikiversity.org';
	} else {
		pg.wiki.hostname = location.hostname; // use in preference to location.hostname for flexibility (?)
	}
	pg.wiki.wikimedia=RegExp('(wiki([pm]edia|source|books|news|quote|versity)|wiktionary|mediawiki)[.]org').test(pg.wiki.hostname);
	pg.wiki.wikia=RegExp('[.]wikia[.]com$', 'i').test(pg.wiki.hostname);
	pg.wiki.isLocal=RegExp('^localhost').test(pg.wiki.hostname);
	pg.wiki.commons=( pg.wiki.wikimedia &amp;&amp; pg.wiki.hostname != 'commons.wikimedia.org') ? 'commons.wikimedia.org' : null;
	pg.wiki.lang = mw.config.get('wgContentLanguage');
	var port = location.port ? ':' + location.port : '';
	pg.wiki.sitebase = pg.wiki.hostname + port;
}

function setTitleBase() {
	var protocol = ( window.popupLocalDebug ? 'http:' : location.protocol );
	pg.wiki.articlePath = mw.config.get('wgArticlePath').replace(/\/\$1/, &quot;&quot;);   // as in http://some.thing.com/wiki/Article
	pg.wiki.botInterfacePath = mw.config.get('wgScript');
	pg.wiki.APIPath = wgScriptPath +&quot;/api.php&quot;;
	// default mediawiki setting is paths like http://some.thing.com/articlePath/index.php?title=foo

	var titletail = pg.wiki.botInterfacePath + '?title=';
	//var titletail2 = joinPath([pg.wiki.botInterfacePath, 'wiki.phtml?title=']);

	// other sites may need to add code here to set titletail depending on how their urls work

	pg.wiki.titlebase   = protocol + '//' + pg.wiki.sitebase + titletail;
	//pg.wiki.titlebase2  = protocol + '//' + joinPath([pg.wiki.sitebase, titletail2]);
	pg.wiki.wikibase    = protocol + '//' + pg.wiki.sitebase + pg.wiki.botInterfacePath;
	pg.wiki.apiwikibase = protocol + '//' + pg.wiki.sitebase + pg.wiki.APIPath;
	pg.wiki.articlebase = protocol + '//' + pg.wiki.sitebase + pg.wiki.articlePath;
	pg.wiki.commonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.botInterfacePath;
	pg.wiki.apicommonsbase = protocol + '//' + pg.wiki.commons  + pg.wiki.APIPath;
	pg.re.basenames = RegExp( '^(' +
				  map( literalizeRegex, [ pg.wiki.titlebase, //pg.wiki.titlebase2,
							  pg.wiki.articlebase ]).join('|') + ')' );
}


//////////////////////////////////////////////////
// Global regexps

function setMainRegex() {
	var reStart='[^:]*://';
	var preTitles = literalizeRegex(wgScriptPath) + '/(?:index[.]php|wiki[.]phtml)[?]title=';
	// slightly ugly hack when pg.wiki.articlePath is empty
	preTitles += '|' + literalizeRegex( ( pg.wiki.articlePath ? pg.wiki.articlePath + '/': ''));

	var reEnd='(' + preTitles + ')([^&amp;?#]*)[^#]*(?:#(.+))?';
	pg.re.main = RegExp(reStart + literalizeRegex(pg.wiki.sitebase) + reEnd);
}

function setRegexps() {
	setMainRegex();
	var sp=nsRe(pg.nsSpecialId);
	pg.re.urlNoPopup=RegExp('((title=|/)' + sp + '(?:%3A|:)|section=[0-9])') ;
	pg.re.contribs  =RegExp('(title=|/)'  + sp + '(?:%3A|:)Contributions' + '(&amp;target=|/|/' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)(.*)') ;
	pg.re.email     =RegExp('(title=|/)'  + sp + '(?:%3A|:)EmailUser'     + '(&amp;target=|/|/(?:' + mw.config.get('wgFormattedNamespaces')[pg.nsUserId]+':)?)(.*)') ;
	pg.re.backlinks =RegExp('(title=|/)'  + sp + '(?:%3A|:)WhatLinksHere' + '(&amp;target=|/)([^&amp;]*)');

//&lt;NOLITE&gt;
	var im=nsReImage();
	// note: tries to get images in infobox templates too, e.g. movie pages, album pages etc
	//                      (^|\[\[)image: *([^|\]]*[^|\] ]) *
	//                      (^|\[\[)image: *([^|\]]*[^|\] ])([^0-9\]]*([0-9]+) *px)?
	//                                                        $4 = 120 as in 120px
	pg.re.image = RegExp('(^|\\[\\[)' + im + ': *([^|\\]]*[^|\\] ])' +
			     '([^0-9\\]]*([0-9]+) *px)?|(?:\\n *[|]?|[|]) *' +
			     '(' + getValueOf('popupImageVarsRegexp') + ')' +
			     ' *= *(?:\\[\\[ *)?(?:' + im + ':)?' +
			     '([^|]*?)(?:\\]\\])? *[|]? *\\n', 'img') ;
	pg.re.imageBracketCount = 6;

	pg.re.category = RegExp('\\[\\[' +nsRe(pg.nsCategoryId) +
				': *([^|\\]]*[^|\\] ]) *', 'i');
	pg.re.categoryBracketCount = 1;

	pg.re.ipUser=RegExp('('+nsRe(pg.nsUserId)+':)?' +
			    '((25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])\\.){3}' +
			    '(25[0-5]|2[0-4][0-9]|1[0-9][0-9]|[1-9][0-9]|[0-9])');

	pg.re.stub= RegExp(getValueOf('popupStubRegexp'), 'im');
	pg.re.disambig=RegExp(getValueOf('popupDabRegexp'), 'im');

//&lt;/NOLITE&gt;
	// FIXME replace with general parameter parsing function, this is daft
	pg.re.oldid=RegExp('[?&amp;]oldid=([^&amp;]*)');
	pg.re.diff=RegExp('[?&amp;]diff=([^&amp;]*)');
}


//////////////////////////////////////////////////
// miscellany

function setupCache() {
	// page caching
	pg.cache.pages = [];
}

function setMisc() {
	pg.current.link=null;
	pg.current.links=[];
	pg.current.linksHash={};

	setupCache();

	pg.timer.checkPopupPosition=null;
	pg.counter.loop=0;

	// ids change with each popup: popupImage0, popupImage1 etc
	pg.idNumber=0;

	// for myDecodeURI
	pg.misc.decodeExtras = [
		{from: '%2C', to: ',' },
		{from: '_',   to: ' ' },
		{from: '%24', to: '$'},
		{from: '%26',   to: '&amp;' } // no ,
		];

}

function leadingInteger(s){
	var n=s.match(/^(\d*)/)[1];
	if (n) { return +n; }
	return null;
}

function setBrowserHacks() {
	var useOriginal=false;
	// browser-specific hacks
	if (typeof window.opera != 'undefined') {
		//if (leadingInteger(opera.version()) &lt; 9)
		{ useOriginal=true; } // v9 beta still seems to have buggy css
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
	} else if (navigator.appName=='Konqueror') {
		setDefault('popupNavLinkSeparator', ' &amp;bull; ');
		pg.flag.isKonq=true;
	} else if ( navigator.vendor &amp;&amp; navigator.vendor.toLowerCase().indexOf('apple computer')===0) {
		pg.flag.isSafari=true;
		var webkit=+navigator.userAgent.replace(RegExp('^.*AppleWebKit[/](\\d+).*', 'i'), '$1');
		if (webkit &lt; 420) { useOriginal=true; }
	} else if (navigator.appName.indexOf(&quot;Microsoft&quot;)!=-1) {
		setDefault('popupNavLinkSeparator', ' &amp;#183; ');
		var ver=+navigator.userAgent.replace(RegExp('^.*MSIE (\\d+).*'), '$1');
		pg.flag.isIE=true;
		pg.flag.IEVersion=ver;
	}
	if (pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 8) {
		useOriginal=true;
	}
	if ((pg.flag.isIE &amp;&amp; pg.flag.IEVersion &lt; 7) || pg.flag.isKonq || (pg.flag.isSafari &amp;&amp; webkit &lt; 420)) {
		pg.flag.linksLikeIE6=true;
	}
	if (useOriginal &amp;&amp; pg.structures.original) {
		setDefault('popupStructure','original');
	}
}

function setupPopups() {
	// NB translatable strings should be set up first (strings.js)
	// basics
	setupDebugging();
	setSiteInfo();
	setTitleBase();
	setOptions(); // see options.js

	// namespaces etc
	setNamespaces();
	setInterwiki();

	// regexps
	setRegexps();
	setRedirs();

	// other stuff
	setBrowserHacks();
	setMisc();
	setupLivePreview();

	// main deal here
	setupTooltips();
	Navpopup.tracker.enable();

	setupPopups.completed = true;
}
// ENDFILE: init.js
// STARTFILE: navlinks.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// navlinks... let the fun begin
//

function defaultNavlinkSpec() {
	var str='';
	str += '&lt;b&gt;&lt;&lt;mainlink|shortcut= &gt;&gt;&lt;/b&gt;';
	if (getValueOf('popupLastEditLink')) {
		str += '*&lt;&lt;lastEdit|shortcut=/&gt;&gt;|&lt;&lt;lastContrib&gt;&gt;|&lt;&lt;sinceMe&gt;&gt;if(oldid){|&lt;&lt;oldEdit&gt;&gt;|&lt;&lt;diffCur&gt;&gt;}';
	}

	// user links
	// contribs - log - count - email - block
	// count only if applicable; block only if popupAdminLinks
	str += 'if(user){&lt;br&gt;&lt;&lt;contribs|shortcut=c&gt;&gt;*&lt;&lt;userlog|shortcut=L|log&gt;&gt;';
	str+='if(ipuser){*&lt;&lt;arin&gt;&gt;}if(wikimedia){*&lt;&lt;count|shortcut=#&gt;&gt;}';
	str+='if(ipuser){}else{*&lt;&lt;email|shortcut=E&gt;&gt;}if(admin){*&lt;&lt;block|shortcut=b&gt;&gt;|&lt;&lt;blocklog|log&gt;&gt;}}';

	// editing links
	// talkpage   -&gt; edit|new - history - un|watch - article|edit
	// other page -&gt; edit - history - un|watch - talk|edit|new
	var editstr='&lt;&lt;edit|shortcut=e&gt;&gt;';
	var editOldidStr='if(oldid){&lt;&lt;editOld|shortcut=e&gt;&gt;|&lt;&lt;revert|shortcut=v|rv&gt;&gt;|&lt;&lt;edit|cur&gt;&gt;}else{' + editstr + '}'
		var historystr='&lt;&lt;history|shortcut=h&gt;&gt;if(mainspace_en){|&lt;&lt;editors|shortcut=E|&gt;&gt;}';
	var watchstr='&lt;&lt;unwatch|unwatchShort&gt;&gt;|&lt;&lt;watch|shortcut=w|watchThingy&gt;&gt;';

	str+='&lt;br&gt;if(talk){' +
		editOldidStr+'|&lt;&lt;new|shortcut=+&gt;&gt;' + '*' + historystr+'*'+watchstr + '*' +
		'&lt;b&gt;&lt;&lt;article|shortcut=a&gt;&gt;&lt;/b&gt;|&lt;&lt;editArticle|edit&gt;&gt;' +
		'}else{' + // not a talk page
		editOldidStr + '*' + historystr + '*' + watchstr + '*' +
		'&lt;b&gt;&lt;&lt;talk|shortcut=t&gt;&gt;&lt;/b&gt;|&lt;&lt;editTalk|edit&gt;&gt;|&lt;&lt;newTalk|shortcut=+|new&gt;&gt;'
		+ '}';

	// misc links
	str += '&lt;br&gt;&lt;&lt;whatLinksHere|shortcut=l&gt;&gt;*&lt;&lt;relatedChanges|shortcut=r&gt;&gt;*&lt;&lt;move|shortcut=m&gt;&gt;';

	// admin links
	str += 'if(admin){&lt;br&gt;&lt;&lt;unprotect|unprotectShort&gt;&gt;|&lt;&lt;protect|shortcut=p&gt;&gt;|&lt;&lt;protectlog|log&gt;&gt;*' +
		'&lt;&lt;undelete|undeleteShort&gt;&gt;|&lt;&lt;delete|shortcut=d&gt;&gt;|&lt;&lt;deletelog|log&gt;&gt;}';
	return str;
}

function navLinksHTML (article, hint, params) { //oldid, rcid) {
	var str = '&lt;span class=&quot;popupNavLinks&quot;&gt;' + defaultNavlinkSpec() + '&lt;/span&gt;';
	// BAM
	return navlinkStringToHTML(str, article, params);
}

function expandConditionalNavlinkString(s,article,z,recursionCount) {
	var oldid=z.oldid, rcid=z.rcid, diff=z.diff;
	// nested conditionals (up to 10 deep) are ok, hopefully! (work from the inside out)
	if (typeof recursionCount!=typeof 0) { recursionCount=0; }
	var conditionalSplitRegex=RegExp(
		//(1     if    \\(    (2    2)    \\)      {(3    3)}  (4   else      {(5     5)}  4)1)
		'(;?\\s*if\\s*\\(\\s*([\\w]*)\\s*\\)\\s*\\{([^{}]*)\\}(\\s*else\\s*\\{([^{}]*?)\\}|))', 'i');
	var splitted=s.parenSplit(conditionalSplitRegex);
	// $1: whole conditional
	// $2: test condition
	// $3: true expansion
	// $4: else clause (possibly empty)
	// $5: false expansion (possibly null)
	var numParens=5;
	var ret = splitted[0];
	for (var i=1; i&lt;splitted.length; i=i+numParens+1) {

		var testString=splitted[i+2-1];
		var trueString=splitted[i+3-1];
		var falseString=splitted[i+5-1];
		if (typeof falseString=='undefined' || !falseString) { falseString=''; }
		var testResult=null;

		switch (testString) {
		case 'user':
			testResult=(article.userName())?true:false;
			break;
		case 'talk':
			testResult=(article.talkPage())?false:true; // talkPage converts _articles_ to talkPages
			break;
		case 'admin':
			testResult=getValueOf('popupAdminLinks')?true:false;
			break;
		case 'oldid':
			testResult=(typeof oldid != 'undefined' &amp;&amp; oldid)?true:false;
			break;
		case 'rcid':
			testResult=(typeof rcid != 'undefined' &amp;&amp; rcid)?true:false;
			break;
		case 'ipuser':
			testResult=(article.isIpUser())?true:false;
			break;
		case 'mainspace_en':
			testResult=isInMainNamespace(article) &amp;&amp;
				pg.wiki.hostname=='en.wikiversity.org';
			break;
		case 'wikimedia':
			testResult=(pg.wiki.wikimedia) ? true : false;
			break;
		case 'diff':
			testResult=(typeof diff != 'undefined' &amp;&amp; diff)?true:false;
			break;
		}

		switch(testResult) {
		case null: ret+=splitted[i];  break;
		case true: ret+=trueString;   break;
		case false: ret+=falseString; break;
		}

		// append non-conditional string
		ret += splitted[i+numParens];
	}
	if (conditionalSplitRegex.test(ret) &amp;&amp; recursionCount &lt; 10) {
		return expandConditionalNavlinkString(ret,article,z,recursionCount+1);
	}
	return ret;
}

function navlinkStringToArray(s, article, params) {
	s=expandConditionalNavlinkString(s,article,params);
	var splitted=s.parenSplit(RegExp('&lt;&lt;(.*?)&gt;&gt;'));
	var ret=[];
	for (var i=0; i&lt;splitted.length; ++i) {
		if (i%2) { // i odd, so s is a tag
			var t=new navlinkTag();
			var ss=splitted[i].split('|');
			t.id=ss[0];
			for (var j=1; j&lt;ss.length; ++j) {
				var sss=ss[j].split('=');
				if (sss.length&gt;1) {
					t[sss[0]]=sss[1];
				}
				else { // no assignment (no &quot;=&quot;), so treat this as a title (overwriting the last one)
					t.text=popupString(sss[0]);
				}
			}
			t.article=article;
			var oldid=params.oldid, rcid=params.rcid, diff=params.diff;
			if (typeof oldid != 'undefined' &amp;&amp; oldid != null) { t.oldid=oldid; }
			if (typeof rcid != 'undefined' &amp;&amp; rcid != null) { t.rcid=rcid; }
			if (typeof diff != 'undefined' &amp;&amp; diff != null) { t.diff=diff; }
			if (!t.text &amp;&amp; t.id != 'mainlink') { t.text=popupString(t.id); }
			ret.push(t);
		}
		else { // plain HTML
			ret.push(splitted[i]);
		}
	}
	return ret;
}


function navlinkSubstituteHTML(s) {
	return s.split('*').join(getValueOf('popupNavLinkSeparator'))
		.split('&lt;menurow&gt;').join('&lt;li class=&quot;popup_menu_row&quot;&gt;')
		.split('&lt;/menurow&gt;').join('&lt;/li&gt;')
		.split('&lt;menu&gt;').join('&lt;ul class=&quot;popup_menu&quot;&gt;')
		.split('&lt;/menu&gt;').join('&lt;/ul&gt;');

}

function navlinkDepth(magic,s) {
	return s.split('&lt;' + magic + '&gt;').length - s.split('&lt;/' + magic + '&gt;').length;
}


// navlinkString: * becomes the separator
//                &lt;&lt;foo|bar=baz|fubar&gt;&gt; becomes a foo-link with attribute bar='baz'
//                                      and visible text 'fubar'
//                if(test){...} and if(test){...}else{...} work too (nested ok)

function navlinkStringToHTML(s,article,params) {
	//limitAlert(navlinkStringToHTML, 5, 'navlinkStringToHTML\n' + article + '\n' + (typeof article));
	var p=navlinkStringToArray(s,article,params);
	var html='';
	var menudepth = 0; // nested menus not currently allowed, but doesn't do any harm to code for it
	var menurowdepth = 0;
	var wrapping = null;
	for (var i=0; i&lt;p.length; ++i) {
		if (typeof p[i] == typeof '') {
			html+=navlinkSubstituteHTML(p[i]);
			menudepth += navlinkDepth('menu', p[i]);
			menurowdepth += navlinkDepth('menurow', p[i]);
//			if (menudepth === 0) {
//				tagType='span';
//			} else if (menurowdepth === 0) {
//				tagType='li';
//			} else {
//				tagType = null;
//			}
		} else if (typeof p[i].type != 'undefined' &amp;&amp; p[i].type=='navlinkTag') {
			if (menudepth &gt; 0 &amp;&amp; menurowdepth === 0) {
				html += '&lt;li class=&quot;popup_menu_item&quot;&gt;' + p[i].html() + '&lt;/li&gt;';
			} else {
				html+=p[i].html();
			}
		}
	}
	return html;
}

function navlinkTag() {
	this.type='navlinkTag';
}

navlinkTag.prototype.html=function () {
	this.getNewWin();
	this.getPrintFunction();
	var html='';
	var opening, closing;
	var tagType='span';
	if (!tagType) {
		opening = ''; closing = '';
	} else {
		opening = '&lt;' + tagType + ' class=&quot;popup_' + this.id + '&quot;&gt;';
		closing = '&lt;/' + tagType + '&gt;';
	}
	if (typeof this.print!='function') {
		errlog ('Oh dear - invalid print function for a navlinkTag, id='+this.id);
	} else {
		html=this.print(this);
		if (typeof html != typeof '') {html='';}
		else if (typeof this.shortcut!='undefined') html=addPopupShortcut(html, this.shortcut);
	}
	return opening + html + closing;
};

navlinkTag.prototype.getNewWin=function() {
	getValueOf('popupLinksNewWindow');
	if (typeof pg.option.popupLinksNewWindow[this.id] === 'undefined') { this.newWin=null; }
	this.newWin=pg.option.popupLinksNewWindow[this.id];
}

navlinkTag.prototype.getPrintFunction=function() { //think about this some more
	// this.id and this.article should already be defined
	if (typeof this.id!=typeof '' || typeof this.article!=typeof {} ) { return; }
	var html='';
	var a,t;

	this.noPopup=1;
	switch (this.id) {
	case 'contribs': case 'history': case 'whatLinksHere':
	case 'userPage': case 'monobook': case 'userTalk':
	case 'talk': case 'article': case 'lastEdit':
		this.noPopup=null;
	}
	switch (this.id) {
	case 'email':     case 'contribs':  case 'block':     case 'unblock':
	case 'userlog':   case 'userSpace': case 'deletedContribs':
		this.article=this.article.userName();
	}

	switch (this.id) {
	case 'userTalk': case 'newUserTalk': case 'editUserTalk':
	case 'userPage': case 'monobook': case 'editMonobook': case 'blocklog':
		this.article=this.article.userName(true);
	// fall through; no break
	case 'pagelog': case 'deletelog': case 'protectlog':
	delete this.oldid;
	}

	if (this.id=='editMonobook' || this.id=='monobook') { this.article.append('/monobook.js'); }

	if (this.id != 'mainlink') {
		// FIXME anchor handling should be done differently with Title object
		this.article=this.article.removeAnchor();
		// if (typeof this.text=='undefined') this.text=popupString(this.id);
	}

	switch (this.id) {
	case 'undelete':       this.print=specialLink; this.specialpage='Undelete'; this.sep='/'; break;
	case 'whatLinksHere':  this.print=specialLink; this.specialpage='Whatlinkshere'; break;
	case 'relatedChanges': this.print=specialLink; this.specialpage='Recentchangeslinked'; break;
	case 'move':           this.print=specialLink; this.specialpage='Movepage'; break;
	case 'contribs':       this.print=specialLink; this.specialpage='Contributions'; break;
	case 'deletedContribs':this.print=specialLink; this.specialpage='Deletedcontributions'; break;
	case 'email':          this.print=specialLink; this.specialpage='EmailUser'; this.sep='/'; break;
	case 'block':          this.print=specialLink; this.specialpage='Blockip'; this.sep='&amp;ip='; break;
	case 'unblock':        this.print=specialLink; this.specialpage='Ipblocklist'; this.sep='&amp;action=unblock&amp;ip='; break;
	case 'userlog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;user='; break;
	case 'blocklog':       this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=block&amp;page='; break;
	case 'pagelog':        this.print=specialLink; this.specialpage='Log'; this.sep='&amp;page='; break;
	case 'protectlog':     this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=protect&amp;page='; break;
	case 'deletelog':      this.print=specialLink; this.specialpage='Log'; this.sep='&amp;type=delete&amp;page='; break;
	case 'userSpace':      this.print=specialLink; this.specialpage='PrefixIndex'; this.sep='&amp;namespace=2&amp;prefix='; break;
	case 'search':         this.print=specialLink; this.specialpage='Search'; this.sep='&amp;fulltext=Search&amp;search='; break;
	case 'history': case 'historyfeed': case 'unwatch': case 'watch':
	case 'unprotect': case 'protect':
	this.print=wikiLink; this.action=this.id; break;

	case 'delete':
	this.print=wikiLink; this.action='delete';
	if (this.article.namespaceId()==pg.nsImageId) {
	    var img=this.article.stripNamespace();
	    this.action+='&amp;image='+img;
	}
	break;

	case 'markpatrolled':
	case 'edit': // editOld should keep the oldid, but edit should not.
	delete this.oldid; // fall through
	case 'view': case 'purge': case 'render':
	this.print=wikiLink;
	this.action=this.id; break;
	case 'raw':
	this.print=wikiLink; this.action='raw&amp;ctype=text/css'; break;
	case 'new':
	this.print=wikiLink; this.action='edit&amp;section=new'; break;
	case 'mainlink':
	if (typeof this.text=='undefined') { this.text=this.article.toString().entify(); }
	if (getValueOf('popupSimplifyMainLink') &amp;&amp; isInStrippableNamespace(this.article)) {
	    var s=this.text.split('/'); this.text=s[s.length-1];
	    if (this.text=='' &amp;&amp; s.length &gt; 1) { this.text=s[s.length-2]; }
	}
	this.print=titledWikiLink;
	if (typeof this.title=='undefined' &amp;&amp; pg.current.link &amp;&amp; typeof pg.current.link.href != 'undefined') {
	    this.title=safeDecodeURI((pg.current.link.originalTitle)?pg.current.link.originalTitle:this.article);
	    if (typeof this.oldid != 'undefined' &amp;&amp; this.oldid) {
		this.title=tprintf('Revision %s of %s', [this.oldid, this.title]);
	    }
	}
	this.action='view'; break;
	case 'userPage':
	case 'article':
	case 'monobook':
	case 'editMonobook':
	case 'editArticle':
	delete this.oldid;
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.article=this.article.articleFromTalkOrArticle();
	//alert(this.id+'\n'+this.article + '\n'+ typeof this.article);
	this.print=wikiLink;
	if (this.id.indexOf('edit')==0) {
	    this.action='edit';
	} else { this.action='view';}
	break;
	case 'userTalk':
	case 'talk':
	this.article=this.article.talkPage();
	delete this.oldid;
	this.print=wikiLink;
	this.action='view'; break;
	case 'arin':
	this.print=arinLink; break;
	case 'count':
	this.print=editCounterLink; break;
	case 'google':
	this.print=googleLink; break;
	case 'editors':
	this.print=editorListLink; break;
	case 'globalsearch':
	this.print=globalSearchLink; break;
	case 'lastEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the last edit');
	this.from='prev'; this.to='cur'; break;
	case 'oldEdit':
	this.print=titledDiffLink;
	this.title=popupString('Show the edit made to get revision') + ' ' + this.oldid;
	this.from='prev'; this.to=this.oldid; break;
	case 'editOld':
	this.print=wikiLink; this.action='edit'; break;
	case 'undo':
	this.print=wikiLink; this.action='edit&amp;undo='; break;
	case 'markpatrolled':
	this.print=wikiLink; this.action='markpatrolled';
	case 'revert':
	this.print=wikiLink; this.action='revert'; break;
	case 'nullEdit':
	this.print=wikiLink; this.action='nullEdit'; break;
	case 'diffCur':
	this.print=titledDiffLink;
	this.title=tprintf('Show changes since revision %s', [this.oldid]);
	this.from=this.oldid; this.to='cur'; break;
	case 'editUserTalk':
	case 'editTalk':
	delete this.oldid;
	this.article=this.article.talkPage();
	this.action='edit'; this.print=wikiLink; break;
	case 'newUserTalk':
	case 'newTalk':
	this.article=this.article.talkPage();
	this.action='edit&amp;section=new'; this.print=wikiLink; break;
	case 'lastContrib':
	case 'sinceMe':
	this.print=magicHistoryLink;
	break;
	case 'togglePreviews':
	this.text=popupString(pg.option.simplePopups ? 'enable previews' : 'disable previews');
	case 'disablePopups': case 'purgePopups':
	this.print=popupMenuLink;
	break;
	default:
	this.print=function () {return 'Unknown navlink type: '+this.id+''};
	}
};
//
//  end navlinks
//////////////////////////////////////////////////
//&lt;/NOLITE&gt;
// ENDFILE: navlinks.js
// STARTFILE: shortcutkeys.js
//&lt;NOLITE&gt;
function popupHandleKeypress(evt) {
	var keyCode = window.event ? window.event.keyCode : ( evt.keyCode ? evt.keyCode : evt.which);
	if (!keyCode || !pg.current.link || !pg.current.link.navpopup) { return; }
	if (keyCode==27) { // escape
		killPopup();
		return false; // swallow keypress
	}

	var letter=String.fromCharCode(keyCode);
	var links=pg.current.link.navpopup.mainDiv.getElementsByTagName('A');
	var startLink=0;
	var i,j;

	if (popupHandleKeypress.lastPopupLinkSelected) {
		for (i=0; i&lt;links.length; ++i) {
			if (links[i]==popupHandleKeypress.lastPopupLinkSelected) { startLink=i; }
		}
	}
	for (j=0; j&lt;links.length; ++j) {
		i=(startLink + j + 1) % links.length;
		if (links[i].getAttribute('popupkey')==letter) {
			if (evt &amp;&amp; evt.preventDefault) evt.preventDefault();
			links[i].focus();
			popupHandleKeypress.lastPopupLinkSelected=links[i];
			return false; // swallow keypress
		}
	}

	// pass keypress on
	if (document.oldPopupOnkeypress) { return document.oldPopupOnkeypress(evt); }
	return true;
}

function addPopupShortcuts() {
	if (document.onkeypress!=popupHandleKeypress) {
		document.oldPopupOnkeypress=document.onkeypress;
	}
	document.onkeypress=popupHandleKeypress;
}

function rmPopupShortcuts() {
	popupHandleKeypress.lastPopupLinkSelected=null;
	try {
		if (document.oldPopupOnkeypress &amp;&amp; document.oldPopupOnkeypress==popupHandleKeypress) {
			// panic
			document.onkeypress=null; //function () {};
			return;
		}
		document.onkeypress=document.oldPopupOnkeypress;
	} catch (nasties) { /* IE goes here */ }
}


function addLinkProperty(html, property) {
	// take &quot;&lt;a href=...&gt;...&lt;/a&gt; and add a property
	// not sophisticated at all, easily broken
	var i=html.indexOf('&gt;');
	if (i&lt;0) { return html; }
	return html.substring(0,i) + ' ' + property + html.substring(i);
}

function addPopupShortcut(html, key) {
	if (!getValueOf('popupShortcutKeys')) { return html; }
	var ret= addLinkProperty(html, 'popupkey=&quot;'+key+'&quot;');
	if (key==' ') { key=popupString('spacebar'); }
	return ret.replace(RegExp('^(.*?)(title=&quot;)(.*?)(&quot;.*)$', 'i'),'$1$2$3 ['+key+']$4');
}
//&lt;/NOLITE&gt;
// ENDFILE: shortcutkeys.js
// STARTFILE: diffpreview.js
//&lt;NOLITE&gt;
function loadDiff(article, oldid, diff, navpop) {
	navpop.diffData={};
	var oldRev, newRev;
	switch (diff) {
	case 'cur':
		switch ( oldid ) {
		case null:
		case '':
		case 'prev':
			// eg newmessages diff link
			oldRev='0&amp;direction=prev';
			newRev=0;
			break;
		default:
			oldRev = oldid;
			newRev = 0;
		}
		break;
	case 'prev':
		oldRev = ( oldid || 0 ) + '&amp;direction=prev'; newRev = oldid; break;
	case 'next':
		oldRev = oldid; newRev = oldid + '&amp;direction=next';
		break;
	default:
		oldRev = oldid || 0; newRev = diff || 0; break;
	}
	oldRev = oldRev || 0;
	newRev = newRev || 0;

	var go = function() {
		pendingNavpopTask(navpop);
		getWiki(article, doneDiffNew, newRev, navpop);

		pendingNavpopTask(navpop);
		getWiki(article, doneDiffOld, oldRev, navpop);

		var tz = Cookie.read('popTz');
		if (getValueOf('popupAdjustDiffDates') &amp;&amp; tz===null) {
		    pendingNavpopTask(navpop);
		    getPageWithCaching(pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;meta=userinfo&amp;uiprop=options',
				       function(d) {
					       completedNavpopTask(navpop);
					       setTimecorrectionCookie(d);
					       if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
				       },  navpop);
		}
		return true; // remove hook once run
	}
	if (navpop.visible || !getValueOf('popupLazyDownloads')) { go(); }
	else { navpop.addHook(go, 'unhide', 'before', 'DOWNLOAD_DIFFS'); }
}

function setTimecorrectionCookie(d) {
	try {
		var jsobj=getJsObj(d.data);
		var tz=jsobj.query.userinfo.options.timecorrection;
	} catch (someError) {
		logerr( 'setTimecorretion failed' );
		return;
	}
    Cookie.create( 'popTz', getTimeOffset(tz), 1);
}

function doneDiff(download, isOld) {
	if (!download.owner || !download.owner.diffData) { return; }
	var navpop=download.owner;
	var label= (isOld) ? 'Old' : 'New';
	var otherLabel=(isOld) ? 'New' : 'Old';
	navpop.diffData[label]=download;
	completedNavpopTask(download.owner);
	if (diffDownloadsComplete(navpop)) { insertDiff(navpop); }
}

function diffDownloadsComplete(navpop) {
	if ( Cookie.read('popTz')===null) { return false; }
	return navpop.diffData.Old &amp;&amp; navpop.diffData.New;
}

function doneDiffNew(download) { doneDiff(download, false); }
function doneDiffOld(download) { doneDiff(download, true);  }

function rmBoringLines(a,b,context) {

	if (typeof context == 'undefined') { context=2; }
	// this is fairly slow... i think it's quicker than doing a word-based diff from the off, though
	var aa=[], aaa=[];
	var bb=[], bbb=[];
	var i, j;

	// first, gather all disconnected nodes in a and all crossing nodes in a and b
	for (i=0; i&lt;a.length; ++i ) {
		if(!a[i].paired) { aa[i]=1; }
		else if (countCrossings(b,a,i, true)) {
			aa[i]=1;
			bb[ a[i].row ] = 1;
		}
	}

	// pick up remaining disconnected nodes in b
	for (i=0; i&lt;b.length; ++i ) {
		if (bb[i]==1) { continue; }
		if(!b[i].paired) { bb[i]=1; }
	}

	// another pass to gather context: we want the neighbours of included nodes which are not yet included
	// we have to add in partners of these nodes, but we don't want to add context for *those* nodes in the next pass
	for (i=0; i&lt;b.length; ++i) {
		if ( bb[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(b.length, i+context); ++j) {
				if ( !bb[j] ) { bb[j] = 1; aa[ b[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;a.length; ++i) {
		if ( aa[i] == 1 ) {
			for (j=max(0,i-context); j &lt; min(a.length, i+context); ++j) {
				if ( !aa[j] ) { aa[j] = 1; bb[ a[j].row ] = 0.5; }
			}
		}
	}

	for (i=0; i&lt;bb.length; ++i) {
		if (bb[i] &gt; 0) { // it's a row we need
			if (b[i].paired) { bbb.push(b[i].text); } // joined; partner should be in aa
			else {
				bbb.push(b[i]);
			}
		}
	}
	for (i=0; i&lt;aa.length; ++i) {
		if (aa[i] &gt; 0) { // it's a row we need
			if (a[i].paired) { aaa.push(a[i].text); } // joined; partner should be in aa
			else {
				aaa.push(a[i]);
			}
		}
	}

	return { a: aaa, b: bbb};
}

function stripOuterCommonLines(a,b,context) {
	var i=0;
	while (i&lt;a.length &amp;&amp; i &lt; b.length &amp;&amp; a[i]==b[i]) { ++i; }
	var j=a.length-1; var k=b.length-1;
	while ( j&gt;=0 &amp;&amp; k&gt;=0 &amp;&amp; a[j]==b[k] ) { --j; --k; }

	return { a: a.slice(max(0,i - 1 - context), min(a.length+1, j + context+1)),
			    b: b.slice(max(0,i - 1 - context), min(b.length+1, k + context+1)) };
}

function insertDiff(navpop) {
	// for speed reasons, we first do a line-based diff, discard stuff that seems boring, then do a word-based diff
	// FIXME: sometimes this gives misleading diffs as distant chunks are squashed together
	var oldlines=navpop.diffData.Old.data.split('\n');
	var newlines=navpop.diffData.New.data.split('\n');
	var inner=stripOuterCommonLines(oldlines,newlines,getValueOf('popupDiffContextLines'));
	oldlines=inner.a; newlines=inner.b;
	var truncated=false;
	getValueOf('popupDiffMaxLines');
	if (oldlines.length &gt; pg.option.popupDiffMaxLines || newlines.length &gt; pg.option.popupDiffMaxLines) {
		// truncate
		truncated=true;
		inner=stripOuterCommonLines(oldlines.slice(0,pg.option.popupDiffMaxLines),
					    newlines.slice(0,pg.option.popupDiffMaxLines),
					    pg.option.popupDiffContextLines);
		oldlines=inner.a; newlines=inner.b;
	}

	var lineDiff=diff(oldlines, newlines);
	var lines2=rmBoringLines(lineDiff.o, lineDiff.n);
	var oldlines2=lines2.a; var newlines2=lines2.b;

	var simpleSplit = !String.prototype.parenSplit.isNative;
	var html='&lt;hr&gt;';
	if (getValueOf('popupDiffDates')) {
		html += diffDatesTable(navpop.diffData.Old, navpop.diffData.New);
		html += '&lt;hr&gt;';
	}
	html += shortenDiffString(
		diffString(oldlines2.join('\n'), newlines2.join('\n'), simpleSplit),
		getValueOf('popupDiffContextCharacters') ).join('&lt;hr&gt;');
	setPopupTipsAndHTML(html.split('\n').join('&lt;br&gt;') +
		     (truncated ? '&lt;hr&gt;&lt;b&gt;'+popupString('Diff truncated for performance reasons')+'&lt;/b&gt;' : '') ,
			    'popupPreview', navpop.idNumber);
}

function diffDatesTable( oldDl, newDl ) {
	var html='&lt;table class=&quot;popup_diff_dates&quot;&gt;';
	html += diffDatesTableRow( newDl, tprintf('New revision'));
	html += diffDatesTableRow( oldDl, tprintf('Old revision'));
	html += '&lt;/table&gt;';
	return html;
}
function diffDatesTableRow( dl, label ) {
	var txt='';
	if (!dl) {
		txt=popupString('Something went wrong :-(');
	} else if (!dl.lastModified) {
		txt= (/^\s*$/.test(dl.data)) ?
			popupString('Empty revision, maybe non-existent') : popupString('Unknown date');
	} else {
		var datePrint=getValueOf('popupDiffDatePrinter');
		if (typeof dl.lastModified[datePrint] == 'function') {
			if (getValueOf('popupAdjustDiffDates')) {
				var off;
				if (off=Cookie.read('popTz')) {
					var d2=adjustDate(dl.lastModified, off);
					txt = dayFormat(d2, true) + ' ' + timeFormat(d2, true);
				}
			} else {
				txt = dl.lastModified[datePrint]();
			}
		} else {
			txt = tprintf('Invalid %s %s', ['popupDiffDatePrinter', datePrint]);
		}
	}
	var revlink = generalLink({url: dl.url.replace(/&amp;.*?(oldid=[0-9]+(?:&amp;direction=[^&amp;]*)?).*/, '&amp;$1'),
				   text: label, title: label});
	return simplePrintf('&lt;tr&gt;&lt;td&gt;%s&lt;/td&gt;&lt;td&gt;%s&lt;/td&gt;&lt;/tr&gt;', [ revlink, txt ]);
}
//&lt;/NOLITE&gt;
// ENDFILE: diffpreview.js
// STARTFILE: links.js
//&lt;NOLITE&gt;
/////////////////////
// LINK GENERATION //
/////////////////////

// titledDiffLink --&gt; titledWikiLink --&gt; generalLink
// wikiLink       --&gt; titledWikiLink --&gt; generalLink
// editCounterLink --&gt; generalLink

function titledDiffLink(l) { // article, text, title, from, to) {
	return titledWikiLink({article: l.article, action: l.to + '&amp;oldid=' + l.from,
				newWin: l.newWin,
				noPopup: l.noPopup,
				text: l.text, title: l.title,
				/* hack: no oldid here */
				actionName: 'diff'});
}


function wikiLink(l) {
	//{article:article, action:action, text:text, oldid, newid}) {
	if (! (typeof l.article == typeof {}
	       &amp;&amp; typeof l.action == typeof '' &amp;&amp; typeof l.text==typeof '')) return null;
	if (typeof l.oldid == 'undefined') { l.oldid=null; }
	var savedOldid = l.oldid;
	if (!/^(edit|view|revert|render)$|^raw/.test(l.action)) { l.oldid=null; }
	var hint=popupString(l.action + 'Hint'); // revertHint etc etc etc
	var oldidData=[l.oldid, safeDecodeURI(l.article)];
	var revisionString = tprintf('revision %s of %s', oldidData);
	log('revisionString='+revisionString);
	switch (l.action) {
	case 'edit&amp;section=new': hint = popupString('newSectionHint');  break;
	case 'edit&amp;undo=':
		if (l.diff &amp;&amp; l.diff != 'prev' &amp;&amp; savedOldid ) {
		  l.action += l.diff + '&amp;undoafter=' + savedOldid;
		} else if (savedOldid) {
		  l.action += savedOldid;
		}
		hint = popupString('undoHint');
		break;
	case 'raw&amp;ctype=text/css': hint=popupString('rawHint'); break;
	case 'revert':
		var p=parseParams(pg.current.link.href);
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=' + revertSummary(l.oldid, p.diff);
		if (p.diff=='prev') {
			l.action += '&amp;direction=prev';
			revisionString = tprintf('the revision prior to revision %s of %s', oldidData);
		}
		if (getValueOf('popupRevertSummaryPrompt')) { l.action += '&amp;autosummaryprompt=true'; }
		if (getValueOf('popupMinorReverts')) { l.action += '&amp;autominor=true'; }
		log('revisionString is now '+revisionString);
		break;
	case 'nullEdit':
		l.action='edit&amp;autoclick=wpSave&amp;actoken=' + autoClickToken() + '&amp;autosummary=null';
		break;
	case 'historyfeed':
		l.action='history&amp;feed=rss';
		break;
	case 'markpatrolled':
		l.action='markpatrolled&amp;rcid='+l.rcid;
	}

	if (hint) {
		if (l.oldid) {
			hint = simplePrintf(hint, [revisionString]);
		}
		else {
			hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
		}
	}
	else {
		hint = safeDecodeURI(l.article + '&amp;action=' + l.action) + (l.oldid) ? '&amp;oldid='+l.oldid : '';
	}

	return titledWikiLink({article: l.article, action: l.action, text: l.text, newWin:l.newWin,
				title: hint, oldid: l.oldid, noPopup: l.noPopup});
}

function revertSummary(oldid, diff) {
	var ret='';
	if (diff == 'prev') {
		ret=getValueOf('popupQueriedRevertToPreviousSummary');
	} else { ret = getValueOf('popupQueriedRevertSummary'); }
	return ret + '&amp;autorv=' + oldid;
}

function titledWikiLink(l) {
	// possible properties of argument:
	// article, action, text, title, oldid, actionName, className, noPopup
	// oldid = null is fine here

	// article and action are mandatory args

	if (typeof l.article == 'undefined' || typeof l.action=='undefined') {
		errlog('got undefined article or action in titledWikiLink');
		return null;
	}

	var base = pg.wiki.titlebase +  l.article.urlString();
	var url=base;

	if (typeof l.actionName=='undefined' || !l.actionName) { l.actionName='action'; }

	// no need to add &amp;action=view, and this confuses anchors
	if (l.action != 'view') { url = base + '&amp;' + l.actionName + '=' + l.action; }

	if (typeof l.oldid!='undefined' &amp;&amp; l.oldid) { url+='&amp;oldid='+l.oldid; }

	var cssClass=pg.misc.defaultNavlinkClassname;
	if (typeof l.className!='undefined' &amp;&amp; l.className) { cssClass=l.className; }

	return generalNavLink({url: url, newWin: l.newWin,
				title: (typeof l.title != 'undefined') ? l.title : null,
				text: (typeof l.text!='undefined')?l.text:null,
				className: cssClass, noPopup:l.noPopup});
}

function getLastContrib(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processLastContribInfo(x,{page: wikipage, newWin: newWin})});
}
function processLastContribInfo(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: an odd thing happened. Please retry.'); return; }
	if(!info.firstNewEditor) {
		alert(tprintf('Only found one editor: %s made %s edits', [info.edits[0].editor,info.edits.length]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+info.firstNewEditor.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function getDiffSinceMyEdit(wikipage, newWin) {
	getHistoryInfo(wikipage, function(x){processDiffSinceMyEdit(x,{page: wikipage, newWin: newWin})});
}
function processDiffSinceMyEdit(info, stuff) {
	if(!info.edits || !info.edits.length) { alert('Popups: something fishy happened. Please try again.'); return; }
	var friendlyName=stuff.page.split('_').join(' ');
	if(!info.myLastEdit) {
		alert(tprintf('Couldn\'t find an edit by %s\nin the last %s edits to\n%s',
			      [info.userName, getValueOf('popupHistoryLimit'), friendlyName]));
		return;
	}
	if(info.myLastEdit.index==0) {
		alert(tprintf(&quot;%s seems to be the last editor to the page %s&quot;, [info.userName, friendlyName]));
		return;
	}
	var newUrl=pg.wiki.titlebase + new Title(stuff.page).urlString() + '&amp;diff=cur&amp;oldid='+ info.myLastEdit.oldid;
	displayUrl(newUrl, stuff.newWin);
}
function displayUrl(url, newWin){
	if(newWin) { window.open(url); }
	else { document.location=url; }
}

function purgePopups() {
	processAllPopups(true);
	setupCache(); // deletes all cached items (not browser cached, though...)
	pg.option={};
	abortAllDownloads();
}

function processAllPopups(nullify, banish) {
	for (var i=0; i&lt;pg.current.links.length; ++i) {
		if (!pg.current.links[i].navpopup) { continue; }
		(nullify || banish) &amp;&amp; pg.current.links[i].navpopup.banish();
		pg.current.links[i].simpleNoMore=false;
		nullify &amp;&amp; (pg.current.links[i].navpopup=null);
	}
}

function disablePopups(){
	processAllPopups(false, true);
	setupTooltips(null, true);
}

function togglePreviews() {
	processAllPopups(true, true);
	pg.option.simplePopups=!pg.option.simplePopups;
	abortAllDownloads();
}

function magicHistoryLink(l) {
	// FIXME use onclick change href trick to sort this out instead of window.open

	var jsUrl='', title='';
	switch(l.id) {
	case 'lastContrib':
		jsUrl=simplePrintf('javascript:getLastContrib(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('lastContribHint');
		break;
	case 'sinceMe':
		jsUrl=simplePrintf('javascript:getDiffSinceMyEdit(\'%s\',%s)',
			[l.article.toString(true).split(&quot;'&quot;).join(&quot;\\'&quot;), l.newWin]);
		title=popupString('sinceMeHint');
		break;
	}

	return generalNavLink({url: jsUrl, newWin: false, // can't have new windows with JS links, I think
				title: title, text: l.text, noPopup: l.noPopup});
}

function popupMenuLink(l) {
	var jsUrl=simplePrintf('javascript:%s()', [l.id]);
	var title=popupString(simplePrintf('%sHint', [l.id]));
	return generalNavLink({url: jsUrl, newWin:false, title:title, text:l.text, noPopup:l.noPopup});
}

function specialLink(l) {
	// properties: article, specialpage, text, sep
	if (typeof l.specialpage=='undefined'||!l.specialpage) return null;
	var base = pg.wiki.titlebase +  mw.config.get('wgFormattedNamespaces')[pg.nsSpecialId]+':'+l.specialpage;
	if (typeof l.sep == 'undefined' || l.sep===null) l.sep='&amp;target=';
	var article=l.article.urlString({keepSpaces: l.specialpage=='Search'});
	var hint=popupString(l.specialpage+'Hint');
	switch (l.specialpage) {
	case 'Log':
	    switch (l.sep) {
	    case '&amp;user=': hint=popupString('userLogHint'); break;
	    case '&amp;type=block&amp;page=': hint=popupString('blockLogHint'); break;
	    case '&amp;page=': hint=popupString('pageLogHint'); break;
	    case '&amp;type=protect&amp;page=': hint=popupString('protectLogHint'); break;
	    case '&amp;type=delete&amp;page=': hint=popupString('deleteLogHint'); break;
	    default: log('Unknown log type, sep=' + l.sep); hint='Missing hint (FIXME)';
	    }
	    break;
	case 'PrefixIndex': article += '/'; break;
	}
	if (hint) hint = simplePrintf(hint, [safeDecodeURI(l.article)]);
	else hint = safeDecodeURI(l.specialpage+':'+l.article) ;

	var url = base + l.sep + article;
	return generalNavLink({url: url, title: hint, text: l.text, newWin:l.newWin, noPopup:l.noPopup});
}

function generalLink(l) {
	// l.url, l.text, l.title, l.newWin, l.className, l.noPopup
	if (typeof l.url=='undefined') return null;

	// only quotation marks in the url can screw us up now... I think
	var url=l.url.split('&quot;').join('%22');

	var ret='&lt;a href=&quot;' + url + '&quot;';
	if (typeof l.title!='undefined' &amp;&amp; l.title) { ret += ' title=&quot;' + mw.html.escape(l.title) + '&quot;'; }
	if (l.noPopup) { ret += ' noPopup=1'; }
	var newWin;
	if (typeof l.newWin=='undefined' || l.newWin===null) { newWin=getValueOf('popupNewWindows'); }
	else { newWin=l.newWin; }
	if (newWin) { ret += ' target=&quot;_blank&quot;'; }
	if (typeof l.className!='undefined'&amp;&amp;l.className) { ret+=' class=&quot;'+l.className+'&quot;'; }
	ret += '&gt;';
	if (typeof l.text==typeof '') { ret+= l.text; }
	ret +='&lt;/a&gt;';
	return ret;
}

function appendParamsToLink(linkstr, params) {
	var sp=linkstr.parenSplit(RegExp('(href=&quot;[^&quot;]+?)&quot;', 'i'));
	if (sp.length&lt;2) return null;
	var ret=sp.shift() + sp.shift();
	ret += '&amp;' + params + '&quot;';
	ret += sp.join('');
	return ret;
}

function changeLinkTargetLink(x) { // newTarget, text, hint, summary, clickButton, minor, title (optional) {
	if (x.newTarget) {
		log ('changeLinkTargetLink: newTarget=' + x.newTarget);
	}
	// optional: oldTarget (in wikitext)
	// if x.newTarget omitted or null, remove the link

	x.clickButton=encodeURI(x.clickButton);

	// FIXME: first character of page title as well as namespace should be case insensitive
	// eg [[category:foo]] and [[Category:Foo]] are equivalent
	// this'll break if charAt(0) is nasty
	var cA=literalizeRegex(x.oldTarget);
	var chs=cA[0].toUpperCase();
	chs='['+chs + chs.toLowerCase()+']';
	var currentArticleRegexBit=encodeURIComponent(chs+cA.substring(1));
	currentArticleRegexBit=currentArticleRegexBit
		.split(RegExp('[_ ]+', 'g')).join('[_ ]+')
		.split( &quot;%20&quot; ).join('[_ ]+')
		.split('\\(').join('(?:%2528|\\()')
		.split('\\)').join('(?:%2529|\\))');
	// leading and trailing space should be ignored, and anchor bits optional:
	currentArticleRegexBit = '\\s*(' + currentArticleRegexBit + '(?:#[^\\[\\|]*)?)\\s*';
	// e.g. Computer (archaic) -&gt; \s*([Cc]omputer[_ ](?:%2528|\()archaic(?:%2528|\)))\s*

	// autoedit=s~\[\[([Cc]ad)\]\]~[[Computer-aided%20design|$1]]~g;s~\[\[([Cc]AD)[|]~[[Computer-aided%20design|~g

	var title=x.title || mw.config.get('wgPageName').split('_').join(' ');
	var lk=titledWikiLink({article: new Title(title), newWin:x.newWin,
						action:  'edit',
						text:    x.text,
						title:   x.hint,
						className: 'popup_change_title_link'
						});
	var cmd='';
	if (x.newTarget) {
		// escape '&amp;' and other nasties
		var t=encodeURIComponent(x.newTarget);
		var s=encodeURIComponent(literalizeRegex(x.newTarget));
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~[['+t+'|$1]]~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|]~[['+t+'|~g;';
		cmd += 's~\\[\\['+s + '\\|' + s + '\\]\\]~[[' + t + ']]~g';
	} else {
		cmd += 's~\\[\\['+currentArticleRegexBit+'\\]\\]~$1~g;';
		cmd += 's~\\[\\['+currentArticleRegexBit+'[|](.*?)\\]\\]~$2~g';
	}
	cmd += '&amp;autoclick='+x.clickButton + '&amp;actoken=' + autoClickToken();
	cmd += ( x.minor == null ) ? '' : '&amp;autominor='+x.minor;
	cmd += ( x.watch == null ) ? '' : '&amp;autowatch='+x.watch;
	cmd += '&amp;autosummary='+encodeURIComponent(x.summary);
	return appendParamsToLink(lk, 'autoedit='+cmd);
}


function redirLink(redirMatch, article) {
	// NB redirMatch is in wikiText
	var ret='';

	if (getValueOf('popupAppendRedirNavLinks') &amp;&amp; getValueOf('popupNavLinks')) {
		ret += '&lt;hr&gt;';
		if (getValueOf('popupFixRedirs') &amp;&amp; typeof autoEdit != 'undefined' &amp;&amp; autoEdit) {
			log('redirLink: newTarget=' + redirMatch);
			ret += addPopupShortcut(
				changeLinkTargetLink(
				{newTarget: redirMatch, text: popupString('Redirects'),
					hint: popupString('Fix this redirect'),
						summary: simplePrintf(getValueOf('popupFixRedirsSummary'),
								      [article.toString(), redirMatch ]),
						oldTarget: article.toString(),
						clickButton: getValueOf('popupRedirAutoClick'), minor: true,
						watch: getValueOf('popupWatchRedirredPages')})
				, 'R');
			ret += popupString(' to ');
		}
		else ret += popupString('Redirects') + popupString(' to ');
		return ret;
	}

	else return '&lt;br&gt; ' + popupString('Redirects') + popupString(' to ') +
		     titledWikiLink({article: new Title().fromWikiText(redirMatch), action: 'view',  /* FIXME: newWin */
						      text: safeDecodeURI(redirMatch), title: popupString('Bypass redirect')});
}

function arinLink(l) {
	if (!saneLinkCheck(l)) { return null; }
	if ( ! l.article.isIpUser() || ! pg.wiki.wikimedia) return null;

	var uN=l.article.userName();

	return generalNavLink({url:'http://ws.arin.net/cgi-bin/whois.pl?queryinput=' + encodeURIComponent(uN), newWin:l.newWin,
				title: tprintf('Look up %s in ARIN whois database', [uN]),
				text: l.text, noPopup:1});
}

function toolDbName(cookieStyle) {
	var ret = mw.config.get('wgDBname');
	if (!cookieStyle) { ret+= '_p'; }
	return ret;
}

function saneLinkCheck(l) {
	if (typeof l.article != typeof {} || typeof l.text != typeof '') { return false; }
	return true;
}
function editCounterLink(l) {
	if(!saneLinkCheck(l)) return null;
	if (! pg.wiki.wikimedia) return null;
	var uN=l.article.userName();
	var tool=getValueOf('popupEditCounterTool');
	var url;
	var soxredToolUrl='http://toolserver.org/~soxred93/count/index.php?name=$1&amp;lang=$2&amp;wiki=$3';
	var kateToolUrl='http://toolserver.org/~$3/cgi-bin/Tool1/wannabe_kate?username=$1&amp;site=en.wikiversity.org&amp;$2';

	switch(tool) {
	case 'custom':
		url=simplePrintf(getValueOf('popupEditCounterUrl'), [ encodeURIComponent(uN), toolDbName() ]);
		break;
	case 'kate':
	case 'interiot':
		url=simplePrintf(kateToolUrl, [ encodeURIComponent(uN), toolDbName(), tool ]);
		break;
	default:
	    var theWiki=pg.wiki.hostname.split('.');
		url=simplePrintf(soxredToolUrl, [ encodeURIComponent(uN), theWiki[0], theWiki[1] ]);
	}
	return generalNavLink({url:url, title: tprintf('editCounterLinkHint', [uN]),
				newWin:l.newWin, text: l.text, noPopup:1});
}


function globalSearchLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://vs.aka-online.de/cgi-bin/globalwpsearch.pl?timeout=120&amp;search=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + article, newWin:l.newWin,
				title: tprintf('globalSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function googleLink(l) {
	if(!saneLinkCheck(l)) return null;

	var base='http://www.google.com/search?q=';
	var article=l.article.urlString({keepSpaces:true});

	return generalNavLink({url:base + '%22' + article + '%22', newWin:l.newWin,
				title: tprintf('googleSearchHint', [safeDecodeURI(l.article)]),
				text: l.text, noPopup:1});
}

function editorListLink(l) {
	if(!saneLinkCheck(l)) return null;
	var article= l.article.articleFromTalkPage() || l.article;
        var theWiki=pg.wiki.hostname.split('.');
        var base='http://toolserver.org/~soxred93/articleinfo/index.php?&amp;uselang=' + wgUserLanguage +
            'lang=' + theWiki[0] + '&amp;wiki=' + theWiki[1] + '&amp;begin=&amp;end=&amp;article='
	return generalNavLink({url:base+article.urlString(),
				title: tprintf('editorListHint', [article]),
				newWin:l.newWin, text: l.text, noPopup:1});
}

function generalNavLink(l) {
	l.className = (l.className==null) ? 'popupNavLink' : l.className;
	return generalLink(l);
}

//////////////////////////////////////////////////
// magic history links
//

function getHistoryInfo(wikipage, whatNext) {
	log('getHistoryInfo');
	getHistory(wikipage, whatNext ? function(d){whatNext(processHistory(d));} : processHistory);
}

// FIXME eliminate pg.idNumber ... how? :-(

function getHistory(wikipage, onComplete) {
	log('getHistory');
	var url = pg.wiki.apiwikibase + '?format=json&amp;action=query&amp;prop=revisions&amp;titles=' +
			new Title(wikipage).urlString() + '&amp;rvlimit=' + getValueOf('popupHistoryLimit');
	log('getHistory: url='+url);
	if (pg.flag.isIE) {
		url = url + '&amp;*'; //to circumvent https://bugzilla.wikimedia.org/show_bug.cgi?id=28840
	}
	return startDownload(url, pg.idNumber+'history', onComplete);
}

function processHistory(download) {
	var jsobj = getJsObj(download.data);
	try {
		window.x=jsobj;
		var p=jsobj['query']['pages']
		for (var pageid in p) {
			var revisions=p[pageid]['revisions'];
			// we only get the first one
			break;
		}
	} catch (someError) {
		log('Something went wrong with JSON business');
		return finishProcessHistory([]);
	}
	var edits=[];
	for (var i=0; i&lt;revisions.length; ++i) {
		edits.push({ oldid: revisions[i]['revid'], editor: revisions[i]['user'] });
	}
	log('processed ' + edits.length + ' edits');
	return finishProcessHistory(edits, mw.config.get('wgUserName'));
}


function finishProcessHistory(edits, userName) {
	var histInfo={};

	histInfo.edits=edits;
	histInfo.userName=userName;

	for (var i=0; i&lt;edits.length; ++i) {
		if (typeof histInfo.myLastEdit == 'undefined' &amp;&amp; userName &amp;&amp; edits[i].editor==userName) {
			histInfo.myLastEdit={index: i, oldid: edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
		if (typeof histInfo.firstNewEditor == 'undefined' &amp;&amp; edits[i].editor != edits[0].editor) {
			histInfo.firstNewEditor={index:i, oldid:edits[i].oldid, previd: (i==0 ? null : edits[i-1].oldid)};
		}
	}
	//pg.misc.historyInfo=histInfo;
	return histInfo;
}
//&lt;/NOLITE&gt;
// ENDFILE: links.js
// STARTFILE: options.js
//////////////////////////////////////////////////
// options

// check for cookies and existing value, else use default
function defaultize(x) {
	var val=null;
	if (x!='popupCookies') {
		defaultize('popupCookies');
		if (pg.option.popupCookies &amp;&amp; (val=Cookie.read(x))) {
			pg.option[x]=val;
			return;
		}
	}
	if (pg.option[x]===null || typeof pg.option[x]=='undefined') {
		if (typeof window[x] != 'undefined' ) pg.option[x]=window[x];
		else pg.option[x]=pg.optionDefault[x];
	}
}

function newOption(x, def) {
	pg.optionDefault[x]=def;
}

function setDefault(x, def) {
	return newOption(x, def);
}

function getValueOf(varName) {
	defaultize(varName);
	return pg.option[varName];
}

function useDefaultOptions() { // for testing
	for (var p in pg.optionDefault) {
		pg.option[p]=pg.optionDefault[p];
		if (typeof window[p]!='undefined') { delete window[p]; }
	}
}

function setOptions() {
	// user-settable parameters and defaults
	var userIsSysop = false;
	if ( mw.config.get('wgUserGroups') ) {
		for ( var g = 0; g &lt; mw.config.get('wgUserGroups').length; ++g ) {
			if ( mw.config.get('wgUserGroups')[g] == &quot;sysop&quot; )
				userIsSysop = true
		}
	}

	// Basic options
	newOption('popupDelay',               0.5);
	newOption('popupHideDelay',           0.5);
	newOption('simplePopups',             false);
	newOption('popupStructure',           'shortmenus');   // see later - default for popupStructure is 'original' if simplePopups is true
	newOption('popupActionsMenu',         true);
	newOption('popupSetupMenu',           true);
	newOption('popupAdminLinks',          userIsSysop);
	newOption('popupShortcutKeys',        false);
	newOption('popupHistoricalLinks',     true);
	newOption('popupOnlyArticleLinks',    true);
	newOption('removeTitles',             true);
	newOption('popupMaxWidth',            350);
	newOption('popupInitialWidth',        false); // integer or false
	newOption('popupSimplifyMainLink',    true);
	newOption('popupAppendRedirNavLinks', true);
	newOption('popupTocLinks',            false);
	newOption('popupSubpopups',           true);
	newOption('popupDragHandle',          false /* 'popupTopLinks'*/);
	newOption('popupLazyPreviews',        true);
	newOption('popupLazyDownloads',       true);
	newOption('popupAllDabsStubs',        false);
	newOption('popupDebugging',           false);
	newOption('popupAdjustDiffDates',     true);
	newOption('popupActiveNavlinks',      true);
	newOption('popupModifier',            false); // ctrl, shift, alt or meta
	newOption('popupModifierAction',      'enable'); // or 'disable'
	newOption('popupDraggable',           true);

//&lt;NOLITE&gt;
	// images
	newOption('popupImages',                 true);
	newOption('imagePopupsForImages',        true);
	newOption('popupNeverGetThumbs',         false);
	//newOption('popupImagesToggleSize',       true);
	newOption('popupThumbAction',            'imagepage'); //'sizetoggle');
	newOption('popupImageSize',              60);
	newOption('popupImageSizeLarge',         200);

	// redirs, dabs, reversion
	newOption('popupFixRedirs',             false);
	newOption('popupRedirAutoClick',        'wpDiff');
	newOption('popupFixDabs',               false);
	newOption('popupRevertSummaryPrompt',   false);
	newOption('popupMinorReverts',          false);
	newOption('popupRedlinkRemoval',        false);
	newOption('popupWatchDisambiggedPages', null);
	newOption('popupWatchRedirredPages',    null);
	newOption('popupDabWiktionary',         'last');

	// navlinks
	newOption('popupNavLinks',          true);
	newOption('popupNavLinkSeparator',  ' &amp;sdot; ');
	newOption('popupLastEditLink',      true);
	newOption('popupEditCounterTool',   'soxred');
	newOption('popupEditCounterUrl',    '');
	newOption('popupExtraUserMenu',     '');
//&lt;/NOLITE&gt;

	// previews etc
	newOption('popupPreviews',             true);
	newOption('popupSummaryData',          true);
	newOption('popupMaxPreviewSentences',  5);
	newOption('popupMaxPreviewCharacters', 600);
	newOption('popupLastModified',         true);
	newOption('popupPreviewKillTemplates', true);
	newOption('popupPreviewRawTemplates',  true);
	newOption('popupPreviewFirstParOnly',  true);
	newOption('popupPreviewCutHeadings',   true);
	newOption('popupPreviewButton',        false);
	newOption('popupPreviewButtonEvent',   'click');

//&lt;NOLITE&gt;
	// diffs
	newOption('popupPreviewDiffs',          true);
	newOption('popupDiffMaxLines',          100);
	newOption('popupDiffContextLines',      2);
	newOption('popupDiffContextCharacters', 40);
	newOption('popupDiffDates',             true);
	newOption('popupDiffDatePrinter',       'toLocaleString');

	// edit summaries. God, these are ugly.
	newOption('popupFixDabsSummary',           popupString('defaultpopupFixDabsSummary') );
	newOption('popupExtendedRevertSummary',    popupString('defaultpopupExtendedRevertSummary') );
	newOption('popupTimeOffset',               null);
	newOption('popupRevertSummary',            popupString('defaultpopupRevertSummary') );
	newOption('popupRevertToPreviousSummary',  popupString('defaultpopupRevertToPreviousSummary') );
	newOption('popupQueriedRevertSummary',            popupString('defaultpopupQueriedRevertSummary') );
	newOption('popupQueriedRevertToPreviousSummary',  popupString('defaultpopupQueriedRevertToPreviousSummary') );
	newOption('popupFixRedirsSummary',         popupString('defaultpopupFixRedirsSummary') );
	newOption('popupRedlinkSummary',           popupString('defaultpopupRedlinkSummary') );
	newOption('popupRmDabLinkSummary',         popupString('defaultpopupRmDabLinkSummary') );
//&lt;/NOLITE&gt;
	// misc
	newOption('popupCookies',             false);
	newOption('popupHistoryLimit',        50);
//&lt;NOLITE&gt;
	newOption('popupFilters',             [popupFilterStubDetect,     popupFilterDisambigDetect,
					       popupFilterPageSize,       popupFilterCountLinks,
					       popupFilterCountImages,    popupFilterCountCategories,
					       popupFilterLastModified]);
	newOption('extraPopupFilters',        []);
	newOption('popupOnEditSelection', 'cursor');
	newOption('popupPreviewHistory',      true);
	newOption('popupImageLinks',          true);
	newOption('popupCategoryMembers',     true);
	newOption('popupUserInfo',            true);
	newOption('popupHistoryPreviewLimit', 25);
	newOption('popupContribsPreviewLimit',25);
	newOption('popupRevDelUrl',          '//en.wikiversity.org/wiki/Wikiversity:Revision_deletion');
//&lt;/NOLITE&gt;

	// new windows
	newOption('popupNewWindows',     false);
	newOption('popupLinksNewWindow', {'lastContrib': true, 'sinceMe': true});

	// regexps
	newOption('popupDabRegexp', '([{][{]\\s*disambig|disambig\\s*[}][}]|disamb\\s*[}][}]|dab\\s*[}][}])|[{][{]\\s*(((geo|hn|road?|school|number)dis)|[234][lc][acw]|shipindex)(\\s*[|][^}]*)?\\s*[}][}]|is a .*disambiguation.*page');
	newOption('popupAnchorRegexp', 'anchors?'); //how to identify an anchors template
	newOption('popupStubRegexp', '(sect)?stub[}][}]|This .*-related article is a .*stub');
	newOption('popupImageVarsRegexp', 'image|image_(?:file|skyline|name|flag|seal)|cover|badge|logo');
}
// ENDFILE: options.js
// STARTFILE: strings.js
//&lt;NOLITE&gt;
//////////////////////////////////////////////////
// Translatable strings
//////////////////////////////////////////////////
//
// See instructions at
// //en.wikipedia.org/wiki/Wikipedia:Tools/Navigation_popups/Translation

pg.string = {
	/////////////////////////////////////
	// summary data, searching etc.
	/////////////////////////////////////
	'article': 'article',
	'category': 'category',
	'categories': 'categories',
	'image': 'image',
	'images': 'images',
	'stub': 'stub',
	'section stub': 'section stub',
	'Empty page': 'Empty page',
	'kB': 'kB',
	'bytes': 'bytes',
	'day': 'day',
	'days': 'days',
	'hour': 'hour',
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    <title>Nanomedicine</title>
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      <comment>project box(es)</comment>
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      <text bytes="16735" sha1="4e67sivkd4i3d9naqitfqgh5wni1ktt" xml:space="preserve">{{pharmacy}}
Dr SHOEB MUSTAFA, DEPT. OF MICROBIOLOGY,&lt;br&gt;
J.N.MEDICAL COLLEGE AND HOSPITAL,A.M.U, ALIGARH&lt;br&gt;
E MAIL:SHOEBMUSTAFA82@INDIATIMES.COM

•	Nanomedicine is the medical application of nanotechnology. It covers areas such as nanoparticle drug delivery and possible future applications of molecular nanotechnology (MNT) and nanovaccinology.
   Nanopharmacology can be defined as the application of nanotechnology to the development and/or discovery of methods to deliver drugs. In this context a nanodrug can be a vector (nanovector) designed to deliver a pharmacological agent (drug). The prefix &quot;nano&quot; originates from the word νάννος (Greek for dwarf
•	The most important innovations are taking place in drug delivery within the human body, which involves developing nanoscale particles or molecules to improve permeable bioavailability.
•	In vivo imaging, ultra sonic waves, is another area where tools and devices are being developed. Using nanoparticle contrast agents, images such as ultrasound and MRI have a favorable distribution and improved contrast.
•	The new drug delivery therapies and the outside monitors eg. Like a stopwatch for treatment, monitoring, dosage &amp; routine maintenance, can help with daily regime control &amp; possibly help contain &amp; retract, &amp; or dissipate or cessate certain disease within the human body.

== PHARMACOLOGICAL POTENTIAL ==
Nanopharmocology is the use of nanotechnology for pharmacology applications such as: the formation &amp; delivery of novel nanoscopic entities &lt;ref&gt;http://www.nanopharmacology.com/&lt;/ref&gt;, exploring and matching specific compounds to individual patients chemistry, for maximum effectiveness, and for advanced pharmaceutical delivery systems, targeting discovery of new pharmacological molecular entities; selection of pharmaceuticals for gene proximity, therapy, in treating individuals, &amp; to maximize effectiveness and minimize side effects (2), standard delivery of pharmaceuticals to targeted locations or tissues within the body.     Nanoparticles can render targeted, time allocated, and sustained delivery of biological compounds to specific tissues with a minimum of systemic side effects.

Nanoparticles, have extraordinary properties, that can be used to improve drug delivery. 
•	Whereas, larger particles would have been cleared from the body, now remaining cells take up these nanoparticles because of their size.
•	The particulates from drug delivery systems, lower the volume of distribution, and reduce the effect on non-target tissue.
•	Development of completely new drugs with more useful behavior and less side effects.
===Some applications of nanopharmacology===
*•	Diagnose conditions and disclose pathogens.
*•	Identify optimal drug agents, to   treat the exsisting condition, or targeted pathogens.
*•	Fuel high-yield production of matched pharmaceuticals.
*•	Locate, embed, or attach integrated
or  enter target tissue; configurations   or pathogens.
*•	Dispense the ideal mass dosage of matched biological compound to the specific target locations.

== TARGETTED DRUG DELIVERY-ROLE OF NANOCAPSULES ==
•	Nanocapsule, means sandy, biodegrable, nanoparticle, that consists of a shell and a space, in which desired substances may be placed. Drug-filled nanocapsules can be covered with antibodies or cell-surface receptors that bind to cancer or various cells and release their biological compound on contact with that tissue. Nanocapsules have been made using molecules called phospholipids, which are hydrophobic (water-repellant) on one end and hydrophilic (water-loving) on the other. When such molecules are placed in an aqueous environment, they can spontaneously form capsules in which the hydrophobic portions are inside (3), protecting them from contact with water.The walls of our cells are in fact made up of a double layer of such molecules. Inside the cells, similar capsules, called liposomes (literally, fat bodies), are used to transport material. 

== BIOSENSOR CHIPS ==
•	Nanotechnology chips with biosensors can find genes, guide drug discovery, monitor body functioning, and identify biologic and chemical pathogens. As nanotechnology and genetics advance, medibots and engineered beneficial microorganisms may be integrated into nanomedibots. Nanomedibots will be used to diagnosis and treat healing conditions that resist diagnosis and curing by current biomedical research.
Medibots  are robots or robotic systems that provide physicians with greater flexibility, precision of motion, and/or remote procedure capability in the diagnosis or treatment of medical conditions.
Concerning macro-scale medibots (4), improvements in the conveyance of visual and directional information with sophisticated consoles and remote-controlled hardware are already enabling surgeons to conduct an increasing array of surgical procedures in a minimally invasive manner. 

== ONCOLOGY ==

1.	Nanoparticles of cadmium selenide (quantum dots) glow when exposed to ultraviolet light. When injected, they seep into cancer tumors. The surgeon can see the glowing tumor, and use it as a guide for more accurate tumor removal.
2.	Sensor test chips containing thousands of nanowires, able to detect proteins and other biomarkers left behind by cancer cells, could enable the detection and diagnosis of cancer in the early stages from a few drops of a patient's blood. [5]
3.	Researchers at Rice University have demonstrated the use of 120nm diameter nanoshells coated with gold to kill cancer tumors in mice. The nanoshells can be targeted to bond to cancerous cells by conjugating antibodies or peptides to the nanoshell surface. By irradiating the area of the tumor with an infrared laser, which passes through flesh without heating it, the gold is heated sufficiently to cause death to the cancer cells [6].
4.	Dendrimer molecule has over a hundred hooks on it that allow it to attach to cells in the body for a variety of purposes. These molecules have also shown potential for targeted chemotherapy against tumor cells.


== SURGERY ==

•	At Rice University, a flesh welder is used to fuse two pieces of chicken meat into a single piece. The two pieces of chicken are placed together touching. A greenish liquid containing gold-coated nanoshells is dribbled along the seam. An infrared laser is traced along the seam, causing the two sides to weld together.
•	This could solve the difficulties and blood leaks caused when the surgeon tries to restitch the arteries he/she has cut during a kidney or heart transplant. The flesh welder could meld the artery into a perfect seal.


== ORTHOPEDIC SURGERY (Arthrobotics) ==
· Arthrobotics is the application of robotic technology to help orthopedic surgeons in the healing, repair, and replacement of joint-related conditions. Current applications of arthrobotics involve arthroscopic automation and place enhancements, such as automated motion of the arthroscope, position sensors to guide it, and force sensors for tissue proximity control. Future arthrobotic usages might incorporate complete joint replacement with bionic bionics and neuro-computer interfaces for limb control from neural impulses in the brain.

== RADIOLOGY (DIAGNOSTIC AND INTERVENTIONAL) AND NUCLEAR MEDICINE ==
•	Nanodevices could be observed at work inside the body using MRI, using mostly 13C atoms rather than the natural 12C isotope of carbon, since 13C has a nonzero nuclear magnetic moment.
•	Medical nanodevices would first be injected into a human body, and would then go to work in a specific organ or tissue mass.
•	 The doctor will monitor the progress, and make certain that the nanodevices have gotten to the correct target treatment region.
•	 The doctor can actually see the nanodevices congregate around their target (a tumor mass, etc.).
•	Tracking movement can help determine how well drugs are being distributed or how substances are metabolized.

== NANOROBOTS ==

•	There are somewhat speculative  claims that using nanorobots [7] [8] in medicine, would totally change the world of medicine once it is realized.
•	Nanomedicine [9] [10] would make use of these nanorobots, introduced into the body, to repair or detect damages and infections. 
•	According to Robert Freitas of the Institute for Molecular Manufacturing, a typical blood borne medical nanorobot would be between 0.5-3 micrometres in size, because that is the maximum size possible due to capillary passage requirement.
•	 Carbon would be the primary element used to build these nanorobots due to the inherent strength and other characteristics of some forms of carbon (diamond/fullerene composites), and nanorobots would be fabricated in desktop nanofactories [11] specialized for this purpose.
•	 Nanorobots could counter the problem of identifying and isolating cancer cells as they could be introduced into the bloodstream. These nanorobots would search out cancer affected cells using certain molecular markers. Medical nanorobots would then destroy these cells, and only these cells.
•	Nanomedicines could be a very helpful and hopeful therapy for patients, since current treatments like radiation therapy and chemotherapy often end up destroying more healthy cells than cancerous ones. 
•	Nanorobots could also be useful in precision tissue- and cell-targeted drug delivery [12] [13], in performing nanosurgery [14], and in treatments for hypoxemia and respiratory illness[15] [16], dentistry [17] [18], bacteremic infections[19], physical trauma [20], gene therapy via chromosome replacement therapy [21] [22], and even biological aging [23].
•	
== RESPIROCYTE ==
: One very simple nanorobot that was designed a few years ago is, the artificial mechanical red cell, a &quot;respirocyte.&quot; (24) that   can deliver 236 times more oxygen per unit volume than a natural red cell.
Some possible applications using nanorobots are as follows:
•	To cure skin diseases, a cream containing nanorobots may be used. 
•	A mouthwash full of smart nanomachines could identify and destroy pathogenic bacteria while allowing normal commensals to grow.
•	Medical nanodevices could augment the immune system by finding and disabling unwanted bacteria and viruses just like leucocyte.
•	Devices working in the bloodstream could nibble away at arteriosclerosis deposits, widening the affected blood vessels. 
•	Cell herding devices could restore artery walls and artery linings to prevent most heart attacks.


== NEURO-ELECTRONIC INTERFACES (NEUROLOGICAL APPLICATIONS) ==
•	Neuro-electronic interfaces are a visionary goal dealing with the construction of nanodevices that will permit computers to be joined and linked to the nervous system. 
•       This idea requires the building of a molecular structure that will permit control and detection of nerve impulses by an external computer.
•	The computers will be able to interpret, register, and respond to signals the body gives off when it feels sensations. 
•	The demand for such structures is huge because many diseases involve the decay of the nervous system (ALS and multiple sclerosis). Also, many injuries and accidents may impair the nervous system resulting in dysfunctional systems and paraplegia.
•	 If computers could control the nervous system through neuro-electronic interface, problems that impair the system could be controlled so that effects of diseases and injuries could be overcome.
•	 PROSPECTS:                                           
•	Treatment of paraplegia, hemiplegia and spondylosis following accidental injuries, vascular and due to other causes.

== CELL REPAIR MACHINES (REGENERATIVE MEDICINE) ==
•	Using drugs and surgery, doctors can only encourage tissues to repair themselves. With molecular machines, there will be more direct repairs. 
•	The possibilities of these cell repair machines are impressive. Comparable to the size of viruses or bacteria, their compact parts will allow them to be more complex. 
•	As they open and close cell membranes or travel through tissue and enter cells and viruses, machines will only be able to correct a single molecular disorder like DNA damage or enzyme deficiency.
•	 Nanocomputers will be needed to guide these machines. These computers will direct machines to examine, take apart, and rebuild damaged molecular structures. 

== ENDOCRINOLOGY ==

•	An example of the state of the nanobiotechnological art is Tejal Desai's(Boston University) artificial pancreas. Dr. Desai has encased her mouse pancreatic cells in a membrane studded with &quot;nanopores&quot; a mere seven nanometres across. As glucose from the blood washes in through the nanopores (25), the enclosed islet cells respond by releasing insulin. At 7 nanometres, the pores are big enough to allow the passage of glucose and insulin,but antibodies, which are significantly larger, cannot squeeze through, and so cannot damage the islet cells. 

== CARBON NANOTUBE MUSCLE ==
Artificial muscles have been made from millions of carbon nanotubes. Like natural muscles, providing an electrical charge causes the individual fibres to expand and the whole structure to move (26). An artificial muscle with strength and speed equal to that of a human muscle may soon be possible. 
A new wave of technology and medicine is being created and its impact on the world is going to be monumental. From the possible applications such as drug delivery and in vivo imaging to the potential machines of the future, advancements in nanomedicine are being made every day. 

==Single Molecule Detection in Signaling Pathways==
Novel photon correlation spectroscopy and fluorescence-based techniques allow the visualization of single biomolecules such as specific proteins, enzymes, hormones, nucleic acids, and so on, in living cells and tissues.&lt;ref&gt;http://wiki.planetphysics.info:8888/index.php/Main_Page#PlanetPhysics.org:_Organizational_Links Nanoscience journals and projects&lt;/ref&gt;

==References and Notes==

&lt;references/&gt;

==Bibliography==
*1. [http://www.nanopharmacology.com/ Nano-Pharmacology]
*2.http://www.nanopharmaceutix.com/
*3.http://www.ajetudes.club.fr/ nano/nanocapsules.htm
*4.http://medibots.info/
*5 http://en.wikipedia.org/wiki/_note-0
*6 http://en.wikipedia.org/wiki/_note-1
*7. Freitas, Robert A. ''&quot;Current Status of Nanomedicine and Medical Nanorobotics Journal of Computational and Theoretical Nanoscience&quot;'', Volume '''2''', Number 1, March 2005 , pp. 1-25(25)
*8. Robert A.Freitas,Jr. &quot;Current Status of Nanomedicine andMedical Nanorobotics&quot;. ''Journal of computational and Theoretical Nanoscience'',Vol'''.2''',1: 25,2005.
*9. Nanomedicine, Volume I: Basic Capabilities,1999 Robert A. Freitas Jr.
*10. Nanomedicine, Volume IIA: Biocompatibility, 2003Robert A. Freitas Jr. 
*11. http://www.molecularassembler.com/Nanofactory/
*12.Freitas RA. Pharmacytes: an ideal vehicle for targeted drug delivery.
J Nanosci Nanotechnol. 2006 Sep-Oct;6(9-10):2769-75.
*13. Pharmacytes:An Ideal Vehicle for Targeted Drug Delivery Robert A.Freitas,Jr. Journal of
Nanoscience and NanotechnologyVol.6,2769-2775 2006
14.International Journal of Surgery (2005) - , - e -www.int-journal-surgery.com
15Freitas RA.Exploratory design in medical nanotechnology: a mechanical artificial red cell. Artif Cells Blood Substit Immobil Biotechnol. 1998 Jul;26(4):411-30. PMID: 9663339 [PubMed - indexed for MEDLINE]
16.http://www.foresight.org/Nanomedicine/Respirocytes.
17 Nanodentistry.Freitas RA.Zyvex Corp., Richardson, Texas 75081, USA J Am Dent Assoc. 2000 Nov;131(11):1559-65.
18 Robert A. Freitas Jr., “Nanodentistry,” J. Amer. Dent. Assoc. 131(November 2000):1559-1566. (Cover story)
19 Robert A. Freitas Jr., Journal of Evolution and Technology - Vol. 14 - April 2005
http://jetpress.org/volume14/freitas.html
20 IMM Report Number 18: Nanomedicine
In conjunction with Foresight Update 41
Clottocytes: Artificial Mechanical Platelets
ByRobertA.Freitas Jr.
Research Scientist, Zyvex LLC
21 The future of nanofabrication and molecular scale devices in nanomedicine.Freitas RA.
Zyvex Corp, Richardson, Texas, USA Stud Health Technol Inform. 2002;80:45-59
22 The Future of Nanofabrication and Molecular Scale Devices in Nanomedicine
Robert A. Freitas Jr.,Research Scientist, Zyvex Corp.published July 2002  http://www.rfreitas.com/Nano/FutureNanofabNMed.htm
23 Death Is An Outrage Robert A. Freitas Jr.
Lecture delivered by the author at the Fifth Alcor Conference on Extreme Life Extension, 16 November 2002, Newport Beach, CA, http://www.rfreitas.com/Nano/DeathIsAnOutrage. 
24.  Robert F. Jr. Nanotechnology Magazine 2 (1996) 8. Robert F. Jr. Artificial Cells 26 (1998) 411.
25.  http://www.pnl.gov/energyscience/06-01/ws.htm
26. http://www.mondolithic.com
[[Category:Nanoscience]]</text>
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== Writing and Research in the Disciplines ==
This is a resource for students who are writing research projects in various disciplines. The sections that follow contain information about writing conventions in major citation style guides, sources for information in different fields of study, and helpful advice for developing a thesis and organizing material when writing a research paper.

== Writing ==
=== How to Take Notes ===
When researching for a paper, taking notes is an essential part to the paper’s actual success. It is also a great way to avoid plagiarism and get as much original information into the paper as possible. 

To start out, 3 x 5 note cards are great sources to write on, but regular loose leaf paper could be used just as well. It’s good to write down points, but summarizing and paraphrasing can be good too. I find that the best way is to take in a couple of sentences at a time. Read the small bit of information and then from what you can recollect in your mind without looking at the source, write down what you remember. This way you can avoid copying word for word and in the end avoid reiterating that exact information of ideas or actual words in your paper. 

Make sure that you write down the major issues; you can go into details later. In order to take advantage of the time in which you are given to take notes, start with bold prints or look for main subject words, and then if you have time later, go back and highlight the specifics you might have missed to begin with. Also before you begin taking notes, you might want to start out with a source card so that you can go back and reference and cite your information later. Number the source cards according to the information contained in the note cards.

Melissa Collins' Work Cited Page

Brizee, H. Allen. &lt;u&gt;Writing a Research Paper&lt;/u&gt;. 1995-2004: Internet. http://owl.english.purdue.edu/workshops/hypertext/ResearchW/notes.html
Apr 11, 2008.

=== How to Summarize ===

Summarizing is one of the most important tools needed in education. It is the basis for interpreting and translating text into one’s own words. Summarizing is taking the main idea of a text and putting it in fewer words to get the general idea of the material (Jones). When we summarize, we extract what the most important parts are to show the main essence of the material (Jones). There are some general ideas and guidelines that many agree on when teaching to summarize. 

Some useful ways to start the summarizing process while reading the material include underlining or highlighting important words or passages and then writing down the main ideas in a column or separate sheet of paper (“How to….”). Multiple readings of the original source are often helpful, as well as reading it quickly to only pick up the most important ideas (“How to…”).  After quickly reading the material, it is helpful to go through the material more in-depth to dissect each section. 

The main point to remember about a summary is that it should be put into the writer’s own words to avoid any suspicion of plagiarism. Not only is it important to not use the exact same words as the original author, but it is also important to not use the same sentence structure (“Learn to…”). To avoid exactly copying the original source, it is helpful to set the original source out of view, and then trying to write a brief overview in your own words. It is important to stay dedicated to the original source, keeping its main essence and idea, without copying it exactly (“Learn to…”).

“How To Summarize.” Mantex. 2007. Mantex. 10 April 2008. &lt;http://www.mantex.co.uk/samples/summary.htm&gt;.

Jones, Raymond. “Summarizing.” Reading Quest. 3 February 2007. ReadingQuest.org. 10 April 2008. &lt; http://www.readingquest.org/strat/summarize.html&gt;.

“Learn to Summarize.” University of Houston Victoria. 2006. Academic Center University of Houston Victoria. 10 April 2008. &lt;http://www.uhv.edu/ac/research/write/summary.asp&gt;.

=== How to Paraphrase ===

Paraphrasing is something that everyone should know how to do and do it correctly. Paraphrasing is often confused with summarizing. They are not the same thing and can produce very different results to the reader. To summarize something will leave only a very general idea. Paraphrasing is taking someone else’s ideas and putting them in your own, unique words. 

	It is important, when paraphrasing someone, to give credit to the author. If you don’t give credit where it is due, it is considered plagiarism.

&lt;blockquote&gt;
Here are a few basic guidelines for solid paraphrasing from Ms. Driscoll at Purdue University:
1.	Reread the original passage until you understand its full meaning.
2.	Set the original aside, and write your paraphrase on a note card.
3.	Jot down a few words below your paraphrase to remind you later how you envision using this material. At the top of the note card, write a key word or phrase to indicate the subject of your paraphrase.
4.	Check your rendition with the original to make sure that your version accurately expresses all the essential information in a new form.
5.	Use quotation marks to identify any unique term or phraseology you have borrowed exactly from the source.
6.	Record the source (including the page) on your note card so that you can credit it easily if you decide to incorporate the material into your paper. (Driscoll, 1)
&lt;/blockquote&gt;

Mr. Plotnick gives a great example of what not to do when paraphrasing another person’s writing. Given this excerpt from Oliver Sack’s essay “An Anthropologist on Mars”:
&lt;blockquote&gt;
“The cause of autism has also been a matter of dispute. Its incidence is about one in a thousand, and it occurs throughout the world, its features remarkably consistent even in extremely different cultures. It is often not recognized in the first year of life, but tends to become obvious in the second or third year. Though Asperger regarded it as a biological defect of affective contact—innate, inborn, analogous to a physical or intellectual defect—Kanner tended to view it as a psychogenic disorder, a reflection of bad parenting, and most especially of a chillingly remote, often professional, &quot;refrigerator mother.&quot; At this time, autism was often regarded as &quot;defensive&quot; in nature, or confused with childhood schizophrenia. A whole generation of parents—mothers, particularly—were made to feel guilty for the autism of their children.”
&lt;/blockquote&gt;
Here is an example of poor paraphrasing:
&lt;blockquote&gt;
“The cause of the condition autism has been disputed. It occurs in approximately one in a thousand children, and it exists in all parts of the world, its characteristics strikingly similar in vastly differing cultures. The condition is often not noticeable in the child's first year, yet it becomes more apparent as the child reaches the ages of two or three. Although Asperger saw the condition as a biological defect of the emotions that was inborn and therefore similar to a physical defect, Kanner saw it as psychological in origin, as reflecting poor parenting and particularly a frigidly distant mother. During this period, autism was often seen as a defense mechanism, or it was misdiagnosed as childhood schizophrenia. An entire generation of mothers and fathers (but especially mothers) were made to feel responsible for their offspring's autism (Sacks 247-48).”
Notice how most of the sentences have only a few words rearranged or changed for synonyms. The sentence structure and paragraph layout are even almost identical to the original. Just because you cite the page numbers at the end of your paragraph doesn’t mean that you’re in the clear for plagiarism (Plotnick, 1).
&lt;/blockquote&gt;

                                            -Brandon Evans

Driscoll, Dana Lynn. “Paraphrase: Write it in Your Own Words.” The Owl at Purdue.
	1995. University of Purdue. April 11, 2008.	
	[http://owl.english.purdue.edu/owl/resource/619/01/]

Plotnick, Jerry. “Paraphrase and Summary.” University College: Writing Workshop.
2007. University of Toronto. April 11, 2008. [http://www.utoronto.ca/ucwriting/paraphrase.html]


=== How to Organize ===
One of the toughest things about writing a paper is figuring out just how to organize it. Where do you begin? How do you begin? What do you include? What order do you put it in? How do you conclude your paper? Well below is a list of websites that may assist you in your organizational writing process. Included is also a brief summary of the positive and negative points of each website to help you further narrow your search.

1) How to Organize a Research Paper
http://www.geocities.com/athens/oracle/4184
A Research Paper is a Tree

good: This provides a simple explanation of what to include in your paper, how to organize the basics of your paper, and what section to include specific information in. It gives an example of how an outline is a tree and how each aspect of your paper is like a specific part of the tree. This makes it easy to visually see where each piece of information should fall in your paper.

bad: It takes the example of the outline being a tree a bit far. It focuses more on making that analogy than it does presenting valuable information about writing a paper.

2) How to Organize Your Paper
http://www.lasalle.edu/services/sheekey/organize.htm

good: It is a list of links to several websites to help with specific organizational problems such as having trouble putting ideas into the proper format in a paper, having trouble relating the different concepts in the paper, and having trouble getting started/getting organized.

bad: This site contains no actual information itself; it merely provides links to other sites that may be useful.

3) How to Organize a Research Paper
http://www.ehow.com/how_138072_organize-research-paper.html

good: It contains a very cleat set of 8 steps to prepare for and organize your research paper. It also contains tips, warnings, and links to related articles and example research papers. 

bad: It contains no examples of an actual paper, just links.

4) Research Guide for Students
http://www.aresearchguide.com/1steps.html
How to Write an A+ Research Paper

good: It contains a very clear list of steps to go through including choosing a topic, finding information, stating your thesis, making a tentative outline, organizing your notes, https://sites.google.com/site/bestessaywritingservicereview/ writing your first draft, and revising your final outline and draft. It includes a detailed explanation of each step as well as examples and links to find further information. It also contains a series of checklists to help ensure that you included everything and have written an effective paper.

bad: It unfortunately doesn't focus too much on actually writing the paper other than a brief discussion of the introduction, body, and conclusion.

5)How to write a Term Paper
http://gale.cengage.com/free_resources/term_paper/begin.htm
Begin and Organize a Research Paper

good: It contains a very detailed outline of instructions on essentially how to go about formatting your thoughts, creating a detailed outline, and different methods to implement following the creation of and outline.

bad: It only has a few examples of how to actually carry out each step of the given process which may make it a little more difficult to thoroughly follow.

=== How to Create a Thesis ===
1. Defining Your Research Topic and Starting Your Search http://www.camellia.shc.edu/literacy/tableversion/lessons/lesson3/defining2.htm

Summary: 
The site seemed to be a broader, not quite as in-depth, website. The main reason I found it to be a useful resource is that it provided a very helpful analogy regarding narrowing a topic. The author compared it to two lakes, a smaller lake and a larger lake. The smaller lake was deep, but the large was shallow. The point was to emphasize how if you choose the larger lake, your topic will be more vague and broad, but by choosing the smaller, deeper lake you are able to go more into detail on your topic. 

2. How To Write A Thesis Statement 
http://www.indiana.edu/~wts/pamphlets/thesis_statement.shtml

Summary: 
I liked this website because it was more specific as far as discussing certain points of developing a topic which would then turn into a thesis statement. What I found most interesting is the site had two sections which provided two approaches to developing the statement depending on whether or not the topic was assigned. Despite being given a topic, one must develop their own thesis. It also gave tips on deciding upon a topic if one is not assigned. I liked where the author stated that, &quot;In general, your thesis statement will accomplish these goals if you think of the thesis as the answer to the question your paper explores.&quot; Very well put.

3. Developing a Central Claim
http://uwp.duke.edu/wstudio/documents/developing_claim_000.pdf

Summary:
This Duke University Writer's Studio webpage was a useful resource for explaining the development of a research question/thesis statement. It was a bit more detailed that most of the sites I have viewed, but I believe that is a good thing. It contained a lot of information, but it was well-organized into a paragraph layout, and it was easy to read. I liked one of the points in the second paragraph stating that, &quot;Several sentences might be necessary to convery your thesis or central claim&quot;. I think many are taught that a thesis is a single sentence, and the website addresses that appropriately.

5. Creating A Thesis Statement
http://owl.english.purdue.edu/owl/resource/545/01

Summary:
I was glad to find a page on the Owl site because I have found it to be a useful database for writing in the past. The design of the page is simple and clearcut, making it easy to find information about the desired subject. The webpage provides several great ideas for developing a thesis as well as provides examples. There was not as much information as I had thought there might be, but the information provided was useful and to-the-point.

=== How to illustrate with the second degree ===
The second degree can make a text attractive or pleasant, but can also introduce a malaise when not mastered (eg: to ask to keep an eye on your text to a one-eyed person).

One way to be inspired and warned is to learn the [[w:idiom|idioms]], [[w:Stylistic device|stylistic devices]] and other [[w:Figure of speech|figures of speech]] which are typical of the destination language.

Apart from those conventional tools, it exists [http://faux-amis.fr/Eng_Index.html many different ways] to build a proper style, and become proud of [[w:Jakobson's functions of language|the communication poetic function]], especially with the help of homonyms and false-friends.

== How to Find Sources ==
=== Reliable and Unreliable Sources ===
Searching for information and developing the knowledge needed to discuss your topic in depth can be the most nerve-racking step in writing a research paper. Finding credible and reliable sources of information from which to draw your conclusions has become increasingly difficult in today’s information drenched world but here are a few steps that you can take to better insure the credibility of any particular source.

Take a moment to ask yourself these questions when you are presented with a new potential source.

What is the author’s motivation for presenting the information provided in this source? 
*Is it to report facts or data?
*Is the writer trying to attract attention to a cause? 
:*If so, what is the cause?
*Is the work geared toward advertising a product or Idea? 
*Is this motivation apparent or was it hidden? 
*Do any objectives of the source create a bias that is pertinent to your issue? 
*Has the information presented been verified?
:*How has the information been verified? 
:*Does the verifying party have any bias toward the issue? Do they stand to gain from the presentation of this information?

If the work has been published, check out the publishing company.
*What other works have been published by the company?
*Are the works popular? Are they scholarly? Are they accurate?

If the name of the Author is available research their previous works and background.
*Is the author experienced in the field he or she has written about?
*How has the public and/ or the academic community responded to the authors past work?

Finding reliable sources on the internet can be extremely difficult because of the publishing freedom that is found online.
The site below has a lot of helpful information on determining the reliability of a web source. There is even a section that teaches you to decode a URL and discover all the information that is hidden within it

http://www.wesleyan.edu/libr/tut/websearch/evaluate.html-.

The Wikipedia policy on [[w:Wikipedia:Reliable_sources|Reliable Sources]] also provides valuable guidance.

=== Biology ===
Finding resources can be overwhelming at first. With all the information that is out there, how are you supposed to know where to find all of it? The first place that you should go to is your local library and searches their online databases for the specific topic that you are working on. A great database to use in the field of biology is PubMed.  [http://www.ncbi.nlm.nih.gov/pubmed/] It has over 11 million documents, some with full text that you can view. Another very broad database is the Biological and Agricultural Index Plus. It has a great variety of full text sources that one can utilize. Another database that you can search from your own home is called EurekAlert!  [http://www.eurekalert.org/] This site is regularly updated and includes links to article and databases dealing with science and technology.

Internet sources
If you want to do a simple internet search on your topic, there are a few things that you need to keep in mind. Make sure that it is a scholarly website, primarily .org or .edu. Make sure that the author is credible. If the article isn’t peer reviewed, do a background check to make sure the author is trustworthy. 

If you are stuck and can’t find any sources, try checking the bibliographies of the books you already have. These usually contain relative information on the topic that you are researching and should provide a good starting point to lead you to other sources. If all else fails, just ask a librarian. They will be more than happy to assist you in finding information for a topic. Even if they don’t have the information in the library, they will either order it for you or send you to a place where you can get it.


=== Search Engines for Business Related Disciplines ===

There are a number of professional online journals that cover current business topics. These include magazines concerned with the connection between business and environment and even running businesses from home.
Others include…

[http://galenet.galegroup.com/servlet/BCRC?locID=tusc49521]
[http://www.entrepreneur.com/]
[http://www.businesshistory.net/]


=== Business Journals ===

[http://www.greenbiz.com/]
[http://www.homebusinessmag.com/]
[http://www.thebhc.org/publications/BEHonline/beh.html]
[http://www.businessweek.com/]
[http://www.inbusinessmagazine.com/]
[http://www.bizjournals.com/]

=== Advertising Techniques ===

[http://www.pandecta.com/sell.html]
[http://www.mediaworkshop.org/bwc/johnston_gonzalez/ads/glossary.html]
[http://www.foothilltech.org/rgeib/english/media_literacy/advertising_techniques.htm]


== APA ==
=== Citing Sources ===
Citing Sources using APA*

In APA, the works cited list at the end of a paper is called &quot;References.&quot; The order, punctuation, and capitalization of the information in a citation are all very important, so here are general guidelines for citing sources using APA.

Listing a Publication’s Author(s)
Authors are listed by last name and first (and possibly middle) initial, followed by the year of publication in parenthesis. Up to six authors may be listed in this format, placing “&amp;” before the last author’s name. For something with more than six authors, the first six should be listed followed by “et al.” which means “and others.” If the author is unknown, the title of the publication is written before the date of publication.

Capitalization of Titles
In APA format, only journal titles follow traditional capitalization techniques. For all other titles, only capitalize the first letter of the first word of a title (and subtitle), proper nouns, and the first word in a title to come after a colon or dash (excluding hyphenated compound words.)

Citing a Book
Author, X. Y. (Publication Year). Title of Book: Subtitle. Publication City: Publisher.
—For a book with an editor, the editor’s name is written in parentheses after the book title, followed by “Ed.” (or “Eds.”)

Citing an Article in a Periodical
Author, X. Y. (Year). Title of Article. Name of Periodical. Volume(Issue). Page-Range.

—If the article being cited is a letter to the editor, this is indicated by adding “[Letter to the Editor]” between the title and the name of the periodical.
—If a review is being cited, the title of the review is given followed by “[Review of the book]” and the book title.

Citing an Electronic Source
Author, X. Y. (Date of Update). Title of Document on Site. In Title of Website. Retrieved Date of Access, from URLofWebsite.com
—If there is no date of publication, it is replaced by “(n.d.)” 
—For an article from an online periodical which also appears in a printed journal, “[Electronic Version]” is added after the article title.
—If the source is obtained from a university program’s website, include the program name in the “Retrieved” statement.

Article from Database
Author, X. Y. (Date of Publication). Title of Article. Name of Periodical. Volume(Issue). Pages. Retrieved Date of Access, from Database Name database (Document number).


For more specific and in-depth guidelines, and to view citation examples within each category, go to http://owl.english.purdue.edu/owl/resource/560/05/


Adapted from 
Hacker, D. (2007). A writer's reference (6th ed.). Boston: Bedford/St. Martins. 
and from 
Neyhart, D. &amp; Karper, E. (2008, April 9). APA formatting and style guide. In The owl at Purdue. Retrieved April 10, 2008, from http://owl.english.purdue.edu/owl/resource/560/01/


=== Formatting ===

The following is a very helpful web link to a sample paper done in APA style - &lt;u&gt;http://www.vanguard.edu/uploadedFiles/Faculty/DDegelman/psychapa.doc.&lt;/u&gt;

Also, another good reference tool is Diana Hacker’s 6th Edition of ''A Writer’s Reference''. Pages 414 through 459 give you all sorts of advice when creating a paper to be done in APA. 
Another sample paper is given in pages 451 through 459 of the Hacker book. 

Formatting your paper in APA style can be a little tedious, but the process is quite simple once you understand the rules. For example, you are allowed to insert visuals such as graphs, comics, or any type of pictures. Make sure each visual has a title and number (like Table 1, Table 2, Table 3, etc.) posted above the artwork and place this fragment in a paragraph that addresses its purpose. 

'''Basic Rules:'''

'''Margins''' = 1 inch

'''Double Space?''' Yes and No – do double space your actual paper (this includes in-text citations), but single space footnotes.

'''Quotations:'''If you want to use a quote that is longer than 40 words, don’t use quotation marks. Instead, you need to indent the quotation 5 space bar clicks from the left margin (if this confuses you – check out a sample paper to get a more hands-on approach).

'''Headings:'''Not required, but can be very useful for addressing your main points. Center your headings.

'''Page Numbers:'''If you have a title page, label it i (where? far upper right) …if you have an abstract page, label it ii. One of the most noticeable characteristics of APA style papers are the page numbers partnered with a title. The title can be a shortened version of your main title. Here is an example:

Main Title:    ''Bee Keeping Journals of the Late 1860’s: The Value of These Collections to American Science''

Heading of page 2 in an APA type paper:         Bee Keeping Journals 2

'''Works Cited:'''You’ll actually label your “Works Cited” page, as “References”. This will be the final page of your paper, one that still deserves a heading, and will be double spaced. When typing authors’ names, you will use initials instead of first names (Ex: “Mallory Durham” would be cited as “Durham, M.”). Secondly, don’t use quotations when citing article titles. Instead you will ''italicize''.

'''''IMPORTANT''''': A distinct trait of APA style reference pages is the format. Alphabetize by the first letter of authors’ last name(s) – if there is no author, then type out the source name (Ex: March for Cancer Foundation - in this case you would use the “M” from “March” to alphabetize). Don’t number your sources. The first line (starting with author name(s) or other sources) is typed with no indention, but all of the lines following the first one will be shifted 5 space bar clicks from the left margin.

=== Links ===

'''Free APA bibliography generator'''

If you have never composed a cited bibliography in APA, MLA or CSE before, this website could be the answer to all your questions. Simply create a new folder on the website, fill in the citation type, format, author, title, publication year and a few more optional boxes, hit format and it’s completed! Another great feature about this site is that you can either print it from the website directly, or download it to another document. 
www.carmun.com 

'''APA formatting'''

Need help formatting your paper? Learn the basics for writing an APA style research paper. It is user friendly with great links to more detailed features that go into writing a research paper. Most cites like this are not free and very hard to navigate through. The home page contains an example of a term paper with all the correct formats. However, I was still slightly confused after skimming though the given work. To fix this problem, the creators of English Works provide links to general guidelines of APA, how to avoid plagiarism, guides to writing a thesis, introduction and conclusion, prewriting strategies, and guide to paraphrasing. If you are a first time APA style writer, I highly recommend checking out this cite!
http://depts.gallaudet.edu/englishworks/writing/apa_sample.html 


'''Everything you need to know about writing an APA paper'''

This cite is a hypertext which is perfect for this class since we have been dealing with them! It is focused towards writing psychology papers but its main purpose is to guide another in writing and giving examples on an APA paper. Everything is listed on the helpful cite: style details, abbreviations, numbers, citations in text, quotations, title page, introduction, methods, references, the body, and conclusions. If you are still confused and want examples there is an appendix of example title pages and reference sections.
http://www.uwsp.edu/PSYCH/apa4b.htm

'''Tips For Citing Your Academic Paper In APA Format'''

A brief lesson on how students and researchers can learn the basics of constructing a properly formatted paper that meets APA guidelines.
https://canvas.elsevier.com/eportfolios/9904/Home/Five_Tips_For_Citing_Your_Academic_Paper_In_APA_Format

=== Citing In-Text ===

'' In-text Citation of Sources in APA Style''

In APA style, not only direct quotes used within a paper must be cited.  In addition to these, in-text citations must include all ideas borrowed from any other source.  This may be paraphrased material or it may even be something like statistics.  Visuals such as cartoons and graphs must also be cited.  General information known by many and appearing in numerous other sources is not cited.

There is a three-part system that is accepted by the APA.  First, the authors’ names are included in a “signal phrase” and the publication date in parentheses.  Second, a page number in parentheses follows the cited material.  Finally, the last page of the paper must be an alphabetical list of sources cited in the paper.

== CMS ==

CMS writing style stands for the Chicago Manual of Style first used at the University of Chicago in 1890. It is known for being one of the easiest and most informative citing methods. CMS is usually used in the humanities such as art, literature, or history because of its importance placed on the author of the work instead of other details: date and placed published. Here are the rules for the CMS citation. [http://www.sourceaid.com/reference/pdf/citation-guide.pdf]

=== Bibliography ===

1. The title is centered an inch below the top of the page

2. Citations are arranged in alphabetical order

3. Citations are double-spaced between entries, but single within the entry

4. The first line of each citation is aligned with the left margin and the subsequent lines are indented five spaces.  
  

=== In-Text citation ===

1.  All in-text citations direct the reader to the appropriate source in the Endnotes at the end of the text.

2.  Endnotes are a list of the source ordered and numbered according to the sequential number of the corresponding in-text citation.

3. The first in-text citation is superscripted with a 1, the second in-text citation is superscripted with a 2 (no really), and the numbers continue on.


=== Footnotes ===

1. Footnotes are used to provide complete publication information for unoriginal content or structure of a text.

2. Any text, for which there is information in the Footnotes, is superscripted with a corresponding number. The number is found in the Footnotes section at the bottom of the page.


=== Endnotes ===

1.  Endnotes are used to provide complete publication information for each unoriginal idea or concept in the writing.

2.  Any text, for which there is information in the endnotes, is superscripted again with a number and that number can be found in the endnotes with the citation.

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      </contributor>
      <comment>/* Special */ + [[Special:GlobalWatchlist]]</comment>
      <origin>2810294</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="17015" sha1="16mpb2vcdqsp8g8j14tko5zfl4dk8pg" xml:space="preserve">{{TOCright}}
''A loose, personal (i.e., somewhat idiosynchratic) organisation of Wikiversity-related how-tos and links.''
==To sort==
{|style=&quot;background:transparent;&quot;
|valign=top|
* [http://tools.wikimedia.de/~magnus/commonshelper.php commonshelper]
* [[User:Jtneill/Wikification|Wikification]]
* [[w:Help:Interwiki_linking#Project_titles_and_shortcuts|Interwiki linking]]
* [[Wikiversity:Activity bars]]
* [[Wikiversity:Percent complete]]
|valign=top|
* [[Wikiversity:Import|import]]
* [[Wikiversity:Maintenance]]
* [[Wikiversity:Namespaces]]
* [[Wikiversity:Naming conventions]]
|valign=top|
* [[Wikiversity:Participants]]
* [[Wikiversity:Peer review]]
* [[Wikiversity:Review board]]
* [[Wikiversity:Searching]]
* [[How to be a Wikimedia sysop]]
|}

==Anchor==
* [[Template:Anchor]], e.g., [[#test]] will go to &lt;code&gt;&lt;nowiki&gt;{{anchor|test}}&lt;/nowiki&gt;&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{anchor|anchor=test}}&lt;/nowiki&gt;&lt;/code&gt; (should go to end of page)

==Archiving==
* Example of autoarchiving: [[User talk:Terra]]

==Blogging==
* [[Wikiversity Blog howto]]

==Boxes==
[[User:Jtneill/Sandbox/Tables and boxes]]

The simplest of boxes

{| class=&quot;messagebox&quot;
|-
| ABC
XYZ
|}

&lt;blockquote style=&quot;padding-left:1.0em; padding-right:1.0em; background-color:#eaf8f4;&quot;&gt;
Its good that it works in practice, because it certainly doesn’t work in theory[https://blogs.ch.cam.ac.uk/pmr/2007/10/14/the-thing-about-wikipedia-is-that-it-only-works-in-practice-in-theory-it-can-never-work/] 
&lt;/blockquote&gt;

==Categories==
It is possible to change the order in which a page’s categories are displayed. By default, categories are displayed in the order they appear in the wikitext. Wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480]

Using titleparts
&lt;nowiki&gt;[[Category:{{#titleparts:{{PAGENAME}}|1}}]]&lt;/nowiki&gt;

==[[/Centering/]]==
{{User:Jtneill/Wikiversity/Centering}}

==Chat==
* [[irc:wikiversity-en|#wikiversity-en]]

==Citations and referencing==
* [[w:Help:Citation tools|Citation tools]]
* [[:Category:Citation templates]]
* [[mw:Help:Cite]]
* [[Template:Citation]]
* [[WV:REF]]
* Example: Outward Bound Process Model&lt;ref&gt;Walsh, V., &amp; Golins, G. L. (1976). ''[http://wilderdom.com/theory/OutwardBoundProcessModel.html The exploration of the Outward Bound process]''.  Denver, CO: Colorado Outward Bound School.&lt;/ref&gt;

;References
{{reflist|1}}

==Collapse boxes==
{{collapse top|Mary had a little lamb}}
Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb,
Its fleece was white as snow

And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went
The lamb was sure to go

It followed her to school one day
School one day, school one day
It followed her to school one day
Which was against the rules.

It made the children laugh and play,
Laugh and play, laugh and play,
It made the children laugh and play
To see a lamb at school

And so the teacher turned it out,
Turned it out, turned it out,
And so the teacher turned it out,
But still it lingered near

And waited patiently about,
Patiently about, patiently about,
And waited patiently about
Till Mary did appear

&quot;Why does the lamb love Mary so?&quot;
Love Mary so? Love Mary so?
&quot;Why does the lamb love Mary so?&quot;
The eager children cry

&quot;Why, Mary loves the lamb, you know.&quot;
Loves the lamb, you know, loves the lamb, you know
&quot;Why, Mary loves the lamb, you know.&quot;
The teacher did reply
{{collapse bottom}}

==Colour==
* [[Wikiversity web page colors|Color tables]] | [[Wikiversity:Color names|Color names]]
* e.g., Font: {{font|color=green|Green}}, Background: &lt;span style=&quot;background:hotpink; color:white;&quot;&gt;Pink&lt;/span&gt;

==Columns==
===Column breaks===
{|
|-
| Works on all browsers (col-begin/break/end):
{{col-begin}}
{{col-break}}
* Col1
{{col-break}}
* Col2
{{col-break}}
* Col3
{{col-end}}

Works on all browsers (col/break/colend):
{{col}}
{{break}}
* Col1
{{break}}
* Col2
{{break}}
* Col3
{{col/end}}
|}

===Moz-column===
Easier to use, but doesn't work on all browsers:
&lt;div style=&quot;column-count:3;-moz-column-count:3;-webkit-column-count:3&quot;&gt;
* Ant
* Bee
* Buzzard
* Cat
* Dog
* Egret
* Elephant
* Tiger
* Whale
* Worm
&lt;/div&gt;

==Conversions==
===HTML===
* [[w:Wikipedia:Tools/Editing_tools#From_HTML]]
* [http://www.ebruni.it/en/software/os/i_love_wiki/index.mpl i love wiki]
* {{tick}} [http://diberri.dyndns.org/wikipedia/html2wiki/index.html HTML::WikiConverter]
* {{tick}} [http://openfacts2.berlios.de/html2wiki/index.php HTML::WikiConverter]] Add URL

==CSS==
* [[MediaWiki:Common.css]]

==Custodianship==
* [[Wikiversity:Custodianship]]
** [[Wikiversity:Candidates for Custodianship]]
** [[Wikiversity:Notices for custodians]]
** [[Wikiversity:Request custodian action]]
** [[:Category:Wikiversity custodians]]

==Edit page==
Create an internal link to the edit source page using:
[[Special:EditPage/{{FULLPAGENAME}}|Edit source]]

&lt;nowiki&gt;
{{edit page}}
&lt;/nowiki&gt;

gives:
{{edit page}}

&lt;nowiki&gt;
{{edit page box}}
&lt;/nowiki&gt;

gives:
{{edit page box}}

==Extensions==
* [[Special:Version#Extensions]]
* [[/CategoryTree|CategoryTree]]
* [http://www.sandboxserver.org/wiki/index.php?title=Testing_Mediawiki_extensions Sandbox server - testing extensions]
* [[User:Jtneill/WYSIWIG|WYSIWIG]]

==Font==
&lt;p&gt;{{font|face=&quot;courier&quot;|size=medium|courier size 3}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;verdana&quot;|size=large|verdana size 4}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;arial&quot;|size=x-large|arial size 5}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;times new roman&quot;|size=xx-large|times new roman size 6}}&lt;/p&gt;
&lt;p&gt;&lt;b&gt;{{font|face=&quot;verdana&quot;|size=xx-large|verdana bold size 6}}&lt;/b&gt;&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;lucida calligraphy&quot;|size=xx-large|lucida calligraphy size 7}}&lt;/p&gt;

==Formatting==
===Justification===
&lt;div style=&quot;text-align: justify&quot;&gt; This text is right justified (but it doesn't look like unless the paragraph is long enough to go over one line on the page, so this is intentionally a particularly and unnecessarily long sentence in order to demonstrate right justification using &lt;nowiki&gt;&lt;div style=&quot;text-align: justify&quot;&gt;...&lt;/div&gt;&lt;/nowiki&gt;).&lt;/div&gt;
==Line height==
{{center top}}&lt;p style=&quot;line-height: 36px;&quot;&gt;
&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;This uses a&lt;br&gt;line height of 36px&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/p&gt;
&lt;pre&gt;&lt;p style=&quot;line-height: 36px;&quot;&gt;...&lt;/p&gt;&lt;/pre&gt;
{{center bottom}}
===Mouse-over===
* [[Help:Mouse-over]]
* [[Template:H:title]]

==Getting started==
* [[Wikiversity:Guided tour|Guided tour]]
* [[Wikiversity:Introduction|Introduction]] (Wikiversity)
* [[/Introduction|Introduction]] (Jtneill)
* [[/Welcome|Welcome]] (Jtneill)
* [[Introduction to Wiki]] - [[Wiki 101]]
* [[How to use wiki technology as a free learner]]
* [[:Image:Short.ogg|Wikiversity - short intro]] (10 sec. video)
* [[:Image:Editing_tutorial-large.ogg|Wikiversity editing tutorial]] (2 min video)
* [[Wikiversity:Community Portal]]
* [[Wikiversity:Content development]]
* [[Help:Edit summary]]
* [[Making links]]

==Good design==
* [[User:Jtneill/Good design]]

==Icons==
* [[Help:Icons]]
* [[User:McCormack/icons]]

==Images==
===[[Template:Gallery|Gallery]]===
{{Gallery
|title=Gallery of images
|footer=Uses this [[Template:Gallery|template]]
|width=150
|lines=2
||Comment
|File:Wikiversity-logo-Snorky.svg|[[Help:Contents/Links|Links]] can be put in captions.
|File:Wikiversity-logo-Snorky.svg|Full [[MediaWiki]]&lt;br /&gt;[[syntax]] may be used…
|File:Wikiversity-logo-Snorky.svg|
}}

&lt;!-- Fixed image in bottom right which is linked --&gt;
&lt;div id=&quot;template-navbar&quot; style=&quot;position: fixed; left:1; right:0; bottom:0; padding:0; font-size:122%;&quot;&gt;[[Image:Happy.png|right|50px|link=en:Happiness|Happiness]]&lt;/div&gt;

===ImageMap===
* [[mw:Extension:ImageMap|Extension ImageMap]] e.g.,
{{center top}}
&lt;imagemap&gt;File:Treasurchest.svg|center|80px
default [[Special:Random/|Random Wikiversity mainspace page]]
desc none&lt;/imagemap&gt;Click the treasure box to go to a random [[Wikiversity]] page{{center bottom}}

;Explanation

The ImageMap extension allows, among other things, an image to link directly to a page e.g., as an internal link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;
&lt;/pre&gt;

or as an external link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;
&lt;/pre&gt;

==Integrations==
I'm interested to explore possible connections between WV and:
* [http://archive.org Archive.org]
* [[w:Citizendium|Citizendium]]
* [[w:Google Groups]]
* [[Moodle]]
* [[Open University]]
* [http://openlearn.open.ac.uk/course/view.php?name=Cohere Cohere]
* [[WikiMedia Sister Projects]], particularly:
** [[Wikibooks]]
** [[Wikipedia]]
** [[Simple Wikipedia]]

==Licensing==
* My teaching materials are licensed under [[Wikiversity:License tags#Free licenses|creative commons attribution 2.5]] and hosted either on http://wilderdom.com or http://ucspace.canberra.edu.au. I am thinking I should be dual licensing, but am still coming to grips with trying to understand the licensing similarities, differences, and issues. 
* I plan to gradually transfer most of my teaching materials to the various [[w:WikiMedia Foundation|WikiMedia Foundation]] wiki projects, particularly wikiversity. [[m:Polls|Let's just hope Jimbo doesn't put adds on these sites]], otherwise I will be transferring the materials somewhere else (again).
* [http://beta.wikiversity.org/wiki/Wikiversity:IRC_meeting:New_licence_for_Wikiversity_Beta New_licence_for_Wikiversity_Beta]
* {{tl|db-copyvio}}
* {{tl|hangon}}
* [[:Category:Astronomy Images]]

==Links==
* Plain links: e.g., &lt;span class=&quot;plainlinks&quot;&gt;[http://archive.org http://archive.org]&lt;/span&gt;: &lt;br&gt;&lt;nowiki&gt;&lt;span class=&quot;plainlinks&quot;&gt; ... &lt;/span&gt;&lt;/nowiki&gt;
* [[mw:Manual:Opening external links in a new window]]

==Long page warning==
* [[MediaWiki:Longpagewarning]]

==[[Main page]]==
* [[:Category:Main page templates]]
* [[Main Page/Layout 0.5]]
* &lt;span class=&quot;plainlinks&quot;&gt;[http://en.wikiversity.org/w/index.php?title=Wikiversity:Main_Page&amp;oldid=209253 Main page]&lt;/span&gt; (old)

==Map==
&lt;mapframe latitude=&quot;-28.420391&quot; longitude=&quot;136.757813&quot; zoom=&quot;2&quot; width=&quot;200&quot; height=&quot;109&quot; align=&quot;right&quot;&gt;{
  &quot;type&quot;: &quot;FeatureCollection&quot;,
  &quot;features&quot;: [
    {
      &quot;type&quot;: &quot;Feature&quot;,
      &quot;properties&quot;: {},
      &quot;geometry&quot;: {
        &quot;type&quot;: &quot;Point&quot;,
        &quot;coordinates&quot;: [
          149.12419,
          -35.308275
        ]
      }
    }
  ]
}&lt;/mapframe&gt; 
==Namespaces==
* [[Special:NamespaceInfo]]

==Navigation==
{{nav|User:Jtneill}}
* [[Template:nav]]

==Notes==
Small e.g.,
{{attention}} &lt;small&gt;For calendar due dates, see unit outline.&lt;/small&gt;

Notice templates

{{Notice|{{tl|Notice}}}}
{{Note|{{tl|Note}}}}

==Notifications==
* [[Help:Notifications]]

==[[Project:Participants|Participants]]==
===Custodians===
{{user|Adambro}}&lt;br&gt;
{{user|CQ}}&lt;br&gt;
{{user|Cormaggio}}&lt;br&gt;
{{user|Draicone}}&lt;br&gt;
{{user|Erkan Yilmaz}}&lt;br&gt;
{{user|Gbaor}}&lt;br&gt;
{{user|Leighblackall}}&lt;br&gt;
{{user|McCormack}}&lt;br&gt;
{{user|Mike.lifeguard}}&lt;br&gt;
{{user|Mu301}}&lt;br&gt;
{{user|SB_Johnny}}

===Users===
*{{Participant|CQ}} - see Person of the Hour script

*{{Participant|Donek}}
*{{Participant|Dan Polansky}}

==Pedagogy==
* [[Learning by doing]]
* [[Wikiversity:Project incubator]]

==Policy==
* [[w:Wikipedia:Contributing_FAQ#Is_there_a_minimum_age_requirement_to_contribute_or_register.3F|Is there a minimum age requirement?]]
{{Official policies}}
{{Proposed policies}}

==Project boxes==
* [[Help:Resource attribution]]

==Purge==
To purge the cache for a given page, append this to the URL:
?action=purge

[[mw:Manual:Purge]]

==Quotes==
* [[Template:Quote]]
*

==[[Quizzes]]==
* [[Help:Quiz-Simple]]
* [http://www.qedoc.org/en/index.php?title=User:Jtneill My Qedoc user page]
** [http://eduforge.org/forum/forum.php?forum_id=1138 Qedoc now exports quizzes to Wikiversity]

==Referencing==
* [[meta:WMDE Technical Wishes/Sub-referencing]]

==Sandbox==
* http://www.sandboxserver.org/
* [[Wikiversity:Sandbox Server]]
* [[Topic:Sandbox Server 0.5]]
* [http://scratchpad.wikia.com/wiki/Scratchpad_Wiki_Labs Scratchpad]
* [[../Sandbox]]

==Searching==
* [[Help:Google]]
* [[Wikiversity:Colloquium/archives/April 2008#Google search|Google search]] - &lt;nowiki&gt;[[google:wikiversity]]&lt;/nowiki&gt; [[google:wikiversity]]
* Use a + instead of a space

==Search multiple categories==
;Dual category search including one category with subcategories
Search for chapters which [[Template:Clarification templates|need clarification]]:
&lt;inputbox&gt;	
type=search
width=33
default=incategory:&quot;Resources needing clarification&quot;
namespaces=Main**
prefix=Motivation and emotion/Book
searchbuttonlabel=Search book chapters
bgcolor=transparent
break=no
&lt;/inputbox&gt;

==Sitenotice==
* [[MediaWiki:Sitenotice]]
* [[MediaWiki:Sitenotice id]]

==Size==

===Big/small===
* Use &lt;code&gt;&lt;nowiki&gt;&lt;big&gt;...&lt;/big&gt; - could be also &lt;big&gt;&lt;big&gt;...&lt;/big&gt;&lt;/big&gt; etc. and also &lt;small&gt;...&lt;/small&gt;&lt;/nowiki&gt;&lt;/code&gt;

===CSS===
&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;
&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;

==Special==
* [[Special:SpecialPages]]
* Abuse
** [[Special:AbuseFilter]]
** [[Special:AbuseLog]]
* [[Special:AccountSecurity]]
* [[Special:Allpages]]
* [https://auth.wikimedia.org/enwikiversity/wiki/Special:CreateAccount Create account]
* [[Special:GlobalWatchlist]]
* [[Special:ListGroupRights]]
* [[Special:PermanentLink]]
* [[Random]] - [[Special:Random]] - [[Wikiversity:Random]]
* [[Special:ShortPages]]
* [[Special:Version#Installed extensions]]

==Strategy==
* [[Wikiversity:Publicity]]
* [[Wikiversity:Vision]]
* [[Wikiversity:Vision 2009]]

==Statistics==
* [[Wikiversity:Statistics]]
* [[Google Search and Wikiversity]]
* [http://wikistics.falsikon.de/latest/wikiversity/en/ Monthly page hits for wikiversity.en]
* [http://gtools.org/tool/wikipedia-edit-counter/?str=jtneill&amp;project=en.wikiversity Jtneill edit count]
* https://xtools.wmcloud.org/pageinfo/en.wikiversity.org/
* [[Special:Impact]] - [[w:Special:Impact]]

==Sub-pages==
* [[Special:Prefixindex/User:Jtneill]]
* Transclude:
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/User:Jtneill}}&lt;/nowiki&gt;&lt;/code&gt;
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/{{NAMESPACE}}:{{PAGENAME}}}}&lt;/nowiki&gt;&lt;/code&gt;

==Stubs==
* [[:Category:Stub templates]]

==Structure==
* [[Wikiversity:Browse/Concept]]

==Symbols==
🟨🟡⭐💛🟥⭕️❌🟦🔵🟩🟢✅
* [[User:VeronicaJeanAnderson]]

==System messages==
* [[Special:AllMessages]]
* [[#Sitenotice|Site notice]]

==Style==
* [[MoS]]
* [[MediaWiki:Common.css]]

==Tables==
* [[Help:Table]]
* [[User:Jtneill/Sandbox/Tables and boxes]]

==Tagging/notification==
* &lt;nowiki&gt;@[[User:UserName|UserName]]&lt;/nowiki&gt;
* &lt;nowiki&gt;{{ping|UserName}}&lt;/nowiki&gt;

==Templates==
===Page development===
* {{tl|welcome and expand}} - {{tl|we}}
* {{tl|main welcome}}
* {{tl|search}}
* {{tl|draft}}
* {{tl|underconstruction}}
* {{tl|Learning project boilerplate}}
* {{tl|info}}
* {{tl|note}}
* {{tl|notice}}
* {{tl|Nutshell}}
* &lt;nowiki&gt;{{notice|{{findsources}}}}&lt;/nowiki&gt;

===Page navigation===
* [[Template:EasyNavBar]]
* [[Template:Recovery psychology]] (example)
* [[Workshop for Australian education policy]] (example)

===Sister projects===
* [[Template:Sisterprojectsearch]]
* [[Template:Wikibooks]]
* [[Template:Wikipedia]]
* [[Template:Wikiversity]]

===User talk===
* {{tl|Welcomeip}}
* {{tl|Welcome}}
* {{tl|Talk header}}
* [[:Category:User warning templates]]

===Administrative===
* [[Template:Category redirect]]
* [[Template:Warning]]

==Theory==
* [[Learning by engagement]]
* [[User:JWSchmidt/Wiki Scholar]]

==Thoughts==
* [[Red link]]s are doorways to the infinite library ([[w:The Library of Babel|Library of Babel]])

==Tooltips==
{{Tooltip|Tooltips allow additional text to be displayed when cursor hovers over|Pretty cool, eh?}}


==User==
* [[w:Special:GlobalRenameRequest]]
* [[Special:UserGroupRights]]
* [[Special:UserRights]]
* [[m:Steward requests/Permissions]]
* [[meta:Help:Two-factor authentication]]

==Usability==
* [[Wikiversity:Usability]]
* http://usability.wikimedia.org - [http://usability.wikimedia.org/wiki/User:Jtneill Jtneill]

==Video==
* .ogg files can be uploaded and embedded
* See [[/Video]] for examples

==wikEd==
* [[w:User_talk:Cacycle/wikEd]]

==Wiki2Reveal==
* [[Wiki2Reveal]] (slides on the fly from MediaWiki page)

==x Test anchor==
&lt;!-- Test anchor - don't delete! --&gt;
{{anchor|test}}

==See also==
* [[User:Jade Knight/Tools]]</text>
      <sha1>16mpb2vcdqsp8g8j14tko5zfl4dk8pg</sha1>
    </revision>
    <revision>
      <id>2810295</id>
      <parentid>2810294</parentid>
      <timestamp>2026-05-18T22:51:22Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <minor />
      <comment>/* Special */</comment>
      <origin>2810295</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="17020" sha1="kvu9vwlm0ew6i2j9vvat8wbx407jxxx" xml:space="preserve">{{TOCright}}
''A loose, personal (i.e., somewhat idiosynchratic) organisation of Wikiversity-related how-tos and links.''
==To sort==
{|style=&quot;background:transparent;&quot;
|valign=top|
* [http://tools.wikimedia.de/~magnus/commonshelper.php commonshelper]
* [[User:Jtneill/Wikification|Wikification]]
* [[w:Help:Interwiki_linking#Project_titles_and_shortcuts|Interwiki linking]]
* [[Wikiversity:Activity bars]]
* [[Wikiversity:Percent complete]]
|valign=top|
* [[Wikiversity:Import|import]]
* [[Wikiversity:Maintenance]]
* [[Wikiversity:Namespaces]]
* [[Wikiversity:Naming conventions]]
|valign=top|
* [[Wikiversity:Participants]]
* [[Wikiversity:Peer review]]
* [[Wikiversity:Review board]]
* [[Wikiversity:Searching]]
* [[How to be a Wikimedia sysop]]
|}

==Anchor==
* [[Template:Anchor]], e.g., [[#test]] will go to &lt;code&gt;&lt;nowiki&gt;{{anchor|test}}&lt;/nowiki&gt;&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{anchor|anchor=test}}&lt;/nowiki&gt;&lt;/code&gt; (should go to end of page)

==Archiving==
* Example of autoarchiving: [[User talk:Terra]]

==Blogging==
* [[Wikiversity Blog howto]]

==Boxes==
[[User:Jtneill/Sandbox/Tables and boxes]]

The simplest of boxes

{| class=&quot;messagebox&quot;
|-
| ABC
XYZ
|}

&lt;blockquote style=&quot;padding-left:1.0em; padding-right:1.0em; background-color:#eaf8f4;&quot;&gt;
Its good that it works in practice, because it certainly doesn’t work in theory[https://blogs.ch.cam.ac.uk/pmr/2007/10/14/the-thing-about-wikipedia-is-that-it-only-works-in-practice-in-theory-it-can-never-work/] 
&lt;/blockquote&gt;

==Categories==
It is possible to change the order in which a page’s categories are displayed. By default, categories are displayed in the order they appear in the wikitext. Wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480]

Using titleparts
&lt;nowiki&gt;[[Category:{{#titleparts:{{PAGENAME}}|1}}]]&lt;/nowiki&gt;

==[[/Centering/]]==
{{User:Jtneill/Wikiversity/Centering}}

==Chat==
* [[irc:wikiversity-en|#wikiversity-en]]

==Citations and referencing==
* [[w:Help:Citation tools|Citation tools]]
* [[:Category:Citation templates]]
* [[mw:Help:Cite]]
* [[Template:Citation]]
* [[WV:REF]]
* Example: Outward Bound Process Model&lt;ref&gt;Walsh, V., &amp; Golins, G. L. (1976). ''[http://wilderdom.com/theory/OutwardBoundProcessModel.html The exploration of the Outward Bound process]''.  Denver, CO: Colorado Outward Bound School.&lt;/ref&gt;

;References
{{reflist|1}}

==Collapse boxes==
{{collapse top|Mary had a little lamb}}
Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb,
Its fleece was white as snow

And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went
The lamb was sure to go

It followed her to school one day
School one day, school one day
It followed her to school one day
Which was against the rules.

It made the children laugh and play,
Laugh and play, laugh and play,
It made the children laugh and play
To see a lamb at school

And so the teacher turned it out,
Turned it out, turned it out,
And so the teacher turned it out,
But still it lingered near

And waited patiently about,
Patiently about, patiently about,
And waited patiently about
Till Mary did appear

&quot;Why does the lamb love Mary so?&quot;
Love Mary so? Love Mary so?
&quot;Why does the lamb love Mary so?&quot;
The eager children cry

&quot;Why, Mary loves the lamb, you know.&quot;
Loves the lamb, you know, loves the lamb, you know
&quot;Why, Mary loves the lamb, you know.&quot;
The teacher did reply
{{collapse bottom}}

==Colour==
* [[Wikiversity web page colors|Color tables]] | [[Wikiversity:Color names|Color names]]
* e.g., Font: {{font|color=green|Green}}, Background: &lt;span style=&quot;background:hotpink; color:white;&quot;&gt;Pink&lt;/span&gt;

==Columns==
===Column breaks===
{|
|-
| Works on all browsers (col-begin/break/end):
{{col-begin}}
{{col-break}}
* Col1
{{col-break}}
* Col2
{{col-break}}
* Col3
{{col-end}}

Works on all browsers (col/break/colend):
{{col}}
{{break}}
* Col1
{{break}}
* Col2
{{break}}
* Col3
{{col/end}}
|}

===Moz-column===
Easier to use, but doesn't work on all browsers:
&lt;div style=&quot;column-count:3;-moz-column-count:3;-webkit-column-count:3&quot;&gt;
* Ant
* Bee
* Buzzard
* Cat
* Dog
* Egret
* Elephant
* Tiger
* Whale
* Worm
&lt;/div&gt;

==Conversions==
===HTML===
* [[w:Wikipedia:Tools/Editing_tools#From_HTML]]
* [http://www.ebruni.it/en/software/os/i_love_wiki/index.mpl i love wiki]
* {{tick}} [http://diberri.dyndns.org/wikipedia/html2wiki/index.html HTML::WikiConverter]
* {{tick}} [http://openfacts2.berlios.de/html2wiki/index.php HTML::WikiConverter]] Add URL

==CSS==
* [[MediaWiki:Common.css]]

==Custodianship==
* [[Wikiversity:Custodianship]]
** [[Wikiversity:Candidates for Custodianship]]
** [[Wikiversity:Notices for custodians]]
** [[Wikiversity:Request custodian action]]
** [[:Category:Wikiversity custodians]]

==Edit page==
Create an internal link to the edit source page using:
[[Special:EditPage/{{FULLPAGENAME}}|Edit source]]

&lt;nowiki&gt;
{{edit page}}
&lt;/nowiki&gt;

gives:
{{edit page}}

&lt;nowiki&gt;
{{edit page box}}
&lt;/nowiki&gt;

gives:
{{edit page box}}

==Extensions==
* [[Special:Version#Extensions]]
* [[/CategoryTree|CategoryTree]]
* [http://www.sandboxserver.org/wiki/index.php?title=Testing_Mediawiki_extensions Sandbox server - testing extensions]
* [[User:Jtneill/WYSIWIG|WYSIWIG]]

==Font==
&lt;p&gt;{{font|face=&quot;courier&quot;|size=medium|courier size 3}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;verdana&quot;|size=large|verdana size 4}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;arial&quot;|size=x-large|arial size 5}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;times new roman&quot;|size=xx-large|times new roman size 6}}&lt;/p&gt;
&lt;p&gt;&lt;b&gt;{{font|face=&quot;verdana&quot;|size=xx-large|verdana bold size 6}}&lt;/b&gt;&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;lucida calligraphy&quot;|size=xx-large|lucida calligraphy size 7}}&lt;/p&gt;

==Formatting==
===Justification===
&lt;div style=&quot;text-align: justify&quot;&gt; This text is right justified (but it doesn't look like unless the paragraph is long enough to go over one line on the page, so this is intentionally a particularly and unnecessarily long sentence in order to demonstrate right justification using &lt;nowiki&gt;&lt;div style=&quot;text-align: justify&quot;&gt;...&lt;/div&gt;&lt;/nowiki&gt;).&lt;/div&gt;
==Line height==
{{center top}}&lt;p style=&quot;line-height: 36px;&quot;&gt;
&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;This uses a&lt;br&gt;line height of 36px&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/p&gt;
&lt;pre&gt;&lt;p style=&quot;line-height: 36px;&quot;&gt;...&lt;/p&gt;&lt;/pre&gt;
{{center bottom}}
===Mouse-over===
* [[Help:Mouse-over]]
* [[Template:H:title]]

==Getting started==
* [[Wikiversity:Guided tour|Guided tour]]
* [[Wikiversity:Introduction|Introduction]] (Wikiversity)
* [[/Introduction|Introduction]] (Jtneill)
* [[/Welcome|Welcome]] (Jtneill)
* [[Introduction to Wiki]] - [[Wiki 101]]
* [[How to use wiki technology as a free learner]]
* [[:Image:Short.ogg|Wikiversity - short intro]] (10 sec. video)
* [[:Image:Editing_tutorial-large.ogg|Wikiversity editing tutorial]] (2 min video)
* [[Wikiversity:Community Portal]]
* [[Wikiversity:Content development]]
* [[Help:Edit summary]]
* [[Making links]]

==Good design==
* [[User:Jtneill/Good design]]

==Icons==
* [[Help:Icons]]
* [[User:McCormack/icons]]

==Images==
===[[Template:Gallery|Gallery]]===
{{Gallery
|title=Gallery of images
|footer=Uses this [[Template:Gallery|template]]
|width=150
|lines=2
||Comment
|File:Wikiversity-logo-Snorky.svg|[[Help:Contents/Links|Links]] can be put in captions.
|File:Wikiversity-logo-Snorky.svg|Full [[MediaWiki]]&lt;br /&gt;[[syntax]] may be used…
|File:Wikiversity-logo-Snorky.svg|
}}

&lt;!-- Fixed image in bottom right which is linked --&gt;
&lt;div id=&quot;template-navbar&quot; style=&quot;position: fixed; left:1; right:0; bottom:0; padding:0; font-size:122%;&quot;&gt;[[Image:Happy.png|right|50px|link=en:Happiness|Happiness]]&lt;/div&gt;

===ImageMap===
* [[mw:Extension:ImageMap|Extension ImageMap]] e.g.,
{{center top}}
&lt;imagemap&gt;File:Treasurchest.svg|center|80px
default [[Special:Random/|Random Wikiversity mainspace page]]
desc none&lt;/imagemap&gt;Click the treasure box to go to a random [[Wikiversity]] page{{center bottom}}

;Explanation

The ImageMap extension allows, among other things, an image to link directly to a page e.g., as an internal link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;
&lt;/pre&gt;

or as an external link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;
&lt;/pre&gt;

==Integrations==
I'm interested to explore possible connections between WV and:
* [http://archive.org Archive.org]
* [[w:Citizendium|Citizendium]]
* [[w:Google Groups]]
* [[Moodle]]
* [[Open University]]
* [http://openlearn.open.ac.uk/course/view.php?name=Cohere Cohere]
* [[WikiMedia Sister Projects]], particularly:
** [[Wikibooks]]
** [[Wikipedia]]
** [[Simple Wikipedia]]

==Licensing==
* My teaching materials are licensed under [[Wikiversity:License tags#Free licenses|creative commons attribution 2.5]] and hosted either on http://wilderdom.com or http://ucspace.canberra.edu.au. I am thinking I should be dual licensing, but am still coming to grips with trying to understand the licensing similarities, differences, and issues. 
* I plan to gradually transfer most of my teaching materials to the various [[w:WikiMedia Foundation|WikiMedia Foundation]] wiki projects, particularly wikiversity. [[m:Polls|Let's just hope Jimbo doesn't put adds on these sites]], otherwise I will be transferring the materials somewhere else (again).
* [http://beta.wikiversity.org/wiki/Wikiversity:IRC_meeting:New_licence_for_Wikiversity_Beta New_licence_for_Wikiversity_Beta]
* {{tl|db-copyvio}}
* {{tl|hangon}}
* [[:Category:Astronomy Images]]

==Links==
* Plain links: e.g., &lt;span class=&quot;plainlinks&quot;&gt;[http://archive.org http://archive.org]&lt;/span&gt;: &lt;br&gt;&lt;nowiki&gt;&lt;span class=&quot;plainlinks&quot;&gt; ... &lt;/span&gt;&lt;/nowiki&gt;
* [[mw:Manual:Opening external links in a new window]]

==Long page warning==
* [[MediaWiki:Longpagewarning]]

==[[Main page]]==
* [[:Category:Main page templates]]
* [[Main Page/Layout 0.5]]
* &lt;span class=&quot;plainlinks&quot;&gt;[http://en.wikiversity.org/w/index.php?title=Wikiversity:Main_Page&amp;oldid=209253 Main page]&lt;/span&gt; (old)

==Map==
&lt;mapframe latitude=&quot;-28.420391&quot; longitude=&quot;136.757813&quot; zoom=&quot;2&quot; width=&quot;200&quot; height=&quot;109&quot; align=&quot;right&quot;&gt;{
  &quot;type&quot;: &quot;FeatureCollection&quot;,
  &quot;features&quot;: [
    {
      &quot;type&quot;: &quot;Feature&quot;,
      &quot;properties&quot;: {},
      &quot;geometry&quot;: {
        &quot;type&quot;: &quot;Point&quot;,
        &quot;coordinates&quot;: [
          149.12419,
          -35.308275
        ]
      }
    }
  ]
}&lt;/mapframe&gt; 
==Namespaces==
* [[Special:NamespaceInfo]]

==Navigation==
{{nav|User:Jtneill}}
* [[Template:nav]]

==Notes==
Small e.g.,
{{attention}} &lt;small&gt;For calendar due dates, see unit outline.&lt;/small&gt;

Notice templates

{{Notice|{{tl|Notice}}}}
{{Note|{{tl|Note}}}}

==Notifications==
* [[Help:Notifications]]

==[[Project:Participants|Participants]]==
===Custodians===
{{user|Adambro}}&lt;br&gt;
{{user|CQ}}&lt;br&gt;
{{user|Cormaggio}}&lt;br&gt;
{{user|Draicone}}&lt;br&gt;
{{user|Erkan Yilmaz}}&lt;br&gt;
{{user|Gbaor}}&lt;br&gt;
{{user|Leighblackall}}&lt;br&gt;
{{user|McCormack}}&lt;br&gt;
{{user|Mike.lifeguard}}&lt;br&gt;
{{user|Mu301}}&lt;br&gt;
{{user|SB_Johnny}}

===Users===
*{{Participant|CQ}} - see Person of the Hour script

*{{Participant|Donek}}
*{{Participant|Dan Polansky}}

==Pedagogy==
* [[Learning by doing]]
* [[Wikiversity:Project incubator]]

==Policy==
* [[w:Wikipedia:Contributing_FAQ#Is_there_a_minimum_age_requirement_to_contribute_or_register.3F|Is there a minimum age requirement?]]
{{Official policies}}
{{Proposed policies}}

==Project boxes==
* [[Help:Resource attribution]]

==Purge==
To purge the cache for a given page, append this to the URL:
?action=purge

[[mw:Manual:Purge]]

==Quotes==
* [[Template:Quote]]
*

==[[Quizzes]]==
* [[Help:Quiz-Simple]]
* [http://www.qedoc.org/en/index.php?title=User:Jtneill My Qedoc user page]
** [http://eduforge.org/forum/forum.php?forum_id=1138 Qedoc now exports quizzes to Wikiversity]

==Referencing==
* [[meta:WMDE Technical Wishes/Sub-referencing]]

==Sandbox==
* http://www.sandboxserver.org/
* [[Wikiversity:Sandbox Server]]
* [[Topic:Sandbox Server 0.5]]
* [http://scratchpad.wikia.com/wiki/Scratchpad_Wiki_Labs Scratchpad]
* [[../Sandbox]]

==Searching==
* [[Help:Google]]
* [[Wikiversity:Colloquium/archives/April 2008#Google search|Google search]] - &lt;nowiki&gt;[[google:wikiversity]]&lt;/nowiki&gt; [[google:wikiversity]]
* Use a + instead of a space

==Search multiple categories==
;Dual category search including one category with subcategories
Search for chapters which [[Template:Clarification templates|need clarification]]:
&lt;inputbox&gt;	
type=search
width=33
default=incategory:&quot;Resources needing clarification&quot;
namespaces=Main**
prefix=Motivation and emotion/Book
searchbuttonlabel=Search book chapters
bgcolor=transparent
break=no
&lt;/inputbox&gt;

==Sitenotice==
* [[MediaWiki:Sitenotice]]
* [[MediaWiki:Sitenotice id]]

==Size==

===Big/small===
* Use &lt;code&gt;&lt;nowiki&gt;&lt;big&gt;...&lt;/big&gt; - could be also &lt;big&gt;&lt;big&gt;...&lt;/big&gt;&lt;/big&gt; etc. and also &lt;small&gt;...&lt;/small&gt;&lt;/nowiki&gt;&lt;/code&gt;

===CSS===
&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;
&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;

==Special==
* [[Special:SpecialPages]]
* Abuse
** [[Special:AbuseFilter]]
** [[Special:AbuseLog]]
* [[Special:AccountSecurity]]
* [[Special:Allpages]]
* [https://auth.wikimedia.org/enwikiversity/wiki/Special:CreateAccount Create account]
* [[meta:Special:GlobalWatchlist]]
* [[Special:ListGroupRights]]
* [[Special:PermanentLink]]
* [[Random]] - [[Special:Random]] - [[Wikiversity:Random]]
* [[Special:ShortPages]]
* [[Special:Version#Installed extensions]]

==Strategy==
* [[Wikiversity:Publicity]]
* [[Wikiversity:Vision]]
* [[Wikiversity:Vision 2009]]

==Statistics==
* [[Wikiversity:Statistics]]
* [[Google Search and Wikiversity]]
* [http://wikistics.falsikon.de/latest/wikiversity/en/ Monthly page hits for wikiversity.en]
* [http://gtools.org/tool/wikipedia-edit-counter/?str=jtneill&amp;project=en.wikiversity Jtneill edit count]
* https://xtools.wmcloud.org/pageinfo/en.wikiversity.org/
* [[Special:Impact]] - [[w:Special:Impact]]

==Sub-pages==
* [[Special:Prefixindex/User:Jtneill]]
* Transclude:
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/User:Jtneill}}&lt;/nowiki&gt;&lt;/code&gt;
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/{{NAMESPACE}}:{{PAGENAME}}}}&lt;/nowiki&gt;&lt;/code&gt;

==Stubs==
* [[:Category:Stub templates]]

==Structure==
* [[Wikiversity:Browse/Concept]]

==Symbols==
🟨🟡⭐💛🟥⭕️❌🟦🔵🟩🟢✅
* [[User:VeronicaJeanAnderson]]

==System messages==
* [[Special:AllMessages]]
* [[#Sitenotice|Site notice]]

==Style==
* [[MoS]]
* [[MediaWiki:Common.css]]

==Tables==
* [[Help:Table]]
* [[User:Jtneill/Sandbox/Tables and boxes]]

==Tagging/notification==
* &lt;nowiki&gt;@[[User:UserName|UserName]]&lt;/nowiki&gt;
* &lt;nowiki&gt;{{ping|UserName}}&lt;/nowiki&gt;

==Templates==
===Page development===
* {{tl|welcome and expand}} - {{tl|we}}
* {{tl|main welcome}}
* {{tl|search}}
* {{tl|draft}}
* {{tl|underconstruction}}
* {{tl|Learning project boilerplate}}
* {{tl|info}}
* {{tl|note}}
* {{tl|notice}}
* {{tl|Nutshell}}
* &lt;nowiki&gt;{{notice|{{findsources}}}}&lt;/nowiki&gt;

===Page navigation===
* [[Template:EasyNavBar]]
* [[Template:Recovery psychology]] (example)
* [[Workshop for Australian education policy]] (example)

===Sister projects===
* [[Template:Sisterprojectsearch]]
* [[Template:Wikibooks]]
* [[Template:Wikipedia]]
* [[Template:Wikiversity]]

===User talk===
* {{tl|Welcomeip}}
* {{tl|Welcome}}
* {{tl|Talk header}}
* [[:Category:User warning templates]]

===Administrative===
* [[Template:Category redirect]]
* [[Template:Warning]]

==Theory==
* [[Learning by engagement]]
* [[User:JWSchmidt/Wiki Scholar]]

==Thoughts==
* [[Red link]]s are doorways to the infinite library ([[w:The Library of Babel|Library of Babel]])

==Tooltips==
{{Tooltip|Tooltips allow additional text to be displayed when cursor hovers over|Pretty cool, eh?}}


==User==
* [[w:Special:GlobalRenameRequest]]
* [[Special:UserGroupRights]]
* [[Special:UserRights]]
* [[m:Steward requests/Permissions]]
* [[meta:Help:Two-factor authentication]]

==Usability==
* [[Wikiversity:Usability]]
* http://usability.wikimedia.org - [http://usability.wikimedia.org/wiki/User:Jtneill Jtneill]

==Video==
* .ogg files can be uploaded and embedded
* See [[/Video]] for examples

==wikEd==
* [[w:User_talk:Cacycle/wikEd]]

==Wiki2Reveal==
* [[Wiki2Reveal]] (slides on the fly from MediaWiki page)

==x Test anchor==
&lt;!-- Test anchor - don't delete! --&gt;
{{anchor|test}}

==See also==
* [[User:Jade Knight/Tools]]</text>
      <sha1>kvu9vwlm0ew6i2j9vvat8wbx407jxxx</sha1>
    </revision>
    <revision>
      <id>2810373</id>
      <parentid>2810295</parentid>
      <timestamp>2026-05-19T03:41:16Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>+ Pages</comment>
      <origin>2810373</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16906" sha1="qkxijw1anc0lg6t5zs4luejl4m1l4z7" xml:space="preserve">{{TOCright}}
''A loose, personal (i.e., somewhat idiosynchratic) organisation of Wikiversity-related how-tos and links.''
==To sort==
{|style=&quot;background:transparent;&quot;
|valign=top|
* [http://tools.wikimedia.de/~magnus/commonshelper.php commonshelper]
* [[User:Jtneill/Wikification|Wikification]]
* [[w:Help:Interwiki_linking#Project_titles_and_shortcuts|Interwiki linking]]
* [[Wikiversity:Activity bars]]
* [[Wikiversity:Percent complete]]
|valign=top|
* [[Wikiversity:Import|import]]
* [[Wikiversity:Maintenance]]
* [[Wikiversity:Namespaces]]
* [[Wikiversity:Naming conventions]]
|valign=top|
* [[Wikiversity:Participants]]
* [[Wikiversity:Peer review]]
* [[Wikiversity:Review board]]
* [[Wikiversity:Searching]]
* [[How to be a Wikimedia sysop]]
|}

==Anchor==
* [[Template:Anchor]], e.g., [[#test]] will go to &lt;code&gt;&lt;nowiki&gt;{{anchor|test}}&lt;/nowiki&gt;&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{anchor|anchor=test}}&lt;/nowiki&gt;&lt;/code&gt; (should go to end of page)

==Archiving==
* Example of autoarchiving: [[User talk:Terra]]

==Blogging==
* [[Wikiversity Blog howto]]

==Boxes==
[[User:Jtneill/Sandbox/Tables and boxes]]

The simplest of boxes

{| class=&quot;messagebox&quot;
|-
| ABC
XYZ
|}

&lt;blockquote style=&quot;padding-left:1.0em; padding-right:1.0em; background-color:#eaf8f4;&quot;&gt;
Its good that it works in practice, because it certainly doesn’t work in theory[https://blogs.ch.cam.ac.uk/pmr/2007/10/14/the-thing-about-wikipedia-is-that-it-only-works-in-practice-in-theory-it-can-never-work/] 
&lt;/blockquote&gt;

==Categories==
It is possible to change the order in which a page’s categories are displayed. By default, categories are displayed in the order they appear in the wikitext. Wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480]

Using titleparts
&lt;nowiki&gt;[[Category:{{#titleparts:{{PAGENAME}}|1}}]]&lt;/nowiki&gt;

==[[/Centering/]]==
{{User:Jtneill/Wikiversity/Centering}}

==Chat==
* [[irc:wikiversity-en|#wikiversity-en]]

==Citations and referencing==
* [[w:Help:Citation tools|Citation tools]]
* [[:Category:Citation templates]]
* [[mw:Help:Cite]]
* [[Template:Citation]]
* [[WV:REF]]
* Example: Outward Bound Process Model&lt;ref&gt;Walsh, V., &amp; Golins, G. L. (1976). ''[http://wilderdom.com/theory/OutwardBoundProcessModel.html The exploration of the Outward Bound process]''.  Denver, CO: Colorado Outward Bound School.&lt;/ref&gt;

;References
{{reflist|1}}

==Collapse boxes==
{{collapse top|Mary had a little lamb}}
Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb,
Its fleece was white as snow

And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went
The lamb was sure to go

It followed her to school one day
School one day, school one day
It followed her to school one day
Which was against the rules.

It made the children laugh and play,
Laugh and play, laugh and play,
It made the children laugh and play
To see a lamb at school

And so the teacher turned it out,
Turned it out, turned it out,
And so the teacher turned it out,
But still it lingered near

And waited patiently about,
Patiently about, patiently about,
And waited patiently about
Till Mary did appear

&quot;Why does the lamb love Mary so?&quot;
Love Mary so? Love Mary so?
&quot;Why does the lamb love Mary so?&quot;
The eager children cry

&quot;Why, Mary loves the lamb, you know.&quot;
Loves the lamb, you know, loves the lamb, you know
&quot;Why, Mary loves the lamb, you know.&quot;
The teacher did reply
{{collapse bottom}}

==Colour==
* [[Wikiversity web page colors|Color tables]] | [[Wikiversity:Color names|Color names]]
* e.g., Font: {{font|color=green|Green}}, Background: &lt;span style=&quot;background:hotpink; color:white;&quot;&gt;Pink&lt;/span&gt;

==Columns==
===Column breaks===
{|
|-
| Works on all browsers (col-begin/break/end):
{{col-begin}}
{{col-break}}
* Col1
{{col-break}}
* Col2
{{col-break}}
* Col3
{{col-end}}

Works on all browsers (col/break/colend):
{{col}}
{{break}}
* Col1
{{break}}
* Col2
{{break}}
* Col3
{{col/end}}
|}

===Moz-column===
Easier to use, but doesn't work on all browsers:
&lt;div style=&quot;column-count:3;-moz-column-count:3;-webkit-column-count:3&quot;&gt;
* Ant
* Bee
* Buzzard
* Cat
* Dog
* Egret
* Elephant
* Tiger
* Whale
* Worm
&lt;/div&gt;

==Conversions==
===HTML===
* [[w:Wikipedia:Tools/Editing_tools#From_HTML]]
* [http://www.ebruni.it/en/software/os/i_love_wiki/index.mpl i love wiki]
* {{tick}} [http://diberri.dyndns.org/wikipedia/html2wiki/index.html HTML::WikiConverter]
* {{tick}} [http://openfacts2.berlios.de/html2wiki/index.php HTML::WikiConverter]] Add URL

==CSS==
* [[MediaWiki:Common.css]]

==Custodianship==
* [[Wikiversity:Custodianship]]
** [[Wikiversity:Candidates for Custodianship]]
** [[Wikiversity:Notices for custodians]]
** [[Wikiversity:Request custodian action]]
** [[:Category:Wikiversity custodians]]

==Edit page==
Create an internal link to the edit source page using:
[[Special:EditPage/{{FULLPAGENAME}}|Edit source]]

&lt;nowiki&gt;
{{edit page}}
&lt;/nowiki&gt;

gives:
{{edit page}}

&lt;nowiki&gt;
{{edit page box}}
&lt;/nowiki&gt;

gives:
{{edit page box}}

==Extensions==
* [[Special:Version#Extensions]]
* [[/CategoryTree|CategoryTree]]
* [http://www.sandboxserver.org/wiki/index.php?title=Testing_Mediawiki_extensions Sandbox server - testing extensions]
* [[User:Jtneill/WYSIWIG|WYSIWIG]]

==Font==
&lt;p&gt;{{font|face=&quot;courier&quot;|size=medium|courier size 3}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;verdana&quot;|size=large|verdana size 4}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;arial&quot;|size=x-large|arial size 5}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;times new roman&quot;|size=xx-large|times new roman size 6}}&lt;/p&gt;
&lt;p&gt;&lt;b&gt;{{font|face=&quot;verdana&quot;|size=xx-large|verdana bold size 6}}&lt;/b&gt;&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;lucida calligraphy&quot;|size=xx-large|lucida calligraphy size 7}}&lt;/p&gt;

==Formatting==
===Justification===
&lt;div style=&quot;text-align: justify&quot;&gt; This text is right justified (but it doesn't look like unless the paragraph is long enough to go over one line on the page, so this is intentionally a particularly and unnecessarily long sentence in order to demonstrate right justification using &lt;nowiki&gt;&lt;div style=&quot;text-align: justify&quot;&gt;...&lt;/div&gt;&lt;/nowiki&gt;).&lt;/div&gt;
==Line height==
{{center top}}&lt;p style=&quot;line-height: 36px;&quot;&gt;
&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;This uses a&lt;br&gt;line height of 36px&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/p&gt;
&lt;pre&gt;&lt;p style=&quot;line-height: 36px;&quot;&gt;...&lt;/p&gt;&lt;/pre&gt;
{{center bottom}}
===Mouse-over===
* [[Help:Mouse-over]]
* [[Template:H:title]]

==Getting started==
* [[Wikiversity:Guided tour|Guided tour]]
* [[Wikiversity:Introduction|Introduction]] (Wikiversity)
* [[/Introduction|Introduction]] (Jtneill)
* [[/Welcome|Welcome]] (Jtneill)
* [[Introduction to Wiki]] - [[Wiki 101]]
* [[How to use wiki technology as a free learner]]
* [[:Image:Short.ogg|Wikiversity - short intro]] (10 sec. video)
* [[:Image:Editing_tutorial-large.ogg|Wikiversity editing tutorial]] (2 min video)
* [[Wikiversity:Community Portal]]
* [[Wikiversity:Content development]]
* [[Help:Edit summary]]
* [[Making links]]

==Good design==
* [[User:Jtneill/Good design]]

==Icons==
* [[Help:Icons]]
* [[User:McCormack/icons]]

==Images==
===[[Template:Gallery|Gallery]]===
{{Gallery
|title=Gallery of images
|footer=Uses this [[Template:Gallery|template]]
|width=150
|lines=2
||Comment
|File:Wikiversity-logo-Snorky.svg|[[Help:Contents/Links|Links]] can be put in captions.
|File:Wikiversity-logo-Snorky.svg|Full [[MediaWiki]]&lt;br /&gt;[[syntax]] may be used…
|File:Wikiversity-logo-Snorky.svg|
}}

&lt;!-- Fixed image in bottom right which is linked --&gt;
&lt;div id=&quot;template-navbar&quot; style=&quot;position: fixed; left:1; right:0; bottom:0; padding:0; font-size:122%;&quot;&gt;[[Image:Happy.png|right|50px|link=en:Happiness|Happiness]]&lt;/div&gt;

===ImageMap===
* [[mw:Extension:ImageMap|Extension ImageMap]] e.g.,
{{center top}}
&lt;imagemap&gt;File:Treasurchest.svg|center|80px
default [[Special:Random/|Random Wikiversity mainspace page]]
desc none&lt;/imagemap&gt;Click the treasure box to go to a random [[Wikiversity]] page{{center bottom}}

;Explanation

The ImageMap extension allows, among other things, an image to link directly to a page e.g., as an internal link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;
&lt;/pre&gt;

or as an external link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;
&lt;/pre&gt;

==Integrations==
I'm interested to explore possible connections between WV and:
* [http://archive.org Archive.org]
* [[w:Citizendium|Citizendium]]
* [[w:Google Groups]]
* [[Moodle]]
* [[Open University]]
* [http://openlearn.open.ac.uk/course/view.php?name=Cohere Cohere]
* [[WikiMedia Sister Projects]], particularly:
** [[Wikibooks]]
** [[Wikipedia]]
** [[Simple Wikipedia]]

==Licensing==
* My teaching materials are licensed under [[Wikiversity:License tags#Free licenses|creative commons attribution 2.5]] and hosted either on http://wilderdom.com or http://ucspace.canberra.edu.au. I am thinking I should be dual licensing, but am still coming to grips with trying to understand the licensing similarities, differences, and issues. 
* I plan to gradually transfer most of my teaching materials to the various [[w:WikiMedia Foundation|WikiMedia Foundation]] wiki projects, particularly wikiversity. [[m:Polls|Let's just hope Jimbo doesn't put adds on these sites]], otherwise I will be transferring the materials somewhere else (again).
* [http://beta.wikiversity.org/wiki/Wikiversity:IRC_meeting:New_licence_for_Wikiversity_Beta New_licence_for_Wikiversity_Beta]
* {{tl|db-copyvio}}
* {{tl|hangon}}
* [[:Category:Astronomy Images]]

==Links==
* Plain links: e.g., &lt;span class=&quot;plainlinks&quot;&gt;[http://archive.org http://archive.org]&lt;/span&gt;: &lt;br&gt;&lt;nowiki&gt;&lt;span class=&quot;plainlinks&quot;&gt; ... &lt;/span&gt;&lt;/nowiki&gt;
* [[mw:Manual:Opening external links in a new window]]

==Long page warning==
* [[MediaWiki:Longpagewarning]]

==[[Main page]]==
* [[:Category:Main page templates]]
* [[Main Page/Layout 0.5]]
* &lt;span class=&quot;plainlinks&quot;&gt;[http://en.wikiversity.org/w/index.php?title=Wikiversity:Main_Page&amp;oldid=209253 Main page]&lt;/span&gt; (old)

==Map==
&lt;mapframe latitude=&quot;-28.420391&quot; longitude=&quot;136.757813&quot; zoom=&quot;2&quot; width=&quot;200&quot; height=&quot;109&quot; align=&quot;right&quot;&gt;{
  &quot;type&quot;: &quot;FeatureCollection&quot;,
  &quot;features&quot;: [
    {
      &quot;type&quot;: &quot;Feature&quot;,
      &quot;properties&quot;: {},
      &quot;geometry&quot;: {
        &quot;type&quot;: &quot;Point&quot;,
        &quot;coordinates&quot;: [
          149.12419,
          -35.308275
        ]
      }
    }
  ]
}&lt;/mapframe&gt; 
==Namespaces==
* [[Special:NamespaceInfo]]

==Navigation==
{{nav|User:Jtneill}}
* [[Template:nav]]

==Notes==
Small e.g.,
{{attention}} &lt;small&gt;For calendar due dates, see unit outline.&lt;/small&gt;

Notice templates

{{Notice|{{tl|Notice}}}}
{{Note|{{tl|Note}}}}

==Notifications==
* [[Help:Notifications]]

==Pages==
* [[Special:AllPages]]
* Number of pages in category: &lt;nowiki&gt;{{PAGESINCATEGORY:User:Jtneill}}&lt;/nowiki&gt;

==[[Project:Participants|Participants]]==
*[[Wikiversity:Support staff]]

===Users===
*{{Participant|CQ}} - see Person of the Hour script

*{{Participant|Donek}}
*{{Participant|Dan Polansky}}

==Pedagogy==
* [[Learning by doing]]
* [[Wikiversity:Project incubator]]

==Policy==
* [[w:Wikipedia:Contributing_FAQ#Is_there_a_minimum_age_requirement_to_contribute_or_register.3F|Is there a minimum age requirement?]]
{{Official policies}}
{{Proposed policies}}

==Project boxes==
* [[Help:Resource attribution]]

==Purge==
To purge the cache for a given page, append this to the URL:
?action=purge

[[mw:Manual:Purge]]

==Quotes==
* [[Template:Quote]]
*

==[[Quizzes]]==
* [[Help:Quiz-Simple]]
* [http://www.qedoc.org/en/index.php?title=User:Jtneill My Qedoc user page]
** [http://eduforge.org/forum/forum.php?forum_id=1138 Qedoc now exports quizzes to Wikiversity]

==Referencing==
* [[meta:WMDE Technical Wishes/Sub-referencing]]

==Sandbox==
* http://www.sandboxserver.org/
* [[Wikiversity:Sandbox Server]]
* [[Topic:Sandbox Server 0.5]]
* [http://scratchpad.wikia.com/wiki/Scratchpad_Wiki_Labs Scratchpad]
* [[../Sandbox]]

==Searching==
* [[Help:Google]]
* [[Wikiversity:Colloquium/archives/April 2008#Google search|Google search]] - &lt;nowiki&gt;[[google:wikiversity]]&lt;/nowiki&gt; [[google:wikiversity]]
* Use a + instead of a space

==Search multiple categories==
;Dual category search including one category with subcategories
Search for chapters which [[Template:Clarification templates|need clarification]]:
&lt;inputbox&gt;	
type=search
width=33
default=incategory:&quot;Resources needing clarification&quot;
namespaces=Main**
prefix=Motivation and emotion/Book
searchbuttonlabel=Search book chapters
bgcolor=transparent
break=no
&lt;/inputbox&gt;

==Sitenotice==
* [[MediaWiki:Sitenotice]]
* [[MediaWiki:Sitenotice id]]

==Size==

===Big/small===
* Use &lt;code&gt;&lt;nowiki&gt;&lt;big&gt;...&lt;/big&gt; - could be also &lt;big&gt;&lt;big&gt;...&lt;/big&gt;&lt;/big&gt; etc. and also &lt;small&gt;...&lt;/small&gt;&lt;/nowiki&gt;&lt;/code&gt;

===CSS===
&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;
&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;

==Special==
* [[Special:SpecialPages]]
* Abuse
** [[Special:AbuseFilter]]
** [[Special:AbuseLog]]
* [[Special:AccountSecurity]]
* [[Special:Allpages]]
* [https://auth.wikimedia.org/enwikiversity/wiki/Special:CreateAccount Create account]
* [[meta:Special:GlobalWatchlist]]
* [[Special:ListGroupRights]]
* [[Special:PermanentLink]]
* [[Random]] - [[Special:Random]] - [[Wikiversity:Random]]
* [[Special:ShortPages]]
* [[Special:Version#Installed extensions]]

==Strategy==
* [[Wikiversity:Publicity]]
* [[Wikiversity:Vision]]
* [[Wikiversity:Vision 2009]]

==Statistics==
* [[Wikiversity:Statistics]]
* [[Google Search and Wikiversity]]
* [http://wikistics.falsikon.de/latest/wikiversity/en/ Monthly page hits for wikiversity.en]
* [http://gtools.org/tool/wikipedia-edit-counter/?str=jtneill&amp;project=en.wikiversity Jtneill edit count]
* https://xtools.wmcloud.org/pageinfo/en.wikiversity.org/
* [[Special:Impact]] - [[w:Special:Impact]]

==Sub-pages==
* [[Special:Prefixindex/User:Jtneill]]
* Transclude:
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/User:Jtneill}}&lt;/nowiki&gt;&lt;/code&gt;
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/{{NAMESPACE}}:{{PAGENAME}}}}&lt;/nowiki&gt;&lt;/code&gt;

==Stubs==
* [[:Category:Stub templates]]

==Structure==
* [[Wikiversity:Browse/Concept]]

==Symbols==
🟨🟡⭐💛🟥⭕️❌🟦🔵🟩🟢✅
* [[User:VeronicaJeanAnderson]]

==System messages==
* [[Special:AllMessages]]
* [[#Sitenotice|Site notice]]

==Style==
* [[MoS]]
* [[MediaWiki:Common.css]]

==Tables==
* [[Help:Table]]
* [[User:Jtneill/Sandbox/Tables and boxes]]

==Tagging/notification==
* &lt;nowiki&gt;@[[User:UserName|UserName]]&lt;/nowiki&gt;
* &lt;nowiki&gt;{{ping|UserName}}&lt;/nowiki&gt;

==Templates==
===Page development===
* {{tl|welcome and expand}} - {{tl|we}}
* {{tl|main welcome}}
* {{tl|search}}
* {{tl|draft}}
* {{tl|underconstruction}}
* {{tl|Learning project boilerplate}}
* {{tl|info}}
* {{tl|note}}
* {{tl|notice}}
* {{tl|Nutshell}}
* &lt;nowiki&gt;{{notice|{{findsources}}}}&lt;/nowiki&gt;

===Page navigation===
* [[Template:EasyNavBar]]
* [[Template:Recovery psychology]] (example)
* [[Workshop for Australian education policy]] (example)

===Sister projects===
* [[Template:Sisterprojectsearch]]
* [[Template:Wikibooks]]
* [[Template:Wikipedia]]
* [[Template:Wikiversity]]

===User talk===
* {{tl|Welcomeip}}
* {{tl|Welcome}}
* {{tl|Talk header}}
* [[:Category:User warning templates]]

===Administrative===
* [[Template:Category redirect]]
* [[Template:Warning]]

==Theory==
* [[Learning by engagement]]
* [[User:JWSchmidt/Wiki Scholar]]

==Thoughts==
* [[Red link]]s are doorways to the infinite library ([[w:The Library of Babel|Library of Babel]])

==Tooltips==
{{Tooltip|Tooltips allow additional text to be displayed when cursor hovers over|Pretty cool, eh?}}


==User==
* [[w:Special:GlobalRenameRequest]]
* [[Special:UserGroupRights]]
* [[Special:UserRights]]
* [[m:Steward requests/Permissions]]
* [[meta:Help:Two-factor authentication]]

==Usability==
* [[Wikiversity:Usability]]
* http://usability.wikimedia.org - [http://usability.wikimedia.org/wiki/User:Jtneill Jtneill]

==Video==
* .ogg files can be uploaded and embedded
* See [[/Video]] for examples

==wikEd==
* [[w:User_talk:Cacycle/wikEd]]

==Wiki2Reveal==
* [[Wiki2Reveal]] (slides on the fly from MediaWiki page)

==x Test anchor==
&lt;!-- Test anchor - don't delete! --&gt;
{{anchor|test}}

==See also==
* [[User:Jade Knight/Tools]]</text>
      <sha1>qkxijw1anc0lg6t5zs4luejl4m1l4z7</sha1>
    </revision>
    <revision>
      <id>2810374</id>
      <parentid>2810373</parentid>
      <timestamp>2026-05-19T03:43:00Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>/* Pages */ + hitcounter</comment>
      <origin>2810374</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16957" sha1="369trvfvxnz1uv4rbp2fmkcgnng4it0" xml:space="preserve">{{TOCright}}
''A loose, personal (i.e., somewhat idiosynchratic) organisation of Wikiversity-related how-tos and links.''
==To sort==
{|style=&quot;background:transparent;&quot;
|valign=top|
* [http://tools.wikimedia.de/~magnus/commonshelper.php commonshelper]
* [[User:Jtneill/Wikification|Wikification]]
* [[w:Help:Interwiki_linking#Project_titles_and_shortcuts|Interwiki linking]]
* [[Wikiversity:Activity bars]]
* [[Wikiversity:Percent complete]]
|valign=top|
* [[Wikiversity:Import|import]]
* [[Wikiversity:Maintenance]]
* [[Wikiversity:Namespaces]]
* [[Wikiversity:Naming conventions]]
|valign=top|
* [[Wikiversity:Participants]]
* [[Wikiversity:Peer review]]
* [[Wikiversity:Review board]]
* [[Wikiversity:Searching]]
* [[How to be a Wikimedia sysop]]
|}

==Anchor==
* [[Template:Anchor]], e.g., [[#test]] will go to &lt;code&gt;&lt;nowiki&gt;{{anchor|test}}&lt;/nowiki&gt;&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{anchor|anchor=test}}&lt;/nowiki&gt;&lt;/code&gt; (should go to end of page)

==Archiving==
* Example of autoarchiving: [[User talk:Terra]]

==Blogging==
* [[Wikiversity Blog howto]]

==Boxes==
[[User:Jtneill/Sandbox/Tables and boxes]]

The simplest of boxes

{| class=&quot;messagebox&quot;
|-
| ABC
XYZ
|}

&lt;blockquote style=&quot;padding-left:1.0em; padding-right:1.0em; background-color:#eaf8f4;&quot;&gt;
Its good that it works in practice, because it certainly doesn’t work in theory[https://blogs.ch.cam.ac.uk/pmr/2007/10/14/the-thing-about-wikipedia-is-that-it-only-works-in-practice-in-theory-it-can-never-work/] 
&lt;/blockquote&gt;

==Categories==
It is possible to change the order in which a page’s categories are displayed. By default, categories are displayed in the order they appear in the wikitext. Wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480]

Using titleparts
&lt;nowiki&gt;[[Category:{{#titleparts:{{PAGENAME}}|1}}]]&lt;/nowiki&gt;

==[[/Centering/]]==
{{User:Jtneill/Wikiversity/Centering}}

==Chat==
* [[irc:wikiversity-en|#wikiversity-en]]

==Citations and referencing==
* [[w:Help:Citation tools|Citation tools]]
* [[:Category:Citation templates]]
* [[mw:Help:Cite]]
* [[Template:Citation]]
* [[WV:REF]]
* Example: Outward Bound Process Model&lt;ref&gt;Walsh, V., &amp; Golins, G. L. (1976). ''[http://wilderdom.com/theory/OutwardBoundProcessModel.html The exploration of the Outward Bound process]''.  Denver, CO: Colorado Outward Bound School.&lt;/ref&gt;

;References
{{reflist|1}}

==Collapse boxes==
{{collapse top|Mary had a little lamb}}
Mary had a little lamb,
Little lamb, little lamb,
Mary had a little lamb,
Its fleece was white as snow

And everywhere that Mary went,
Mary went, Mary went,
Everywhere that Mary went
The lamb was sure to go

It followed her to school one day
School one day, school one day
It followed her to school one day
Which was against the rules.

It made the children laugh and play,
Laugh and play, laugh and play,
It made the children laugh and play
To see a lamb at school

And so the teacher turned it out,
Turned it out, turned it out,
And so the teacher turned it out,
But still it lingered near

And waited patiently about,
Patiently about, patiently about,
And waited patiently about
Till Mary did appear

&quot;Why does the lamb love Mary so?&quot;
Love Mary so? Love Mary so?
&quot;Why does the lamb love Mary so?&quot;
The eager children cry

&quot;Why, Mary loves the lamb, you know.&quot;
Loves the lamb, you know, loves the lamb, you know
&quot;Why, Mary loves the lamb, you know.&quot;
The teacher did reply
{{collapse bottom}}

==Colour==
* [[Wikiversity web page colors|Color tables]] | [[Wikiversity:Color names|Color names]]
* e.g., Font: {{font|color=green|Green}}, Background: &lt;span style=&quot;background:hotpink; color:white;&quot;&gt;Pink&lt;/span&gt;

==Columns==
===Column breaks===
{|
|-
| Works on all browsers (col-begin/break/end):
{{col-begin}}
{{col-break}}
* Col1
{{col-break}}
* Col2
{{col-break}}
* Col3
{{col-end}}

Works on all browsers (col/break/colend):
{{col}}
{{break}}
* Col1
{{break}}
* Col2
{{break}}
* Col3
{{col/end}}
|}

===Moz-column===
Easier to use, but doesn't work on all browsers:
&lt;div style=&quot;column-count:3;-moz-column-count:3;-webkit-column-count:3&quot;&gt;
* Ant
* Bee
* Buzzard
* Cat
* Dog
* Egret
* Elephant
* Tiger
* Whale
* Worm
&lt;/div&gt;

==Conversions==
===HTML===
* [[w:Wikipedia:Tools/Editing_tools#From_HTML]]
* [http://www.ebruni.it/en/software/os/i_love_wiki/index.mpl i love wiki]
* {{tick}} [http://diberri.dyndns.org/wikipedia/html2wiki/index.html HTML::WikiConverter]
* {{tick}} [http://openfacts2.berlios.de/html2wiki/index.php HTML::WikiConverter]] Add URL

==CSS==
* [[MediaWiki:Common.css]]

==Custodianship==
* [[Wikiversity:Custodianship]]
** [[Wikiversity:Candidates for Custodianship]]
** [[Wikiversity:Notices for custodians]]
** [[Wikiversity:Request custodian action]]
** [[:Category:Wikiversity custodians]]

==Edit page==
Create an internal link to the edit source page using:
[[Special:EditPage/{{FULLPAGENAME}}|Edit source]]

&lt;nowiki&gt;
{{edit page}}
&lt;/nowiki&gt;

gives:
{{edit page}}

&lt;nowiki&gt;
{{edit page box}}
&lt;/nowiki&gt;

gives:
{{edit page box}}

==Extensions==
* [[Special:Version#Extensions]]
* [[/CategoryTree|CategoryTree]]
* [http://www.sandboxserver.org/wiki/index.php?title=Testing_Mediawiki_extensions Sandbox server - testing extensions]
* [[User:Jtneill/WYSIWIG|WYSIWIG]]

==Font==
&lt;p&gt;{{font|face=&quot;courier&quot;|size=medium|courier size 3}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;verdana&quot;|size=large|verdana size 4}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;arial&quot;|size=x-large|arial size 5}}&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;times new roman&quot;|size=xx-large|times new roman size 6}}&lt;/p&gt;
&lt;p&gt;&lt;b&gt;{{font|face=&quot;verdana&quot;|size=xx-large|verdana bold size 6}}&lt;/b&gt;&lt;/p&gt;
&lt;p&gt;{{font|face=&quot;lucida calligraphy&quot;|size=xx-large|lucida calligraphy size 7}}&lt;/p&gt;

==Formatting==
===Justification===
&lt;div style=&quot;text-align: justify&quot;&gt; This text is right justified (but it doesn't look like unless the paragraph is long enough to go over one line on the page, so this is intentionally a particularly and unnecessarily long sentence in order to demonstrate right justification using &lt;nowiki&gt;&lt;div style=&quot;text-align: justify&quot;&gt;...&lt;/div&gt;&lt;/nowiki&gt;).&lt;/div&gt;
==Line height==
{{center top}}&lt;p style=&quot;line-height: 36px;&quot;&gt;
&lt;big&gt;&lt;big&gt;&lt;big&gt;&lt;big&gt;This uses a&lt;br&gt;line height of 36px&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/big&gt;&lt;/p&gt;
&lt;pre&gt;&lt;p style=&quot;line-height: 36px;&quot;&gt;...&lt;/p&gt;&lt;/pre&gt;
{{center bottom}}
===Mouse-over===
* [[Help:Mouse-over]]
* [[Template:H:title]]

==Getting started==
* [[Wikiversity:Guided tour|Guided tour]]
* [[Wikiversity:Introduction|Introduction]] (Wikiversity)
* [[/Introduction|Introduction]] (Jtneill)
* [[/Welcome|Welcome]] (Jtneill)
* [[Introduction to Wiki]] - [[Wiki 101]]
* [[How to use wiki technology as a free learner]]
* [[:Image:Short.ogg|Wikiversity - short intro]] (10 sec. video)
* [[:Image:Editing_tutorial-large.ogg|Wikiversity editing tutorial]] (2 min video)
* [[Wikiversity:Community Portal]]
* [[Wikiversity:Content development]]
* [[Help:Edit summary]]
* [[Making links]]

==Good design==
* [[User:Jtneill/Good design]]

==Icons==
* [[Help:Icons]]
* [[User:McCormack/icons]]

==Images==
===[[Template:Gallery|Gallery]]===
{{Gallery
|title=Gallery of images
|footer=Uses this [[Template:Gallery|template]]
|width=150
|lines=2
||Comment
|File:Wikiversity-logo-Snorky.svg|[[Help:Contents/Links|Links]] can be put in captions.
|File:Wikiversity-logo-Snorky.svg|Full [[MediaWiki]]&lt;br /&gt;[[syntax]] may be used…
|File:Wikiversity-logo-Snorky.svg|
}}

&lt;!-- Fixed image in bottom right which is linked --&gt;
&lt;div id=&quot;template-navbar&quot; style=&quot;position: fixed; left:1; right:0; bottom:0; padding:0; font-size:122%;&quot;&gt;[[Image:Happy.png|right|50px|link=en:Happiness|Happiness]]&lt;/div&gt;

===ImageMap===
* [[mw:Extension:ImageMap|Extension ImageMap]] e.g.,
{{center top}}
&lt;imagemap&gt;File:Treasurchest.svg|center|80px
default [[Special:Random/|Random Wikiversity mainspace page]]
desc none&lt;/imagemap&gt;Click the treasure box to go to a random [[Wikiversity]] page{{center bottom}}

;Explanation

The ImageMap extension allows, among other things, an image to link directly to a page e.g., as an internal link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [[Motivation and emotion/Book/2015|Motivation and emotion Book - 2015]]
&lt;/imagemap&gt;
&lt;/pre&gt;

or as an external link:
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;

The syntax is:
&lt;pre style=&quot;overflow:auto&quot;&gt;
&lt;imagemap&gt;
File:Treasurchest.svg|center|150px|alt=Alt text
default [https://www.psychologytoday.com/basics/motivation Motivation (Psychology Today)]
&lt;/imagemap&gt;
&lt;/pre&gt;

==Integrations==
I'm interested to explore possible connections between WV and:
* [http://archive.org Archive.org]
* [[w:Citizendium|Citizendium]]
* [[w:Google Groups]]
* [[Moodle]]
* [[Open University]]
* [http://openlearn.open.ac.uk/course/view.php?name=Cohere Cohere]
* [[WikiMedia Sister Projects]], particularly:
** [[Wikibooks]]
** [[Wikipedia]]
** [[Simple Wikipedia]]

==Licensing==
* My teaching materials are licensed under [[Wikiversity:License tags#Free licenses|creative commons attribution 2.5]] and hosted either on http://wilderdom.com or http://ucspace.canberra.edu.au. I am thinking I should be dual licensing, but am still coming to grips with trying to understand the licensing similarities, differences, and issues. 
* I plan to gradually transfer most of my teaching materials to the various [[w:WikiMedia Foundation|WikiMedia Foundation]] wiki projects, particularly wikiversity. [[m:Polls|Let's just hope Jimbo doesn't put adds on these sites]], otherwise I will be transferring the materials somewhere else (again).
* [http://beta.wikiversity.org/wiki/Wikiversity:IRC_meeting:New_licence_for_Wikiversity_Beta New_licence_for_Wikiversity_Beta]
* {{tl|db-copyvio}}
* {{tl|hangon}}
* [[:Category:Astronomy Images]]

==Links==
* Plain links: e.g., &lt;span class=&quot;plainlinks&quot;&gt;[http://archive.org http://archive.org]&lt;/span&gt;: &lt;br&gt;&lt;nowiki&gt;&lt;span class=&quot;plainlinks&quot;&gt; ... &lt;/span&gt;&lt;/nowiki&gt;
* [[mw:Manual:Opening external links in a new window]]

==Long page warning==
* [[MediaWiki:Longpagewarning]]

==[[Main page]]==
* [[:Category:Main page templates]]
* [[Main Page/Layout 0.5]]
* &lt;span class=&quot;plainlinks&quot;&gt;[http://en.wikiversity.org/w/index.php?title=Wikiversity:Main_Page&amp;oldid=209253 Main page]&lt;/span&gt; (old)

==Map==
&lt;mapframe latitude=&quot;-28.420391&quot; longitude=&quot;136.757813&quot; zoom=&quot;2&quot; width=&quot;200&quot; height=&quot;109&quot; align=&quot;right&quot;&gt;{
  &quot;type&quot;: &quot;FeatureCollection&quot;,
  &quot;features&quot;: [
    {
      &quot;type&quot;: &quot;Feature&quot;,
      &quot;properties&quot;: {},
      &quot;geometry&quot;: {
        &quot;type&quot;: &quot;Point&quot;,
        &quot;coordinates&quot;: [
          149.12419,
          -35.308275
        ]
      }
    }
  ]
}&lt;/mapframe&gt; 
==Namespaces==
* [[Special:NamespaceInfo]]

==Navigation==
{{nav|User:Jtneill}}
* [[Template:nav]]

==Notes==
Small e.g.,
{{attention}} &lt;small&gt;For calendar due dates, see unit outline.&lt;/small&gt;

Notice templates

{{Notice|{{tl|Notice}}}}
{{Note|{{tl|Note}}}}

==Notifications==
* [[Help:Notifications]]

==Pages==
* [[Special:AllPages]]
* Number of pages in category: &lt;nowiki&gt;{{PAGESINCATEGORY:User:Jtneill}}&lt;/nowiki&gt;
* {{hitcounter}} - &lt;nowiki&gt;{{hitcounter}}&lt;/nowiki&gt;

==[[Project:Participants|Participants]]==
*[[Wikiversity:Support staff]]

===Users===
*{{Participant|CQ}} - see Person of the Hour script

*{{Participant|Donek}}
*{{Participant|Dan Polansky}}

==Pedagogy==
* [[Learning by doing]]
* [[Wikiversity:Project incubator]]

==Policy==
* [[w:Wikipedia:Contributing_FAQ#Is_there_a_minimum_age_requirement_to_contribute_or_register.3F|Is there a minimum age requirement?]]
{{Official policies}}
{{Proposed policies}}

==Project boxes==
* [[Help:Resource attribution]]

==Purge==
To purge the cache for a given page, append this to the URL:
?action=purge

[[mw:Manual:Purge]]

==Quotes==
* [[Template:Quote]]
*

==[[Quizzes]]==
* [[Help:Quiz-Simple]]
* [http://www.qedoc.org/en/index.php?title=User:Jtneill My Qedoc user page]
** [http://eduforge.org/forum/forum.php?forum_id=1138 Qedoc now exports quizzes to Wikiversity]

==Referencing==
* [[meta:WMDE Technical Wishes/Sub-referencing]]

==Sandbox==
* http://www.sandboxserver.org/
* [[Wikiversity:Sandbox Server]]
* [[Topic:Sandbox Server 0.5]]
* [http://scratchpad.wikia.com/wiki/Scratchpad_Wiki_Labs Scratchpad]
* [[../Sandbox]]

==Searching==
* [[Help:Google]]
* [[Wikiversity:Colloquium/archives/April 2008#Google search|Google search]] - &lt;nowiki&gt;[[google:wikiversity]]&lt;/nowiki&gt; [[google:wikiversity]]
* Use a + instead of a space

==Search multiple categories==
;Dual category search including one category with subcategories
Search for chapters which [[Template:Clarification templates|need clarification]]:
&lt;inputbox&gt;	
type=search
width=33
default=incategory:&quot;Resources needing clarification&quot;
namespaces=Main**
prefix=Motivation and emotion/Book
searchbuttonlabel=Search book chapters
bgcolor=transparent
break=no
&lt;/inputbox&gt;

==Sitenotice==
* [[MediaWiki:Sitenotice]]
* [[MediaWiki:Sitenotice id]]

==Size==

===Big/small===
* Use &lt;code&gt;&lt;nowiki&gt;&lt;big&gt;...&lt;/big&gt; - could be also &lt;big&gt;&lt;big&gt;...&lt;/big&gt;&lt;/big&gt; etc. and also &lt;small&gt;...&lt;/small&gt;&lt;/nowiki&gt;&lt;/code&gt;

===CSS===
&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 200%&quot;&gt;200% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;
&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;font-size: 150%&quot;&gt;150% text&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;

==Special==
* [[Special:SpecialPages]]
* Abuse
** [[Special:AbuseFilter]]
** [[Special:AbuseLog]]
* [[Special:AccountSecurity]]
* [[Special:Allpages]]
* [https://auth.wikimedia.org/enwikiversity/wiki/Special:CreateAccount Create account]
* [[meta:Special:GlobalWatchlist]]
* [[Special:ListGroupRights]]
* [[Special:PermanentLink]]
* [[Random]] - [[Special:Random]] - [[Wikiversity:Random]]
* [[Special:ShortPages]]
* [[Special:Version#Installed extensions]]

==Strategy==
* [[Wikiversity:Publicity]]
* [[Wikiversity:Vision]]
* [[Wikiversity:Vision 2009]]

==Statistics==
* [[Wikiversity:Statistics]]
* [[Google Search and Wikiversity]]
* [http://wikistics.falsikon.de/latest/wikiversity/en/ Monthly page hits for wikiversity.en]
* [http://gtools.org/tool/wikipedia-edit-counter/?str=jtneill&amp;project=en.wikiversity Jtneill edit count]
* https://xtools.wmcloud.org/pageinfo/en.wikiversity.org/
* [[Special:Impact]] - [[w:Special:Impact]]

==Sub-pages==
* [[Special:Prefixindex/User:Jtneill]]
* Transclude:
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/User:Jtneill}}&lt;/nowiki&gt;&lt;/code&gt;
** &lt;code&gt;&lt;nowiki&gt;{{Special:Prefixindex/{{NAMESPACE}}:{{PAGENAME}}}}&lt;/nowiki&gt;&lt;/code&gt;

==Stubs==
* [[:Category:Stub templates]]

==Structure==
* [[Wikiversity:Browse/Concept]]

==Symbols==
🟨🟡⭐💛🟥⭕️❌🟦🔵🟩🟢✅
* [[User:VeronicaJeanAnderson]]

==System messages==
* [[Special:AllMessages]]
* [[#Sitenotice|Site notice]]

==Style==
* [[MoS]]
* [[MediaWiki:Common.css]]

==Tables==
* [[Help:Table]]
* [[User:Jtneill/Sandbox/Tables and boxes]]

==Tagging/notification==
* &lt;nowiki&gt;@[[User:UserName|UserName]]&lt;/nowiki&gt;
* &lt;nowiki&gt;{{ping|UserName}}&lt;/nowiki&gt;

==Templates==
===Page development===
* {{tl|welcome and expand}} - {{tl|we}}
* {{tl|main welcome}}
* {{tl|search}}
* {{tl|draft}}
* {{tl|underconstruction}}
* {{tl|Learning project boilerplate}}
* {{tl|info}}
* {{tl|note}}
* {{tl|notice}}
* {{tl|Nutshell}}
* &lt;nowiki&gt;{{notice|{{findsources}}}}&lt;/nowiki&gt;

===Page navigation===
* [[Template:EasyNavBar]]
* [[Template:Recovery psychology]] (example)
* [[Workshop for Australian education policy]] (example)

===Sister projects===
* [[Template:Sisterprojectsearch]]
* [[Template:Wikibooks]]
* [[Template:Wikipedia]]
* [[Template:Wikiversity]]

===User talk===
* {{tl|Welcomeip}}
* {{tl|Welcome}}
* {{tl|Talk header}}
* [[:Category:User warning templates]]

===Administrative===
* [[Template:Category redirect]]
* [[Template:Warning]]

==Theory==
* [[Learning by engagement]]
* [[User:JWSchmidt/Wiki Scholar]]

==Thoughts==
* [[Red link]]s are doorways to the infinite library ([[w:The Library of Babel|Library of Babel]])

==Tooltips==
{{Tooltip|Tooltips allow additional text to be displayed when cursor hovers over|Pretty cool, eh?}}


==User==
* [[w:Special:GlobalRenameRequest]]
* [[Special:UserGroupRights]]
* [[Special:UserRights]]
* [[m:Steward requests/Permissions]]
* [[meta:Help:Two-factor authentication]]

==Usability==
* [[Wikiversity:Usability]]
* http://usability.wikimedia.org - [http://usability.wikimedia.org/wiki/User:Jtneill Jtneill]

==Video==
* .ogg files can be uploaded and embedded
* See [[/Video]] for examples

==wikEd==
* [[w:User_talk:Cacycle/wikEd]]

==Wiki2Reveal==
* [[Wiki2Reveal]] (slides on the fly from MediaWiki page)

==x Test anchor==
&lt;!-- Test anchor - don't delete! --&gt;
{{anchor|test}}

==See also==
* [[User:Jade Knight/Tools]]</text>
      <sha1>369trvfvxnz1uv4rbp2fmkcgnng4it0</sha1>
    </revision>
  </page>
  <page>
    <title>Help:Resources by subject</title>
    <ns>12</ns>
    <id>57656</id>
    <revision>
      <id>2810268</id>
      <parentid>2787448</parentid>
      <timestamp>2026-05-18T22:25:51Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>+new</comment>
      <origin>2810268</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6633" sha1="cuc41oyzrqeth2zeqolah9w36uy6460" xml:space="preserve">&lt;noinclude&gt;{{Project boxes/Nav}}&lt;/noinclude&gt;

This page is a guide to using [[Help:project boxes|project boxes]] to tag and categorise your '''resources by subject'''. The Wikiversity [[Help:Project boxes|project boxes]] system allows you to insert an easy and attractive project box into your resource which does a lot of handy things behind the scenes, such as classifying your resource and making it accessible in the navigation system. Just follow the instructions below. Traditionally, the following colour scheme was employed for project boxes. 
* Green: school (K-12, pre-tertiary).
* Mauve: university
* Brown: [[Help:Resources by language|languages]]
* Blue: non-formal education
It is sufficient to write the shortcut into your wiki-markup. Just copy and paste (or type) the code given into your page '''''including the double curly brackets'''''. The project box will align itself on the right-hand side of your page. The project box will also automatically categorise the resource into a special category which puts your resource into the category tree of the equivalent portal. The project box also adds a link to the relevant portal. All of this is automatic - you just type in the code shown, and the rest is done for you.

{{usbktop}}
{{usbk|mathematics|shortcut=maths}}
{{usbk|English}}
{{usbk|history}}
{{usbk|environmental science}}
{{usbk|geography}}
{{usbk|biology}}
{{usbk|chemistry}}
{{usbk|physics}}
{{usbk|music}}
{{usbk|art and design|shortcut=artdes|description=Template &quot;art&quot; already exists and has other purposes.}}
{{usbk|sports|shortcut=sport}}
{{usbk|statistics|shortcut=stats}}
{{usbk|religion}}
{{usbk|languages|description=In addition, you can add a language-specific project box (see [[Help:Resources by language|here]]).}}
{{usbk|literature}}
{{usbk|writing}}
{{usbk|information technology|shortcut=it}}
{{usbk|networking}}
{{usbk|cs}}
{{usbk|science}}
{{usbk|sociology}}
{{usbk|economics}}
{{usbk|finance}}
{{usbk|philosophy}}
{{usbk|christianity}}
{{usbk|Esl|description=Technically this is a language-specific project box (see [[Help:Resources by language|here]]). Distinguish carefully from English for native speakers (above).}}
{{usbk|astronomy}}
{{usbk|education|description=Everything is educational on Wikiversity. It is suggested that this tag should be reserved for resources on topics such as educational science and other meta-educational matters.}}
{{usbk|law}}
{{usbk|medicine}}
{{usbk|psychology}}
{{usbk|pharmacy}}
{{usbk|engineering}}
{{usbk|technology}}
{{usbk|humanities}}
{{usbk|PoliSci}}
{{usbk|film}}
{{usbk|design}}
{{usbk|bloom|shortcut=flower}}
{{usbk|wikimedia studies|shortcut=wms}}
{{usbkbottom}}

=== Project boxes for tagging language-learning resources by language ===

See [[Help:Resources by language]].

=== Miscellaneous subject-related project boxes ===

{{usbktop}}
{{usbk|unknown subject|shortcut=unksub|description=Neutral.}}
{{usbk|unknown subject 2|shortcut=unksub2|description=Fun.}}
{{usbkbottom}}

=== Requests for change of  subjects ===

Can't create a project box? Then just request it here instead. Please sign your name with &lt;nowiki&gt;~~~~&lt;/nowiki&gt; after your request.

* Topic: Career development and employment (including career selection, job finding, dealing with unemployment and so on) [[User:BillBell|BillBell]] 20:53, 15 December 2010 (UTC)
* Topic:Journalism and Mass Communications (i.e. reporting, copy editing, advertising, public relations, broadcast, etc.) --[[User:Jp07|Jp07]] 13:44, 1 July 2011 (UTC)
*:Imoye[[User:Imoye|Imoye]] ([[User talk:Imoye|discuss]] • [[Special:Contributions/Imoye|contribs]]) 15:41, 2 December 2023 (UTC) &lt;nowiki&gt;{{Music}}&lt;/nowiki&gt;
*:I need a box for securing online training kits   and projects that will enable me create job in online music education : songs and instrumental composition, piano works, guitar, and voice training skills [[User:Imoye|Imoye]] ([[User talk:Imoye|discuss]] • [[Special:Contributions/Imoye|contribs]]) 15:46, 2 December 2023 (UTC)
* Topic: Critical Care Nursing[[User:Holly Northam|Holly Northam]] ([[User talk:Holly Northam|talk]]) 09:02, 11 August 2012 (UTC)
* I am developing several courses in the &quot;[[Wisdom/Curriculum|Applied Wisdom]]&quot; curriculum. I would like a box to help me link these to a subject. Can you please create a box for a subject called &quot;Applied Wisdom&quot; Thanks! --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|talk]]) 01:58, 1 September 2012 (UTC)
* Topic: Software Localization [[User:Nlyubimova|Nlyubimova]] 1:13, 1 February 2017 (UTC)
* Topic: Classics and Ancient Languages --[[User:Whovian z|Whovian z]] ([[User talk:Whovian z|discuss]] • [[Special:Contributions/Whovian z|contribs]]) 11:16, 9 May 2018 (UTC)
*Topic: Psychophysics [[User:Jeaucques Quœure|Jeaucques Quœure]] ([[User talk:Jeaucques Quœure|discuss]] • [[Special:Contributions/Jeaucques Quœure|contribs]]) 08:35, 26 September 2020 (UTC)

== Frequent questions ==

Q: '''''I'm not sure which of these templates to use for my resource.'''''
:A: ''You don't have to pin yourself to one of them. If you're trying to make up your mind between two of them, use both.''

Q: '''''My resource is cross-disciplinary.'''''
:A: ''You are welcome to apply more than one of these project boxes to your resource.''

Q: '''''Where should I put this on my page?'''''
:A: ''Probably either at the very top or the very bottom. It's really a question of your own taste. User boxes have traditionally been placed at the top of user pages, so if you can't decide, put your project boxes at the top as well.''

Q: '''''Can I combine these with other project boxes, such as educational-level project boxes and completion-status project boxes?'''''
:A: ''Yes. In fact, please do. This is the idea. The project boxes are designed to stack up in a matching group, and create a full metadata classification for your resource.''

Q: '''''I find these subject classifications too broad. Can I create a project box with a finer subject classification?'''''
:A: ''Yes. In fact, please do. This is the idea. When you list your project box for use, please ensure that the presentation on this page remains user-friendly. For example, if you create 20 project boxes for different sub-fields of particle physics, you may wish to create a sub-page on which to list them.''

Q: '''''Do I have to include project boxes in my resource?'''''
:A: ''No. You are welcome to just add appropriate [[Wikiversity:Categories]] to your resource instead. Most Wikiversity resources do not use project boxes.''

== See also ==
* [[Help:project boxes]]

&lt;noinclude&gt;
[[Category:Help]]
[[Category:Project boxes]]
&lt;/noinclude&gt;</text>
      <sha1>cuc41oyzrqeth2zeqolah9w36uy6460</sha1>
    </revision>
  </page>
  <page>
    <title>Featured content/9</title>
    <ns>0</ns>
    <id>60510</id>
    <revision>
      <id>2810372</id>
      <parentid>449795</parentid>
      <timestamp>2026-05-19T03:35:30Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>-1 for the count</comment>
      <origin>2810372</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="467" sha1="a15jitr7x3xbv98ghw2247sc2byv932" xml:space="preserve">{{FOTD|link=Economic Classroom Experiments|name=Economic Classroom Experiments|image=Monty open door chances.svg|blurb=Economic Classroom Experiments is a growing collection (currently {{#expr: {{PAGESINCATEGORY:Economic classroom experiments}} - 1}} resources) of lesson plans and ideas for games in the economics classroom. The experiments are suitable for both secondary and tertiary education. Economics teachers and others are welcome to add to the collection.}}</text>
      <sha1>a15jitr7x3xbv98ghw2247sc2byv932</sha1>
    </revision>
  </page>
  <page>
    <title>Variance</title>
    <ns>0</ns>
    <id>63545</id>
    <revision>
      <id>2810307</id>
      <parentid>298232</parentid>
      <timestamp>2026-05-18T23:11:53Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>some sections</comment>
      <origin>2810307</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="820" sha1="1ykagowaum9djyztoa03res9qpnjptj" xml:space="preserve">{{statistics-stub}}
In [[probability theory]] and [[statistics]], the '''variance''' of a [[random variable]], [[probability distribution]], or [[sample (statistics)|sample]] is one measure of [[statistical dispersion]], averaging the squared distance of its possible values from the [[expected value]] (mean).  Whereas the mean is a way to describe the location of a distribution, the variance is a way to capture its scale or degree of being spread out.  The [[w:Units of measurement|unit]] of variance is the square of the unit of the original variable.  The positive [[w:square root|square root]] of the variance, called the [[standard deviation]], has the same units as the original variable and can be easier to interpret for this reason.

== Resources ==

== See also ==

* [[Statistics]]

[[Category:Statistics]]</text>
      <sha1>1ykagowaum9djyztoa03res9qpnjptj</sha1>
    </revision>
  </page>
  <page>
    <title>Introduction to Diplomatic History</title>
    <ns>0</ns>
    <id>66297</id>
    <revision>
      <id>2810241</id>
      <parentid>2809888</parentid>
      <timestamp>2026-05-18T20:47:06Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>re-adding PROD with reasoning</comment>
      <origin>2810241</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7033" sha1="goy57c44gket24nr1cescoio69izmen" xml:space="preserve">{{Prod|Course has not been developed since 2008; no actual content has been developed beyond the terms listed at the bottom of the page (for ex, no pages/lectures/notes}}
&lt;div style=&quot;float: right; border:solid darkgreen 1px; margin: 1px;&quot;&gt;
{| cellspacing=&quot;0&quot; style=&quot;width: 238px; background: goldenrod;&quot;
| style=&quot;width: 35px; height: 45px; background: darkgreen; text-align: center; font-size: {{{8|{{{id-s|24}}}}}}pt; color: {{{id-fc|white}}};&quot; | '''D'''
| style=&quot;font-size: {{{info-s|8}}}pt; padding: 4pt; line-height: 1.25em; color: {{{info-fc|black}}};&quot; | This lesson is a part of the '''Denelder Homeschooling Series on History'''.
|}&lt;/div&gt;&lt;noinclude&gt;

'''DIPL 1001: Introduction to Diplomatic History''' is a survey of the history of diplomacy throughout recorded history. This course is meant to introduce new students to the study of diplomatic history by explaining the concept of diplomacy, terms that the student will use often in the [[Topic:Diplomatic History|Department of Diplomatic History]], and a broad history of international relations on a global scale. This is the first course students new to the department should complete as it will be the foundation for successive courses.

Courses within the Department of Diplomatic History will be primarily self-study, placing the educational responsibility on the student rather than the professor. Although the professor will provide a plan for study and general information, it is the responsibility of the student to fulfil the goals and expectations of the course by completing the readings, studying the provided lesson, and performing independent research to prove comprehension. This course is also designed for homeschooling use, with information for the homeschool instructor to aid the student in successful completion. Recommendations for further study will be provided with each homeschooling lesson to expand upon the basic course. 

==Denelder Homeschooling Series on History==
As denoted by the infobox above, this course is a lesson created by [[User:Dr_Denelder|Dr. Jason Denelder]] as a part of his lesson series for homeschooled students. This lesson was designed as an aid for homeschoolers to further their knowledge on a specific topic, not to replace regular homeschooling lesson plans and resources. The Introduction to Diplomatic History is intended as the first lesson in the Department of Diplomatic History and is classified as HS-DH001 in the Homeschooling Series.

==Suggested Readings==
*[http://www.diplom.org/Zine/S1995R/Szykman/History.html Diplomacy: An Historical Perspective] Simon Szykman. Spring 1995. Carnegie Mellon University.
*[http://www.ediplomat.com/nd/history.htm A Brief History of Diplomacy]  eDiplomat.
*[http://diplo.diplomacy.edu/books/mdiplomacy_book/langhorne/langhorne.htm History and the Evolution of Diplomacy] Richard Langhorne.
*[http://diplo.diplomacy.edu/books/mdiplomacy_book/petrovski/petrovski.htm Diplomacy as an Instrument of Good Governance] Vladimir Petrovsky.

==Course Syllabus==
===Goals and Expectations===
That students will understand the concept of diplomacy in a historical sense, will understand the basic terms of diplomatic research, and will gain an understanding of international relations on a global scale throughout history. That students will be able to implement their newly gained knowledge and successfully demonstrate their understanding by developing a researched essay on a general topic of diplomatic history.

===Reading Schedule===

===Essay===
The purpose of the essay is to demonstrate an understanding of the basics of diplomacy in the context of diplomatic history. As this is considered a university first-year course, grammar, spelling, and rhetoric should be correct and consistent throughout. Substance, however, is the most important component of a successful essay, demonstrating comprehension of the idea of diplomacy and its practical uses. Students have open control over the topic of their choice as long as it relates to the course material. Essays should be at least two pages long, although this should not be looked upon as a maximum. As the purpose is to demonstrate comprehension, the student should not write a descriptive essay, but rather an analytical essay. This means that the student should analyze a topic in diplomatic history, discussing the consequences of such an action and possible alternate paths and their consequences, using terms and concepts from the lesson.

Since this is an introductory course that encompasses the entire history of international relations, possible topics are endless in scope. In the essay, it is better to narrow in on a particular incident rather than discuss a broad topic. Do not analyze the diplomacy of Europe during the First World War, rather, analyze the effects of the War Guilt Clause on relations between Germany and the United Kingdom. Be specific in your analysis. 

For those students wishing for constructive criticism of their essays may email them to Dr. Denelder at jason.denelder@yahoo.com. He will read your essay, making comments and noting corrections where necessary. If submitting the essay, please allow up to two weeks to accommodate Dr. Denelder's busy schedule.

===Course Completion===
Successful completion of DIPL 1001 is dependent on the student's understanding of the concept of diplomacy and the broad history of international relations demonstrated by the satisfactory completion of an essay on a selected topic of diplomatic history. DIPL 1001 serves as the prerequisite course for continuation into more detailed courses of diplomatic history and should be completed first.

==Lesson Plan/Outline==
===Synopsis===

===Concepts===

===Terms===
*'''Diplomacy:''' the art and practice of conducting negotiations between representatives of groups or states; also, the employment of tact to gain strategic advantage or to find mutually acceptable solutions to a common challenge
*'''International Diplomacy:''' the conduct of international relations through the intercession of professional diplomats with regard to issues of peace-making, trade, war, economics, and culture
*'''Diplomatic Immunity:''' a form of legal immunity and a policy held between governments, which ensures that diplomats are given safe passage and are considered not susceptible to lawsuit or prosecution under the host country's laws
*'''Diplomatic Recognition:''' a unilateral political act, with domestic and international legal consequences, whereby a state acknowledges an act or status of another state or government
*'''Paradiplomacy:''' the international relations conducted by subnational, regional, local or non-central governments

===Important Figures===

===Timeline===

==Course Roster==
*--[[User:Jolie|Jolie]] 22:22, 9 October 2008 (UTC)

==Professorship==
* [[User:Dr_Denelder|Dr. Jason Denelder]] - For questions, concerns, discussion, or comment, please use my [[User talk:Dr_Denelder|talk page]] or email me at jason.denelder@yahoo.com.

[[Category:History]]
[[Category:Introductions]]</text>
      <sha1>goy57c44gket24nr1cescoio69izmen</sha1>
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  </page>
  <page>
    <title>Wikiversity talk:Main Page/News</title>
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    <id>67093</id>
    <revision>
      <id>2810394</id>
      <parentid>2809745</parentid>
      <timestamp>2026-05-19T09:45:43Z</timestamp>
      <contributor>
        <username>~2026-30030-49</username>
        <id>3077934</id>
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      <comment>/* YAHOO! DIGITAL TRANSFORMATION AND RECOVERY PLAN */ new section</comment>
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      <format>text/x-wiki</format>
      <text bytes="15674" sha1="i21l60f00hgye30kb63kw5zup4uybiv" xml:space="preserve">=== Semi ===

Should this page be full protected? Obviously all the custodians should have it watchlisted, but no one other than a custodian has ever edited it. [[User:Salmon of Doubt|Salmon of Doubt]] 11:44, 13 September 2008 (UTC)
* The idea of the complex protection system on the various main page templates was to leave this particular page semi-protected only so that ordinary users can add news items. This page should only be fully protected if it becomes a repeated target for vandalism, which is not yet the case. --[[User:McCormack|McCormack]] 12:07, 13 September 2008 (UTC)

== Possible use of dynamicpagelist ==

{{#invoke:DynamicPageList
|show
|category=Completed resources
|namespace=
|count=10
|mode=unordered
|ordermethod=categoryaddlastedit
|orderdate=categoryaddlastdate
|order=descending
}} --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:19, 16 October 2016 (UTC)

So, if I follow current custom, [[Main Page/News]] would appear something like:

'''2016'''
* '''15 October:''' The new courses [[IT Fundamentals]] and [[Assessing Human Rights]] are completed and ready for students and professionals
* '''15 October:''' The new book chapter [[Motivation and emotion/Book/2016/Emotional hijacking|Emotional hijacking]] is ready for use by psychologists and their students
* '''12 October:''' The Python Programming lessons [[Python Programming/Modules|Modules]] and [[Python Programming/Classes|Classes]] are completed and ready for students
* '''15 August:''' '''Wikiversity celebrates its 10-year anniversary!'''
* '''15 August:''' The fall semester begins for the course [[principles of radiation astronomy]].
* '''8 August:''' The [[ENG 099|open course in conversational American English]] for EFL/ESL/ELL/ESOL students starts.
* '''31 July:''' For [[Wikiversity:Year of Science 2016|'''The Wikimedia Year of Science''']], try using the May 9, 2016 [[w:Transit of Mercury]] to improve the [[Stars/Sun/Locating the Sun|location of the Sun]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:22, 16 October 2016 (UTC)

::I'm confused. You wrote that &quot;It would be great to have five to six things to put in the news each week instead of five to six for three to four months!&quot; Are you also wanting to maintain this manually rather than using DynamicPageList to do the updates automatically? If you are working manually, there is no reason to list IT Fundamentals again, as it is only on the DynamicPageList due to vandalism. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:40, 16 October 2016 (UTC)

:::Originally I was intending to try to maintain this subpage manually. Your use of dynamicpagelist suggests that at least this part could be automated. But there appears to be no easy way to include what the resources are, their approximate dates of completion and intended targets. I also wanted to include those News items that are not in that specific category. Combining the two in an automated way would really be great! --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 02:11, 17 October 2016 (UTC)

==Earlier unannounced completed resources==

These would currently have been updated or improved:
{{div col|colwidth=12em}}
{{#invoke:DynamicPageList
|show
|category=Completed resources
|namespace=
|count=10
|mode=unordered
|ordermethod=categoryaddlastedit
|orderdate=categoryaddlastdate
|order=descending
}}
{{Div col end}} --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:54, 25 June 2017 (UTC)

# [[Mathematical Properties]] was announced on 20 January 2018,
# [[Internet Protocol Analysis]] was announced on 15 March 2019,
# [[Overcoming Hate]] was announced on 9 July 2019,
# [[Unleashing Creativity]] was announced on 2 July 2019,
# [[Candor]] was announced on 28 June 2019,
# [[Exploring Social Constructs]] was announced on 31 May 2019,
# [[Applied Programming]] was announced on 17 May 2018,
# [[Finding Courage]] was announced on 17 April 2019,
# [[Moral Reasoning]] was announced on 14 April 2019,
# [[Coping with Ego]] was announced on 17 March 2019,
# [[Resolving Anger]] was announced on 1 February 2019,
# [[Communicating Power]] was announced on 29 January 2019,
# [[What you can change and what you cannot]] was announced on 28 January 2019,
# [[Recognizing Emotions]] was announced on 25 January 2019,
# [[Appraising Emotional Responses]] was announced on 24 January 2019, and
# [[Open Source 3-D Printing]] was announced on 20 January 2019. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 01:35, 15 September 2019 (UTC)

== COVID-19 COBOL programmer shortage? ==

&lt;blockquote&gt;COVID-19 COBOL programmer shortage&lt;/blockquote&gt;
Where can I find information about this topic (from 12 April news item)? Thanks in advance. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 19:13, 21 April 2020 (UTC)
:{{Ping|Ottawahitech}} There's quite a bit you can learn with a search engine. Just from my cursory following of the news, I know that the problem is particularly acute in New Jersey in the banking industry. If you're interested in learning, you may want to track down *How to Learn COBOL in 21 Days*, which is free online. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:28, 21 April 2020 (UTC)
:{{At|Ottawahitech}} A long list of additional resources are included at [[Talk:COBOL]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:29, 21 April 2020 (UTC)
::{{At|Koavf|Dave Braunschweig}} actually there is a story behind my question. Back in 2011 I was trying to insert information into a Bank of America article and was meeting a [https://en.wikipedia.org/w/index.php?oldid=436375222&amp;title=Talk%3ABank_of_America#The_suicide_of_Kevin_Flanagan lot of resistance], even though at the time the information was documented on another Wikipedia article where I first learned about it. The information was about a computer programmer who committed suicide in front of one of Bank of America's properties. According to the the article, he was despondent after losing his job at Bofa, which went to H1B workers. Flanagn and his layed off coleauges all of whom lost their jobs were tasked with training their replacements. 
::To make a long story short, there were two persistent editors guarding information on the Bofa article, and  I eventually moved on to other areas. Those two kept the story out of wikipedia, and months or even years later I found out that the article about Flanagan himself disappreaed as well. Since then I am skeptical about claims  of a  shortage of skilled people made by employers without the corresponding verifiable reliable sources showing a shortage actually exists. Maybe that's just me? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 02:24, 22 April 2020 (UTC)
:::{{ping|Ottawahitech}} Well, that certainly escalated quickly. Without getting into the specifics of any editing disputes from the past or possible criminal disappearances, etc. it seems like your main question is, &quot;Are there ''really'' a shortage of COBOL specialists?&quot; and the answer is 100% yes. This has been a known problem for well over a decade (likely longer) and if you want evidence of that, I would recommend looking at job listings to see how much a company will pay someone with COBOL knowledge versus (e.g.) Python or C+. Having proficiency and especially experience in COBOL is a good way to make money in programming. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:37, 22 April 2020 (UTC)

:::{{At|Ottawahitech}} I'm sorry, but for me this approach crosses the line. I have recommended that you move on from past incidents on other Wikimedia projects.[https://en.wikiversity.org/w/index.php?title=User_talk%3AOttawahitech&amp;type=revision&amp;diff=2141168&amp;oldid=2137899] I have strongly encouraged you to move on from past incidents on other Wikimedia projects. I am now warning you to move on from past incidents on other Wikimedia projects. Wikiversity's [[Wikiversity:Mission|mission]] is to create and host a range of learning projects and learning resources. You need to find a way to contribute to this mission that doesn't involve past edits elsewhere. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:01, 22 April 2020 (UTC)

== Finding Common Ground ==

The course [[Finding Common Ground]] is now complete. May I add it to the news myself or is there some other way to have it added? Thanks. --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 01:40, 14 March 2022 (UTC)

:I've added an announcement of your course's completion to Main Page News, please modify if you wish. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 05:16, 14 March 2022 (UTC)
::Thanks! [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 11:50, 14 March 2022 (UTC)

== bug ==

January 5, 2023 is after December 25, 2023??? [[Special:Contributions/79.185.141.205|79.185.141.205]] ([[User talk:79.185.141.205|discuss]])
:fixed, thanks for bringing this up. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 22:30, 6 January 2024 (UTC)

=== another bug ===


March 6, 2024 is after December 5, 2024??? [[Special:Contributions/109.243.1.105|109.243.1.105]] ([[User talk:109.243.1.105|discuss]])
:Fixed. I'll try to be more attentive to this page. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:10, 18 July 2025 (UTC)

==noinclude==
{{ping|Dave Braunschweig}} I suppose, the offending &lt;code&gt;&lt;nowiki&gt;&lt;/noinclude&gt;&lt;/nowiki&gt;&lt;/code&gt; on the Main Page comes from here. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 21:22, 8 December 2024 (UTC)

:Thanks for the watchful eye {{ping|Watchduck}} I've fixed it up. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:45, 8 December 2024 (UTC)

== write news? ==

here? @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:10, 13 May 2026 (UTC)

:If you are serious about writing news here, I recommend getting together other Wikinews editors (including me: I'm happy to help) to organize at [[School:Journalism]], plan out what we want to do, present any radical proposals (like wholesale rehosting Wikinews here) to the community, and then starting the process of regularly writing news stories if the community agrees to include hosting citizen journalism here as an ongoing activity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:21, 14 May 2026 (UTC)

== YAHOO! DIGITAL TRANSFORMATION AND RECOVERY PLAN ==

{{/header template}}
== PROJECT: YAHOO! DIGITAL TRANSFORMATION AND RECOVERY PLAN ==

'''Prepared by:''' [[ BENASING, AL-RAFFY]] 
 
'''Selected Company:''' Yahoo!  

'''Date:''' May 19, 2026  

---

== 1. CASE STUDY AUDIT (Why did the company decline?) ==
Based on my research on [[Wikipedia]], here are the reasons why this company struggled with its Information System:

* '''Legacy Issue:''' Yahoo! depended heavily on outdated web portal systems and traditional online advertising methods, making it difficult to compete with newer digital platforms.  

* '''Failure to Adapt:''' The company failed to quickly improve its search engine, mobile applications, and cloud-based services during the rapid growth of the internet industry.  

* '''Competitor Edge:''' Competitors such as Google developed faster search systems, smarter algorithms, and more advanced digital ecosystems that attracted more users and advertisers.  

---

== 2. PROPOSED MAINTENANCE &amp; ADAPTATION PLAN ==
If I were the Operations Manager at that time, these are the steps I would take to prevent the company from failing:

=== A. System Upgrade (Evolutionary Maintenance) ===

# '''Search System Improvement:''' Upgrade Yahoo!’s search engine with artificial intelligence and advanced indexing systems for faster and more accurate search results.  

# '''Cloud Infrastructure Integration:''' Move Yahoo!’s email services, databases, and digital platforms into cloud systems to improve scalability and reliability.  

# '''Mobile Platform Development:''' Create modern mobile applications for Yahoo! Mail, News, and Finance to improve user accessibility.  

# '''Digital Advertising Optimization:''' Use AI-driven advertising systems to deliver more personalized and effective online advertisements.  

=== B. Preventive Maintenance (Monthly Checklist) ===

* '''Data Backup:''' Perform automatic daily backups of customer accounts, emails, and advertising data.  

* '''Security Patching:''' Update firewalls and cybersecurity systems monthly to protect user information from hacking and data breaches.  

* '''Performance Monitoring:''' Monitor website traffic, loading speed, and server performance regularly to prevent system downtime.  

* '''User Feedback Audit:''' Analyze user feedback regarding application usability, spam filtering, and search accuracy.  

* '''System Stress Testing:''' Conduct regular stress testing to ensure systems can handle high user traffic without crashing.  

---

== 3. BUSINESS CONTINUITY (The &quot;Plan B&quot;) ==
If the main system crashes, these are the actions we will take:

* '''Backup Server:''' Use distributed cloud servers and redundant databases to maintain access to Yahoo! services during outages.  

* '''Emergency Protocol:''' Notify users and employees immediately through email and mobile alerts within 10 minutes after detecting technical issues.  

* '''Disaster Recovery Plan:''' Restore critical systems using cloud recovery solutions and backup databases to minimize downtime.  

* '''Technical Response Team:''' Maintain a dedicated 24/7 IT support and recovery team to resolve technical failures quickly.  

---

== 4. CONCLUSION ==
Proper '''Information System Operation and Maintenance''' is essential for success in the digital industry. If Yahoo! had continuously modernized its systems, improved its cloud infrastructure, and adapted to technological trends, it could have remained one of the leading internet companies in the world.  

[[Category:Business Information Systems Projects]] [[Special:Contributions/&amp;#126;2026-30030-49|&amp;#126;2026-30030-49]] ([[User talk:&amp;#126;2026-30030-49|talk]]) 09:45, 19 May 2026 (UTC)</text>
      <sha1>i21l60f00hgye30kb63kw5zup4uybiv</sha1>
    </revision>
    <revision>
      <id>2810399</id>
      <parentid>2810394</parentid>
      <timestamp>2026-05-19T10:02:26Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Reverted edit by [[Special:Contributions/~2026-30030-49|~2026-30030-49]] ([[User_talk:~2026-30030-49|talk]]) to last version by [[User:Codename Noreste|Codename Noreste]] using [[Wikiversity:Rollback|rollback]]</comment>
      <origin>2809090</origin>
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      <format>text/x-wiki</format>
      <text bytes="11960" sha1="b21s689fhahqu7thagvorvcfhgi6c1n" xml:space="preserve">=== Semi ===

Should this page be full protected? Obviously all the custodians should have it watchlisted, but no one other than a custodian has ever edited it. [[User:Salmon of Doubt|Salmon of Doubt]] 11:44, 13 September 2008 (UTC)
* The idea of the complex protection system on the various main page templates was to leave this particular page semi-protected only so that ordinary users can add news items. This page should only be fully protected if it becomes a repeated target for vandalism, which is not yet the case. --[[User:McCormack|McCormack]] 12:07, 13 September 2008 (UTC)

== Possible use of dynamicpagelist ==

{{#invoke:DynamicPageList
|show
|category=Completed resources
|namespace=
|count=10
|mode=unordered
|ordermethod=categoryaddlastedit
|orderdate=categoryaddlastdate
|order=descending
}} --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:19, 16 October 2016 (UTC)

So, if I follow current custom, [[Main Page/News]] would appear something like:

'''2016'''
* '''15 October:''' The new courses [[IT Fundamentals]] and [[Assessing Human Rights]] are completed and ready for students and professionals
* '''15 October:''' The new book chapter [[Motivation and emotion/Book/2016/Emotional hijacking|Emotional hijacking]] is ready for use by psychologists and their students
* '''12 October:''' The Python Programming lessons [[Python Programming/Modules|Modules]] and [[Python Programming/Classes|Classes]] are completed and ready for students
* '''15 August:''' '''Wikiversity celebrates its 10-year anniversary!'''
* '''15 August:''' The fall semester begins for the course [[principles of radiation astronomy]].
* '''8 August:''' The [[ENG 099|open course in conversational American English]] for EFL/ESL/ELL/ESOL students starts.
* '''31 July:''' For [[Wikiversity:Year of Science 2016|'''The Wikimedia Year of Science''']], try using the May 9, 2016 [[w:Transit of Mercury]] to improve the [[Stars/Sun/Locating the Sun|location of the Sun]]. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:22, 16 October 2016 (UTC)

::I'm confused. You wrote that &quot;It would be great to have five to six things to put in the news each week instead of five to six for three to four months!&quot; Are you also wanting to maintain this manually rather than using DynamicPageList to do the updates automatically? If you are working manually, there is no reason to list IT Fundamentals again, as it is only on the DynamicPageList due to vandalism. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:40, 16 October 2016 (UTC)

:::Originally I was intending to try to maintain this subpage manually. Your use of dynamicpagelist suggests that at least this part could be automated. But there appears to be no easy way to include what the resources are, their approximate dates of completion and intended targets. I also wanted to include those News items that are not in that specific category. Combining the two in an automated way would really be great! --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 02:11, 17 October 2016 (UTC)

==Earlier unannounced completed resources==

These would currently have been updated or improved:
{{div col|colwidth=12em}}
{{#invoke:DynamicPageList
|show
|category=Completed resources
|namespace=
|count=10
|mode=unordered
|ordermethod=categoryaddlastedit
|orderdate=categoryaddlastdate
|order=descending
}}
{{Div col end}} --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 21:54, 25 June 2017 (UTC)

# [[Mathematical Properties]] was announced on 20 January 2018,
# [[Internet Protocol Analysis]] was announced on 15 March 2019,
# [[Overcoming Hate]] was announced on 9 July 2019,
# [[Unleashing Creativity]] was announced on 2 July 2019,
# [[Candor]] was announced on 28 June 2019,
# [[Exploring Social Constructs]] was announced on 31 May 2019,
# [[Applied Programming]] was announced on 17 May 2018,
# [[Finding Courage]] was announced on 17 April 2019,
# [[Moral Reasoning]] was announced on 14 April 2019,
# [[Coping with Ego]] was announced on 17 March 2019,
# [[Resolving Anger]] was announced on 1 February 2019,
# [[Communicating Power]] was announced on 29 January 2019,
# [[What you can change and what you cannot]] was announced on 28 January 2019,
# [[Recognizing Emotions]] was announced on 25 January 2019,
# [[Appraising Emotional Responses]] was announced on 24 January 2019, and
# [[Open Source 3-D Printing]] was announced on 20 January 2019. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 01:35, 15 September 2019 (UTC)

== COVID-19 COBOL programmer shortage? ==

&lt;blockquote&gt;COVID-19 COBOL programmer shortage&lt;/blockquote&gt;
Where can I find information about this topic (from 12 April news item)? Thanks in advance. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 19:13, 21 April 2020 (UTC)
:{{Ping|Ottawahitech}} There's quite a bit you can learn with a search engine. Just from my cursory following of the news, I know that the problem is particularly acute in New Jersey in the banking industry. If you're interested in learning, you may want to track down *How to Learn COBOL in 21 Days*, which is free online. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:28, 21 April 2020 (UTC)
:{{At|Ottawahitech}} A long list of additional resources are included at [[Talk:COBOL]]. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:29, 21 April 2020 (UTC)
::{{At|Koavf|Dave Braunschweig}} actually there is a story behind my question. Back in 2011 I was trying to insert information into a Bank of America article and was meeting a [https://en.wikipedia.org/w/index.php?oldid=436375222&amp;title=Talk%3ABank_of_America#The_suicide_of_Kevin_Flanagan lot of resistance], even though at the time the information was documented on another Wikipedia article where I first learned about it. The information was about a computer programmer who committed suicide in front of one of Bank of America's properties. According to the the article, he was despondent after losing his job at Bofa, which went to H1B workers. Flanagn and his layed off coleauges all of whom lost their jobs were tasked with training their replacements. 
::To make a long story short, there were two persistent editors guarding information on the Bofa article, and  I eventually moved on to other areas. Those two kept the story out of wikipedia, and months or even years later I found out that the article about Flanagan himself disappreaed as well. Since then I am skeptical about claims  of a  shortage of skilled people made by employers without the corresponding verifiable reliable sources showing a shortage actually exists. Maybe that's just me? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 02:24, 22 April 2020 (UTC)
:::{{ping|Ottawahitech}} Well, that certainly escalated quickly. Without getting into the specifics of any editing disputes from the past or possible criminal disappearances, etc. it seems like your main question is, &quot;Are there ''really'' a shortage of COBOL specialists?&quot; and the answer is 100% yes. This has been a known problem for well over a decade (likely longer) and if you want evidence of that, I would recommend looking at job listings to see how much a company will pay someone with COBOL knowledge versus (e.g.) Python or C+. Having proficiency and especially experience in COBOL is a good way to make money in programming. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:37, 22 April 2020 (UTC)

:::{{At|Ottawahitech}} I'm sorry, but for me this approach crosses the line. I have recommended that you move on from past incidents on other Wikimedia projects.[https://en.wikiversity.org/w/index.php?title=User_talk%3AOttawahitech&amp;type=revision&amp;diff=2141168&amp;oldid=2137899] I have strongly encouraged you to move on from past incidents on other Wikimedia projects. I am now warning you to move on from past incidents on other Wikimedia projects. Wikiversity's [[Wikiversity:Mission|mission]] is to create and host a range of learning projects and learning resources. You need to find a way to contribute to this mission that doesn't involve past edits elsewhere. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:01, 22 April 2020 (UTC)

== Finding Common Ground ==

The course [[Finding Common Ground]] is now complete. May I add it to the news myself or is there some other way to have it added? Thanks. --[[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 01:40, 14 March 2022 (UTC)

:I've added an announcement of your course's completion to Main Page News, please modify if you wish. --[[User:Marshallsumter|Marshallsumter]] ([[User talk:Marshallsumter|discuss]] • [[Special:Contributions/Marshallsumter|contribs]]) 05:16, 14 March 2022 (UTC)
::Thanks! [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 11:50, 14 March 2022 (UTC)

== bug ==

January 5, 2023 is after December 25, 2023??? [[Special:Contributions/79.185.141.205|79.185.141.205]] ([[User talk:79.185.141.205|discuss]])
:fixed, thanks for bringing this up. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 22:30, 6 January 2024 (UTC)

=== another bug ===


March 6, 2024 is after December 5, 2024??? [[Special:Contributions/109.243.1.105|109.243.1.105]] ([[User talk:109.243.1.105|discuss]])
:Fixed. I'll try to be more attentive to this page. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:10, 18 July 2025 (UTC)

==noinclude==
{{ping|Dave Braunschweig}} I suppose, the offending &lt;code&gt;&lt;nowiki&gt;&lt;/noinclude&gt;&lt;/nowiki&gt;&lt;/code&gt; on the Main Page comes from here. --[[User:Watchduck|Watchduck]] &lt;small&gt;([[User talk:Watchduck|quack]])&lt;/small&gt; 21:22, 8 December 2024 (UTC)

:Thanks for the watchful eye {{ping|Watchduck}} I've fixed it up. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:45, 8 December 2024 (UTC)

== write news? ==

here? @[[User:Koavf|Koavf]] [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 22:10, 13 May 2026 (UTC)

:If you are serious about writing news here, I recommend getting together other Wikinews editors (including me: I'm happy to help) to organize at [[School:Journalism]], plan out what we want to do, present any radical proposals (like wholesale rehosting Wikinews here) to the community, and then starting the process of regularly writing news stories if the community agrees to include hosting citizen journalism here as an ongoing activity. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:21, 14 May 2026 (UTC)</text>
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  <page>
    <title>Emotion</title>
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      <text bytes="3855" sha1="1522c5jtvsq33yly5rbjhef59hd59m0" xml:space="preserve">'''Emotion''' refers to short-lasting affective states which occur in response to daily life events. 

Emotions are complex—they involve physiological, cognitive, behavioural, and social aspects, as well as subjective feelings. Different emotions each serve distinct [[motivation]]al function. There appear to be six to eight basic emotions (see Figure 1).
{{TOCright}}

==What is emotion?==
'''[[Emotion]]''' is not easily defined. It involves the complex [[w:psychophysiology|psychophysiological]] experience of an individual's state of mind as interacting with [[w:biochemical|biochemical]] and [[w:environmental|environmental]] influences. In [[w:human|human]]s, emotion fundamentally involves &quot;[[w:physiological arousal|physiological arousal]], expressive [[w:behavior|behaviour]]s, and [[w:consciousness|conscious experience]]&quot;.&lt;ref&gt;Myers, D. G. (2004). Theories of emotion. ''Psychology'' (7th ed.). Worth Publishers, p. 500.&lt;/ref&gt;

More simply, it's how we feel about things. Many of the chapters which follow will delve into conceptualising emotion and particular aspects of emotion - both what affects emotion and how emotion affects behaviour and thinking. 

* &quot;short-lived, feeling-purposive-expressive-bodily responses that help us adapt to the opportunities and challenges we face during important life events&quot; (Reeve, 2018, p. 288)
* &quot;synchronised brain-based systems that coordinate feeling, bodily response, purpose, and expression so to ready the individual to adapt successfully to life circumstances&quot; (Reeve, 2018, p. 289)
* &quot;short-lived psychological-physiological phenomena that represent efficient modes of adaptation to changing environmental demands&quot; (Levenson, 1994, p. 123)

==Questions about emotion==
* What is an emotion?
* What causes an emotion?
* What type of emotions are there?
* What functions do emotions serve?
* How can we regulate emotions?
* What is the difference between emotion and mood?
* How can emotion be measured?
* What are the consequences of emotion?
* How can emotion be changed?
* How and why did emotions evolve?
* How are the emotions of animals and humans similar and how do they vary?

==Types of emotion==
[[File:Emotions wheel.png|right|450px|thumb|''Figure 1''. An emotions wheel. Basic emotions are depicted in the centre (inner ring). Less intense aspects of basic emotions are shown in lighter colours (middle ring). More intense aspects of basic emotions are shown in darker colours (outer ring).]]
Some of the main types of emotion are:
* [[w:Fear|Fear]]
* [[w:Anger|Anger]]
* [[w:Sadness|Sadness]]
* [[w:Disgust|Disgust]]
* [[w:Contempt|Contempt]]
* [[w:Guilt|Guilt]]
* [[w:Surprise|Surprise]]
* [[w:Joy|Joy]]

==Emotion causes==
[[File:What causes an emotion.jpg|center|400px|thumb|Model of emotion (Reeve, 2015)]]

The causes of emotion are debated; they could be caused primarily by:
* physiological responses first, followed by cognitive interpretation
* cognitive responses first, followed by physiological responses
* a combination of physiological and cognitive responses

==Emotion images==
What emotions do you think are depicted in each of these images?
{{center|
&lt;gallery&gt;
File:Expression of the Emotions Figure 20.png
File:Child's Angry Face.jpg
File:Disgust expression cropped.jpg
File:Depression.jpg
File:Interest.jpg
File:B&amp;W Happiness.jpg
File:SURPRISE.jpg
File:Contempt.jpg
&lt;/gallery&gt;
}}

To find more emotion pictures, visit the [[Motivation_and_emotion/Gallery|Motivation and Emotion gallery]] or go to the [[commons:Category:Emotions|emotions category on Wikimedia Commons]].

==See also==
# [[w:Emotion|Emotion]] (Wikipedia)
# [[Mood]]
# [[Motivation]]
# [[Motivation and emotion]]

==References==
{{reflist}}
Reeve, J. (2018). ''[[Motivation and emotion/Readings/Textbooks/Reeve/2018|Understanding motivation and emotion]]'' (7th ed.). Wiley.

[[Category:Emotion]]</text>
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'''Emotion''' refers to short-lasting affective states which occur in response to daily life events. 

Emotions are complex—they involve physiological, cognitive, behavioural, and social aspects, as well as subjective feelings. Different emotions each serve distinct [[motivation]]al function. There appear to be six to eight basic emotions (see Figure 1).
{{TOCright}}

==What is emotion?==
'''[[Emotion]]''' is not easily defined. It involves the complex [[w:psychophysiology|psychophysiological]] experience of an individual's state of mind as interacting with [[w:biochemical|biochemical]] and [[w:environmental|environmental]] influences. In [[w:human|human]]s, emotion fundamentally involves &quot;[[w:physiological arousal|physiological arousal]], expressive [[w:behavior|behaviour]]s, and [[w:consciousness|conscious experience]]&quot;.&lt;ref&gt;Myers, D. G. (2004). Theories of emotion. ''Psychology'' (7th ed.). Worth Publishers, p. 500.&lt;/ref&gt;

More simply, it's how we feel about things. Many of the chapters which follow will delve into conceptualising emotion and particular aspects of emotion - both what affects emotion and how emotion affects behaviour and thinking. 

* &quot;short-lived, feeling-purposive-expressive-bodily responses that help us adapt to the opportunities and challenges we face during important life events&quot; (Reeve, 2018, p. 288)
* &quot;synchronised brain-based systems that coordinate feeling, bodily response, purpose, and expression so to ready the individual to adapt successfully to life circumstances&quot; (Reeve, 2018, p. 289)
* &quot;short-lived psychological-physiological phenomena that represent efficient modes of adaptation to changing environmental demands&quot; (Levenson, 1994, p. 123)

==Questions about emotion==
* What is an emotion?
* What causes an emotion?
* What type of emotions are there?
* What functions do emotions serve?
* How can we regulate emotions?
* What is the difference between emotion and mood?
* How can emotion be measured?
* What are the consequences of emotion?
* How can emotion be changed?
* How and why did emotions evolve?
* How are the emotions of animals and humans similar and how do they vary?

==Types of emotion==
[[File:Emotions wheel.png|right|450px|thumb|''Figure 1''. An emotions wheel. Basic emotions are depicted in the centre (inner ring). Less intense aspects of basic emotions are shown in lighter colours (middle ring). More intense aspects of basic emotions are shown in darker colours (outer ring).]]
Some of the main types of emotion are:
* [[w:Fear|Fear]]
* [[w:Anger|Anger]]
* [[w:Sadness|Sadness]]
* [[w:Disgust|Disgust]]
* [[w:Contempt|Contempt]]
* [[w:Guilt|Guilt]]
* [[w:Surprise|Surprise]]
* [[w:Joy|Joy]]

==Emotion causes==
[[File:What causes an emotion.jpg|center|400px|thumb|Model of emotion (Reeve, 2015)]]

The causes of emotion are debated; they could be caused primarily by:
* physiological responses first, followed by cognitive interpretation
* cognitive responses first, followed by physiological responses
* a combination of physiological and cognitive responses

==Emotion images==
What emotions do you think are depicted in each of these images?
{{center|
&lt;gallery&gt;
File:Expression of the Emotions Figure 20.png
File:Child's Angry Face.jpg
File:Disgust expression cropped.jpg
File:Depression.jpg
File:Interest.jpg
File:B&amp;W Happiness.jpg
File:SURPRISE.jpg
File:Contempt.jpg
&lt;/gallery&gt;
}}

To find more emotion pictures, visit the [[Motivation_and_emotion/Gallery|Motivation and Emotion gallery]] or go to the [[commons:Category:Emotions|emotions category on Wikimedia Commons]].

==See also==
# [[w:Emotion|Emotion]] (Wikipedia)
# [[Mood]]
# [[Motivation]]
# [[Motivation and emotion]]

==References==
{{reflist}}
Reeve, J. (2018). ''[[Motivation and emotion/Readings/Textbooks/Reeve/2018|Understanding motivation and emotion]]'' (7th ed.). Wiley.

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== Asadbek2003 ==

asadbek alijonf [[Special:Contributions/&amp;#126;2026-29869-26|&amp;#126;2026-29869-26]] ([[User talk:&amp;#126;2026-29869-26|talk]]) 14:34, 18 May 2026 (UTC)</text>
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== ~2026-28792-52 ==

Please block [[Special:Contribs/~2026-28792-52]], vandalism. Appears to be same user as above. [[User:Tenshi Hinanawi|Tenshi Hinanawi]] ([[User talk:Tenshi Hinanawi|トーク]] • [[Special:Contributions/Tenshi Hinanawi|投稿記録]]) 17:38, 12 May 2026 (UTC)
: Blocked locally by Barras. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:46, 12 May 2026 (UTC)

== New User Exceeded New Page Limit  ==

Hello, my action of creating a Portal for Banjo learning (Portal:Banjo) was denied as I am a user whose had my account for a while but not written before today. My actions are constructive, but if you would rather me wait and let the system work as it intends to then that's okay too. 
--[[User:Kirby - Electrotechnics|Kirby - Electrotechnics]] ([[User talk:Kirby - Electrotechnics|discuss]] • [[Special:Contributions/Kirby - Electrotechnics|contribs]]) 01:13, 17 May 2026 (UTC)

:That is standard and the rate limit will fall off as you stay and edit; it has some pretty easy barriers to cross. I can create a blank [[Portal:Banjo]] if you want, but to be clear, portal pages are usually much broader topics that can help orient you to specific pages. Do you think there will be that many pages about the topic of banjo playing? If not, then you can just continue editing [[Banjo]]. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 03:36, 17 May 2026 (UTC)

== Disable [[Special:AbuseFilter/3]] ==

Please disable [[Special:AbuseFilter/3]] because it is redundant with [[m:Special:AbuseFilter/104|a global filter]] that disallows the same type of spam that filter 3 would have caught. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:06, 19 May 2026 (UTC)</text>
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== ~2026-28792-52 ==

Please block [[Special:Contribs/~2026-28792-52]], vandalism. Appears to be same user as above. [[User:Tenshi Hinanawi|Tenshi Hinanawi]] ([[User talk:Tenshi Hinanawi|トーク]] • [[Special:Contributions/Tenshi Hinanawi|投稿記録]]) 17:38, 12 May 2026 (UTC)
: Blocked locally by Barras. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 17:46, 12 May 2026 (UTC)

== New User Exceeded New Page Limit  ==

Hello, my action of creating a Portal for Banjo learning (Portal:Banjo) was denied as I am a user whose had my account for a while but not written before today. My actions are constructive, but if you would rather me wait and let the system work as it intends to then that's okay too. 
--[[User:Kirby - Electrotechnics|Kirby - Electrotechnics]] ([[User talk:Kirby - Electrotechnics|discuss]] • [[Special:Contributions/Kirby - Electrotechnics|contribs]]) 01:13, 17 May 2026 (UTC)

:That is standard and the rate limit will fall off as you stay and edit; it has some pretty easy barriers to cross. I can create a blank [[Portal:Banjo]] if you want, but to be clear, portal pages are usually much broader topics that can help orient you to specific pages. Do you think there will be that many pages about the topic of banjo playing? If not, then you can just continue editing [[Banjo]]. ―[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''&lt;span style=&quot;color:black&quot;&gt;v&lt;/span&gt;f&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 03:36, 17 May 2026 (UTC)

== Disable [[Special:AbuseFilter/3]] ==

Please disable [[Special:AbuseFilter/3]] because it is redundant with [[m:Special:AbuseFilter/104|a global filter]] that disallows the same type of spam that filter 3 would have caught. Thank you. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:06, 19 May 2026 (UTC)
: [[Special:AbuseFilter/history/3/diff/prev/454|Done]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:15, 19 May 2026 (UTC)</text>
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  <page>
    <title>Openness</title>
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Openness is a [[free culture]] philosophy and an important foundational concept in many social and technical systems. For example, openness is critical to [[w:democracy|democracy]].

==Learning outcomes==
These learning outcomes aim to provide a framework for exploring openness encouraging critical thinking, interdisciplinary engagement, and reflective practice.

* Define openness:
** Articulate a personal understanding of openness and compare it with perspectives from scholars like David Wiley.
** Investigate contrasting views on openness and its antithesis, considering how it manifests in various contexts.
* Evaluate the advantages and disadvantages of openness:
** Critically assess the impact of openness on societal, technological, and individual levels, weighing factors such as transparency, collaboration, innovation, and privacy.
** Analyze case studies or real-world examples to understand the nuanced implications of embracing or restricting openness.
* Identify domains where openness is crucial:
** Explore the significance of openness in diverse fields such as governance, education, science, technology, and culture.
** Examine how openness fosters trust, accountability, and progress within these domains.
* Connect to related Wikiversity resources:
** Engage with existing materials on Wikiversity to deepen understanding of openness in research and education, exploring its ethical, practical, and pedagogical dimensions.
** Collaborate with peers to contribute insights or perspectives to enhance collective knowledge on the topic.
* Explore personal philosophy regarding openness:
** Reflect on how principles of openness align with or challenge personal beliefs, values, and goals.
** Consider ethical dilemmas or practical considerations that arise when navigating the tensions between openness and other priorities.

==Learning tasks==
There are several learning tasks participants are invited to engage with on this page:
* Define openness: What is openness? How would you define it? How do others define it? For example, consider how David Wiley describes openness in his article &quot;Defining 'Open'&quot;. What is the opposite of openness?
* What are the pros and cons of openness? e.g., create a [[w:SWOT|SWOT]] analysis Evaluate the advantages and disadvantages of open versus closed/non-open approaches, considering factors such as transparency, collaboration, innovation, and privacy.
* In what domains is openness important?
* Explore related Wikiversity resources discussing openness in research and education to gain a deeper understanding of its implications.
* [[w:Open by default|Open by default]] vs. closed by default - When should open by default practices be adopted?
* Explore how openness relate to your personal philosophy (e.g., create a sub-page)

==Defining openness==
* [http://opencontent.org/blog/archives/1123 Defining “Open”] David Wiley, 2009
{{cquote|Instead of secrecy, openness should reign, and I can very well imagine the day when two persons will no longer keep any secrets from one another because they will have no secrets from anyone, because the subjective life will be a fact, as totally open as the objective life.|30px|30px|Jean-Paul Sartre|Wolfgang Schirmacher, “[http://www.egs.edu/faculty/schirmacher/privacy.html Privacy as an Ethical Problem in the Computer Society],” trans. Virginia Cutrufelli, June 2005}}

==Create a sub-page==
You are welcome to add a sub-page about '''{{PAGENAME}}'''. Enter a title that is not already on the list below and start a draft. If you wish to change your title, or have any other questions, visit us at ''[[Wikiversity:Colloquium]]''.
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==See also==
{{wp}}
* [[Open academia]]
* [[Openness and flexibility]]

==External links==
* [https://www.gnu.org/education/edu-schools.html Why schools should exclusively use free software]] (Richard Stallman)

[[Category:Open essay collections]]
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    <title>Ask Me 3</title>
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Nearly half of all American adults, 90 million people, have difficulty understanding and using health information that they are given (Partnership for Clear Health Communication, 2007).  This statistic is important because health literacy skills – the ability to read, understand and effectively use basic medical instructions and information – are linked with an individual’s health status (Partnership for Clear Health Communication, 2007); which means the lower your health literacy skills are, the more likely you are to become sick or have lower than average health.  This is why clear communication between patients and health care providers is essential (Partnership for Clear Health Communication, 2007).  The better the communication between the health care provider and their patients, the more likely it is that the patient will have a better understanding of what their health problems are and why they need to follow their physician’s advice, and in turn can be one step closer to becoming a healthier person.  The Ask Me 3 program is designed to do just that - to help patients increase their health literacy and, as a result, also raise their health.    


'''What Questions to Ask'''
 
The Ask Me 3 program is centered on three important universal questions that were developed to help increase health literacy.  These three questions are (Partnership for Clear Health Communication, 2007): 

*What is my main problem?
*What do I need to do? 
*Why is it important for me to do this?

These questions should be asked when patients are seeing any health care providers or pharmacists, when preparing for a medical test or procedure or when picking up medicine so you they will become a more informed consumer of their healthcare (Partnership for Clear Health Communication, 2007).  


'''Advantages of Ask Me 3'''  

There are many important advantages to asking these questions, such as keeping patients safe when taking their medication at home, helping them understand how to get better and being to better understand what procedures may be performed on them (Partnership for Clear Health Communication, 2007).  They may also be able to spend less money on healthcare by making fewer trips to their healthcare provider because main questions were answered during the first visit instead of during consequential visits.  

    	
'''Other Important Questions to Ask'''  

The Ask Me 3 questions are not the only important questions that patients should ask their health care provider or pharmacist.  It is also important that any other questions they thought of on their own are answered.  These questions can be used to supplement the Ask Me 3 questions.
Partnership for Clear Health Communication.  (2007).  Ask Me 3.  Retrieved from http://www.npsf.org/askme3/  
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{{secondary}}
== Creative Writing Activity ==

Sometimes it's difficult to get students started with writing.  Here's a fun activity that can reinforce the elements of fiction and give students a chance to brainstorm using each other as resources:

'''Story-Go-Round'''

*First, place students in circular groups. Groups of 4-6 work well.  
*Explain to the students that they will each start a story and that they will have a specific amount of time to complete each step before passing their paper to the right or to the left (that part doesn't matter, as long as everyone passes the same way).  
*Time each step carefully.  For beginners, a minute to a minute and a half is sufficient for step 1.  Add about ten seconds to each subsequent step to give them time to read.  Don't tell the students you are adding the time, as they will never notice because they will be too busy working! 
*Depending on your audience, you may want to set some ground rules about what topics are off-limits.  Topics that are typically off limits are illegal activities, drugs and weapons, profanity, and sexual references.
*Write the steps on the board or project them using an overhead, LCD projector or Smartboard.  The steps are as follows:

#Describe a setting (time and place)
#Introduce a protagonist (if your students are younger, you may want to use the term &quot;main character&quot;)
#Introduce a second character/antagonist
#Describe a conflict
#Bring the conflict to its climax
#Resolve the conflict

*Make sure you explain that students may ONLY work on ONE step at a time.  If they jump ahead and introduce the conflict while they are describing the antagonist, the next person who gets the paper won't know what to do.
*Once the activity is complete, have each group share the best story and explain which member came up with which element(s).
*As an extension activity, you can have each student revise their original paper and turn in the final copy.

This is a fun activity that takes little prep time and students usually really enjoy it, even at the college level.  I did this in my teaching methods class when I was a senior in college, and we all had a lot of fun with our crazy stories!

--[[User:Lessouth|Lessouth]] 14:06, 3 March 2010 (UTC)
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==Engine Sizing==

===Civil Engines===

Modern  (i.e. high bypass ratio) civil engines are normally sized to meet the thrust requirements at the Top-of-Climb, which is often the design condition for the engine. 

The throttle setting used at Take-Off depends upon the aircraft configuration: i.e. whether it has two, three or four-engines fitted. In the Western World, civil engines operate to a &quot;set and forget&quot;  throttle setting throughout Take-off. If the thrust of one engine is lost during the Take Off, the remaining engine/s must have sufficient total thrust to allow the aircraft to clear any immediate obstruction beyond the end of the runway (e.g. buildings). 

So if one engine is lost on a twin engine aircraft (e.g. Boeing 777) during Take-off, the remaining 50% of thrust must be sufficient to meet the above criteria. Consequently the implied nominal T/O thrust must be very high, which results in the aircraft having a very steep climb-out from the airport. 

On the other hand, if one engine is lost during Take-off on a four engined aircraft (e.g. Boeing 747),  there is still 75% of the nominal total thrust to meet the above criteria. So the implied nominal T/O thrust can be relatively low, resulting in the aircraft having a shallower climb-out.

===Military Engines===

The sizing point for a military engine is very much dependent upon the aircraft application. 

As example, the Pegasus engine fitted in the Harrier is sized to meet the thrust requirements for a vertical landing in a hot climate, with a high level of reaction control bleed from the HP compressor. These severe requirements mean there is more than sufficient thrust for normal wing-borne operation and so, in-flight, the engine is significantly derated (i.e. throttled back).

==Husk plot==

A Husk Plot is a concise way of summarizing the performance of a jet engine. The following sections describe how the plot is generated and can be used.

===Thrust/SFC loops===

Specific Fuel Consumption (i.e. SFC), defined as fuel flow/net thrust, is an important parameter reflecting the overall thermal (or fuel) efficiency of an engine. 

As an engine is throttled back there will be a variation of SFC with net thrust, because of changes in the engine cycle (e.g. lower overall pressure ratio) and variations in component performance (e.g. compressor efficiency). When plotted, the resultant curve is known as a thrust/SFC loop. A family of these curves can be generated at Sea Level, Standard Day, conditions over a range of flight speeds. A Husk Plot (RHS) can be developed using this family of curves. The net thrust scale is simply relabeled &lt;math&gt;Fn/{\delta}\, &lt;/math&gt;, where &lt;math&gt;{\delta}\, &lt;/math&gt; is relative ambient pressure , whilst the SFC scale is relabeled &lt;math&gt;SFC/\sqrt{\theta}\, &lt;/math&gt;, where &lt;math&gt;{\theta}\, &lt;/math&gt; is relative ambient temperature. The resulting plot can be used to estimate engine net thrust and SFC at any altitude, flight speed and climate  for a range of throttle setting.[[Image:huskplot.gif|thumb|200px|right|Typical Husk Plot]]

Selecting a point on the plot, net thrust is calculated as follows:

'''&lt;math&gt;Fn = (Fn/{\delta}) \cdot {\delta}&lt;/math&gt;'''

Clearly, net thrust falls with altitude, because of the decrease in ambient pressure.

The corresponding SFC is calculated as follows:

'''&lt;math&gt;SFC = (SFC/\sqrt{\theta}) \cdot \sqrt{\theta}&lt;/math&gt;'''

At a given point on the Husk Plot, SFC falls with decreasing ambient temperature (e.g. increasing altitude or colder climate).The basic reason why SFC increases with flight speed is the implied increase in ram drag.

Although a Husk Plot is a concise way of summarizing the performance of a jet engine, the predictions obtained at altitude will be slightly
optimistic. For instance, because ambient temperature remains constant above 11,000 m (36,089 ft) altitude, at a fixed non-dimensional point the Husk plot would yield no change in SFC with increasing altitude. In reality, there would be a small, steady, increase in SFC, owing to the falling [[w:Reynolds number|Reynolds number]].

===Thrust lapse===

The nominal net thrust quoted for a jet engine usually refers to the Sea Level Static (SLS) condition, either for the International Standard Atmosphere (ISA) or a hot day condition (e.g. ISA+10 °C). As an example, the GE90-76B has a take-off static thrust of 76,000 [[w:pound-force|lbf]] (360 [[w:kilonewton|kN]]) at SLS, ISA+15 °C.

Naturally, net thrust will decrease with altitude, because of the lower air density. There is also, however, a flight speed effect. 

Initially as the aircraft gains speed down the runway, there will be little increase in nozzle pressure and temperature, because the ram rise in the intake is very small. There will also be little change in mass flow. Consequently, nozzle gross thrust initially only increases marginally with flight speed. However, being an air breathing engine (unlike a conventional rocket) there is a penalty for taking on-board air from the atmosphere. This is known as ram drag. Although the penalty is zero at static conditions, it rapidly increases with flight speed causing the net thrust to be eroded. 

As flight speed builds up after take-off, the ram rise in the intake starts to have a significant effect upon nozzle pressure/temperature and intake airflow, causing nozzle gross thrust to climb more rapidly. This term now starts to offset the still increasing ram drag, eventually causing net thrust to start to increase. In some engines, the net thrust at say Mach 1.0, sea level can even be slightly greater than the static thrust. Above Mach 1.0, with a subsonic inlet design, shock losses tend to decrease net thrust, however a suitably designed supersonic inlet can give a lower reduction in intake pressure recovery, allowing net thrust to continue to climb in the supersonic regime.

The thrust lapse described above depends on the design specific thrust and, to a certain extent, on how the engine is rated with intake temperature. Three possible ways of rating an engine are depicted on the above Husk Plot. The engine could be rated at constant turbine entry temperature, shown on the plot as '''&lt;math&gt;SOT/{\theta}\, &lt;/math&gt;'''. Alternatively, a constant mechanical shaft speed could be assumed, depicted as '''&lt;math&gt;N_F/\sqrt{\theta}\, &lt;/math&gt;'''. A further alternative is a constant compressor corrected speed, shown as '''&lt;math&gt;N_F/\sqrt{\theta}_T\, &lt;/math&gt;'''. The variation of net thrust with flight Mach number can be clearly seen on the Husk Plot.

===Other trends===

The Husk Plot can also be used to indicate trends in the following parameters:

1) turbine entry temperature

'''&lt;math&gt;SOT = (SOT/{\theta}) \cdot  {\theta}\, &lt;/math&gt;'''

So as ambient temperature falls (through increasing altitude or a cooler climate), turbine entry temperature must also fall to stay at the same non-dimensional
point on the Husk Plot. All the other non-dimensional groups (e.g. corrected flow, axial and peripheral Mach numbers, pressure ratios, efficiencies, etc will also stay constant).

2) mechanical shaft speed

'''&lt;math&gt;N_F = (N_F/\sqrt{\theta}) \cdot  \sqrt{\theta}\, &lt;/math&gt;'''

Again as ambient temperature falls (through increasing altitude or a cooler climate), mechanical shaft speed must also decrease to remain at the same non-dimemsional point. 

By definition, compressor corrected speed, '''&lt;math&gt;N_F/\sqrt{\theta}_T\, &lt;/math&gt;''', must remain constant at a given non-dimensional point.

==Rated Performance==
====Civil====
[[Image:Civilrating.png|thumb|right|400px|Typical civil rating system]] Nowadays, civil engines are usually flat-rated on net thrust up to a 'kink-point' climate. So at a given flight condition, net thrust is held approximately constant over a very wide range of ambient temperature, by increasing (HP) turbine rotor inlet temperature (RIT or SOT). However, beyond the kink-point, SOT is held constant and net thrust starts to fall for further increases in ambient temperature. Consequently, aircraft fuel load and/or payload must be decreased.

Usually, for a given rating, the kink-point SOT is held constant, regardless of altitude or flight speed.

Some engines have a special rating, known as the 'Denver Bump'. This invokes a higher RIT than normal, to enable fully laden aircraft to Take-off safely from Denver, CO in the summer months. Denver Airport is extremely hot in the summer and the runways are over a mile above sea level. Both of these factors affect engine thrust.

====Military====
[[Image:militaryrating.gif|thumb|left|400px|Typical military rating system]] The rating systems used on military engines vary from engine to engine. A typical military rating structure is shown on the left. Such a rating system maximises the thrust available from the engine cycle chosen, whilst respecting the aerodynamic and mechanical limits imposed on the turbomachinery. If there is adequate thrust to meet the aircraft's mission in a particular range of intake temperature, the engine designer may elect to truncate the schedule shown, to lower the turbine rotor inlet temperature and, thereby, improve engine life.

At low intake temperatures, the engine tends to operate at maximum [[w:corrected speed|corrected speed]] or [[w:corrected flow|corrected flow]]. As intake temperature rises, a limit on (HP) turbine rotor inlet temperature (SOT) takes effect, progressively reducing corrected flow. At even higher intake temperatures, a limit on compressor delivery temperature (''T''&lt;sub&gt;3&lt;/sub&gt;) is invoked, which decreases both SOT and corrected flow.

[[Image:T1design.gif|thumb|right|400px|Impact of design intake temperature]] The impact of design intake temperature is shown on the right hand side. 

An engine with a low design ''T''&lt;sub&gt;1&lt;/sub&gt; combines high corrected flow with high rotor turbine temperature (SOT), maximizing net thrust at low ''T''&lt;sub&gt;1&lt;/sub&gt; conditions (e.g. Mach 0.9, 30000 ft, ISA). However, although turbine rotor inlet temperature stays constant as ''T''&lt;sub&gt;1&lt;/sub&gt; increases, there is a steady decrease in corrected flow, resulting in poor net thrust at high ''T''&lt;sub&gt;1&lt;/sub&gt; conditions (e.g. Mach 0.9, sea level, ISA).

Although an engine with a high design ''T''&lt;sub&gt;1&lt;/sub&gt; has a high corrected flow at low ''T''&lt;sub&gt;1&lt;/sub&gt; conditions, the SOT is low, resulting in a poor net thrust. Only at high ''T''&lt;sub&gt;1&lt;/sub&gt; conditions is there the combination of a high corrected flow and a high SOT, to give good thrust characteristics.

A compromise between these two extremes would be to design for a medium intake temperature (say 290 K).

As ''T''&lt;sub&gt;1&lt;/sub&gt; increases along the SOT plateau, the engines will throttle back, causing both a decrease in corrected airflow and overall pressure ratio. As shown, the chart implies a common ''T''&lt;sub&gt;3&lt;/sub&gt; limit for both the low and high design ''T''&lt;sub&gt;1&lt;/sub&gt; cycles. Roughly speaking, the ''T''&lt;sub&gt;3&lt;/sub&gt; limit will correspond to a common overall pressure ratio at the ''T''&lt;sub&gt;3&lt;/sub&gt; breakpoint. Although both cycles will increase throttle setting as ''T''&lt;sub&gt;1&lt;/sub&gt; decreases, the low design ''T''&lt;sub&gt;1&lt;/sub&gt; cycle has a greater 'spool-up' before hitting the corrected speed limit. Consequently, the low design ''T''&lt;sub&gt;1&lt;/sub&gt; cycle has a higher design overall pressure ratio.

==Nomenclature==

*'''&lt;math&gt;A\, &lt;/math&gt;'''   flow area
*'''&lt;math&gt;A_{\mathrm{8calc}}\, &lt;/math&gt;'''  calculated nozzle effective throat area
*'''&lt;math&gt;A_{\mathrm{8 des pt}}\, &lt;/math&gt;''' design point nozzle effective throat area  
*'''&lt;math&gt;A_{\mathrm{8 geometricdesign}}\, &lt;/math&gt;''' nozzle geometric throat area 
*'''&lt;math&gt;{\alpha}\, &lt;/math&gt;''' shaft angular acceleration 
*'''&lt;math&gt;{\beta}\, &lt;/math&gt;''' arbitrary lines which dissect the corrected speed lines on a compressor characteristic  
*'''&lt;math&gt;C_{\mathrm{pc}}\, &lt;/math&gt;''' specific heat at constant pressure for air
*'''&lt;math&gt;C_{\mathrm{pt}}\,&lt;/math&gt;'''  specific heat at constant pressure for combustion products
*'''&lt;math&gt;C_{\mathrm{dcalc}}\, &lt;/math&gt;''' calculated nozzle discharge coefficient 
*'''&lt;math&gt;C_x\, &lt;/math&gt;''' thrust coefficient
*'''&lt;math&gt;{\delta}\, &lt;/math&gt;''' ambient pressure/Sea Level ambient pressure
*'''&lt;math&gt;({\delta}H/T)_{\mathrm{turb}} \, &lt;/math&gt;''' turbine enthalpy drop/inlet temperature
*'''&lt;math&gt;{\delta}N\, &lt;/math&gt;'''  change in mechanical shaft speed
*'''&lt;math&gt;{\delta}P_w\, &lt;/math&gt;''' excess shaft power
*'''&lt;math&gt;{\delta}\,{\tau}\, &lt;/math&gt;'''  excess shaft torque
*'''&lt;math&gt;{\eta}_{\mathrm{pc}}\, &lt;/math&gt;''' compressor polytropic efficiency
*'''&lt;math&gt;{\eta}_{\mathrm{pt}}\, &lt;/math&gt;'''  turbine polytropic efficiency
*'''&lt;math&gt;g\, &lt;/math&gt;'''   acceleration of gravity
*'''&lt;math&gt;F_g\, &lt;/math&gt;'''  gross thrust
*'''&lt;math&gt;F_n\, &lt;/math&gt;'''  net thrust
*'''&lt;math&gt;F_r\, &lt;/math&gt;'''  ram drag
*'''&lt;math&gt;{\gamma}_{\mathrm{c}}\, &lt;/math&gt;'''  ratio of specific heats for air
*'''&lt;math&gt;{\gamma}_{\mathrm{t}}\, &lt;/math&gt;'''  ratio of specific heats for combustion products
*'''&lt;math&gt;I\, &lt;/math&gt;'''   spool inertia
*'''&lt;math&gt;J\, &lt;/math&gt;'''   mechanical equivalent of heat
*'''&lt;math&gt;K\, &lt;/math&gt;'''   constant
*'''&lt;math&gt;K_1\, &lt;/math&gt;'''   constant
*'''&lt;math&gt;K_2\, &lt;/math&gt;'''   constant
*'''&lt;math&gt;M\, &lt;/math&gt;'''   flight Mach number
*'''&lt;math&gt;N\, &lt;/math&gt;''' compressor mechanical shaft speed
*'''&lt;math&gt;N_{\mathrm{cor}}\, &lt;/math&gt;''' compressor corrected shaft speed
*'''&lt;math&gt;N_{\mathrm{turb cor}}\, &lt;/math&gt;''' turbine corrected shaft speed
*'''&lt;math&gt;p\, &lt;/math&gt;'''   static pressure
*'''&lt;math&gt;P\, &lt;/math&gt;'''   stagnation (or total) pressure
*'''&lt;math&gt;P_3/P_2\, &lt;/math&gt;''' compressor pressure ratio
*'''&lt;math&gt;prf\, &lt;/math&gt;'''  intake pressure recovery factor
*'''&lt;math&gt;R\, &lt;/math&gt;'''   gas constant
*'''&lt;math&gt;{\rho}\, &lt;/math&gt;''' density
*'''&lt;math&gt;SFC\, &lt;/math&gt;''' specific fuel consumption  
*'''&lt;math&gt;SOT\, &lt;/math&gt;''' stator outlet temperature
*'''&lt;math&gt;RIT\, &lt;/math&gt;''' (turbine) rotor inlet temperature
*'''&lt;math&gt;t\, &lt;/math&gt;'''   static temperature or time
*'''&lt;math&gt;T\, &lt;/math&gt;'''  stagnation (or total) temperature
*'''&lt;math&gt;T_1\, &lt;/math&gt;'''  intake stagnation temperature
*'''&lt;math&gt;T_3\, &lt;/math&gt;'''  compressor delivery total temperature
*'''&lt;math&gt;{\theta}\, &lt;/math&gt;''' ambient temperature/Sea Level, Standard Day, ambient temperature
*'''&lt;math&gt;{\theta}_T\, &lt;/math&gt;''' total temperature/Sea Level, Standard Day, ambient temperature
*'''&lt;math&gt;V\, &lt;/math&gt;'''  velocity
*'''&lt;math&gt;w\, &lt;/math&gt;''' mass flow
*'''&lt;math&gt;w_{\mathrm{4cor calc}}\, &lt;/math&gt;''' calculated turbine entry corrected flow
*'''&lt;math&gt;w_{\mathrm{2cor}}\, &lt;/math&gt;''' compressor corrected inlet flow 
*'''&lt;math&gt;w_{\mathrm{4cor des pt}}\, &lt;/math&gt;''' design point turbine entry corrected flow 
*'''&lt;math&gt;w_{\mathrm{4cor turb char}}\, &lt;/math&gt;''' corrected entry flow from turbine characteristic (or map) 
*'''&lt;math&gt;w_{\mathrm{fe}}\, &lt;/math&gt;''' combustor fuel flow

==Notes==
{{Reflist}}

==References==
* Kerrebrock, Jack L. (1992), ''Aircraft Engines and Gas Turbines'', The MIT Press, Cambridge, Massachusetts USA.  {{ISBN|0 262 11162 4}}

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&lt;div style=&quot;background:white; border:2px SteelBlue solid; padding:12px;&quot;&gt;
My name is James Neill (''he/him''). I'm an Assistant Professor in the [https://www.canberra.edu.au/about-uc/faculties/health/study/psychology Discipline of Psychology] at the [[University of Canberra]], Australia.

I'm passionate about [[open academia]]—I like to share knowledge openly.

On English Wikiversity, I'm a [[WV:Custodianship|custodian]] and [[WV:Bureaucratship|bureaucrat]]&lt;small&gt;&lt;sup&gt;[https://en.wikiversity.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Jtneill (verify)]&lt;/sup&gt;&lt;/small&gt;. Since 2005, I've made:
* ~[https://xtools.wmcloud.org/ec/en.wikiversity.org/Jtneill 80,000 edits] on  [[Main page|Wikiversity]]
* ~[https://xtools.wmcloud.org/ec/en.wikipedia/Jtneill 4,600 edits] on [[w:|Wikipedia]]
* ~[https://xtools.wmcloud.org/ec/en.commons/Jtneill 2,200 edits] on [[c:|Wikimedia Commons]].

My [[User:Jtneill/Teaching/Philosophy|teaching philosophy]] is based on experiential learning. [[/Teaching|I teach]] a 3rd-year undergraduate [[psychology]] unit, [[motivation and emotion]], and a 4th-year Honours unit about [[research methods in psychology]].

{{/Research}}

[[/Presentations|I also present]] about open education, wikis in higher education, and collaborative development of open educational resources. 

Currently, I'm working on:
[[User:Jtneill/Presentations/Open wiki assignments for authentic learning|Open wiki assignments for authentic learning]].

Most recently, I presented on:
[[User:Jtneill/Presentations/Interactive classroom exercises using Google Forms and Sheets|Interactive classroom exercises using Google Forms and Sheets]].

Hobbies include exploring outdoors, mountain biking, and [[w:guerilla gardening|guerilla gardening]].

[[/Contact|Feel free to connect.]]
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&lt;div style=&quot;font-size: 1pt&quot;&gt;&lt;br /&gt;&lt;/div&gt;
{{edit page box}}

&lt;!-- LOCAL TIME --&gt;
{{center top}}&lt;small&gt;Local &lt;!-- day/ --&gt;time: &lt;!-- {{ #time: l | {{CURRENTDAYNAME}} +10 hours}} --&gt; {{ #time: H:i | {{CURRENTTIME}} +11 hours }} ([[w:UTC|UTC]]+10)&lt;/small&gt;{{center bottom}}

[[Category:User en|{{PAGENAME}}]]
[[Category:User en-N|{{PAGENAME}}]]
[[Category:User es-0|{{PAGENAME}}]]
[[Category:Wikiversity custodians|Jtneill]]
[[Category:Wikiversitans]]
[[Category:{{FULLPAGENAME}}| ]]
[[Category:University of Canberra/Staff]]
[[Category:Wiki participants with committed identities]]
[[Category:Teachers of Health Professionals]]
[[Category:Wikiversity bureaucrats]]</text>
      <sha1>go2hlxrgqo6rn8d0h1j3ufv837xnkog</sha1>
    </revision>
    <revision>
      <id>2810117</id>
      <parentid>2810116</parentid>
      <timestamp>2026-05-18T12:13:18Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>/* */</comment>
      <origin>2810117</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3119" sha1="cg99pgyviwix48opo4x4djnec44v96n" xml:space="preserve">__NOTOC__
&lt;div style=&quot;background:white; border:2px SteelBlue solid; padding:12px;&quot;&gt;
My name is James Neill (''he/him''). I'm an Assistant Professor in the [https://www.canberra.edu.au/about-uc/faculties/health/study/psychology Discipline of Psychology] at the [[University of Canberra]], Australia.

I'm passionate about [[open academia]]—I like to share knowledge openly.

On English Wikiversity, I'm a [[WV:Custodianship|custodian]] and [[WV:Bureaucratship|bureaucrat]]&lt;small&gt;&lt;sup&gt;[https://en.wikiversity.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Jtneill (verify)]&lt;/sup&gt;&lt;/small&gt;. Since 2005, I've made:
* ~[https://xtools.wmcloud.org/ec/en.wikiversity.org/Jtneill 80,000 edits] on  [[Main page|Wikiversity]]
* ~[https://xtools.wmcloud.org/ec/en.wikipedia/Jtneill 4,600 edits] on [[w:|Wikipedia]]
* ~[https://xtools.wmcloud.org/ec/en.commons/Jtneill 2,200 edits] on [[c:|Wikimedia Commons]].

My [[User:Jtneill/Teaching/Philosophy|teaching philosophy]] is based on experiential learning. [[/Teaching|I teach]] a 3rd-year undergraduate [[psychology]] unit, [[motivation and emotion]], and a 4th-year Honours unit about [[research methods in psychology]].

{{/Research}}

[[/Presentations|I also present]] about open education, wikis in higher education, and collaborative development of open educational resources. 

Currently, I'm working on:
[[User:Jtneill/Presentations/Open wiki assignments for authentic learning|Open wiki assignments for authentic learning]].
&lt;!--
Most recently, I presented on:
[[User:Jtneill/Presentations/Interactive classroom exercises using Google Forms and Sheets|Interactive classroom exercises using Google Forms and Sheets]].
--&gt;
Hobbies include exploring outdoors, mountain biking, and [[w:guerilla gardening|guerilla gardening]].

[[/Contact|Feel free to connect.]]
&lt;/div&gt;
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type=search
width=20
namespaces=User
prefix={{FULLPAGENAME}}
searchbuttonlabel=Search User:Jtneill
bgcolor=transparent
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&lt;!-- SUBPAGES --&gt;
{{Collapse box|1=[[/Subpages/]]|2=&lt;nowiki&gt;&lt;/nowiki&gt;
{{/Subpages}}
}}

&lt;!-- Gateways Box --&gt;
{{Collapse box|1=[[Template:Gateways|Wikiversity Gateways]]|2=
{{center top}}
&lt;div style=&quot;float:right; width:100%&quot;&gt;
{{gateways}}
&lt;/div&gt;
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}}

&lt;!-- SISTERPROJECTS --&gt;
{{Collapse box|1=[[Template:Sisterprojects/Projects|Sister projects]]|2=
{{center top}}
{{Sisterprojects/Projects}}
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}}

&lt;!--DIT PAGE BOX --&gt;
&lt;div style=&quot;font-size: 1pt&quot;&gt;&lt;br /&gt;&lt;/div&gt;
{{edit page box}}

&lt;!-- LOCAL TIME --&gt;
{{center top}}&lt;small&gt;Local &lt;!-- day/ --&gt;time: &lt;!-- {{ #time: l | {{CURRENTDAYNAME}} +10 hours}} --&gt; {{ #time: H:i | {{CURRENTTIME}} +11 hours }} ([[w:UTC|UTC]]+10)&lt;/small&gt;{{center bottom}}

[[Category:User en|{{PAGENAME}}]]
[[Category:User en-N|{{PAGENAME}}]]
[[Category:User es-0|{{PAGENAME}}]]
[[Category:Wikiversity custodians|Jtneill]]
[[Category:Wikiversitans]]
[[Category:{{FULLPAGENAME}}| ]]
[[Category:University of Canberra/Staff]]
[[Category:Wiki participants with committed identities]]
[[Category:Teachers of Health Professionals]]
[[Category:Wikiversity bureaucrats]]</text>
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  </page>
  <page>
    <title>Uthumphon Phisai District</title>
    <ns>0</ns>
    <id>100689</id>
    <revision>
      <id>2810144</id>
      <parentid>619192</parentid>
      <timestamp>2026-05-18T19:02:58Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>PROD</comment>
      <origin>2810144</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3705" sha1="3q0gpd81ps55q085mpb56pcay7zzvg7" xml:space="preserve">{{Prod|15+ years with no further development or integration into a bigger learning project; may be suitable for Wikivoyage}}
'''The history of Uthumphon Phisai District'''
Uthumphon Phisai District was established in 1911. In the past, it was called Prajim District by the district west of Ban Somrong, Tambon Samrong. Paprachumchuntunikon was the first leader of the district.
In 1914 Mr. Bunma Sinparaya became leader of the district. He considered that around the district there were many fig trees that are the symbol of the district. So, he changed the name of the district from Prajim into Uthumphon Phisai that means “Place of the big fig tree.” 
In 1937, Mr. Sayar Sukrud became leader of the district. He moved the district from Ban Somrong to Bam Tumye that was near the railway &lt;from Bangkok to    Ubon Ratchathani&gt; that is the district place now.
In 1948, Mr. Pawong Sriboonrhu became leader of the district. He developed the district and got the funded to make the district place, police station, and house of government.
Now, Uthumphon Phisai is a district in the western part of Sisaket Province, northeastern Thailand.


The district is subdivided into 25 subdistricts. There are further 25 subdistricts administrative organizations.
1.	Kamphaeng
2.	I Lam
3.	Kan Lueang
4.	Thung Chai
5.	Samrong
6.	Khaem
7.	Nong Hai
8.	Khayung
10.	Ta Ket
11.	Hua Chang
12.	Rang Raeng
14.	Tae
15.	Khae
16.	Pho Chai
17.	Pa Ao
18.	Nong Hang
22.	Sa Kamphaeng Yai
24.	Khok Lam
25.	Khok Chan		


'''The history of Prasat Hin Wat Sa Kamphaeng Yai'''
Located in Prasat Hin Wat Sa Kamphaeng Yai, Tambon Sa Kamphaeng Yai, Uthumphonphisai district, Sisaket Province.
Prasat Hin Wat Sa Kamphaeng Yai is the biggest and most perfect Khmer Ruins in the province. The Khmer Ruins comprises three stupas on the same base lining in North-South direction and facing east. The main stupa, at the middle, made from sandstone and bricks in some part, houses carved lintel depicting God Indra on the back of Erawan Heavenly Elephant above the Kiattimukha. Other two stupas are made of brick with sandstone decorations such as lintel, gable frame and door frame. Behind the southern stupa is another brick stupa. Before all are two brick vihara surrounded with walls made from laterite and sandstone and 4 Gopuras (doors) at all directions. Brick vihara at north houses a carved lintel depicting Reclining Vishnu. The southern brick vihara houses a lintel depicting God Shiva and Goddess Uma seated on Nonthi Cow. Presently, this Khmer Ruins belongs to the division of Archeology, Fine Arts Department. Many antiques are found from this site such as lintels depicting Shiva God, Krissana God fighting Vattana Cow, Buddha statue in the attitude of meditation under naga, Buddha statue in attitude of meditation, and terra cotta Buddha images. By the style appearing on gables, lintels, and antique, particularly inscription at the doorframe of Sa Kamphaeng Yai Khmer Ruins, this ruins was probably build in the 11th Century with Bapuan Art style of Khmer. It was served as shrine for God Shiva before changing into Mahayana Buddhist temple in 13th Century. 

'''How to go there?'''
Prasat Hin Wat Sa Kamphaeng Yai is 26 kilometers from away Sisaket Province and 2 kilometres from Uthumphonphisai district, via highway 226.


'''References'''

http://www.teawmuangthai.com/sisaket/001/
 
http://guideubon.com/news/view.php?t=69&amp;s_id=18&amp;d_id=18
 
http://www.mistercleanweb.com/sisaket_station/sisaket-wat-srakhampheangyai.html
 
http://www.ezytrip.com/Thailand/th/NorthEast/SiSaKet/UthumphonPhisai/PrasatWatSaKamphaengYai/PrasatWatSaKamphaengYai.htm
 
http://www.hotelsguidethailand.com/travel/travel_detail.php?l=th&amp;code=1524</text>
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  <page>
    <title>Template:Userbox/doc</title>
    <ns>10</ns>
    <id>115360</id>
    <revision>
      <id>2810264</id>
      <parentid>2661309</parentid>
      <timestamp>2026-05-18T22:03:10Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <comment>+</comment>
      <origin>2810264</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="15750" sha1="9dtmtbdlkdd0e9p3k0fw5nfviz3d2ki" xml:space="preserve">{{Documentation subpage}}
{{Lua|Module:Userbox}}
{{TemplateStyles|Template:Userbox/styles.css}}
&lt;!-- Categories go at the bottom of this page and interwikis go in Wikidata. --&gt;

This template can be used to quickly create a [[Wikiversity:Userboxes|userbox]] for display on a user's [[Wikiversity:User pages|user page]] without having to know HTML or Wikitable syntax.

'''''[[WV:NFCC|Nonfree]] images must not be displayed in userboxes, and are subject to summary removal by any editor without any notice being required.'''''

== Sandbox reminder==
* Always practice or experiment in the [[Template:Userbox/sandbox]] or [[Template:Userbox/testcases]]
* Once you are satisfied: Copy your code!
* In your Browser's address bar, change &quot;sandbox&quot; or &quot;testcases&quot; to the name of your new Userbox.
** Example: 
** '''CHANGE''' [{{Fullurl:Template:Userbox/sandbox}} http://en.wikiversity.org/wiki/Template:Userbox/sandbox]&lt;!--Display http://, but allow possibility of https:// access.--&gt;
** '''TO''' [{{Fullurl:Template:Userbox/WhateverYourNewBoxNameIs}} https://en.wikiversity.org/wiki/Template:Userbox/WhateverYourNewBoxNameIs]
** If the name of your new Userbox is taken, create a different name.
* You will be prompted to Start or Create your new Template Userbox!
* Paste your code into the space provided.

== Usage ==
&lt;!-- Abstract usage of the template, one variable per row. --&gt;
&lt;syntaxhighlight lang=&quot;wikitext&quot; style=&quot;overflow: auto&quot;&gt;
{{userbox
| bodyclass     = &lt;!--Adds an HTML class attribute to the entire template's HTML table, to allow for styling, emission of microformats, etc.--&gt;
| border-c      = &lt;!--border color (default=id-c or #999999)--&gt;
| border-s      = &lt;!--border width in pixels (default=1)--&gt;
| float         = &lt;!--left|right|none (default=left)--&gt;
| id            = &lt;!--id image or text (image size should normally not exceed 90x45px)--&gt;
| id-a          = &lt;!--id horizontal alignment left/center/right/justify (default=center)--&gt;
| id-c          = &lt;!--id background color (default=#DDDDDD)--&gt;
| id-fc         = &lt;!--id font color (default=info-fc or black)--&gt;
| id-h          = &lt;!--id box height in pixels (default=45)--&gt;
| id-lh         = &lt;!--id line height (default=1.25em)--&gt;
| id-op         = &lt;!--id other CSS parameters--&gt;
| id-p          = &lt;!--id cell padding (default=0 1px 0 0)--&gt;
| id-s          = &lt;!--id text size in points (default=14)--&gt;
| id-w          = &lt;!--id box width in pixels (default=45)--&gt;
| info-class    = &lt;!--Adds an HTML class attribute to the &quot;info&quot; HTML table-row, to allow for styling, emission of microformats, etc.--&gt;
| info          = &lt;!--info text or image--&gt;
| info-a        = &lt;!--info horizontal alignment left/center/right/justify (default=left)--&gt;
| info-c        = &lt;!--info background color (default=#EEEEEE)--&gt;
| info-fc       = &lt;!--info font color (default=black)--&gt;
| info-lh       = &lt;!--info line height (default=1.25em)--&gt;
| info-op       = &lt;!--info other CSS parameters--&gt;
| info-p        = &lt;!--info padding (default=0 4px 0 4px)--&gt;
| info-s        = &lt;!--info text size in points (default=8)--&gt;
| nocat         = &lt;!--block page category declarations; see [[WP:NOCAT]] (default=false)--&gt;
| usercategory  = &lt;!--user category (optional, unlinked and without the &quot;Category:&quot; part)--&gt;
| usercategory2 = &lt;!--user category (optional)--&gt;
| usercategory3 = &lt;!--user category (optional)--&gt;
| usercategory4 = &lt;!--user category (optional)--&gt;
| usercategory5 = &lt;!--user category (optional)--&gt;
}}
&lt;/syntaxhighlight&gt;
* All parameters are optional.
* Images should normally be scaled to x45px or less.
&lt;!-- Explain what this template's parameters do -- if no params, delete the definition. --&gt;

Most HTML-based tables use only a handful of these attributes. The following subset can be used to quickly convert an HTML userbox into the format used here:

&lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;
{{userbox
| border-c = 
| id       = 
| id-c     = 
| id-fc    = 
| id-s     = 
| info     = 
| info-c   = 
| info-fc  = 
| info-lh  = 
| info-s   = 
}}&lt;/syntaxhighlight&gt;

== Examples ==
{|
! style=&quot;width: 300px;&quot; | Code
! Result
|-
| &lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;{{userbox
| border-c      = #aaffaa
| border-s      = 2
| id            = foo
| id-c          = #ffffee
| id-s          = 20
| info          = ''foo bar''
| info-c        = #ffeeff
| info-s        = 12
}}&lt;/syntaxhighlight&gt; || {{userbox|id=foo|id-s=20|id-c=#ffffee|info=''foo bar''|info-c=#ffeeff|info-s=12|border-c=#aaffaa|border-s=2}}
|-
| colspan=&quot;2&quot;| Below example shows the default appearance of a userbox, which is (much) higher than the 45px.&lt;br&gt;Compare the height of the one below with the above userbox.
|-
| &lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;{{userbox
| border-c      = #aaffaa
| border-s      = 2
| id            = foo logo
| id-c          = #ffffee
| info          = ''We are trying to see 
default distance in between text 
lines, see the distance in 
between cell content and its border, 
and also see total height.''
| info-c        = #ffeeff
}}&lt;/syntaxhighlight&gt; || {{userbox|id=foo logo|id-c=#ffffee|info=''We are trying to see default distance in between text lines, see the distance in between cell content and its border, and also see total height.''|info-c=#ffeeff|border-c=#aaffaa|border-s=2}}
|-
| colspan=&quot;2&quot;| Below example shows how we can change that userbox and further specify parameters to bring down&lt;br&gt;the overall height of the userbox to the recommended height of 45px, even with four text lines.&lt;br&gt;Cell padding parameter &quot;''info-p''&quot; can also be set at &quot;''1pt 1pt 1pt 2pt''&quot;, or &quot;''1pt 2pt''&quot; for better appearance,&lt;br&gt;when there are 4 text lines.
|-
| &lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;{{userbox
| border-c      = #aaffaa
| border-s      = 1
| id            = foo logo
| id-c          = #ffffee
| id-lh         = 1.1em
| id-s          = 14
| info          = ''We have specified values 
to lessen the distance between 
text lines and padding space between 
cell content and its border.''
| info-c        = #ffeeff
| info-lh       = 1.05em
| info-p        = 1pt
| info-s        = 8
}}&lt;/syntaxhighlight&gt; || {{userbox|id=foo logo|id-s=14|id-lh=1.1em|id-c=#ffffee|info=''We have specified values to lessen the distance between text lines and padding space between cell content and its border.''|info-c=#ffeeff|info-s=8|info-p=1pt|info-lh=1.05em|border-c=#aaffaa|border-s=1}}
|-
| colspan=&quot;2&quot;| Below example is for advanced users, showing how we can specify other [[:w:Cascading Style Sheets|CSS]] properties,for example, &quot;''font-family''&quot;,&lt;br&gt;to change the font or &quot;''text-decoration''&quot; to add lines around the text. Below, on the right side are two userboxes:&lt;br&gt;the top one is displayed without either parameters; and the bottom userbox is displayed by using the below code,&lt;br&gt;with the help of the &quot;''info-op''&quot; field. 
|-
| &lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;{{userbox
| border-c      = #afa
| border-s      = 2
| id            = foo logo
| id-c          = #ffe
| id-lh         = 1.1em
| id-s          = 14
| info          = foo bar
| info-c        = #fef
| info-op       = font-family: 'Courier New', monospace; text-decoration: wavy overline green;
| info-s        = 14
}}&lt;/syntaxhighlight&gt; || colspan=&quot;2&quot;| {{Userbox|id=foo logo|id-s=14|id-lh=1.1em|id-c=#ffe|info=foo bar|info-c=#fef|info-s=14|border-c=#afa|border-s=2}} &lt;br style=&quot;clear:both&quot;&gt;&amp;#160;&lt;br /&gt; {{Userbox|id=foo logo|id-s=14|id-lh=1.1em|id-c=#ffe|info=foo bar|info-c=#fef|info-s=14|info-op=font-family: 'Courier New', monospace; text-decoration: wavy overline green;|border-c=#afa|border-s=2}}
|}

==Microformats==
; bodyclass : This parameter is inserted into the &quot;class&quot; attribute for the userbox as a whole.
; info-class : This parameter is inserted into the &quot;class&quot; attribute for the info component.

This template supports the addition of [[:w:microformat|microformat]] information. This is done by adding &quot;class&quot; attributes to various data cells, indicating what kind of information is contained within. To flag a userbox as containing [[:w:hCard|hCard]] information about a person, for example, add the following parameter:

&lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;
| bodyclass     = vcard
&lt;/syntaxhighlight&gt;

''or''

&lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;
| info-class    = vcard
&lt;/syntaxhighlight&gt;

''then'' (for example):

&lt;syntaxhighlight lang=&quot;wikitext&quot;&gt;&lt;nowiki&gt;
| title         = …the books of &lt;span class=&quot;fn&quot;&gt;[[Iain Banks]]&lt;/span&gt;
&lt;/nowiki&gt;&lt;/syntaxhighlight&gt;

...and so forth.

Examples include:

* &lt;code&gt;{{tlu|User:UBX/Iain Banks}}&lt;/code&gt; - person
* {{tlx|User Microformats}} - group (WikiProject Microformats)
* {{tlx|User Brum}} - place (Birmingham)

See [[Wikipedia:WikiProject Microformats]] for more information on adding microformat information to Wikipedia.

== Template Data ==
{{TemplateData header}}

&lt;TemplateData&gt;{
	&quot;description&quot;: &quot;This template can be used to quickly create a userbox for display on a user's user page without having to know HTML or Wikitable syntax.&quot;,
	&quot;params&quot;: {
		&quot;bodyclass&quot;: {
			&quot;label&quot;: &quot;Body class&quot;,
			&quot;description&quot;: &quot;Adds an HTML class attribute to the entire template's HTML table, to allow for styling, emission of microformats, etc.&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;required&quot;: false
		},
		&quot;border-c&quot;: {
			&quot;label&quot;: &quot;Border color&quot;,
			&quot;description&quot;: &quot;Color of the outer border&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;default&quot;: &quot;#999&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;border-color&quot;
			]
		},
		&quot;border-s&quot;: {
			&quot;label&quot;: &quot;Border width&quot;,
			&quot;description&quot;: &quot;border width in pixels&quot;,
			&quot;type&quot;: &quot;number&quot;,
			&quot;default&quot;: &quot;1&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;border-width&quot;
			]
		},
		&quot;float&quot;: {
			&quot;label&quot;: &quot;Float&quot;,
			&quot;description&quot;: &quot;left|right|none&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;default&quot;: &quot;left&quot;,
			&quot;required&quot;: false,
			&quot;suggestedvalues&quot;: [
				&quot;left&quot;,
				&quot;right&quot;,
				&quot;none&quot;
			]
		},
		&quot;id&quot;: {
			&quot;label&quot;: &quot;Logo&quot;,
			&quot;description&quot;: &quot;id image or text&quot;,
			&quot;type&quot;: &quot;content&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;3&quot;,
				&quot;logo&quot;
			],
			&quot;suggested&quot;: true
		},
		&quot;id-a&quot;: {
			&quot;label&quot;: &quot;Logo content horizontal alignment&quot;,
			&quot;description&quot;: &quot;Horizontal alignment of logo content; left/center/right/justify&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;default&quot;: &quot;center&quot;,
			&quot;required&quot;: false,
			&quot;suggestedvalues&quot;: [
				&quot;left&quot;,
				&quot;center&quot;,
				&quot;right&quot;,
				&quot;justify&quot;
			]
		},
		&quot;id-c&quot;: {
			&quot;label&quot;: &quot;id-c&quot;,
			&quot;description&quot;: &quot;Two-in-one alias for border color and logo background color. Lower priority than border-c and logo-background&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;1&quot;
			],
			&quot;example&quot;: &quot;#d0d0d0&quot;
		},
		&quot;id-fc&quot;: {
			&quot;label&quot;: &quot;Logo font color&quot;,
			&quot;description&quot;: &quot;Logo font color; if not specified, defaults to info font color&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;default&quot;: &quot;black&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;logo-color&quot;
			]
		},
		&quot;id-h&quot;: {
			&quot;label&quot;: &quot;Logo height&quot;,
			&quot;description&quot;: &quot;Logo box height in pixels&quot;,
			&quot;type&quot;: &quot;number&quot;,
			&quot;default&quot;: &quot;45&quot;,
			&quot;required&quot;: false,
			&quot;aliases&quot;: [
				&quot;logo-height&quot;
			]
		},
		&quot;id-lh&quot;: {
			&quot;label&quot;: &quot;Logo line height&quot;,
			&quot;description&quot;: &quot;Logo line height&quot;,
			&quot;type&quot;: &quot;string&quot;,
			&quot;default&quot;: &quot;1.25em&quot;,
			&quot;required&quot;: false,
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==See also==
{{UBT}}
&lt;includeonly&gt;{{Sandbox other||
&lt;!-- Categories go here and interwikis go in Wikidata. --&gt;
[[Category:Userboxes|*]]
[[Category:User namespace templates]]
[[Category:Wikiversity metatemplates]]
}}&lt;/includeonly&gt;</text>
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  <page>
    <title>Spiders</title>
    <ns>0</ns>
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    <revision>
      <id>2810361</id>
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        <username>Jtneill</username>
        <id>10242</id>
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      <comment>Add more specific category</comment>
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      <text bytes="4705" sha1="0j1hy62nf2uhisonsmzq6r1ubrstora" xml:space="preserve">Spiders are abundant terrestrial arthropods. Actually more than 40,000 species are known (World Spider Catalog, 2015). They produce venom for defense and prey capture and only a few species are dangerous for humans. They succeed in almost every terrestrial environment and are regulators of insect populations for their abundance (Haddad et al. 2004, Chatterjee et al. 2009). Spiders are very important in ecological studies as environment quality indicators and as biologic control agents in agroecosystems, therefore they are ideal organisms for biological monitoring (Pearce &amp; Venier 2006, Cristofoli et al. 2010). Almost all arachnids are good ecosystem degradation indicators, because they are very sensitive to environmental changes caused by human activity. They are closely associated with environmental conditions and vegetation. Most spiders have specific ecological requirements, making them useful indicators of spatial and temporal variation in terrestrial ecosystems (Pearce &amp; Venier 2006). They are important in trophic networks as predators, as well as because of their abundance, biomass and species diversity (Wise 1993, 2006). They feed on all kinds of invertebrates, especially insects, and some little vertebrates and they are eaten by birds, reptiles, amphibians and several groups of mammals.

=== Spiders in Agroecosystems ===
In the last decades there has been an important increase in the number of studies focusing on the use of spiders as biological control agents (Riechert and Lockley, 1984, Young and Edwards, 1990; Sunderland, 1999). They are highlighted for their abundance, biomass and species richness and for their participation in the control of phytophagous species, decomposition and pollination.

It has been mentioned that spiders in the field usually consume about one appropriate-sized insect per day (Nyffeler and Benz, 1987), however they will kill many more insects than they consume (Maupin and Riechert, 2001). In conjunction with other natural enemies (parasitoids, pathogens and other predators) spiders may tip the balance in biological control (Sunderland, 1999), particularly those species called “agrobiont” spiders by Luczak (1979). These spiders have life history characteristics that allow them to reach adulthood and reproduce during the main crop vegetation period, exhibiting high dominance in strong abiotically driven and frequently disturbed habitat types, like agroecosystems (Luczak, 1979, Nyffeler and Benz, 1987, Samu and Szinetár, 2002). 

== Subpages ==
{{Subpages/List}}

== See Also ==
* [[Topic:Arachnology]]

== References ==
* Chatterjee, S., Isaia, M. &amp; Venturino E. (2009). Spiders as biological controllers in the agroecosystem. Journal of Theoretical Biology, 258, 352–362.
* Cristofoli, S., Mahy, G., Kekenbosch, R. &amp; Lambeets, K. (2010). Spider communities as evaluation tools for wet heathland restoration. Ecological Indicators, 10, 773–780.
* Haddad, C. R., Louw, S. M. &amp; Dippenaar-Schoeman, A. S. (2004). An assessment of the biological control potential of Heliophanus pistaciae (Araneae: Salticidae) on Nysius natalensis (Hemiptera: Lygaeidae), a pest of pistachio nuts. Biological Control, 31, 83-90.
* Luczak, J. (1979). Spiders in agrocoenoses. Polish Ecological Studies, 5, 151-200. 
* Maupin, J. L. &amp; Riechert, S. E. (2001). Superfluous killing in spiders: a consequence of adaptation to food-limited environments? Behavioural Ecology, 12 (5), 569–576.
* Nyffeler, M. &amp; Benz, G. (1987). Spiders in natural pest control: a review. Journal of Applied Entomology, 103, 321-339.
* Pearce, J. L. &amp; Venier, L. A. (2006). The use of ground beetles (Coleoptera: Carabidae) and spiders (Araneae) as bioindicators of sustainable forest management: A review. Ecological Indicators, 6, 780–793.
* Riechert, S. E. &amp; Lockley, T. (1984). Spiders as biological control agents. Annual Review of Entomology, 29, 299-320.
* Samu, F. &amp; Szinetar, C. (2002). On the nature of agrobiont spiders. Journal of Arahnology, 30, 389- 402
* Sunderland, K. (1999). Mechanisms underlying the effects of spiders on pest populations. Journal of Arachnology, 27, 308-316.
* Wise, D. H. (1993). Spiders in ecological webs. Cambridge, University.
* Wise, D. H. (2006). Cannibalism, food limitation, intraspecific competition and the regulation of spider populations. Annual Review of Entomology, 51, 441-465.
* World Spider Catalog (2015). World Spider Catalog. Natural History Museum Bern, online at http://wsc.nmbe.ch, version 16.5, accessed on November 2015.
* Young, O. P. &amp; Edwards, G. B. (1990). Spiders in United States field crops and their potential affect on crop pests. Journal of Arachnology, 18, 1-29.

[[Category:Spiders| ]]</text>
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  <page>
    <title>Walsh permutation</title>
    <ns>0</ns>
    <id>118704</id>
    <revision>
      <id>2810402</id>
      <parentid>2745870</parentid>
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      <text bytes="8795" sha1="8is5jxqi9vylx3djjzguoby1387b7t6" xml:space="preserve">The term '''''Walsh permutation''''' was chosen by [[User:Watchduck|the author]] for permutations that permute [[w:Walsh function|Walsh functions]] into other Walsh functions.&lt;br&gt;
A Walsh permutation of degree ''n'' has length 2&lt;sup&gt;''n''&lt;/sup&gt;, and corresponds to an ''n''×''n'' matrix in the {{w|general linear group}} of degree ''n'' over the {{w|finite field}}.&lt;br&gt;
This matrix will sometimes be called ''compression matrix'', and its expression as a vector of ''n'' integers &lt;math&gt;\in \{ 1, ... , 2^n-1\}&lt;/math&gt; will be called ''compression vector''.

There are {{oeis|A002884}}(''n'') Walsh permutations of degree ''n''.

[[File:Walsh permutation wp(8,12,2,3) * wp(6,9,1,2).svg|frame|center|Product of two Walsh permutations: ''wp''( 8,12, 2, 3) * ''wp''( 6, 9, 1, 2) = ''wp''(14,11, 8,12)&lt;br&gt;&lt;small&gt;(the product of two Walsh permutations [[Walsh permutation; bent functions#Some products|related to bent functions]])&lt;/small&gt;]]
[[File:Walsh permutation wp(8,12,2,3) * wp(6,9,1,2) small.svg|frame|center|Product of the compression matrices]]

Not all vectors &lt;math&gt;(v_1,...,v_n)&lt;/math&gt; with different elements &lt;math&gt;\in \{ 1, ... , 2^n-1\}&lt;/math&gt; correspond to Walsh permutations, as the following example shows:

{| class=&quot;collapsible collapsed&quot; style=&quot;width: 100%; border: 1px solid #cccccc;&quot;
! bgcolor=&quot;#dddddd&quot;|No Walsh permutation ''wp''(1,2,3,4)
|-
|

{| style=&quot;width:100%&quot;
|-
|[[File:No Walsh permutation 1 2 3 4.svg|thumb|350px|center|This is not a permutation of 16 elements,&lt;br&gt;so there is no Walsh permutation &lt;math&gt;wp(1,2,3,4)&lt;/math&gt;.]]
|
The corresponding compression matrix would be&lt;br&gt;
[[File:No Walsh permutation 1 2 3 4 small.svg]]&lt;br&gt;which has determinant 0.
|}

|}

==Notation warning==

This article and its subpages currently use two different ways to name and display Walsh permutations. In older files the direction of the compression vector is horizontal, and the permutation is vertical. In new files both compression vector and permutation are horizontal. The old files are gradually replaced. [[3-bit Walsh permutation]] already uses new files.

{| style=&quot;width: 100%;&quot;
|- style=&quot;vertical-align: top;&quot;
| [[File:Walsh permutation 135.svg|thumb|left|x300px|''wp''(1, 3, 5) '''new''' &lt;br&gt;&lt;small&gt;= wp(7, 2, 4) old&lt;/small&gt;]]
| [[File:Walsh permutation 135 Walsh.svg|thumb|center|270px|Ambiguity of ''wp''(1, 3, 5)&lt;br&gt;&lt;br&gt;'''new''': horizontal (0, 1, 3, 2, 5, 4, 6, 7)&lt;br&gt;'''old''': vertical (0, 7, 2, 5, 4, 3, 6, 1)]]
| [[File:Walsh permutation wp( 1,14, 4, 8).svg|thumb|right|x300px|''wp''(1, 14, 4, 8) '''old'''&lt;br&gt;&lt;small&gt;= ''wp''(1, 2, 6, 10) new&lt;/small&gt;]]
|}

=={{rdrdo}} [[Walsh permutation/sequences|Sequences]]==

There are mainly two ways to express the number of Walsh permutations as a product:
* number of bases of an ''n''-dimensional vector space over GF(2) &amp;nbsp; · &amp;nbsp; ''n''!
* product of the first ''n'' powers of two {1, 2, 4, 8, ...} &amp;nbsp; · &amp;nbsp; product of the first ''n'' Mersenne numbers {1, 3, 7, 15, ...} 

{{Walsh permutation/sequences/A002884}}

==[[Schoute permutation]]==
[[File:Walsh permutation wp( 2, 1, 8, 4).svg|thumb|]]
When a simple permutation of n elements is applied on the binary digits of numbers from 0 to 2&lt;sup&gt;n&lt;/sup&gt;-1 the result is a permutation of the numbers from 0 to 2&lt;sup&gt;n&lt;/sup&gt;-1.&lt;br&gt;
The example on the right corresponds to the simple permutation that swaps the first two and the last two digits of the 4-bit binary numbers.&lt;br&gt;
Probably the most important bit permutation is the [[w:Bit-reversal permutation|bit-reversal permutation]].


&lt;br style=&quot;clear: both;&quot;&gt;
=={{rdrdo}} [[Walsh permutation; nimber multiplication|Nimber multiplication]]==
[[File:Nimbers 0...15 multiplication.svg|thumb|]]
The rows of each [[w:Nimber|nimber]] multiplication table are Walsh permutations (except row 0).&lt;br&gt;
They are not only closed under multiplication (function composition), but even under addition (bitwise XOR).
&lt;br style=&quot;clear: both;&quot;&gt;

=={{Rdrdo}} [[Gray code permutation powers]]==
[[File:Cyclic group Z4; Cayley table; powers of Gray code permutation (small).svg|thumb|Cayley table with compression matrices]]
Powers of the [[w:Gray code|Gray code]] permutation have very simple compression matrices and vectors.&lt;br&gt;
In each vector all entries follow from the first one, and the first entries follow from the rows of the [[w:Sierpinski triangle|Sierpinski triangle]].

See also [[Algebraic normal form]].

&lt;br style=&quot;clear: both;&quot;&gt;

=={{rdrdo}} [[Walsh permutation; sequency ordered Walsh matrix|Sequency ordered Walsh matrix]]==
[[File:Natural and sequency ordered Walsh 16.svg|thumb|]]
The permutation that changes the natural ordered into the sequency ordered [[w:Walsh matrix|Walsh matrix]] is the product of the [[w:Gray code|Gray code]] permutation and the [[w:Bit-reversal permutation|bit-reversal permutation]].
&lt;br style=&quot;clear: both;&quot;&gt;

=={{rdrdo}} [[Walsh permutation; bent functions|Bent functions]]==
[[File:From bent function 0111 1000 1000 1000 to wp( 2, 1, 8, 4).svg|thumb|500px|right|From 0111 1000 1000 1000 to ''wp''(2,1,8,4)]]
Each [[w:Bent function|bent function]] corresponds to a Walsh permutation.&lt;br&gt;
This can be seen when all rows of its [[Equivalence classes of Boolean functions#sec|''sec'']] matrix are [[w:Exclusive or|XOR]]&lt;nowiki&gt;ed&lt;/nowiki&gt; with the function itself (second step in the example on the right).
&lt;br style=&quot;clear: both;&quot;&gt;

=={{rdrdo}} [[Order 4 magic squares; Walsh permutations|Magic squares]]==
{| align=&quot;right&quot;
|style=&quot;vertical-align:top;&quot;|[[File:Multigrade operator XOR diamond.svg|thumb|Multigrade operator [[w:Exclusive or|XOR]]&lt;br&gt;These matrices are found in the dual matrices of the magic squares.]]
|style=&quot;vertical-align:top;&quot;|[[File:Square 00-11-07-12---14-05-09-02---13-06-10-01---03-08-04-15.svg|thumb|The [[w:Melencolia I|Melencolia]] square, corresponding to ''wp''(11, 7,14,13)]]
|}
There are 24*9=216 Walsh permutations that correspond to magic squares of order 4.&lt;br&gt;
One my say that only 6 of them are essentially different.
&lt;br style=&quot;clear: both;&quot;&gt;

=={{rdrdo}} [[Walsh permutation; inversions|Inversions]]==
{| style=&quot;width:550px&quot; align=&quot;right&quot;
|style=&quot;vertical-align:top;&quot;|[[File:Inversion set 16; Walsh (15, 14, 13, 11).svg|thumb|center|140px|''wp''(13,11, 7,15)]]
|style=&quot;vertical-align:top;&quot;|[[File:Inversion set 16; Walsh (14, 13, 11, 7).svg|thumb|center|140px|''wp''(14,13,11, 7)]]
|style=&quot;vertical-align:top;&quot;|[[File:Inversion set 16; Walsh (4, 8, 1, 2).svg|thumb|center|140px|''wp''( 4, 8, 1, 2)]]
|}
Some inversion sets of Walsh permutations are very regular.&lt;br&gt;
E.g. there are 2&lt;sup&gt;n&lt;/sup&gt;-1 n-bit Walsh permutations with horizontally striped inversion sets (like the left one of the examples).&lt;br&gt;
The pattern of the stripes is that of Walsh functions.
&lt;br style=&quot;clear: both;&quot;&gt;

=={{Rdrdo}} [[2-bit Walsh permutation|2-bit]]==
{{multiple image
 | align = right  | total_width = 300
 | image1 = Walsh permutation 31.svg
 | image2 = Walsh permutation 31 transform.svg
 | footer = ''wp''(3, 1)
}}
The {{oeis|A002884}}(2) = 6 2-bit Walsh permutations form [[w:General linear group|general linear group]] GL(2,2), which is also the [[w:Symmetric group|symmetric group]] [[w:Dihedral group of order 6|S&lt;sub&gt;3&lt;/sub&gt;]].
&lt;br style=&quot;clear: both;&quot;&gt;

=={{Rdrdo}} [[3-bit Walsh permutation|3-bit]]==
{{multiple image
 | align = right
 | image1 = Walsh permutation 357 Fano red.svg
 | width1 = 200
 | caption1 = ''wp''(5,3,7) as a permutation of the [[w:Fano plane|Fano plane]]
 | image2 =
 | width2 = 457
 | caption2 = Connection between permutation and matrix patterns
 | footer = ''wp''(5,3,7) has permutation pattern 73, matrix pattern 74.b, and its inversion set is [[Walsh_permutation;_inversions#Stripes|striped]].
}}
The {{oeis|A002884}}(3) = 168 3-bit Walsh permutations correspond to the [[w:Collineation|collineations]] of the [[w:Fano plane|Fano plane]].

[http://pastebin.com/Uw3P9rZd Compression vectors], [http://pastebin.com/bJTXnBwY Permutations]

&lt;br style=&quot;clear: both;&quot;&gt;

==4-bit==
There are {{oeis|A002884}}(4) = 20160 4-bit Walsh permutations.

[http://pastebin.com/96smcp6G Compression vectors]

=={{anchor|splice}}Relationship to [[Seal (discrete mathematics)|seals]]==

The fixed points of an ''n''-bit Walsh permutation are [[Seal (discrete mathematics)|seals]] of arity ''n''.&lt;br&gt;

The '''splice''' of a Walsh permutation is the XOR of its values and indices. It is a set partition.&lt;br&gt;
The set of its values also describes a seal.

{{multiple image
 | align = right
 | image1 = Walsh permutation 564.svg
 | width1 = 200
 | caption1 = ''wp''(5,6,4)
 | image2 = Setpart of size 8; intpart 2·4; blocks (0, 3, 4, 7), (1, 2, 5, 6).svg
 | width = 150
 | caption2 = seal &lt;code&gt;1001 1001&lt;/code&gt; (compare matrix 12 in [[:File:Z2%5E4;_subgroups_list.svg#File|this list]])
 | footer = 
}}


[[Category:Walsh permutation]]</text>
      <sha1>8is5jxqi9vylx3djjzguoby1387b7t6</sha1>
    </revision>
  </page>
  <page>
    <title>VHDL programming in plain view</title>
    <ns>0</ns>
    <id>121359</id>
    <revision>
      <id>2810136</id>
      <parentid>2809666</parentid>
      <timestamp>2026-05-18T18:21:45Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Data */</comment>
      <origin>2810136</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2278" sha1="p8imkxbte832aipwrduvzdcycw3pyrw" xml:space="preserve">&lt;!----------------------------------------------------------------------&gt;

== Flip Flop and Latch ==
* FFLatch.Overview.1.A ([[Media:FFLatch.Overview.1.A.20111103.pdf|pdf]])
* Counter.74LS193.1.A ([[Media:Counter.74LS193.1.A.20111108.pdf|pdf]])
* Clock.Overview.1.A ([[Media:Clock.Overview.1.A.20111108.pdf|pdf]])
* Function.Overview.1.A ([[Media:Function.Overview.1.A.20111201.pdf|pdf]])
&lt;br&gt; 

== Versions of VHDL ==
* VHDL Versions ([[Media:VHDL.1.A.Versions.20120619.pdf|pdf]])
* VHDL Libraries ([[Media:VHDL.1.A.Libraries.20140219.pdf|pdf]])
&lt;br&gt;

== Basic Features of VHDL ==
==== Data ====
* Data Objects ([[Media:Data.Object.1A.20260518.pdf|A]], [[Media:Data.Object.1B.20260512.pdf|B]])
* Data Types ([[Media:Data.Type.2A.20260512.pdf|A]], [[Media:Data.Type.2B.20260512.pdf|B]])
* Packages ([[Media:Data.Package.3A.20251206.pdf|pdf]])
* Signal Types ([[Media:Signal.Type.1A.20250614.pdf|pdf]])
* Attributes ([[Media:Data.4.A.Attribute.20251021.pdf|pdf]])
&lt;br&gt;

==== Signals &amp; Variables ====
* Signals &amp; Variables ([[Media:Signal.1A.SigVar.20250614.pdf|pdf]])
* Sequential Signal Assignments ([[Media:Signal.4A.Sequential.20250612.pdf|pdf]])
* Concurrent &amp; Sequential Signal Assignments ([[Media:Signal.1.A.ConSeq.20120611.pdf|pdf]])
* Inertial &amp; Transport Delay Models ([[Media:Signal.2.A.InertTrans.20120704.pdf|pdf]])
* Simulation &amp; Synthesis ([[Media:Signal.3.A.SimSyn.20120504.pdf|pdf]])


&lt;br&gt;

==== Structure ====
* Component ([[Media:Struct.1.A.Component.20120804.pdf|pdf]])
* Configuration ([[Media:Struct.1.A.Configuration.20121003.pdf|pdf]])
* Generic ([[Media:Struct.1.A.Generic.20120802.pdf|pdf]])
&lt;/br&gt;

==== Entity and Architecture ====

&lt;br&gt; 
==== Block Statement ====

&lt;br&gt; 
==== Process Statement ====

&lt;br&gt;
==== Operators ====

&lt;br&gt;
==== Assignment Statement ====

&lt;br&gt; 
==== Concurrent Statement ====

&lt;br&gt; 
==== Sequential Control Statement ====

&lt;br&gt;
==== Function ====
* Function.1.A Usage ([[Media:Function.1.A.Usage.20120611.pdf|pdf]])
* Function.2.A Conversion Function ([[Media:Function.2.A.Conversion.pdf|pdf]])
* Function.3.A Resolution Function ([[Media:Function.3.A.Resolution.pdf|pdf]])

&lt;br&gt;
==== Procedure ====


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

[[Category:VHDL]]
[[Category:FPGA]]</text>
      <sha1>p8imkxbte832aipwrduvzdcycw3pyrw</sha1>
    </revision>
    <revision>
      <id>2810138</id>
      <parentid>2810136</parentid>
      <timestamp>2026-05-18T18:33:03Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Data */</comment>
      <origin>2810138</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2278" sha1="6hrrhpwtqhk0k3hejwkidwjf1jph82o" xml:space="preserve">&lt;!----------------------------------------------------------------------&gt;

== Flip Flop and Latch ==
* FFLatch.Overview.1.A ([[Media:FFLatch.Overview.1.A.20111103.pdf|pdf]])
* Counter.74LS193.1.A ([[Media:Counter.74LS193.1.A.20111108.pdf|pdf]])
* Clock.Overview.1.A ([[Media:Clock.Overview.1.A.20111108.pdf|pdf]])
* Function.Overview.1.A ([[Media:Function.Overview.1.A.20111201.pdf|pdf]])
&lt;br&gt; 

== Versions of VHDL ==
* VHDL Versions ([[Media:VHDL.1.A.Versions.20120619.pdf|pdf]])
* VHDL Libraries ([[Media:VHDL.1.A.Libraries.20140219.pdf|pdf]])
&lt;br&gt;

== Basic Features of VHDL ==
==== Data ====
* Data Objects ([[Media:Data.Object.1A.20260518.pdf|A]], [[Media:Data.Object.1B.20260518.pdf|B]])
* Data Types ([[Media:Data.Type.2A.20260512.pdf|A]], [[Media:Data.Type.2B.20260512.pdf|B]])
* Packages ([[Media:Data.Package.3A.20251206.pdf|pdf]])
* Signal Types ([[Media:Signal.Type.1A.20250614.pdf|pdf]])
* Attributes ([[Media:Data.4.A.Attribute.20251021.pdf|pdf]])
&lt;br&gt;

==== Signals &amp; Variables ====
* Signals &amp; Variables ([[Media:Signal.1A.SigVar.20250614.pdf|pdf]])
* Sequential Signal Assignments ([[Media:Signal.4A.Sequential.20250612.pdf|pdf]])
* Concurrent &amp; Sequential Signal Assignments ([[Media:Signal.1.A.ConSeq.20120611.pdf|pdf]])
* Inertial &amp; Transport Delay Models ([[Media:Signal.2.A.InertTrans.20120704.pdf|pdf]])
* Simulation &amp; Synthesis ([[Media:Signal.3.A.SimSyn.20120504.pdf|pdf]])


&lt;br&gt;

==== Structure ====
* Component ([[Media:Struct.1.A.Component.20120804.pdf|pdf]])
* Configuration ([[Media:Struct.1.A.Configuration.20121003.pdf|pdf]])
* Generic ([[Media:Struct.1.A.Generic.20120802.pdf|pdf]])
&lt;/br&gt;

==== Entity and Architecture ====

&lt;br&gt; 
==== Block Statement ====

&lt;br&gt; 
==== Process Statement ====

&lt;br&gt;
==== Operators ====

&lt;br&gt;
==== Assignment Statement ====

&lt;br&gt; 
==== Concurrent Statement ====

&lt;br&gt; 
==== Sequential Control Statement ====

&lt;br&gt;
==== Function ====
* Function.1.A Usage ([[Media:Function.1.A.Usage.20120611.pdf|pdf]])
* Function.2.A Conversion Function ([[Media:Function.2.A.Conversion.pdf|pdf]])
* Function.3.A Resolution Function ([[Media:Function.3.A.Resolution.pdf|pdf]])

&lt;br&gt;
==== Procedure ====


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

[[Category:VHDL]]
[[Category:FPGA]]</text>
      <sha1>6hrrhpwtqhk0k3hejwkidwjf1jph82o</sha1>
    </revision>
    <revision>
      <id>2810148</id>
      <parentid>2810138</parentid>
      <timestamp>2026-05-18T19:12:18Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Data */</comment>
      <origin>2810148</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2278" sha1="jatq43lionrxct7whqy844aq8k43hmv" xml:space="preserve">&lt;!----------------------------------------------------------------------&gt;

== Flip Flop and Latch ==
* FFLatch.Overview.1.A ([[Media:FFLatch.Overview.1.A.20111103.pdf|pdf]])
* Counter.74LS193.1.A ([[Media:Counter.74LS193.1.A.20111108.pdf|pdf]])
* Clock.Overview.1.A ([[Media:Clock.Overview.1.A.20111108.pdf|pdf]])
* Function.Overview.1.A ([[Media:Function.Overview.1.A.20111201.pdf|pdf]])
&lt;br&gt; 

== Versions of VHDL ==
* VHDL Versions ([[Media:VHDL.1.A.Versions.20120619.pdf|pdf]])
* VHDL Libraries ([[Media:VHDL.1.A.Libraries.20140219.pdf|pdf]])
&lt;br&gt;

== Basic Features of VHDL ==
==== Data ====
* Data Objects ([[Media:Data.Object.1A.20260518.pdf|A]], [[Media:Data.Object.1B.20260518.pdf|B]])
* Data Types ([[Media:Data.Type.2A.20260518.pdf|A]], [[Media:Data.Type.2B.20260512.pdf|B]])
* Packages ([[Media:Data.Package.3A.20251206.pdf|pdf]])
* Signal Types ([[Media:Signal.Type.1A.20250614.pdf|pdf]])
* Attributes ([[Media:Data.4.A.Attribute.20251021.pdf|pdf]])
&lt;br&gt;

==== Signals &amp; Variables ====
* Signals &amp; Variables ([[Media:Signal.1A.SigVar.20250614.pdf|pdf]])
* Sequential Signal Assignments ([[Media:Signal.4A.Sequential.20250612.pdf|pdf]])
* Concurrent &amp; Sequential Signal Assignments ([[Media:Signal.1.A.ConSeq.20120611.pdf|pdf]])
* Inertial &amp; Transport Delay Models ([[Media:Signal.2.A.InertTrans.20120704.pdf|pdf]])
* Simulation &amp; Synthesis ([[Media:Signal.3.A.SimSyn.20120504.pdf|pdf]])


&lt;br&gt;

==== Structure ====
* Component ([[Media:Struct.1.A.Component.20120804.pdf|pdf]])
* Configuration ([[Media:Struct.1.A.Configuration.20121003.pdf|pdf]])
* Generic ([[Media:Struct.1.A.Generic.20120802.pdf|pdf]])
&lt;/br&gt;

==== Entity and Architecture ====

&lt;br&gt; 
==== Block Statement ====

&lt;br&gt; 
==== Process Statement ====

&lt;br&gt;
==== Operators ====

&lt;br&gt;
==== Assignment Statement ====

&lt;br&gt; 
==== Concurrent Statement ====

&lt;br&gt; 
==== Sequential Control Statement ====

&lt;br&gt;
==== Function ====
* Function.1.A Usage ([[Media:Function.1.A.Usage.20120611.pdf|pdf]])
* Function.2.A Conversion Function ([[Media:Function.2.A.Conversion.pdf|pdf]])
* Function.3.A Resolution Function ([[Media:Function.3.A.Resolution.pdf|pdf]])

&lt;br&gt;
==== Procedure ====


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

[[Category:VHDL]]
[[Category:FPGA]]</text>
      <sha1>jatq43lionrxct7whqy844aq8k43hmv</sha1>
    </revision>
    <revision>
      <id>2810154</id>
      <parentid>2810148</parentid>
      <timestamp>2026-05-18T19:30:52Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Data */</comment>
      <origin>2810154</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2278" sha1="jfmkngq6pxa9lsearo628n0gy4yx4yv" xml:space="preserve">&lt;!----------------------------------------------------------------------&gt;

== Flip Flop and Latch ==
* FFLatch.Overview.1.A ([[Media:FFLatch.Overview.1.A.20111103.pdf|pdf]])
* Counter.74LS193.1.A ([[Media:Counter.74LS193.1.A.20111108.pdf|pdf]])
* Clock.Overview.1.A ([[Media:Clock.Overview.1.A.20111108.pdf|pdf]])
* Function.Overview.1.A ([[Media:Function.Overview.1.A.20111201.pdf|pdf]])
&lt;br&gt; 

== Versions of VHDL ==
* VHDL Versions ([[Media:VHDL.1.A.Versions.20120619.pdf|pdf]])
* VHDL Libraries ([[Media:VHDL.1.A.Libraries.20140219.pdf|pdf]])
&lt;br&gt;

== Basic Features of VHDL ==
==== Data ====
* Data Objects ([[Media:Data.Object.1A.20260518.pdf|A]], [[Media:Data.Object.1B.20260518.pdf|B]])
* Data Types ([[Media:Data.Type.2A.20260518.pdf|A]], [[Media:Data.Type.2B.20260518.pdf|B]])
* Packages ([[Media:Data.Package.3A.20251206.pdf|pdf]])
* Signal Types ([[Media:Signal.Type.1A.20250614.pdf|pdf]])
* Attributes ([[Media:Data.4.A.Attribute.20251021.pdf|pdf]])
&lt;br&gt;

==== Signals &amp; Variables ====
* Signals &amp; Variables ([[Media:Signal.1A.SigVar.20250614.pdf|pdf]])
* Sequential Signal Assignments ([[Media:Signal.4A.Sequential.20250612.pdf|pdf]])
* Concurrent &amp; Sequential Signal Assignments ([[Media:Signal.1.A.ConSeq.20120611.pdf|pdf]])
* Inertial &amp; Transport Delay Models ([[Media:Signal.2.A.InertTrans.20120704.pdf|pdf]])
* Simulation &amp; Synthesis ([[Media:Signal.3.A.SimSyn.20120504.pdf|pdf]])


&lt;br&gt;

==== Structure ====
* Component ([[Media:Struct.1.A.Component.20120804.pdf|pdf]])
* Configuration ([[Media:Struct.1.A.Configuration.20121003.pdf|pdf]])
* Generic ([[Media:Struct.1.A.Generic.20120802.pdf|pdf]])
&lt;/br&gt;

==== Entity and Architecture ====

&lt;br&gt; 
==== Block Statement ====

&lt;br&gt; 
==== Process Statement ====

&lt;br&gt;
==== Operators ====

&lt;br&gt;
==== Assignment Statement ====

&lt;br&gt; 
==== Concurrent Statement ====

&lt;br&gt; 
==== Sequential Control Statement ====

&lt;br&gt;
==== Function ====
* Function.1.A Usage ([[Media:Function.1.A.Usage.20120611.pdf|pdf]])
* Function.2.A Conversion Function ([[Media:Function.2.A.Conversion.pdf|pdf]])
* Function.3.A Resolution Function ([[Media:Function.3.A.Resolution.pdf|pdf]])

&lt;br&gt;
==== Procedure ====


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

[[Category:VHDL]]
[[Category:FPGA]]</text>
      <sha1>jfmkngq6pxa9lsearo628n0gy4yx4yv</sha1>
    </revision>
  </page>
  <page>
    <title>Cricket</title>
    <ns>0</ns>
    <id>135139</id>
    <revision>
      <id>2810330</id>
      <parentid>2771911</parentid>
      <timestamp>2026-05-18T23:32:35Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>project box(es)</comment>
      <origin>2810330</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="788" sha1="dimehwp9q15vq452xy125u5x0uhe1wg" xml:space="preserve">{{sports}}
{{0% done}}
[[File:Pollock to Hussey.jpg|thumbnail|right|A bowler, bowling to a batsman.]]

'''[[w:Cricket|Cricket]]''' is an English sport which is very popular in [[Bangladesh]] [[Pakistan]], [[India]], [[Sri Lanka]], and many other countries of the world. Cricket is played by two teams and each team comprises of eleven players. There are strict rules and regulations which govern the domestic as well as international cricket. Cricket is playing very important roles in promoting trade and commerce both domestically and internationally. Cricket also serves as a means of diplomacy between various countries. Thus, cricket joins cricketing countries together to promote political ties also.
==Subpages==
*[[Cricket/Players]]
{{stub}}

{{wikibooks}}

[[Category:Cricket| ]]</text>
      <sha1>dimehwp9q15vq452xy125u5x0uhe1wg</sha1>
    </revision>
    <revision>
      <id>2810331</id>
      <parentid>2810330</parentid>
      <timestamp>2026-05-18T23:34:45Z</timestamp>
      <contributor>
        <username>BigKrow</username>
        <id>3069766</id>
      </contributor>
      <minor />
      <origin>2810331</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="788" sha1="7agl1ufldwhvzjph65wuocp94ow5scq" xml:space="preserve">{{sports}}
{{0% done}}
[[File:Pollock to Hussey.jpg|thumbnail|right|A bowler, bowling to a batsman.]]

'''[[w:Cricket|Cricket]]''' is an English sport which is very popular in [[Bangladesh]], [[Pakistan]], [[India]], [[Sri Lanka]], and many other countries of the world. Cricket is played by two teams, and each team comprises of eleven players. There are strict rules and regulations which govern the domestic as well as international cricket. Cricket is playing very important roles in promoting trade and commerce both domestically and internationally. Cricket also serves as a means of diplomacy between various countries. Thus, cricket joins cricketing countries together to promote political ties also.
==Subpages==
*[[Cricket/Players]]
{{stub}}

{{wikibooks}}

[[Category:Cricket]]</text>
      <sha1>7agl1ufldwhvzjph65wuocp94ow5scq</sha1>
    </revision>
  </page>
  <page>
    <title>Understanding Arithmetic Circuits</title>
    <ns>0</ns>
    <id>139384</id>
    <revision>
      <id>2810118</id>
      <parentid>2809644</parentid>
      <timestamp>2026-05-18T13:46:45Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Adder */</comment>
      <origin>2810118</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3135" sha1="aiatdj472eq48do97ahya1bmih2utt4" xml:space="preserve">
== Adder ==

* Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]]  )
 
{| class=&quot;wikitable&quot;
|-
!  Adder type      !! Overview !! Analysis !! VHDL Level Design  !! CMOS Level Design  
|-
| '''1. Ripple Carry Adder'''
|| [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]||
|| [[Media:Adder.rca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]]
|-
| '''2. Carry Lookahead Adder'''
|| [[Media:VLSI.Arith.1.A.CLA.20260109.pdf|org]], [[Media:VLSI.Arith.2A.CLA.20260518.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260518.pdf|B]] ||
|| [[Media:Adder.cla.20140313.pdf|pdf]]||
|-
| '''3. Carry Save Adder''' 
|| [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]||
|| ||
|-
|| '''4. Carry Select Adder''' 
|| [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]||
|| || 
|-
|| '''5. Carry Skip Adder'''
|| [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]||
|| 
|| [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]]
|- 
|| '''6. Carry Chain Adder'''
|| [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]||
|| [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]],  [[Media:Adder.cca.20140313.pdf|pdf]]
|| [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]]
|- 
|| '''7. Kogge-Stone Adder'''
|| [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]||
|| [[Media:Adder.ksa.20140409.pdf|pdf]]||
|-
|| '''8. Prefix Adder'''
|| [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]||
|| || 
|-
|| '''9.1 Variable Block Adder'''
|| [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]||
|| || 
|-
|| '''9.2 Multi-Level Variable Block Adder'''
|| [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]||
|| || 
|}
&lt;/br&gt;
 
=== Adder Architectures Suitable for FPGA === 
* FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]])
* FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]])
* FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]])
* FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]])
* Carry-Skip Adder
&lt;/br&gt;

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

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

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

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

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

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

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

[[Category:Digital Circuit Design]]
[[Category:FPGA]]</text>
      <sha1>aiatdj472eq48do97ahya1bmih2utt4</sha1>
    </revision>
  </page>
  <page>
    <title>Jump models in financial modelling</title>
    <ns>0</ns>
    <id>140390</id>
    <revision>
      <id>2810404</id>
      <parentid>2777309</parentid>
      <timestamp>2026-05-19T11:31:46Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>project box(es)</comment>
      <origin>2810404</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="13530" sha1="ig5hjkh5wplmd38wwfed9b0c511r9kq" xml:space="preserve">{{finance}}
{{mathematics}}
== Introduction ==

This is an outline of a seminar's contents. 

The main reference for the seminar is 
Rama Cont and Tankov&lt;ref name=&quot;Cont:Tankov:2012&quot; /&gt;. Purely mathematical texts on the same subject are 
Protter&lt;ref name=&quot;Protter2005&quot; /&gt; and Jacod and 
[[Wikipedia:Shiryaev|Shiryaev]]&lt;ref name=&quot;JacodShiryaev1987&quot;/&gt;. Texts being more devoted to finance are Shreve&lt;ref name=&quot;Shreve2004&quot;/&gt; and [[Wikipedia:Shiryaev|Shiryaev]]&lt;ref name=&quot;Shiryaev1999&quot;/&gt;.

=== Home reading ===

Rama Cont and Tankov&lt;ref name=&quot;Cont:Tankov:2012&quot;/&gt;: Chapter 1 and the introduction of each Chapter 2--15.

Protter&lt;ref name=&quot;Protter2005&quot;/&gt;: Chapter I, in particular section 4.

=== Prior knowledge ===

* [[Wikipedia:Measure_%28mathematics%29|measures, measurable functions]] - [[Wikipedia:Radon_nikodym|Radon Nikodym theorem]] - [[Wikipedia:Random_variables|random variables]] - [[Wikipedia:Characteristic_function_%28probability_theory%29|characteristic functions (Fourier transforms), how to find moments from characteristic functions]] - [[Wikipedia:Generating_function|moment generating functions (how to find moments from characteristic functions)]]
	
* special distributions (exponential - gamma - Gaussian)
	
* convergence of random variables (almost sure, in probability, in distribution)
	
* stochastic process - cadlag and caglad - filtrations and histories - non-anticipating (adapted) - stopping time - martingale - optional sampling (stopping) theorem
	
* Levy process - characterization of continuous Levy processes -Poisson process - compensated Poisson process - counting process - compound Poisson process - characteristic function of a compound Poisson process

== Examples of Levy processes ==

=== Concepts and facts ===

* point processes - marked point processes - characterization of Poisson and compound Poisson processes (without proof)
* jump diffusion - Levy measure of jump diffusion - Fourier transform of jump diffusion
* infinitely divisible distribution - convolution semigroups - Levy processes have infinitely divisible distributions - examples (Gaussian, Poisson, compound Poisson, Gamma, Cauchy)
* for every infinitely divisible distribution there is a Levy process (without proof)
* Fourier transform of Levy processes &lt;math&gt;\phi_t(u&lt;/math&gt;) - zeros of &lt;math&gt;\phi_t(u)&lt;/math&gt; - dependence of &lt;math&gt;t&lt;/math&gt; - examples (Gaussian, Poisson, compound Poisson, Gamma, Cauchy)
* Gamma process as limit of compound Poisson processes (via Fourier transforms) - limit behaviour of the Levy measures - Gamma process is FV-process - Levy measure of Gamma process - order of singularity at zero
* Cauchy process as limit of compound Poisson processes (via Fourier transforms) - limit behaviour of the Levy measures - Levy measure of Cauchy process - order of singularity at zero

=== Review questions ===

# Explain the notions of a point process and a marked point process.
# Which Levy processes can be characterized by path properties ?
# Which path properties characterize special Levy processes ?
# What are jump diffusions ? Give the Fourier transform of jump diffusions.
# Explain the notion of infinitely divisible distributions. What is the relation between infinitely divisble distributions and Levy processes ?
# Explain the Gamma process and its Fourier transform.
# Describe, how a Gamma process can be approximated by jump diffusions. What does it tell us about small and large jumps ?
# Explain the Cauchy process and its Fourier transform.
# Describe, how a Cauchy process can be approximated by jump diffusions. What does it tell us about small and large jumps ?
# Which compound Poisson processes can be written as a linear combination of independent Poisson processes ?
\end{enumerate}

=== Problems ===

# Analyze the Levy processes with the following Fourier transforms (expectation, variance, path properties, decomposition as a jump diffusion, Levy measure, jump intensity, jump height distribution, martingale property (yes/no), compensator).
## &lt;math&gt;\log \phi_t(u)=t(-iu-5u^2+e^{2iu}+e^{-iu/2}-2)&lt;/math&gt;
## &lt;math&gt;\log \phi_t(u)=t(iu+3/2e^{2iu}+1/2e^{-iu/2}-2)&lt;/math&gt;
## &lt;math&gt;\log \phi_t(u)=t(iu-u^2)&lt;/math&gt;
## &lt;math&gt;\log \phi_t(u)=t(e^{3iu}-1-3iu)&lt;/math&gt;
# Find the Fourier transform of a jump diffusion with variance 2, jumping with intensity 3, having jump heights +1 and -1 with equal probability.
# Find the Fourier transform of a jump diffusion with variance 1, jumping with intensity 1, having jump heights uniformly distributed on &lt;math&gt;[-2,0]&lt;/math&gt;.
# Find the Levy measure of a sum of five independent Poisson processes with intensities &lt;math&gt;1, 2,\ldots, 5&lt;/math&gt;.
# Find the Levy measure of a linear combination of five independent Poisson processes with intensity 1 and weights &lt;math&gt;1,2,\ldots, 5&lt;/math&gt;.

=== Proofs ===

# Is every driftless (i.e. centered) process a martingale ? (Give a counter example for the general case. Prove it for processes with independent increments.)
# Any finite sum of independent Poisson processes is a Poisson process. Find the Levy measure.
# Any linear combination of independent Poisson processes is a compound Poisson process. Find the Levy measure.
# For every finite measure &lt;math&gt;\nu|\mathcal{B}(\mathbb{R})&lt;/math&gt; there is a compound Poisson process with Levy measure &lt;math&gt;\nu&lt;/math&gt;.
# Show that the characteristic function of a Levy process satisfies &lt;math&gt;\phi_t(u)=\exp(t\psi(u))&lt;/math&gt;.
# Let &lt;math&gt;(X_t)&lt;/math&gt; be a Levy process. Show that &lt;math&gt;Z_t=e^{iuX_t}/E(e^{iuX_t})&lt;/math&gt; is a martingale.

== Jump measures and decomposition of Levy processes ==

=== Concepts and facts ===

* Levy processes with uniformly bounded jumps have moments of all orders (without proof)
* counting measure of a finite set - representation of sums as integrals
* jump measure &lt;math&gt;N_t(B)&lt;/math&gt; of a cadlag process - jump heights in sets &lt;math&gt;B&lt;/math&gt; bounded away from zero - finiteness of the jump measure of a cadlag process
* properties of &lt;math&gt;B\mapsto N_t(B)&lt;/math&gt; - properties of &lt;math&gt;t\mapsto N_t(B)&lt;/math&gt;
* Poissonian jump measure (two properties) - Levy processes have Poissonian jump measures
* Levy measure of a Levy process - Levy measures are bounded on &lt;math&gt;(|x|\ge \epsilon)&lt;/math&gt;, \epsilon&gt;0
* &lt;math&gt;Z_t=\int_B f(x)\,N_t(dx)&lt;/math&gt; is a compound Poisson process for &lt;math&gt;\overline{B}\subseteq\mathbb{R}\setminus\{0\}&lt;/math&gt; - expectation and variance of &lt;math&gt;(Z_t)&lt;/math&gt; - Fourier transform of &lt;math&gt;(Z_t)&lt;/math&gt;
* elimination of big jumps from Levy processes - Levy processes are semimartingales
* moments of Levy processes and Levy measures
* relation between quadratic variation and the singularity of Levy measures
* decomposition of Levy processes (big jumps - continuous part - compensated small jumps) - relation to the Fourier transform - Levy-Khintchine formula - uniquenesss (without proof) - predictable characteristics &lt;math&gt;(a,\sigma^2,\nu)&lt;/math&gt; (w.r.t. a particular centering function &lt;math&gt;h(x)&lt;/math&gt;)
* characterization of FV-Levy processes (without proof)

=== Review questions ===

# How many jumps can occur on a single path of a stochastic process ?
# Explain, why the jump measure of a Levy process leads to Poisson processes.
# What is the Levy measure of a Levy process ?
# Explain the integral representation of sums of jump expressions.
# What is a Poissonian jump measure ? Why are the jump measures of Levy processes of Poissonian type ?
# How to extract big jumps from a stochastic process ?
# Refer the moment properties of integrals w.r.t. Poissonian jump measures.
# Discuss the properties of the singularity of a Levy measure.
# Describe the basic steps of the decomposition of a Levy process. What are the predictable characteristics ? What about uniqueness ?

=== Problems ===

# Let &lt;math&gt;(X_t)&lt;/math&gt; be a Levy process with Levy measure
## &lt;math&gt;\nu=2\epsilon_1+\epsilon_{-1}&lt;/math&gt;,
## &lt;math&gt;\nu(dx)=1_{[-1,1]}(x)\,dx&lt;/math&gt;.
# Find expectation and variance of
## &lt;math&gt;\sum_{s\le t} \Delta X_s\, 1_{(\Delta X_s&gt;1/2)}&lt;/math&gt;
## &lt;math&gt;\sum_{s\le t} (\Delta X_s)^2\, 1_{(\Delta X_s&lt;-1/2)}&lt;/math&gt;
# Find the moments and the Fourier transform of a Levy process with characteristics (let &lt;math&gt;h(x)=x\,1_{(|x|\le 1)}&lt;/math&gt;):
## &lt;math&gt;(-1,0,e^{-x}1_{(x&gt;0)}dx)&lt;/math&gt;
## &lt;math&gt;(0,1,x^{-1/2}1_{(x&gt;0)}dx)&lt;/math&gt;
## &lt;math&gt;(0,0,x^2e^{-x^2}dx)&lt;/math&gt;
## &lt;math&gt;(0,0,1/x^2e^{-x^2}dx)&lt;/math&gt;

=== Proofs ===

# Every Levy measure &lt;math&gt;\nu&lt;/math&gt; satisfies &lt;math&gt;\nu(|x|\ge 1)&lt;\infty&lt;/math&gt;.
# The jump measure of any Levy process is a Poisson jump measure.
# Every Levy process is a semimartingale.
# Let &lt;math&gt;(N_t(B))&lt;/math&gt; be a Poisson jump measure and let &lt;math&gt;\nu(B)&lt;/math&gt; be its Levy measure. Prove the formulas:
## &lt;math&gt;E\Big(\int f(x)\, N_t(dx)\Big)=t\int f(x)\,\nu(dx)&lt;/math&gt; 
## &lt;math&gt;V\Big(\int f(x)\, N_t(dx)\Big)=t\int f^2(x)\,\nu(dx)&lt;/math&gt; 
## &lt;math&gt;E\Big(\exp\Big(\int f(x)\, N_t(dx))\Big)\Big)=\exp\Big(t\int(e^{f(x)}-1)\,\nu(dx)\Big)&lt;/math&gt;
# Every Levy measure &lt;math&gt;\nu&lt;/math&gt; satisfies &lt;math&gt;\int_{|x|\le 1} x^2 \,\nu(dx) &lt;\infty&lt;/math&gt;.

== Stochastic analysis for processes with jumps ==

=== Concepts and facts ===

* general Ito-formula - proof by induction
* Ito-formula for processes with isolated jumps - direct proof
* solving &lt;math&gt;dS_t=S_{t-}\,dX_t&lt;/math&gt; when &lt;math&gt;(X_t)&lt;/math&gt; is a semimartingale with isolated jumps
* Poisson process &lt;math&gt;N_t&lt;/math&gt;: - solving &lt;math&gt;dS_t=S_{t-}\,dN_t&lt;/math&gt; - solving &lt;math&gt;dS_t=\alpha S_{t-}\,dt+\sigma S_{t-}\,dN_t&lt;/math&gt; - martingale solutions


=== Review questions ===

# Explain the solution of &lt;math&gt;dS_t=S_{t-}\,dX_t&lt;/math&gt; when &lt;math&gt;(X_t)&lt;/math&gt; has isolated jumps.
# What is the stochastic exponential of a compound Poisson process ?

=== Problems ===

# Find the solution of &lt;math&gt;dS_t=-S_{t-}dt+2S_{t-}dN_t&lt;/math&gt; where &lt;math&gt;(N_t)&lt;/math&gt; is a Poisson process with intensity &lt;math&gt;\lambda&lt;/math&gt;.
# In the preceding problem choose &lt;math&gt;\lambda&lt;/math&gt; such that &lt;math&gt;(S_t)&lt;/math&gt; is a martingale.
# Find the solution of &lt;math&gt;dS_t=S_{t-}dt-S_{t-}/2dN_t&lt;/math&gt; where &lt;math&gt;(N_t)&lt;/math&gt; is a Poisson process with intensity &lt;math&gt;\lambda&lt;/math&gt;.
# In the preceding problem choose &lt;math&gt;\lambda&lt;/math&gt; such that &lt;math&gt;(S_t)&lt;/math&gt; is a martingale.
# Find the solution of &lt;math&gt;dS_t=-S_{t-}dt+S_{t-}dW_t+2S_{t-}dN_t&lt;/math&gt;  where &lt;math&gt;(W_t)&lt;/math&gt; is a Wiener process and &lt;math&gt;(N_t)&lt;/math&gt; is an independent  Poisson process with intensity &lt;math&gt;\lambda&lt;/math&gt;.
# In the preceding problem choose &lt;math&gt;\lambda&lt;/math&gt; such that &lt;math&gt;(S_t)&lt;/math&gt; is a martingale.
# Let &lt;math&gt;S_t=W_t+N_t&lt;/math&gt; where &lt;math&gt;(W_t)&lt;/math&gt; is a Wiener process and &lt;math&gt;(N_t)&lt;/math&gt; is an independent  Poisson process with intensity &lt;math&gt;\lambda&lt;/math&gt;. Expand &lt;math&gt;e^{t-S_t}&lt;/math&gt; by Ito's formula.
# Let &lt;math&gt;(S_t)&lt;/math&gt; be the solution of  &lt;math&gt;dS_t=-S_{t-}dt+2S_{t-}dN_t&lt;/math&gt; where &lt;math&gt;(N_t)&lt;/math&gt; is a Poisson process with intensity &lt;math&gt;\lambda&lt;/math&gt;. Expand &lt;math&gt;e^{S_t+2t}&lt;/math&gt; by Ito's formula.

== Financial models with jumps, pricing and hedging ==

=== Concepts and facts ===

* equivalent change of measure for Poisson processes (Escher transform) - existence of transforms for arbitrary intensities
* Poissonian stock models - risk neutral models - criterion for NA property - completeness - hedging
* Poisson-diffusion stock models - risk neutral models - criterion for NA property - incompleteness - hedging

=== Review questions ===

# Describe Poissonian stock models. Which of them are risk neutral mdoels ?
# Discuss the NA property for Poissonian stock models.
# Discuss completeness of Poissonian stock models.
# Describe Poisson-diffusion stock models. Which of them are risk neutral mdoels ?
# Discuss the NA property for Poisson-diffusion stock models.
# Discuss completeness of Poisson-diffusion stock models.

=== Proofs ===

# Let &lt;math&gt;(N_t)&lt;/math&gt; be a Poisson process under &lt;math&gt;P&lt;/math&gt;. Show that for every &lt;math&gt;\lambda&gt;0&lt;/math&gt; one may find an equivalent probability measure &lt;math&gt;Q&lt;/math&gt; such that &lt;math&gt;(N_t)&lt;/math&gt; has intensity &lt;math&gt;\lambda&lt;/math&gt;.

== References ==

{{Reflist|
refs=

&lt;ref name=&quot;Cont:Tankov:2012&quot;&gt;{{cite book|author1=Rama Cont|author2=Peter Tankov|title=Financial Modelling with Jump Processes, Second Edition|url=http://books.google.com/books?id=-fZtKgAACAAJ|accessdate=24 January 2013|date=26 October 2012|publisher=CRC PressINC|isbn=978-1-4200-8219-7}}&lt;/ref&gt;
 
&lt;ref name=&quot;Protter2005&quot;&gt;{{cite book|author=Philip Protter|title=Stochastic Integration and Differential Equations: Version 2.1|url=http://books.google.com/books?id=mJkFuqwr5xgC|accessdate=24 January 2013|date=24 May 2005|publisher=Springer|isbn=978-3-540-00313-7}}&lt;/ref&gt; 

&lt;ref name=&quot;JacodShiryaev1987&quot;&gt;{{cite book|author1=Jean Jacod|author2=Albert N. Shiryaev|title=Limit theorems for stochastic processes|url=http://books.google.com/books?id=sUgXKpUIdHwC|accessdate=24 January 2013|date=31 December 1987|publisher=Springer-Verlag|isbn=978-3-540-17882-8}}&lt;/ref&gt; 

&lt;ref name=&quot;Shreve2004&quot;&gt;{{cite book|author=Steven E. Shreve|title=Stochastic Calculus for Finance II: Continuous-Time Models|url=http://books.google.com/books?id=O8kD1NwQBsQC|accessdate=24 January 2013|date=3 June 2004|publisher=Springer|isbn=978-0-387-40101-0}}&lt;/ref&gt;

&lt;ref name=&quot;Shiryaev1999&quot;&gt;{{cite book|author=Albert N. Shiryaev|title=Essentials of Stochastic Finance: Facts, Models, Theory|url=http://books.google.com/books?id=oiIG5FmJxWgC|accessdate=24 January 2013|date=1 February 1999|publisher=World Scientific|isbn=978-981-02-3605-2}}&lt;/ref&gt;

}}
[[Category:Mathematics]]
[[Category:Finance]]</text>
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    <title>Pest Management in Cereal Aphids</title>
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Many pests cause very high yield losses in cereals worldwide. Pest control is as old as agriculture and provides a method to keep crops free form pests. Although many live organisms are considered pests, all of them cause significant damage to plants, measured by the crop yield decrease or by a change in its quality.  
Traditional treatments against plant pests are based on applying excessive amounts of agrochemicals. Additionally, broad spectrum insecticides produce the death of both the target insects and beneficial organisms of those pests. The elimination of natural enemies disrupts the natural balance of crop insects by allowing uncontrolled multiplication of pests, sometimes generating a new pest problem &lt;ref&gt;Debach, Paul, and David Rosen. “Biological Control by Natural Enemies”. Cambridge, UK, Cambridge University Press (1991). 440 pages. {{ISBN|0-521-39191-1}}.&lt;/ref&gt; &lt;ref&gt;Gerson, Uri, and Ephraim Cohen. “Resurgence of Spider Mites (Acari: Tetranychidae) Induced by Synthetic Pyrethroids”. Exp. Appl. Acarol., 6 (1989): 29-46.&lt;/ref&gt; . On the contrary, this aspect is revised in the concept of integrated pest management and its environmental protection practices. This holistic approach to dealing with pests should reduce pesticide use, provide economic savings to farmers and protect both the environment and human health &lt;ref&gt;Ehler, Lester E. “Perspective Integrated Pest Management (IPM): Definition, Historical Development and Implementation, and the Other IPM”. Pest Manag Sci 62 (2006): 787–789.&lt;/ref&gt;.
Aphids belong to the insect family and are considered very harmful pests in cereals. Greenbug and Russian wheat aphid are well- known aphid species. The greenbug damages their hosts by producing chlorosis, reduction of root volume in wheat &lt;ref&gt;Burton, Robert L. &quot;Effect of Greenbug (Homoptera: Aphididae) Damage on Roots and Shoots Biomass in Wheat Seedlings”. Journal of Economic Entomology 79 (1986): 633-636. &lt;/ref&gt; , barley &lt;ref&gt;Arriaga, Héctor O. “Resistance to Greenbug Toxemia”. Barley news 13 (1969): 58-60.&lt;/ref&gt; &lt;ref&gt;Castro, Ana M., Rumi, Clara, and Héctor Arriaga. “Influence of Greenbug on Root Growth of Resistance and Susceptible Barley Genotypes”. Environmental and Experimental Botany 28 (1988): 61-72.&lt;/ref&gt; &lt;ref&gt;Gerloff, E. and E. Ortman. “Physiological Changes in Barley Induced by Feeding Stress”. Crop Science 11 (1971): 174-176.&lt;/ref&gt;  oat and sorghum &lt;ref&gt;Castro, Ana M., and Clara Rumi. “Greenbug Damage on the Aerial Vegetative Growth of Two Barley Cultivars”. Environmental and Experimental Botany 23, no. 3 (1987): 263-271. &lt;/ref&gt; &lt;ref&gt;Castro, Ana M., Rumi, Clara, and Héctor Arriaga. “Alteraciones en el crecimiento radical de cultivares de sorgo infestados con pulgón verde”. Turrialba 41 (1990): 166-171.&lt;/ref&gt;. It also reduces the aerial biomass of wheat &lt;ref&gt;Burton, Robert L. &quot;Effect of Greenbug (Homoptera: Aphididae) Damage on Roots and Shoots Biomass in Wheat Seedlings”. Journal of Economic Entomology 79 (1986): 633-636. &lt;/ref&gt; , barley and rye &lt;ref&gt;Arriaga, Héctor. “El centeno Insave FA. Híbrido sintético resistente a la toxemia del pulgón verde de los cereales”. Revista de la Facultad de Agronomía La Plata XXXII (1956): 190-209.&lt;/ref&gt;. When early attacks occur in oats and barley, a decrease in the movement of protein reserve from the seed to the aerial part of the plant has been recorded &lt;ref&gt;Castro, Ana M., Rumi, Clara, and Héctor Arriaga. “Host Plant Isozymes Profiles of Greenbug Susceptible and Tolerant Barley, Oats and Sorghum Cultivars”. Annals Plant Resistance to Insects Newsletter 13 (1987): 39-40.&lt;/ref&gt; &lt;ref&gt;Castro, Ana M., Rumi, Clara, and Héctor Arriaga. “Oat Production losses Under Greenbug (Schizaphis graminum, Rondani) Infestation and Forward Recovery”. Turrialba 39 (1987): 97-105.&lt;/ref&gt;. Moreover, aphids can inject toxic saliva when feeding from a plant, thus transmitting some viruses. 
In recent years, the most effective strategy for controlling aphid damage is the development of wheat cultivars that carry resistance genes &lt;ref&gt;Porter, David R., Baker C. A. and M. El-Bouhssini. “Resistance in Wheat to a New North American Russian Wheat Aphid Biotype”. Plant Breeding 124 (2005): 603–604.&lt;/ref&gt; &lt;ref&gt;Smith, C. Michael, and Elena V. Boyko. “A Functional Genomics Approach to Identify Temperature Response Genes Modulating Plant Defense Responses to Arthropod Challenge”. In ‘Ecological genomics in Kansas. 4th Ecological Genomics Symposium’. 3–5 Nov. (2006), Kansas City. Pp. 10–14.&lt;/ref&gt; . Those new cultivars are the best resource to obtain durable insect resistance. For this reason, Marker Assisted Selection (MAS) is a helpful tool to accelerate the production of plant materials carrying resistance genes &lt;ref&gt;Yencho, G. C., Cohen, M. B., and P. F. Byrne. “Applications of Tagging and Mapping Insect Resistance Loci in Plants”. Annual Review of Entomology 45 (2000): 393–422. http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.ento.45.1.393&lt;/ref&gt;, speeding up its selection and then its transfer into the genetic background of a new cultivar.

== References ==
&lt;references/&gt;</text>
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    <title>Heresy and the Church in the Mediterranean World</title>
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This resource will identify and study sources on heretics and inquisitors in the Mediterranean world, and will provide opportunity for discussion. We will create subpages on notable individual heretics and Church personalities, taking as a starting place [http://www.ereticopedia.org/system:page-tags/tag/_ereticopedia the page list for ereticopedia.org]. The primary subpages we create should be written like encyclopedia articles, reliably sourced and neutral. Additional material may be added as subpages underneath these, if appropriate, such as original research not reliably published. Pending the creation of pages in English here or elsewhere, we may cite and study sources in Italian, subject to permissions (i.e, copyright), or link to other sources as needed.

Should unresolved conflict appear on the primary subpages, we may fork them, arranging the forks as attributed essays or draft articles underneath the primary subpage.

Discussion should take place on attached Talk pages.

==List of pages==
As this may be large, subpages will be linked from the [[/List/]] subpage.

==Participants==
*[[User:Abd|Abd]] ([[User talk:Abd|discuss]] • [[Special:Contributions/Abd|contribs]]) 19:07, 10 May 2014 (UTC)
* [[User:dsantare7|dsantare7]] ([[User talk:dsantare7|discuss]] • [[Special:Contributions/Santarelli|contribs]]) 20:15, 10 May 2014 (UTC)

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    <title>Wikiversity:Newsletters/Tech News</title>
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      <comment>/* Tech News: 2026-21 */ new section</comment>
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      <text bytes="100574" sha1="i3pamizjuif6xz82s4klerrozl6ni9l" xml:space="preserve">{{Archive box|[[/2014/]] · [[/2015/]] · [[/2016/]] · [[/2017/]] · [[/2018/]] · [[/2019/]] · [[/2020/]] · [[/2021/]] · [[/2022/]] · [[/2023/]] · [[/2024/]] · [[/2025/]]}}
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{{Clear}}

== Tech News: 2026-04 ==

&lt;section begin=&quot;technews-2026-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/04|Translations]] are available.

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* The tray shown on [[Special:Diff|Special:Diff]] in mobile view has been redesigned. It is now collapsed by default, and incorporates a link to undo the edit being viewed, making it easier for mobile editors and reviewers to take action while keeping the interface uncluttered. [https://phabricator.wikimedia.org/T402297] 
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* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the previously observed issue in Vector 2022, where anchor link targets were obscured by the sticky header, has now been addressed. [https://phabricator.wikimedia.org/T406114]

'''Updates for technical contributors'''
* As mentioned in the [[m:Special:MyLanguage/Tech/News/2025/44|October 2025 deprecation announcement]], MediaWiki Interfaces team will begin sunsetting all transform endpoints containing a trailing slash from the MediaWiki REST API the week of January 26. Changes are expected to roll out to all wikis on or before January 30th. All API users currently calling them are encouraged to transition to the non-trailing slash versions. Both endpoint variations can be found, compared, and tested using the [https://test.wikipedia.org/wiki/Special:RestSandbox REST Sandbox]. If you have questions or encounter any problems, please file a ticket in Phabricator to the [https://phabricator.wikimedia.org/project/view/6931/ #MW-Interfaces-Team board].
* Interactive reference documentation for the [[mw:Special:MyLanguage/Wikimedia REST API|Wikimedia REST API]] has moved. Requests to API docs previously hosted through [[mw:Special:MyLanguage/RESTBase|RESTBase]] (e.g.: &lt;code dir=ltr&gt;https://en.wikipedia.org/api/rest_v1/&lt;/code&gt;) are now redirected to the [[w:en:Special:RestSandbox|REST Sandbox]].
* The [[mw:Special:MyLanguage/Wikidata Platform|WMF Wikidata Platform team]] (WDP) has published its [[d:Special:MyLanguage/Wikidata:Wikidata Platform team/Newsletter|January 2026 newsletter]]. It includes updates on the legacy full-graph endpoint decommissioning, the User-Agent policy change, the monthly Blazegraph migration office hours, and efforts to reduce regressions caused by the legacy endpoint shutdown. As a reminder, you can [[m:Special:MyLanguage/Global message delivery/Targets/WDP team updates|subscribe to the WDP newsletter]]!
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.12|MediaWiki]]

'''Meetings and events'''
* The [[mw:Wikimedia Hackathon Northwestern Europe 2026|Wikimedia Hackathon Northwestern Europe 2026]] will take place on 13-14 March 2026 in Arnhem, the Netherlands. Applications opened mid-December and will close soon or when capacity is reached. It's a two-day, technically oriented hackathon bringing together Wikimedians from the region. Hope to see you there!

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W04&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:29, 19 January 2026 (UTC)
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== Tech News: 2026-05 ==

&lt;section begin=&quot;technews-2026-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/05|Translations]] are available.

'''Updates for editors'''
* Wikimedia Foundation invites comments on [[m:Special:MyLanguage/Product and Technology Advisory Council/Year1 Reflections and Proposed Way Forward 2026 Update|proposed future]] of the [[:m:Special:MyLanguage/Product and Technology Advisory Council|Product and Technology Advisory Council]] until 28 February.
* All users with registered accounts can now use passkeys for [[m:Special:MyLanguage/Help:Two-factor authentication|two-factor authentication]] (2FA). Passkeys are a simple way to log in without using a second device. They verify the user's identity using a fingerprint, face scan, or a PIN code. To set up a passkey, first set up a regular 2FA method. Currently, to log in with a passkey, users must also use a password. Later this quarter, passwordless login will allow users to log in with a single click and a passkey. Users with advanced rights will also be required to have 2FA enabled. This is part of the [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security|Account Security]] project.
* Unregistered contributors on blocked IPs or blocked IP ranges can now interact on-wiki to appeal a block by creating a temporary account to appeal a block on the user talk page, unless the &quot;prevent this user from editing their own talk page&quot; is enabled. This solves the problem of logged-out users unable to use the default unblock process via user talk page. [https://phabricator.wikimedia.org/T398673]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the Two-Factor Authentication (2FA) methods description on the management page has been updated. It is now clearer and easier for users to understand and make use of. [https://phabricator.wikimedia.org/T332385]

'''Updates for technical contributors'''
* A new AbuseFilter variable, &lt;code&gt;account_type&lt;/code&gt;, has been added to provide a reliable way to determine the account type being created in the &lt;code&gt;createaccount&lt;/code&gt; and &lt;code&gt;autocreateaccount&lt;/code&gt; actions. As part of this change, the variable &lt;code&gt;accountname&lt;/code&gt; has been renamed to &lt;code&gt;account_name&lt;/code&gt;, and &lt;code&gt;accountname&lt;/code&gt; is now deprecated. Edit filter managers should update any filters that use hardcoded account type checks or the deprecated variable. [https://phabricator.wikimedia.org/T414049]
* Image thumbnails that are requested in non-standard sizes, and using non-standard methods such as direct requests to &lt;code dir=ltr&gt;&lt;nowiki&gt;upload.wikimedia.org/…&lt;/nowiki&gt;&lt;/code&gt; will stop working in the near future. This change is to prevent ongoing external abuse by web-scrapers and bots. Some users with custom CSS/JS, Interface Admins who can fix gadgets and local skins, and Tool-authors, will need to update their code to use standard thumbnail sizes. [[phab:T414805|Details, search-links, and examples of how to fix them, are available in the task]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.13|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W05&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:17, 26 January 2026 (UTC)
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== Tech News: 2026-06 ==

&lt;section begin=&quot;technews-2026-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/06|Translations]] are available.

'''Updates for editors'''
* The &quot;{{int:pageinfo-toolboxlink}}&quot; feature, which gives validating information about a page ([{{fullurl:{{FULLPAGENAME}}|action=info}} example]), now automatically includes a table of contents. If there is a local [[{{ns:8}}:Pageinfo-header]] page created by individual users, it can now be removed. [https://phabricator.wikimedia.org/T363726]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, VisualEditor previously added bold or italic formatting inside link descriptions, making the wikicode complex. This has now been fixed. [https://phabricator.wikimedia.org/T409669]

'''Updates for technical contributors'''
* There was no XML dump on 20 January. Additionally, from now on, dumps will be generated once per month only. [https://phabricator.wikimedia.org/T414389]
* The MediaWiki Interfaces team removed support for all transform endpoints containing a trailing slash from the [https://www.mediawiki.org/wiki/Special:MyLanguage/API:REST%20API MediaWiki REST API]. All API users currently calling those endpoints are encouraged to transition to the non-trailing slash versions. If you have questions or encounter any problems, please file a ticket in phabricator to the [https://phabricator.wikimedia.org/project/view/6931/ #MW-Interfaces-Team board].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.14|MediaWiki]]

'''Weekly highlight'''
* Users are reminded that the Wikimedia Foundation has shared some guiding questions for the July 2026–June 2027 Annual Plan on [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2026-2027/Product &amp; Technology OKRs|Meta]] and ''[[diffblog:2025/12/10/shaping-wikimedia-foundations-2026-2027-annual-goals-key-questions-for-the-wikimedia-movement/|Diff]]''. These focus on global trends, faster and healthier experimentation, better support for newcomers, strengthening editors and advanced users, improving collaboration across projects, and growing and retaining readership. Feedback and ideas are welcome on the [[m:Talk:Wikimedia Foundation Annual Plan/2026-2027|talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W06&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:43, 2 February 2026 (UTC)
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== Tech News: 2026-07 ==

&lt;section begin=&quot;technews-2026-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/07|Translations]] are available.

'''Updates for editors'''
* [[File:Maki-gift-15.svg|12px|link=|class=skin-invert|Wishlist item]] Logged-in contributors who manage large or complex watchlists can now organise and filter watched pages in ways that improve their workflows with the new [[mw:Special:MyLanguage/Help:Watchlist labels|Watchlist labels]] feature. By adding custom labels (for example: pages you created, pages being monitored for vandalism, or discussion pages) users can more quickly identify what needs attention, reduce cognitive load, and respond more efficiently. This improves watchlist usability, especially for highly active editors.
* A new feature available on [[Special:Contributions|Special:Contributions]] shows [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] that are likely operated by the same person, and so makes patrolling less time-consuming. Upon checking contributions of a temporary account, users with access to temporary account IP addresses can now see a view of contributions from the related temporary accounts. The feature looks up all the IPs associated with a given temporary account within the data retention period and shows all the contributions of all temporary accounts that have used these IPs. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts#February 2026: Improvements to the patroller tooling|Learn more]]. [https://phabricator.wikimedia.org/T415674] 
* When editors preview a wikitext edit, the reminder box that they are only seeing a preview (which is shown at the top), now has a grey/neutral background instead of a yellow/warning background. This makes it easier to distinguish preview notes from actual warnings (for example, edit conflicts or problematic redirect targets), which will now be shown in separate warning or error boxes. [https://phabricator.wikimedia.org/T414742]
* The [[m:Special:GlobalWatchlist|Global Watchlist]] lets you view your watchlists from multiple wikis on one page. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] continues to improve — it now properly supports more than one Wikibase site, for example both [[d:|Wikidata]] and [[testwikidata:|testwikidata]]. In addition, issues regarding text direction have been fixed for users who prefer Wikidata or other Wikibase sites in right-to-left (RTL) languages. [https://phabricator.wikimedia.org/T415440][https://phabricator.wikimedia.org/T415458]
* The automatic &quot;magic links&quot; for ISBN, RFC, and PMID numbers have been [[mw:Special:MyLanguage/Help:Magic links|deprecated in wikitext since 2021]] due to inflexibility and difficulties with localization. Several wikis have successfully replaced RFC and PMID magic links with equivalent external links, but a template was often required to replace the functionality of the ISBN magic link. There is now a new [[mw:Special:MyLanguage/Help:Magic words#isbn|built-in parser function]] &lt;code dir=ltr&gt;&lt;nowiki&gt;{{#isbn}}&lt;/nowiki&gt;&lt;/code&gt; available to replace the basic functionality of the ISBN magic link. This makes it easier for wikis who wish to migrate off of the deprecated magic link functionality to do so. [https://phabricator.wikimedia.org/T145604]
* Two new wikis have been created: 
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35401|Jju]] ([[w:kaj:|&lt;code&gt;w:kaj:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T413283]
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q1186896|Nawat]] ([[w:ppl:|&lt;code&gt;w:ppl:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T413273]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. 

'''Updates for technical contributors'''
* A new global user group has been created: [[{{int:grouppage-local-bot}}|{{int:group-local-bot}}]]. It will be used internally by the software to allow community bots to bypass rate limits that are applied to abusive [[w:en:Web scraping|web scrapers]]. Accounts that are approved as bots on at least one Wikimedia wiki will be automatically added to this group. It will not change what user permissions the bot has. [https://phabricator.wikimedia.org/T415588]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.15|MediaWiki]]

'''Meetings and events'''
* The [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Spring 2026|MediaWiki Users and Developers Conference, Spring 2026]] will be held March 25–27 in Salt Lake City, USA. This event is organized by and for the third-party MediaWiki community. You can propose sessions and register to attend. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/AZBWVI46SDEB65PGR5J6E4TYOQQEZXM7/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W07&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:30, 9 February 2026 (UTC)
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== Tech News: 2026-08 ==

&lt;section begin=&quot;technews-2026-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/08|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Wikimedia Site Reliability Engineering|SRE Team]] will be performing a cleanup of Wikimedia's [[m:Special:MyLanguage/Etherpad|Etherpad]] instance, the web-based editor for real-time collaborative document editing. All pads will be permanently deleted after 30 April, 2026 – if there are still migration projects in progress at that point the team can revisit the date on a case by case basis. Please create local backups of any content you wish to keep, as deleted data cannot be recovered. This cleanup helps reduce database size and minimize infrastructure footprint. Etherpad will continue to support real-time collaboration, but long-term storage should not be expected. Additional cleanups may occur in the future without prior notice. [https://phabricator.wikimedia.org/T415237]

'''Updates for editors'''
* The Information Retrieval team will be launching an [[mw:Special:MyLanguage/Readers/Information Retrieval/Phase 1|Android mobile app experiment]] that tests hybrid search capabilities which can handle both semantic and keyword queries. The improvement of on-platform search will enable readers to find what they’re looking for directly on Wikipedia more easily. The experiment will first be launched on Greek Wikipedia in late February, followed by English, French, and Portuguese in March. [https://diff.wikimedia.org/2026/01/08/semantic-search-making-it-easier-to-find-the-information-readers-want/ Read more] on Diff blog. [https://www.mediawiki.org/wiki/Readers/Information_Retrieval]
* The Reader Growth team will run [[mw:Special:MyLanguage/Readers/Reader Growth/WE3.10.2 Mobile Table of Contents|an experiment]] for mobile web users, that adds a table of contents and automatically expands all article sections, to learn more about navigation issues they face. The test will be available on Arabic, Chinese, English, French, Indonesian, and Vietnamese Wikipedias.
* Previously, site notices ([[{{ns:8}}:Sitenotice]] and [[{{ns:8}}:Anonnotice]]) would only render on the desktop site. Now, they will render on all platforms. Users on mobile web will now see these notices and be informed. Site administrators should be prepared to test and fix notices on mobile devices to avoid interference with articles. To opt out, interface admins can add &lt;code dir=&quot;ltr&quot;&gt;#siteNotice { display: none; }&lt;/code&gt; to [[{{ns:8}}:Minerva.css]]. [https://phabricator.wikimedia.org/T138572][https://phabricator.wikimedia.org/T416644]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:19}} community-submitted {{PLURAL:19|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue on [[Special:RecentChanges|Special:RecentChanges]] has been fixed. Previously, clicking hide in the active filters caused the &quot;view new changes since…&quot; button to disappear, though it should have remained visible. The button now behaves as expected. [https://phabricator.wikimedia.org/T406339]

'''Updates for technical contributors'''
* New documentation is now available to help editors debug on-site search features. It supports troubleshooting when pages do not appear in results, when ranking seems unexpected, and when you need to inspect what content is being indexed, helping make search behavior easier to understand and analyze. [[mw:Help:CirrusSearch/Debug|Learn more]]. [https://phabricator.wikimedia.org/T411169]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.16|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W08&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:17, 16 February 2026 (UTC)
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== Tech News: 2026-09 ==

&lt;section begin=&quot;technews-2026-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/09|Translations]] are available.

'''Weekly highlight'''
* [[mw:Special:MyLanguage/Edit check/Reference Check|Reference Check]] has been deployed to English Wikipedia, completing its rollout across all Wikipedias. The feature prompts newcomers to add a citation before publishing new content, helping reduce common citation-related reverts and improve verifiability. In A/B testing, the impact was substantial: newcomers shown Reference Check were approximately 2.2 times more likely to include a reference on desktop and about 17.5 times more likely on mobile web. [https://analytics.wikimedia.org/published/reports/editing/reference_check_ab_test_report_final_2025.html]
'''Updates for editors'''
* The [[mw:Special:MyLanguage/Extension:InterwikiSorting|InterwikiSorting extension]], which allowed for the [[m:Special:MyLanguage/Interwiki sorting order|sorting of interwiki links]], has been undeployed from Wikipedia. As a result, editors who had enabled interwiki link sorting in non-compact mode (full list format) will now see links reordered. The links moving forward will be listed in the alphabetical order of language code. [https://phabricator.wikimedia.org/T253764]
* Later this week, people who are editing a page-section using the mobile visual editor, will notice a new &quot;Edit full page&quot; button. When tapped, you will be able to edit the entire article. This helps when the change you want to make is outside the section you initially opened. [https://phabricator.wikimedia.org/T387175][https://phabricator.wikimedia.org/T409112]
* [[mw:Special:MyLanguage/Readers/Reader Experience|The Reader Experience team]] is inviting editors to assess whether dark mode should still be considered &quot;beta&quot; on their wiki, based on their experience of how well it functions on desktop and mobile. If the feature is deemed mature, editors can update the interface messages in &lt;code dir=ltr&gt;MediaWiki:skin-theme-description&lt;/code&gt; and &lt;code dir=ltr&gt;MediaWiki:Vector-night-mode-beta-tag&lt;/code&gt; to indicate that dark mode is ready and no longer considered beta.
* The improved [[mw:Wikimedia_Apps/Team/iOS/Activity_Tab|Activity tab]] which displays user-insights is now available to all users of the Wikipedia iOS app (version 7.9.0 and later). Following earlier A/B testing that showed higher account creation among users with access to the feature, it has been rolled out to 100% of users along with some updates. The Activity tab now shows your edited articles in the timeline, offers editing impact insights like contribution counts and article view trends, and customization options to improve in-app experience for users.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug that prevented [[mw:Special:MyLanguage/Extension:DiscussionTools|DiscussionTools]] from working on mobile has now been fixed, restoring full functionality. [https://phabricator.wikimedia.org/T415303]

'''Updates for technical contributors'''
* The [[m:Special:GlobalWatchlist|Global Watchlist]] lets you view your watchlists from multiple wikis on one page. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] that makes this possible continues to improve. The latest upgrade is the inclusion of a [[mw:Extension:GlobalWatchlist#hook|new hook]], &lt;code dir=ltr&gt;ext.globalwatchlist.rebuild&lt;/code&gt;, which fires after each watchlist rebuild. This allows you to run gadgets and user scripts for the Special page. [https://phabricator.wikimedia.org/T275159]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.17|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W09&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:03, 23 February 2026 (UTC)
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== Tech News: 2026-10 ==

&lt;section begin=&quot;technews-2026-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/10|Translations]] are available.

'''Weekly highlight'''
* Wikipedia 25 [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments|Birthday mode]] is now live on Betawi, Breton, Chinese, Czech, Dutch, English, French, Gorontalo, Indonesian, Italian, Luxembourgish, Madurese, Sicilian, Spanish, Thai, and Vietnamese Wikipedias! This limited-time campaign feature celebrates 25 years of Wikipedia with a birthday mascot, Baby Globe. When turned on, Baby Globe is shown on [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments/article configuration|~2,500 articles]], waiting to be discovered by readers. Communities can choose to turn Birthday mode on by getting consensus from their community and asking an admin to enable the feature and customize it via [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments#Community Configuration Demo|community configuration]] on the local wiki.

'''Updates for editors'''
* [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|Sub-referencing]], a new feature to re-use references with different details has been released to Swedish Wikipedia, Polish Wikipedia and [[:phab:T418209|a couple of other wikis]]. You can [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#test|try the feature]] on these projects or on testwiki and [https://en.wikipedia.beta.wmcloud.org/wiki/Sub-referencing betawiki]. Learnings from the first pilot wiki German Wikipedia have been [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing/Learnings|published in a report]]. Reach out to the Wikimedia Deutschland team if you are [[:m:Talk:WMDE Technical Wishes/Sub-referencing#Pilot wikis|interested in becoming a pilot wiki]].
* [[mw:Special:MyLanguage/Help:Edit check#Paste check|Paste Check]] will become available at all Wikipedias this week. The feature prompts newcomers who are pasting text they are not likely to have written into VisualEditor to consider whether doing so risks a copyright violation. Paste Check [[mw:Special:MyLanguage/Edit check/Tags|tags]] all edits where it is shown for potential review. Local administrators can configure various aspects of the feature via [[{{#special:EditChecks}}]]. [[mw:Special:MyLanguage/Edit check/Paste Check#A/B Experiment|Research]] across 22 wikis found that Paste Check resulted in an 18% decrease in relative reverted-edits compared to the control group. Translators can [https://translatewiki.net/w/i.php?title=Special%3ATranslate&amp;group=ext-visualeditor-ve-mw-editcheck&amp;filter=&amp;optional=1&amp;action=translate help to localize] this and related features.
* The [[mw:Special:MyLanguage/Readers/Reader Experience|Reader Experience team]] will be standardizing the user menu in the top right for all mobile users so that it is closer to the desktop experience. Currently this user menu is only visible to users with Advanced Mobile Controls (AMC) turned on. The only change is that a couple buttons previously in the left-side menu will move to the top right for users who do not have AMC turned on. This change is expected to go out March 9 and seeks to improve the user interface. [https://phabricator.wikimedia.org/T413912]
* Starting in the week of March 2, the emails sent out when an email address was added, removed, or changed for an account will switch to a substantially nicer and clearer HTML email from the prior plaintext one. [https://phabricator.wikimedia.org/T410807]
* Notifications are currently limited to 2,000 historic entries per user, and extend back to 2013 when the feature was released. This is going to be changed to only store Notifications from the last 5 years, but up to 10,000 of them. This will help with long-term infrastructure health and help to prevent more recent notifications from disappearing too soon. [https://phabricator.wikimedia.org/T383948]
* The [[m:Special:GlobalWatchlist|Global Watchlist]] which lets you view your watchlists from multiple wikis on a single page continues to see improvements. The latest update improves label usage experience. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] now allows activating the [[mw:Special:MyLanguage/Manual:Language#Fallback languages|language fallback system]] for Wikidata items without labels in the viewed language, and showing those labels in the user’s preferred Wikidata language if no &lt;code dir=ltr&gt;uselang=&lt;/code&gt; URL parameter is provided. [https://phabricator.wikimedia.org/T373686][https://phabricator.wikimedia.org/T416111]
* The Wikipedia Android team has started a beta test of [[mw:Special:MyLanguage/Readers/Information Retrieval/Phase 1|hybrid search]] on Greek Wikipedia. Hybrid search capabilities can handle both semantic and keyword queries enabling readers to find what they’re looking for directly on Wikipedia more easily.
* For security reasons, members of certain user groups are [[m:Special:MyLanguage/Mandatory two-factor authentication for users with some extended rights|required to have two-factor authentication]] (2FA) enabled. Currently, 2FA is required to use the group, but not to be a member of it. Given that this model still has some vulnerabilities, the situation will [[phab:T418580|gradually change in March]]. Members of these groups will be unable to disable last 2FA method on their account, and it will be impossible to add users without 2FA to these groups. Users will still be able to add new authentication methods or remove them, as long as at least one method is continuously enabled. In the second half of March, users without 2FA will be removed from these groups. This applies to: CentralNotice administrators, checkusers, interface administrators, suppressors, Wikidata staff, Wikifunctions staff, WMF Office IT and WMF Trust &amp; Safety. Nothing will change for other users. See the linked task for deployment schedule. [https://phabricator.wikimedia.org/T418580]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue preventing users from creating an instance in [https://www.wikibase.cloud/ Wikibase.cloud] has now been fixed. [https://phabricator.wikimedia.org/T416807]

'''Updates for technical contributors'''
* To help ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]], over the next month the Wikimedia Foundation will implement global API rate limits across our APIs. In early March, stricter limits will be applied to unidentified requests from outside Toolforge/WMCS and API requests that are made from web browsers. In April, higher limits will be applied to identified traffic. These limits are intentionally set as high as possible to minimise impact on the community. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]].
* The Wikidata Query Service Linked Data Fragment (LDF) endpoint will be decommissioned in February. This endpoint served limited traffic, which was successfully migrated to other data access methods that were better suited to support existing use cases. The hardware used to support the LDF endpoint will be reallocated to support the ongoing backend migration efforts. [https://phabricator.wikimedia.org/T415696]
* The new Parsoid parser [[mw:Special:MyLanguage/Parsoid/Parser Unification/Updates|continues to be deployed to additional wikis]], improving platform sustainability and making it easier to introduce new reading and editing features. Parsoid is now the default parser on 488 WMF wikis (268 Wikipedias), now covering more than 10% of all Wikipedia page views.
* The process and criteria for [[Special:MyLanguage/Wikimedia Enterprise#Access|requesting exceptional access]] to the high volume feed of the ''Wikimedia Enterprise'' APIs (at no cost for mission-aligned usecases), [[m:Talk:Wikimedia Enterprise#Exceptional access criteria|have now been published]]. This is to provide more thorough and clearer documentation for users.
* [https://techblog.wikimedia.org/ Tech Blog], the blog dedicated to the Wikimedia technical community [https://techblog.wikimedia.org/2026/02/24/a-tech-blog-diff/ will be migrating] to [[diffblog:|Diff]], the community news and event blog. The migration should be complete in April 2026, after which new posts will be accepted for publishing. Readers will be able to access posts – old and new – on the landing page at https://diff.wikimedia.org/techblog.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.18|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W10&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:51, 2 March 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30137798 --&gt;

== Tech News: 2026-11 ==

&lt;section begin=&quot;technews-2026-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/11|Translations]] are available.

'''Weekly highlight'''
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on Wednesday, 25 March 2026 at [https://zonestamp.toolforge.org/1774450800 15:00 UTC]. This is for the datacenter server switchover backup tests, [[wikitech:Deployments/Yearly calendar|which happen twice a year]]. During the switchover, all Wikimedia website traffic is shifted from one primary data center to the backup data center to test availability and prevent service disruption even in emergencies.
* Last week, all wikis had 2 hours of read-only time, and extended unavailability for user-scripts and gadgets. This was due to a security incident which has since been resolved. Work is ongoing to prevent re-occurrences. For current information please see the [[m:Steward's noticeboard#Statement on Meta about today's user script security incident|post on the Stewards' noticeboard]] ([[m:Special:MyLanguage/Wikimedia Foundation/Product and Technology/Product Safety and Integrity/March 2026 User Script Incident|translations]]).

'''Updates for editors'''
* Users facing multiple blocks on mobile will now see the reasons for each block separately, instead of a generic message. This helps them understand why they are blocked and what steps they can take to resolve the issue. For example, users affected for using common VPNs (such as [[Special:MyLanguage/Apple iCloud Private Relay|iCloud Private Relay]]) will receive clearer guidance on what they need to do to start editing again. [https://phabricator.wikimedia.org/T357118]
* Later this week, [[mw:Special:MyLanguage/VisualEditor/Suggestion Mode|Suggestion Mode]] will become available as a beta feature within the visual editor at all Wikipedias. This feature proactively suggests various types of actions that people can consider taking to improve Wikipedia articles, and learn about related guidelines. The feature is locally configurable, and can also be locally expanded with custom Suggestions. Current settings can be seen at [[Special:EditChecks]] and there are [[mw:Special:MyLanguage/Help:Suggestion mode#For administrators %E2%80%93 local customization|instructions for how administrators can customize]] the links to point to local guidelines. The feature is connected to [[mw:Special:MyLanguage/Help:Edit check|Edit check]] which suggests improvements while someone is writing new content. In the future, the Editing team plans to evaluate the feature's impact with newcomers through a controlled experiment. [https://phabricator.wikimedia.org/T404600]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where the cursor became misaligned during the use of CodeMirror’s syntax highlighting, which makes wikitext and code easier to read, has now been fixed. This problem specifically affected users who defined a font rule in a custom stylesheet while creating a new topic with DiscussionTools. [https://phabricator.wikimedia.org/T418793]

'''Updates for technical contributors'''
* API rate limiting update: To help ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]], global API rate limits will be applied this week to requests without a compliant User-Agent that originate from outside Toolforge/WMCS and to unauthenticated requests made from web browsers. Higher limits will be applied to identified traffic in April. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]].
* The new GraphQL API has been released. The API was developed as a flexible alternative to select features of the Wikidata Query Service (WDQS), to improve developer experience and foster adaptability, and efficient data access. Try it out and [[d:Wikidata:Wikibase GraphQL#Feedback and development|give feedback]]. You can also [https://greatquestion.co/wikimediadeutschland/GraphQLAPI/apply sign up for usability tests].
* The [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group|PTAC Unsupported Tools Working Group]] continued improvements to [[commons:Special:MyLanguage/Commons:Video2commons#|Video2Commons]] in February, with fixes addressing authentication errors, large-file handling, task queue visibility, and clearer upload behavior. Work is still ongoing in some areas, including changes related to deprecated server-side uploads. Read [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group#February 2026|this update]] to learn more.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.19|MediaWiki]]

'''In depth'''
* The Article Guidance team invites experienced Wikipedia editors from selected [[mw:Special:MyLanguage/Article guidance/Pilot wikis and collaborators#Collaborators|pilot wikis]] and interested contributors from other Wikipedias to fill out this questionnaire which is available in [https://docs.google.com/forms/d/e/1FAIpQLSfmLeVWnxmsCbPoI_UF2jyRcn73WRGWCVPHzerXb4Cz97X_Ag/viewform English], [https://docs.google.com/forms/d/e/1FAIpQLSd6rzr4XXQw8r4024fE3geTPFe13M_6w7Mitj-YJi0sOlWTAw/viewform?usp=header Arabic], [https://docs.google.com/forms/d/e/1FAIpQLSdok3-RfB18lcugYTUMGkpwmqG_8p760Wv4dCXitOXOszjUDw/viewform?usp=header Bengali], [https://docs.google.com/forms/d/e/1FAIpQLSfjTfYp4jEo0akA4B1e-Nfg3QZPCudUjhJzHzzDi6AHyAaMGA/viewform?usp=header Japanese], [https://docs.google.com/forms/d/e/1FAIpQLScteVoI29Aue4xc72dekk-6RYtvmMgQxzMI900UOawrFrSTWg/viewform?usp=header Portuguese], [https://docs.google.com/forms/d/e/1FAIpQLSetdxnYwL3ub2vqA7awCg5hJZPMIYcDPaiTe12rY9h0GYnVlw/viewform?usp=header Persian], and [https://docs.google.com/forms/d/e/1FAIpQLScNvfJF-Ot-4pzA4qAN771_0QDJ4Li19YcUsaTgSKW8Nc7U_Q/viewform?usp=header Turkish]. Your answers will help the team customize guidance for less experienced editors and help them learn community policies and practices while creating an article. Learn more [[mw:Special:MyLanguage/Article guidance|on the project page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W11&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:53, 9 March 2026 (UTC)
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== Tech News: 2026-12 ==

&lt;section begin=&quot;technews-2026-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/12|Translations]] are available.

'''Updates for editors'''
* The [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature, also known as [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror 6]], has been used for wikitext syntax highlighting since November 2024. It will be promoted out of beta by May 2026 in order to bring improvements and new [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Features|features]] to all editors who use the standard syntax highlighter. If you have any questions or concerns about promoting the feature out of beta, [[mw:Special:MyLanguage/Help talk:Extension:CodeMirror|please share]]. [https://phabricator.wikimedia.org/T259059]
* Some changes to local user groups are performed by stewards on Meta-Wiki and logged there only. Now, interwiki rights changes will be logged both on Meta-Wiki and the wiki of the target user to make it easier to access a full record of user's rights changes on a local wiki. Past log entries for such changes will be backfilled in the coming weeks. [https://phabricator.wikimedia.org/T6055]
* On wikis using [[m:Special:MyLanguage/Flagged Revisions|Flagged Revisions]], the number of pending changes shown on [[{{#Special:PendingChanges}}]] previously counted pages which were no longer pending review, because they have been removed from the system without being reviewed, e.g. due to being deleted, moved to a different namespace, or due to wiki configuration changes. The count will be correct now. On some wikis the number shown will be much smaller than before. There should be no change to the list of pages itself. [https://phabricator.wikimedia.org/T413016]
* Wikifunctions composition language has been rewritten, resulting in a new version of the language. This change aims to increase service stability by reducing the orchestrator's memory consumption. This rewrite also enables substantial latency reduction, code simplification, and better abstractions, which will open the door to later feature additions. Read more about [[f:Special:MyLanguage/Wikifunctions:Status updates/2026-03-11|the changes]].
* Users can now sort search results alphabetically by page title. The update gives an additional option to finding pages more easily and quickly. Previously, results could be sorted by Edit date, Creation date, or Relevance. To use the new option, open 'Advanced Search' on the search results page and select 'Alphabetically' under 'Sorting Order'. [https://phabricator.wikimedia.org/T403775]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:28}} community-submitted {{PLURAL:28|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the bug that prevented UploadWizard on Wikimedia Commons from importing files from Flickr has now been fixed. [https://phabricator.wikimedia.org/T419263]
'''Updates for technical contributors'''
* A new special page, [[{{#special:LintTemplateErrors}}]], has been created to list transcluded pages that are flagged as containing lint errors to help users discover them easily. The list is sorted by the number of transclusions with errors. For example: [[{{#special:LintTemplateErrors}}/night-mode-unaware-background-color]]. [https://phabricator.wikimedia.org/T170874]
* Users of the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature have been using [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] for syntax highlighting when editing JavaScript, CSS, JSON, Vue and Lua content pages, for some time now. Along with promoting CodeMirror 6 out of beta, the plan is to replace CodeEditor as the standard editor for these content models by May 2026. [[mw:Special:MyLanguage/Help talk:Extension:CodeMirror|Feedback or concerns are welcome]]. [https://phabricator.wikimedia.org/T419332]
* The [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] JavaScript modules will soon be upgraded to CodeMirror 6. Leading up to the upgrade, loading the &lt;code dir=ltr&gt;ext.CodeMirror&lt;/code&gt; or &lt;code dir=ltr&gt;ext.CodeMirror.lib&lt;/code&gt; modules from gadgets and user scripts was deprecated in July 2025. The use of the &lt;code dir=ltr&gt;ext.CodeMirror.switch&lt;/code&gt; hook was also deprecated in March 2025. Contributors can now make their scripts or gadgets compatible with CodeMirror 6. See the [[mw:Special:MyLanguage/Extension:CodeMirror#Gadgets and user scripts|migration guide]] for more information. [https://phabricator.wikimedia.org/T373720]
* The MediaWiki Interfaces team is expanding coverage of REST API module definitions to include [[mw:Special:MyLanguage/API:REST API/Extensions|extension APIs]]. REST API modules are groups of related endpoints that can be independently managed and versioned. Modules now exist for [https://phabricator.wikimedia.org/T414470 GrowthExperiments] and [https://phabricator.wikimedia.org/T419053 Wikifunctions] APIs. As we migrate extension APIs to this structure, documentation will move out of the main MediaWiki OpenAPI spec and REST Sandbox view, and will instead be accessible via module-specific options in the dropdown on the [https://test.wikipedia.org/wiki/Special:RestSandbox REST Sandbox] (i.e., [[{{#Special:RestSandbox}}]], available on all wiki projects).
* The [[mw:Special:MyLanguage/Extension:Scribunto|Scribunto]] extension provides different pieces of information about the wiki where the module is being used via the [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual|mw.site]] library. Starting last week, the library also provides a [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#mw.site.wikiId|way]] of accessing the [[mw:Special:MyLanguage/Manual:Wiki ID|wiki ID]] that can be used to facilitate cross-wiki module maintenance. [https://phabricator.wikimedia.org/T146616]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.20|MediaWiki]]

'''In depth'''
* The [[m:Special:MyLanguage/Coolest Tool Award|2026 Coolest Tool Award]] celebrating outstanding community tools, is now open for nominations! Nominate your favorite tool using the [https://wikimediafoundation.limesurvey.net/435684?lang=en nomination survey] form by 23 March 2026. For more information on privacy and data handling, please see the [[foundation:Special:MyLanguage/Legal:Coolest_Tool_Award_2026_Survey_Privacy_Statement|survey privacy statement]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W12&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:35, 16 March 2026 (UTC)
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== Tech News: 2026-13 ==

&lt;section begin=&quot;technews-2026-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/13|Translations]] are available.

'''Weekly highlight'''
* Wikimedia site users can now log in without a password using passkeys. This is a secure method supported by fingerprint, facial recognition, or PIN. With this change, all users who opt for passwordless login will find it easier, faster, and more secure to log in to their accounts using any device. The new passkey login option currently appears as an autofill suggestion in the username field. An additional [[phab:T417120|&quot;Log in with passkey&quot; button]] will soon be available for users who have already registered a passkey. This update will improve security and user experience. The [[c:File:Passwordless_login_screencast.webm|screen recording]] demonstrates the passwordless login process step by step.
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on Wednesday, 25 March 2026 at [https://zonestamp.toolforge.org/1774450800 15:00 UTC]. This is for the datacenter server switchover backup tests, [[wikitech:Deployments/Yearly calendar|which happen twice a year]]. During the switchover, all Wikimedia website traffic is shifted from one primary data center to the backup data center to test availability and prevent service disruption even in emergencies.

'''Updates for editors'''
* Wikimedia site users can now export their notifications older than 5 years using a [[toolforge:echo-chamber|new Toolforge tool]]. This will ensure that users retain their important notifications and avoid them being lost based on the planned change to delete notifications older than 5 years, as previously announced. [https://phabricator.wikimedia.org/T383948]
* Wikipedia editors in Indonesian, Thai, Turkish, and Simple English now have access to Special:PersonalDashboard. This is an [[mw:Special:MyLanguage/Moderator Tools/Dashboard|early version of an experience]] that introduces newer editors to patrolling workflows, making it easier for them to move from making edits to participating in more advanced moderation work on their project. [https://phabricator.wikimedia.org/T402647]
* The [[Special:Block]] now has two minor interface changes. Administrators can now easily perform indefinite blocks through a dedicated radio button in the expiry section. Also, choosing an indefinite expiry provides a different set of common reasons to select from, which can be changed at: [[MediaWiki:Ipbreason-indef-dropdown]]. [https://phabricator.wikimedia.org/T401823]
* Mobile editors [[mw:Special:MyLanguage/Contributors/Account Creation Experiments#Logged-out|at several wikis]] can now see an improved logged-out edit warning, thanks to the recent updates from the Growth team. These changes released last week are part of ongoing efforts and tests to enhance [[mw:Special:MyLanguage/Contributors/Account Creation Experiments|account creation experience on mobile]] and then increase participation. [https://phabricator.wikimedia.org/T408484]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:36}} community-submitted {{PLURAL:36|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the bug that prevented mobile web users from seeing the block information when affected by multiple blocks has been fixed. They can now see messages of all the blocks currently affecting them when they access Wikipedia.

'''Updates for technical contributors'''
* Images built using Toolforge will soon get the upgraded buildpacks version, bringing support for newer language versions and other upstream improvements and fixes. If you use Toolforge Build Service, review the recent [https://lists.wikimedia.org/hyperkitty/list/cloud-announce@lists.wikimedia.org/thread/EMYTA32EV2V5SQ2JIEOD2CL66YFIZEKV/ cloud-announce email] and update your build configuration as necessary to ensure your tools are compatible. [https://wikitech.wikimedia.org/w/index.php?title=Help:Toolforge/Building_container_images&amp;oldid=2392097#Buildpack_environment_upgrade_process][https://phabricator.wikimedia.org/T380127]

* The [https://api.wikimedia.org/wiki/Main_Page API Portal] documentation wiki will shut down in June 2026. API keys created on the API Portal will continue to work normally. api.wikimedia.org endpoints will be deprecated gradually starting in July 2026. Documentation on the API Portal is moving to [[mw:Wikimedia APIs|mediawiki.org]]. Learn more on the [[wikitech:API Portal/Deprecation|project page]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.21|MediaWiki]]

'''In depth'''
* [[m:Special:MyLanguage/WMDE Technical Wishes|WMDE Technical Wishes]] is considering improvements to [[m:WMDE Technical Wishes/References/VisualEditor automatic reference names|automatically generated reference names in VisualEditor]]. Please check out the [[m:WMDE Technical Wishes/References/VisualEditor automatic reference names#Proposed solutions|proposed solutions]] and participate in the [[m:Talk:WMDE Technical Wishes/References/VisualEditor automatic reference names#Request for comment|request for comment]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W13&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:51, 23 March 2026 (UTC)
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== Tech News: 2026-14 ==

&lt;section begin=&quot;technews-2026-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/14|Translations]] are available.

'''Weekly highlight'''
* The Beta version of [[abstract:|Abstract Wikipedia]] a new Wikimedia project which is language-independent, was launched last week. The project allows communities to build Wikipedia articles in their native language, which can be readily accessed by other users in their own languages. The wiki is powered by instructions from Wikifunctions and also based on structured content from Wikidata. [[:f:Special:MyLanguage/Wikifunctions:Status updates/2026-03-26|Read more]].

'''Updates for editors'''
* The Growth team is running an A/B test to evaluate a clearer, more user-friendly message that promotes account creation on wikis. Currently when logged-out mobile users begin editing, they see a jarring warning message that can feel abrupt and discouraging. This also presents temporary account editing as the default rather than encouraging account creation. The test is running on ten Wikipedias, including Arabic, French, Spanish and German. [[mw:Special:MyLanguage/Contributors/Account Creation Experiments#2. Improve logged-out warning message (T415160)|Read more]].
* The Wikimedia Apps team is inviting feedback on [[mw:Special:MyLanguage/Wikimedia Apps/Team/Future of Editing on the Mobile Apps|how editing should work on the Wikipedia mobile apps]]. The discussion focuses on improving how users access editing tools when they tap &quot;Edit&quot;. This is part of a broader effort to convert readers who develop an interest in editing, to access a more user-friendly pathway to start contributing.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:45}} community-submitted {{PLURAL:45|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where citation fetching from the large newspaper archive [https://www.newspapers.com Newspapers.com] was no longer working, due to a block in [[mw:Special:MyLanguage/Citoid|Citoid]] requests, has now been fixed. [https://phabricator.wikimedia.org/T419903]

'''Updates for technical contributors'''
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.22|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W14&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:25, 30 March 2026 (UTC)
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== Tech News: 2026-15 ==

&lt;section begin=&quot;technews-2026-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/15|Translations]] are available.

'''Updates for editors'''

* The [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] now includes a new group goal-setting feature, enabling organizers to set and track event goals such as the number of articles created and participating contributors in real time. Similarly, participants can work toward shared targets and see their collective impact as the event unfolds. The feature is now available on all Wikimedia wikis. Learn more in [[mw:Special:MyLanguage/Help:Extension:CampaignEvents/Registration/Collaborative contributions#Goal setting|the documentation]].
* [[File:Maki-gift-15.svg|12px|link=|class=skin-invert|Wishlist item]] The new [[mw:Special:MyLanguage/Help:Watchlist labels|watchlist labels]] feature (announced in [[m:Special:MyLanguage/Tech/News/2026/07|Tech News 2026-07]]) is now available via VisualEditor, the source editor, and the 'watchstar' (or watch link, for skins that don't have a star icon). Previously it was only possible to assign labels via [[Special:EditWatchlist|EditWatchlist]]. In all three places it is a new field following the expiry field.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where talk pages on mobile with Parsoid are unusable after empty section headers, has now been fixed. [https://phabricator.wikimedia.org/T419171]

'''Updates for technical contributors'''
* The [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|sub-referencing feature]], which lets editors add details to an existing reference without duplicating it, will be gradually rolled out to [[phab:T414094|more wikis]] later this year. Wikis using the [[mw:Special:MyLanguage/Reference Tooltips|Reference Tooltips]] gadget are encouraged to update their version (typically at [[m:MediaWiki:Gadget-ReferenceTooltips.js|MediaWiki:Gadget-ReferenceTooltips.js]] as shown [https://en.wikipedia.org/w/index.php?diff=1344408362 here]) to ensure compatibility. Other reference-related gadgets may also be affected. [https://phabricator.wikimedia.org/T416304]
* All Wikinews editions will be closed and switched to read-only mode on 4 May 2026. Content will remain accessible, but no new edits or articles can be added. This closure was approved by the Board of Trustees of the Wikimedia Foundation following extended discussions. [[m:Wikimedia Foundation Board noticeboard#Board of Trustees Approves Closure of Wikinews|Read more]].
* The [[:mw:Special:MyLanguage/API:Action API|Action API]] has had several formats for requested output. One of them, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;format=php&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, is being removed soon. Please ensure your scripts or bots use the [[mw:Special:MyLanguage/API:Data formats#Output|JSON format]]. This removal should affect very few scripts and bots. [https://phabricator.wikimedia.org/T118538]
* The [[Special:NamespaceInfo|Special:NamespaceInfo]] page now includes namespace aliases. For example &quot;WP&quot; for the &quot;Project&quot; (&quot;Wikipedia&quot;) namespace on the German Wikipedia. [https://phabricator.wikimedia.org/T381455]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.23|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W15&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:19, 6 April 2026 (UTC)
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== Tech News: 2026-16 ==

&lt;section begin=&quot;technews-2026-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/16|Translations]] are available.

'''Weekly highlight'''
* Experienced editors are invited to [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Main_Page test] the [[mw:Special:MyLanguage/Article guidance|Article guidance]] feature, designed to help less-experienced editors create well-structured, policy-compliant Wikipedia articles. Testing instructions are [[mw:Special:MyLanguage/Article guidance/Test feature guide|available]]. Also, after reviewing [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Category:Pages_using_article_guidance the outlines], please provide feedback on the [[mw:Talk:Article guidance|project talk page]]. Based on your input, the feature will be refined and transferred to the pilot Wikipedias to translate and adapt. Check out [[c:File:Article Guidance workflow demo - April 2026.webm|the video]] explaining the feature.
'''Updates for editors'''
* On most wikis, all autoconfirmed users can now use [[Special:ChangeContentModel|Special:ChangeContentModel]] page to [[mw:Special:MyLanguage/Help:ChangeContentModel|create new pages with custom content models]], such as mass message lists, making custom page formats more accessible. Check [[Special:ListGroupRights|Special:ListGroupRights]] for the status of your wiki. [https://phabricator.wikimedia.org/T248294]
* The Growth team has launched an [[mw:Special:MyLanguage/Contributors/Account_Creation_Experiments|account creation experiment]] to evaluate whether adding an account creation button to the mobile web header increases new account registrations and encourages more mobile users to contribute to the wikis. The experiment is currently live on Hindi, Indonesian, Bengali, Thai, and Hebrew Wikipedia, and targets 10% of logged-out mobile web users.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where VisualEditor could get stuck loading on Windows devices with animations turned off, has now been fixed. [https://phabricator.wikimedia.org/T382856]

'''Updates for technical contributors'''
* Starting later this week, {{int:group-abusefilter}} who have the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature enabled will have [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] as the editor at [[Special:AbuseFilter|Special:AbuseFilter]]. This is part of the broader effort to make the user experience more consistent across all editors. [https://phabricator.wikimedia.org/T399673][https://phabricator.wikimedia.org/T419332]
* Tools and bots that access the [[mw:Special:MyLanguage/Notifications/API|Notifications API]] (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;action=query&amp;meta=notifications&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;) will need to update their OAuth or BotPassword grants to also include access to private notifications. [https://phabricator.wikimedia.org/T421991]
* Due to a library upgrade, listings on category pages may be displayed out of order starting on Monday, 20th April. A migration script will be run to correct this, and will take hours to days depending on the size of the wiki (up to a week for English Wikipedia). [https://phabricator.wikimedia.org/T422544]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.24|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W16&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:19, 13 April 2026 (UTC)
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== Tech News: 2026-17 ==

&lt;section begin=&quot;technews-2026-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/17|Translations]] are available.

'''Weekly highlight'''
* After two years of development, [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]], also known as [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror 6]], is to be promoted out of beta on Tuesday, April 21. It brings better code and wikitext readability, reduction in typing errors, and other [[mw:Special:MyLanguage/Help:Extension:CodeMirror|benefits]] to all users of the standard syntax highlighter. A huge thank you to volunteer [https://phabricator.wikimedia.org/p/Bhsd/ Bhsd] who developed many of the new features, including [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Code folding|code folding]], [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Autocompletion|autocompletion]], and [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Linting|linting]]. [https://phabricator.wikimedia.org/T259059]
* A major update to the Wikipedia app for iOS is now rolling out, redesigning the interface to align with Apple's latest &quot;Liquid Glass&quot; visual design. [https://apps.apple.com/us/app/wikipedia/id324715238 Download the latest version] and explore the update.

'''Updates for editors'''
* [[mw:Special:MyLanguage/Readers/Reader Experience/WE3.3.4 Reading lists|Reading lists]] is a feature which allows readers to save articles to a list for reading later. This feature is now in beta on Arabic, French, Indonesian, Vietnamese, and Chinese Wikipedias and by default for all new accounts on all Wikipedias.
* An experiment which explores extending [[mw:Special:MyLanguage/Readers/Reader Growth/Mobile page previews|Page Previews to mobile web]] will be launched in the week of April 20 on Arabic, English, French, Italian, Polish, and Vietnamese Wikipedias. Page Previews are pop-ups that display a thumbnail, lead paragraph, and a link to open the full article of a blue link, thereby improving content discovery. The feature is already available on desktop and in the apps. [[m:Special:MyLanguage/List of experiments in Product and Technology#Template|Read more about this experiment and others]].
* On several wikis, logged-in editors who haven't [[mw:Special:MyLanguage/Help:Email confirmation|confirmed their email addresses]] can now see a banner encouraging them to do so. Having the email address confirmed allows a user to restore access to the account if they lose it. [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security#Encouraging users to confirm their email addresses|Learn more]]. [https://phabricator.wikimedia.org/T421366]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:15}} community-submitted {{PLURAL:15|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where editing very large wiki pages in the 2017 wikitext editor caused slow loading, preview and scrolling lag, and performance issues when selecting, cutting, or pasting content, has now been fixed. [https://phabricator.wikimedia.org/T184857]

'''Updates for technical contributors'''
* As part of the promotion of [[mw:Special:MyLanguage/Help:Extension:CodeMirror|CodeMirror]] from a beta feature, all users will use [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] for syntax highlighting when editing JavaScript, CSS, JSON, Vue and Lua content pages. [https://phabricator.wikimedia.org/T419332]
* The &lt;code&gt;mirrors.wikimedia.org&lt;/code&gt; service for Debian and Ubuntu users will sunset and stop working on May 15. The resources for the service will be replaced with new and better options. Some users may need to switch to a different server which should take about a minute. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/LJYRIS4WB66HIRCAO4GIDTXCMDVZRBMA/ You can read more]. [https://phabricator.wikimedia.org/T416707]
* The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;image&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;oldimage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; table will be removed from [[wikitech:Help:Wiki Replicas|wikireplicas]]. If your tools or queries access &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;image&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;oldimage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; directly, please update them to use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;file&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;filerevision&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; table before 28 May. [https://phabricator.wikimedia.org/T28741]
* Following the recent implementation of global API rate limits on unidentified traffic, the Wikimedia Foundation will continue efforts to ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]] by applying global limits to identified API traffic beginning the last week of April. These limits are intentionally set as high as possible to minimise impact on the community. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]] and [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits/FAQ|Frequently Asked Questions]].
* The [[mw:Special:MyLanguage/Attribution API|Attribution API]] is now available as a [[mw:Special:MyLanguage/Wikimedia APIs/Stability policy|beta]]. The API fetches information for crediting Wikimedia articles and media files wherever they are used. Reference documentation is available through the REST Sandbox special page available on all Wikimedia wikis (such as the [https://en.wikipedia.org/w/index.php?api=attribution.v0-beta&amp;title=Special%3ARestSandbox REST sandbox on English Wikipedia]). Share your feedback on the [[mw:Talk:Attribution API|project talk page]].
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W17&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:00, 20 April 2026 (UTC)
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== Tech News: 2026-18 ==

&lt;section begin=&quot;technews-2026-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/18|Translations]] are available.

'''Updates for editors'''
* There is a change in how new users are autoconfirmed that will improve anti-vandalism protection. Currently, users who have had an account for a few days and made a few edits are automatically added to the [[{{int:grouppage-autoconfirmed/{{CONTENTLANGUAGE}}}}|{{int:group-autoconfirmed}}]] group. This configuration tends to be exploited by some vandals, who create accounts and start to use them only after some time. To mitigate this, the configuration will be updated next week so that – for the purpose of becoming autoconfirmed – the account age will be counted from their first edit, instead of registration date. The numeric value of the age threshold will remain the same. This change will be deployed only to wikis which require at least one edit as part of the autoconfirmation conditions. [https://phabricator.wikimedia.org/T418484]
* All Wikipedia users with new accounts and those who activated the &quot;automatically enable most beta features&quot; option in their preference can now use the [[mw:Special:MyLanguage/Readers/Reader Experience/WE3.3.4 Reading lists|reading lists]] beta feature to save articles for later reading. This helps organize reading interests in one place for convenient access. 
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where infobox images have huge padding in Firefox, has been fixed. [https://phabricator.wikimedia.org/T423676]

'''Updates for technical contributors'''
* As a reminder, the global API rate limits will be applied this week to identified API traffic. This is to help ensure [[mw:MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]]. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, including the actual rate limits, see [[mw:Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]] and [[mw:Wikimedia APIs/Rate limits/FAQ|Frequently Asked Questions]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.26|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W18&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:06, 27 April 2026 (UTC)
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== Tech News: 2026-19 ==

&lt;section begin=&quot;technews-2026-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/19|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Article guidance|Article guidance]] team invites experienced editors of [[mw:Special:MyLanguage/Article guidance/Pilot wikis and collaborators|pilot Wikipedias]]—Arabic, Bangla, Japanese, Portuguese, Persian, Turkish, Simple English, Spanish, and French—to help translate and adapt [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Category:Pages_using_article_guidance sample outlines]. These outlines will guide editors in creating clear, well-structured, and policy-compliant articles when using [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Special:NewArticle the feature] once it is launched in May 2026. [[mw:Special:MyLanguage/Article guidance#Adapting a sample outline in a Wikipedia|Simple instructions]] on how to translate and adapt the outlines are available.
'''Updates for editors'''
* The [[:m:Special:MyLanguage/Product and Technology Advisory Council|Product and Technology Advisory Council]] has published [[:m:Special:MyLanguage/Product and Technology Advisory Council/May 2026 draft PTAC recommendation for feedback|draft recommendations]] on a model that affiliates can follow when contributing to the technical space. Community members are invited to provide feedback on the recommendation until May 8th [[:m:Talk:Product and Technology Advisory Council/May 2026 draft PTAC recommendation for feedback|on the talk page]].
* The number of available thumbnail size preferences in MediaWiki is being reduced to three standardized options—Small (180px), Regular (250px), and Large (400px), as part of ongoing efforts to improve performance and reduce strain on thumbnail services. As a result, existing preferences will be mapped to the nearest new size (for example, smaller selections like 120px or 150px will render at 180px, while larger ones like 300px or 360px will render at 400px). The preferences interface will soon be updated to reflect these changes, and users who wish to opt out or provide feedback can do so. [https://phabricator.wikimedia.org/T424909]
* From now on, even when a permission expires automatically, users will receive an Echo notification similar to the standard notification for permission changes. There is a difference between this and [[m:Special:MyLanguage/Global reminder bot|Global reminder bot]] in that the latter reminds users a week ''before'' the rights are due to expire, so that they can renew the rights.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the problem where the ULS language selector in [[m:Special:Translate|Special:Translate]] would scroll vertically when it shouldn't, has been resolved. Previously, when users opened the &quot;Translate to English&quot; dropdown and typed certain inputs, the dialog would scroll vertically by a few pixels even when there was enough space to display all results. The dropdown no longer shifts unnecessarily when filtering languages. [https://phabricator.wikimedia.org/T358864] 
* The [[m:Special:GlobalWatchlist|Global Watchlist]], which lets you view your watchlists from multiple wikis on a single page, continues to improve. For example, watchlists for Wikibase sites such as [[:d:|Wikidata]] now support [[mw:Special:MyLanguage/Extension:EntitySchema|EntitySchema]] elements for better tracking. The Live Updates mode now refreshes the special page every 60 seconds to comply with the updated [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|global API rate limits]] for improved real-time responsiveness. Additionally, a directionality bug that displayed links as &quot;changes 3&quot; instead of &quot;3 changes&quot; in mixed-direction lists has been fixed. [https://phabricator.wikimedia.org/T415450][https://phabricator.wikimedia.org/T424422][https://phabricator.wikimedia.org/T418091]
'''Updates for technical contributors'''
* The second phase of [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|global API rate limits]] has been rolled out to reduce the [[diffblog:2026/03/26/quo-vadis-crawlers-progress-and-whats-next-on-safeguarding-our-infrastructure/|impact of AI crawlers]] and ensure fair, sustainable access to Wikimedia resources, prioritising human and mission-aligned traffic. [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits#Limits|Limits]] have been shifted from per-hour to per-minute, producing smoother traffic patterns and more predictable API load. Community users are not expected to be affected, and no action is required. Early indications show some User-Agent-based requestors are adjusting behaviour, and around 64% of automated API traffic has been identified. Monitoring continues, and Wikimedia Enterprise remains available for commercial support.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.27|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W19&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:43, 4 May 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30498077 --&gt;

== Tech News: 2026-20 ==

&lt;section begin=&quot;technews-2026-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/20|Translations]] are available.

'''Weekly highlight'''
* Community Tech has published [[m:Special:MyLanguage/Community Wishlist/How to write a good wish|new guidance]] explaining how wishes on Community Wishlist are triaged and prioritized. The documentation is intended to help contributors write stronger proposals by clarifying the factors that influence prioritization decisions. Beyond vote counts, the guidance highlights considerations such as potential impact on the community when determining which wishes move forward.

'''Updates for editors'''
* The Reader Growth team is launching an experiment to test a new [[mw:Special:MyLanguage/Readers/Reader_Growth/Share_Card|Share Card feature]] that allows readers to create visually engaging cards from Wikipedia articles or selected article sections and share them online, with each card linking back to the original article to help expand readership and article discovery. The mobile-only A/B test will be available to a portion of readers on Arabic, Chinese, French, Vietnamese, and English Wikipedia to better understand reading and sharing habits, and is scheduled to begin the week of May 18 and run for four weeks.
* The Android and iOS Wikipedia apps recently released the [[mw:Special:MyLanguage/Wikimedia_Apps/Team/25th_Birthday_Reading_Challenge|25-day reading challenge]] into Beta, as part of efforts to drive reader engagement by encouraging users to complete reading milestones. To track their reading streak during the challenge, App users can add a widget featuring Baby Globe to their home screen. The challenge officially begins May 11.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:17}} community-submitted {{PLURAL:17|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where the global preference for enabling syntax highlighting in wikitext could unexpectedly disable itself after being turned on, has now been fixed. [https://phabricator.wikimedia.org/T425286]

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The ResourceLoader module &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;mediawiki.ui.input&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, deprecated since [[m:Special:MyLanguage/Tech/News/2023/39|September 2023]], will be removed this week. There is a [[mw:Special:MyLanguage/Codex/Migrating_from_MediaWiki_UI|guide for migrating from MediaWiki UI to Codex]] for any tools that use it. [https://phabricator.wikimedia.org/T420125]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.47/wmf.2|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W20&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:20, 11 May 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30524429 --&gt;

== Tech News: 2026-21 ==

&lt;section begin=&quot;technews-2026-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/21|Translations]] are available.

'''Weekly highlight'''
* The Abstract Wikipedia team has identified five potential pilot wikis to assess their interest in adopting abstract articles on their wikis. The pilots are Malayalam, Bengali, Dagbani, Arabic, and Indonesian Wikipedia. The feedback period will be open until May 22. If your community is interested in becoming a pilot, [[m:Talk:Abstract Wikipedia|let us know on Meta]].

'''Updates for editors'''
* An experiment to show [[mw:Special:MyLanguage/Readers/Reader Experience/Reading lists|Reading Lists]] to logged-out readers on mobile web will launch on May 18 across German, Spanish, Italian, Portuguese, Polish, Dutch, Turkish, and Urdu Wikipedias, and will run for one month. The effort supports broader goals of helping readers save and organize articles for later reading, while encouraging habits that could lead to future Wikipedia contributions.
* To support a bookmark button in the Reading List beta feature, the &quot;Tools &gt; Action&quot; menu has been updated to display icons, including the watch star indicator that helps editors identify temporarily watched articles. The icons now also match those used on mobile, improving consistency across platforms. The change is currently limited to the actions menu and mainly affects editors with privileged user rights. [https://phabricator.wikimedia.org/T426008]
* [[mw:Special:MyLanguage/VisualEditor/Suggestion Mode|Suggestion Mode]] was released as an [[w:en:A/B test|A/B test]] for newcomer editors on the mobile website at [[phab:T421189|~15 Wikipedias]]. The experiment will measure the impact that Suggestion Mode has on the proportion of newcomer mobile web edit sessions that result in constructive (un-reverted) article edits. The experiment will also evaluate the feature's impact on editor retention, and monitor changes in revert and block rates.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue in the Wikipedia Android app where images could sometimes fail to load after opening a recommended reading list notification, has now been fixed. [https://phabricator.wikimedia.org/T418231]

'''Updates for technical contributors'''
* The [[mw:Special:MyLanguage/Wikidata Platform|Wikidata Platform team]] has published its [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/Backend Replacement|backend replacement recommendation]] and accompanying [[wikitech:Wikidata Query Service/WDQS Architecture re-design|technical architecture]] for the migration of the Wikidata Query Service (WDQS) away from Blazegraph. Feedback is invited until May 25th 2026, especially on potential gaps and impacts on advanced use cases. Wikidata community members and WDQS users are also encouraged to help identify high-impact tools and workflows that may need attention on [[d:Wikidata:SPARQL query service/WDQS backend update/High-Impact Use Cases|this page]]. Feedback can be shared on the [[d:Wikidata talk:SPARQL query service/WDQS backend update|Migration talk page]] or during the [[d:Special:MyLanguage/Wikidata:Blazegraph Migration Office Hours|next office hour]]. See the [[d:Special:MyLanguage/Wikidata:Wikidata Platform team/Newsletter|WDP team newsletter]] for more details.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.47/wmf.3|MediaWiki]]

'''In depth'''

* On English, French, Japanese, and a few other Wikipedias, there was a [[diffblog:2025/09/02/better-detecting-bots-and-replacing-our-captcha/|trial of hCaptcha]], a third-party bot detection service. The trial showed that hCaptcha effectively detects and deters some bad-faith automated activity, on its own and by giving [[w:en:Wikipedia:Village pump (technical)/Archive 225#Introducing SuggestedInvestigations|checkusers and stewards]] signals to look into. Because the results were positive, hCaptcha will be rolled out across all wikis over the next few weeks. [[mw:Special:MyLanguage/Product Safety and Integrity/Anti-abuse signals/hCaptcha|See the hCaptcha project page]] for technical information about the implementation and privacy protections. [[diffblog:2026/05/04/better-detecting-bots-and-replacing-our-captcha-part-2/|Learn more]].
* The latest Community Tech update is now available, with progress across several Community Wishlist initiatives, including Reading Lists expansion from the mobile app to the website, new language support for &quot;Who Wrote That&quot; and the Personal Dashboard, improvements to 3D rendering and Charts, and upcoming work on talk page sorting, audio playback, and editing workflows. The update also shares current priorities, wishlist status trends, and opportunities for community feedback on future focus areas and the Wikimedia Foundation’s 2026–2027 Annual Plan. [[m:Special:MyLanguage/Community Wishlist/Updates#May 13, 2026: Latest updates from the Community Tech team|Read the full newsletter for details]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W21&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:21, 18 May 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30539262 --&gt;</text>
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    <title>U. S. Government</title>
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      <text bytes="1441" sha1="7i1kluayqlii95w6n23h5t0m0550lak" xml:space="preserve">{{politics}}
{{secondary}}
[[File:January 2025 Official Presidential Portrait of Donald J. Trump.jpg|thumb|Donald J. Trump is the 47th and current President of the USA.]]
[[File:Gilbert Stuart Williamstown Portrait of George Washington.jpg|thumbnail|left|A portrait of George Washington, the 1st president of the United States of America, by Gilbert Stuart Williamstown]]
This project is dedicated for the learning of the U. S. Government and Civics, famous politicians, amendments, laws, and more. 
== Projects ==
*[[U. S. Government/WWII]]

==Current Pages==
*[[U. S. Government/U. S. Branches]]
*[[U. S. Government/Political Principles]]
*[[U. S. Government/Civil War Amendments]]
*[[U. S. Government/Citizenship]]
*[[U. S. Government/Immigrants]]
*[[U. S. Government/Industrialization]]
*[[U. S. Government/Labor Movement]]
*[[U. S. Government/political divisions]] 
*[[U. S. Government/Voting Registration and Participation]]
*[[U. S. Government/Elections]]
*[[U. S. Government/Transportation]]
*[[U. S. Government/Communication in the 1920s]]
*[[U. S. Government/Criminal Law vs. Civil Law Notes]]
*[[U. S. Government/Public Policy]]
*[[U. S. Government/Societal Changes and Opportunities for Minorities]]
*[[U. S. Government/Characteristics of Different Economic Types]]
*[[U. S. Government/Quiz]]

==See also==
*[[American Revolution/Chapter 9: Articles of Confederation]]

[[Category:United States Government| ]]
[[Category:Civics]]</text>
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{{history}}
{{secondary}}
[[File:January 2025 Official Presidential Portrait of Donald J. Trump.jpg|thumb|Donald J. Trump is the 47th and current President of the USA.]]
[[File:Gilbert Stuart Williamstown Portrait of George Washington.jpg|thumbnail|left|A portrait of George Washington, the 1st president of the United States of America, by Gilbert Stuart Williamstown]]
This project is dedicated for the learning of the U. S. Government and Civics, famous politicians, amendments, laws, and more. 
== Projects ==
*[[U. S. Government/WWII]]

==Current Pages==
*[[U. S. Government/U. S. Branches]]
*[[U. S. Government/Political Principles]]
*[[U. S. Government/Civil War Amendments]]
*[[U. S. Government/Citizenship]]
*[[U. S. Government/Immigrants]]
*[[U. S. Government/Industrialization]]
*[[U. S. Government/Labor Movement]]
*[[U. S. Government/political divisions]] 
*[[U. S. Government/Voting Registration and Participation]]
*[[U. S. Government/Elections]]
*[[U. S. Government/Transportation]]
*[[U. S. Government/Communication in the 1920s]]
*[[U. S. Government/Criminal Law vs. Civil Law Notes]]
*[[U. S. Government/Public Policy]]
*[[U. S. Government/Societal Changes and Opportunities for Minorities]]
*[[U. S. Government/Characteristics of Different Economic Types]]
*[[U. S. Government/Quiz]]

==See also==
*[[American Revolution/Chapter 9: Articles of Confederation]]

[[Category:United States Government| ]]
[[Category:Civics]]</text>
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    <title>Emily Dickinson's poems in translation</title>
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The aim of this project is to present translations of Emily Dickinson's poems in various languages. Everyone is welcome to join it, especially those who are interested in Dickinson's legacy, as well as literature/poetry students and teachers. In each of the language sections one may find pages devoted to a discussion of a single poem by Dickinson. The pages contain short history of a given poem, its translations available in a particular language along with their interpretations and comparisons to the original poem. Everyone may learn about various analyses of a poem by clicking on the external links provided on every page. One may also have a look at the manuscripts of a poem, as well as a scansion which shows how to read and accentuate it properly.

== '''Short biography of the poet''' ==
&lt;br&gt;
[[File:Emily_Dickinson_daguerreotype_(cropped).jpg|thumb|350px|right|{{center top}}Emily Dickinson{{center bottom}}]]
[[w:Emily_Dickinson|'''Emily Elizabeth Dickinson''']] (December 10, 1830 – May 15, 1886) was an American [[w:poet|poet]]. Born in [[w:Amherst,_Massachusetts|Amherst, Massachusetts]], to a successful family with strong community ties, she lived a mostly introverted and reclusive life.  After she studied at the [[w:Amherst College#Amherst Academy|Amherst Academy]] for seven years in her youth, she spent a short time at [[w:Mount_Holyoke_Female_Seminary|Mount Holyoke Female Seminary]] before returning to her family's house in Amherst. Considered an eccentric by the locals, she became known for her penchant for white clothing and her reluctance to greet guests or, later in life, even leave her room. Most of her friendships were therefore carried out by correspondence.

While Dickinson was a prolific private poet, fewer than a dozen of her nearly 1,800 poems were published during her lifetime.&lt;ref&gt;Sources differ as to the number of poems that were published, but most put it between seven and ten.&lt;/ref&gt; The work that was published during her lifetime was usually altered significantly by the publishers to fit the conventional poetic rules of the time. Dickinson's poems are unique for the era in which she wrote; they contain short lines, typically lack titles, and often use [[w:Half_rhyme|slant rhyme]] as well as unconventional capitalization and punctuation.&lt;ref name=&quot;Mc2&quot;&gt;McNeil (1986), 2.&lt;/ref&gt; Many of her poems deal with themes of death and immortality, two recurring topics in letters to her friends.

Although most of her acquaintances were probably aware of Dickinson's writing, it was not until after her death in 1886—when Lavinia, Dickinson's younger sister, discovered her cache of poems—that the breadth of Dickinson's work became apparent. Her first collection of poetry was published in 1890 by personal acquaintances [[w:Thomas_Wentworth_Higginson|Thomas Wentworth Higginson]] and [[w:Mabel_Loomis_Todd|Mabel Loomis Todd]], both of whom heavily edited the content. A complete and mostly unaltered collection of her poetry became available for the first time in 1955 when scholar Thomas H. Johnson published ''The Poems of Emily Dickinson''. Despite some unfavorable reviews and some skepticism during the late 19th and early 20th century about Dickinson's literary prowess, Dickinson is now almost universally considered to be one of the most important American poets.&lt;ref name=&quot;Bloo9&quot;&gt;Bloom (1999), 9&lt;/ref&gt;&lt;ref&gt;Ford (1966), 122&lt;/ref&gt;
                                                                    

=='''Languages'''==
* [[/French/]]
* [[/German/]]
* [[/Polish/]]
* Russian
* [[/Spanish/]]
* [[/Kurdish/]]

==''' References'''==
''' Notes'''
[[Category:Poetry translation]]

{{BookCat}}</text>
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    <title>Haskell programming in plain view</title>
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      <comment>/* Lambda Calculus */</comment>
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==Introduction==
* Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]])
* Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]])
* Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]])
* Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]])
* Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]])
&lt;/br&gt;

==Applications==
* Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]])
* Bird's Implementation 
:- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]])
:- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]])
:- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]])
:- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]])

&lt;/br&gt;

==Using GHCi==
* Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]])
&lt;/br&gt;

==Using Libraries==
* Library ([[Media:Library.1.A.20170605.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;


==Types==
* Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]])
* TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]])
* Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]])
* Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]])
* Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]])

==Functions==
* Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]])
* Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]])
* Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]])

==Expressions==
* Expressions I ([[Media:Background.1.D.Expression.20180707.pdf |pdf]])
* Expressions II ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]])
* Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]])
&lt;/br&gt;
&lt;/br&gt;

==Lambda Calculus==
* Lambda Calculus - informal description ([[Media:LCal.1A.informal.20220831.pdf |pdf]])
* Lambda Calculus - Formal definition ([[Media:LCal.2A.formal.20221015.pdf |pdf]])
* Expression Reduction ([[Media:LCal.3A.reduction.20220920.pdf |pdf]])
* Normal Forms ([[Media:LCal.4A.Normal.20220903.pdf |pdf]])
* Encoding Datatypes 
:- Church Numerals ([[Media:LCal.5A.Numeral.20230627.pdf |pdf]])
:- Church Booleans ([[Media:LCal.6A.Boolean.20230815.pdf |pdf]])
:- Functions ([[Media:LCal.7A.Function.20231230.pdf |pdf]])
:- Combinators ([[Media:LCal.8A.Combinator.20241202.pdf |pdf]])
:- Recursions ([[Media:LCal.9A.Recursion.20260518.pdf |A]], [[Media:LCal.9B.Recursion.20260330.pdf |B]])
&lt;/br&gt;
&lt;/br&gt;

==Function Oriented Typeclasses== 
=== Functors ===
* Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]])
* Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]])
* Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]])

=== Applicatives ===
* Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]])
* Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]])
* Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]])
* Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]])

=== Monads I : Background ===
* Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]])
* Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]])
* Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]])
* Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]])
* IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]])
* Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]])

=== Monads II : State Transformer Monads ===
* State Transformer 
: - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]])
: - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]])
: - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]])

* State Monad 
: - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]])
: - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) 
: - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]])

=== Monads III : Mutable State Monads ===
* Mutability Background 
: - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]])
: - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]])
: - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]])
: - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]])
: - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]])

* Mutable Objects
: - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]])
: - Mutable Data Structures  ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]])

* IO Monad 
: - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]])
: - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]])  
: - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]])  

* ST Monad 
: - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]])
: - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]])
: - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]])

=== Monads IV : Reader and Writer Monads ===
* Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]])
* Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]])
* MonadState Class
:: - State &amp; StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]])
:: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]])
* MonadReader Class
:: - Reader &amp; ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]])
:: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]])
* Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]])

=== Monoid ===
* Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]])

=== Arrow ===
* Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]])
&lt;/br&gt;

==Polymorphism==
* Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]])
&lt;/br&gt;

==Concurrent Haskell ==
&lt;/br&gt;


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

==External links==
* [http://learnyouahaskell.com/introduction Learn you Haskell]
* [http://book.realworldhaskell.org/read/ Real World Haskell]
* [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material]


[[Category:Haskell|programming in plain view]]</text>
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    <title>Spiders/Brown Recluse</title>
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      <minor />
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      <text bytes="311" sha1="pw1qwi29hztfbe98d8korzc4lvohlvx" xml:space="preserve">[[File:Brown Recluse.jpg|thumb|right|Brown Recluse]]
The '''Brown Recluse Spider''' is a very poisonous spider in the arachnid family. They are small but very deadly. They can be found in North America.

== Readings ==
* [[Wikipedia: Brown recluse spider]]

== Activities ==
* ''&lt;add learning activities here&gt;''</text>
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      <contributor>
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      <comment>+ [[Category:Spiders]]</comment>
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      <text bytes="333" sha1="3o4m4x27qtg86m5wbgyerfs3b5wau2r" xml:space="preserve">[[File:Brown Recluse.jpg|thumb|right|Brown Recluse]]
The '''Brown Recluse Spider''' is a very poisonous spider in the arachnid family. They are small but very deadly. They can be found in North America.

== Readings ==
* [[Wikipedia: Brown recluse spider]]

== Activities ==
* ''&lt;add learning activities here&gt;''

[[Category:Spiders]]</text>
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  <page>
    <title>Python programming in plain view</title>
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      <contributor>
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        <id>21186</id>
      </contributor>
      <comment>/* Using Libraries */</comment>
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      <text bytes="2647" sha1="5q7witvtzcswb69y50yyj9gxiyoktgg" xml:space="preserve">==''' Part I '''==
&lt;!----------------------------------------------------------------------&gt;
===  Introduction ===

* Overview 
* Memory 
* Number 

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


=== Python for C programmers ===

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

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


=== Using Libraries ===

* Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]])
* Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]])
* Packages ([[Media:Python.Work2.Package.1A.20241207.pdf |pdf]])
* Libraries ([[Media:Python.Work2.Library.1A.20260518.pdf |pdf]])
* Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]])


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

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

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

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

=== Handling a Big Work ===

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

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

=== Handling Series of Data ===

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

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

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


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

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

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

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

==External links==
* [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering]</text>
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    <title>NCERT/Textbook Solutions/Class VII/Mathematics</title>
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      <minor />
      <comment>/* See Also */</comment>
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      <text bytes="1468" sha1="hgtfua1w2eebqcspd5xg4aq4m3p10p8" xml:space="preserve">[[Wikipedia: National Council of Educational Research and Training|'''NCERT''']] books are based upon the curriculum/syllabus defined by [[Wikipedia: Central Board of Secondary Education|CBSE]]. These syllabus are periodically reviewed and revised. The NCERT book for a particular subject is divided into various chapters and every chapter has a set of questions following the chapter. This section provides answers to the questions at the end of each chapter in the '''Maths''' book, for  [[NCERT/Textbook_Solutions#Solutions_to_Textbooks_of_Class_VII|'''Class-VII''']].

==Chapter 01 Integers==

==Chapter 02 Fractions and Decimals==

==Chapter 03 Data Handling==

==Chapter 04 Simple Equations==

==Chapter 05 Lines and Angles==

==Chapter 06 Triangles and its properties==

==Chapter 07 Congruence of Triangles==

==Chapter 08 Comparing Quantities==

==Chapter 09 Rational Numbers==

==Chapter 10 Practical Geometry==

==Chapter 11 Perimeter and Area==

==Chapter 12 Algebraic Expressions==

==Chapter 13 Exponents and Powers==

==Chapter 14 Symmetry==

==Chapter 15 Visualising Solid Shapes==

==See Also==
* [[NCERT/Textbook_Solutions]]

* [[NCERT/Textbook_Solutions#Solutions_to_Textbooks_of_Class_VII]]
* [https://www.edzy.ai/ Edzy.ai]

==External Links==
* [http://www.ncert.nic.in/index.html Official website of NCERT]
* [http://epathshala.nic.in/e-pathshala-4/flipbook/ NCERT textbooks available online]

==References==
{{Reflist}}

[[Category:Mathematics]]</text>
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      <text bytes="6613" sha1="6gkqgwwoxmj2wp1v5hbx2am3lx2e438" xml:space="preserve">{{biology}}
==Scope &amp; Objectives of the Book==

This book deals with the basic understanding and mysteries of human fetal growth, development and maturation inside the mother’s womb up to the 2nd trimester.&lt;ref&gt;Bhattacharya, Niranjan, Stubblefield, Phillip G. (Eds.),m Human Fetal Growth and Development, First and Second Trimesters, Page No. XII, Introduction. {{ISBN|978-3-319-14873-1}}, 1st Edition, 2016.&lt;/ref&gt;

With ever growing knowledge in the field of genetics, this book has tried to disseminate the knowledge of the impact of genetics and its factors that influence the growth and maturation of the fetus and its future implications in the individual’s health and development.  Various important factors like maternal nutrition, environment of the fetus and the mother’s womb, genetics of the fetus and nutrition of the mother all helps in the production of a healthy or an unhealthy baby. The current book encompasses areas and topics pertaining to the fields of obstetrics, gynecology, biochemistry, genetics, stem cells and their regulations during the fetal growth and development, molecular biology, clinical and futuristic medicine including modern topics pertaining to clinical and surgical interventions of in utero fetal surgery and fetal cord blood transfusion and advancements in the field of neonatology. The book proposes that these modern topics will help in incorporating the students, researchers and a wide group of biomedical scientists to update their current clinical and surgical knowledge apart from their existing knowledge and thereby prompting futuristic and cutting edge research.&lt;ref&gt;Bhattacharya, Niranjan, Stubblefield, Phillip G. (Eds.),m Human Fetal Growth and Development, First and Second Trimesters, Page No. XV, Introduction. {{ISBN|978-3-319-14873-1}}, 1st Edition, 2016.&lt;/ref&gt;

The two editors Prof. Niranjan Bhattacharya and Prof. Phillip Stubblefield are both stalwarts in the field of Obstetrics and Gynecology and Stem cell and Regenerative Medicine. Prof. Niranjan Bhattacharya was the pioneer of Cord Blood Transfusion since 1999 and Prof. Stubblefield an emeritus professor of Boston University. With their varied and multidiscipline knowledge the following editors felt they could use their expertise to help in develop a book that will help in global dissemination of specialized knowledge in the field of regenerative medicine, growth and maturation, its implication from a multi-dimensional point of view and help in developing a cutting edge knowledge in the field of fetal growth and development.

This book is also dedicated to two renowned scientists in the field of Reproductive Immunology, Prof. Alan Beer and physiologist and biochemist Dr. Chameli Ganguly.&lt;ref&gt;Bhattacharya, Niranjan, Stubblefield, Phillip G. (Eds.),m Human Fetal Growth and Development, First and Second Trimesters,Opening,{{ISBN|978-3-319-14873-1}}, 1st Edition, 2016.&lt;/ref&gt; The aim of this book is to currently meant to bring together embryologists, medical scientists, clinical practitioners, gynecologists, endocrinologists, reproductive and molecular biologists and geneticists and integrate and combine different knowledge and discipline to enhance the knowledge in understanding the mysteries of fetal tissue and development.

==Chapters of the Book==
Different chapters of this book deals with the basic medical science of the growth, development, metabolism and biological synthesis of the individual fetal organ during the development process in the mother’s womb. Studies like fetus and their origin, measurement also termed as Anthropometric measurements at various gestational age group has been mentioned in details with observational datas. Development of the fetal immune system, hematopoiesis has been described in details by eminent immunologists including a very basic, fundamental and interesting thoughts on vaccination of the unborn using tetanus toxoid used for the first time by one of the editors of this book, Prof. Niranjan Bhattacharya and Prof. K.L.Mukherjee as a safe and cheap abortifacient.

Importance of glucose uptake, fetomaternal circulation, and metabolism in Chapter No.11 as it is an important biological mechanism involving lipid, carbohydrate and protein metabolism for the fetus including genetic factors controlling the role of organ development and function. These all have been explained in details in the book in Chapter no.6, 7, 8 &amp; 9.
The book further deals with the intricacies of fetal protein, carbohydrate and urea synthesis like very little amount of urea is synthesized by the fetal liver which increases with the increase in gestational time. This increase in urea synthesis is although still very minute when compared to the adult liver urea synthesis. Further questions like distinguishing the different adultogenic layer in Chapter No.10 have also been detailed.

Epigenetic and genetic studies of the fetus and the fetus controlling the fetal development are discussed in Chapter no.13 whereas Chapter No.14 deals with a bio-philosophical and an extremely important ethical and debatable concept of “When does the fetus attains a person hood. Is it after the beating of the heart or after the formation of the zygote.”
Questions in the form of chapters on topics like “How does the fetus survives in the mother’s womb for 9 months and why it is not rejected are highlighted with different concepts, theories, hypothesis and scientific explanations involving the laws of classical immunology. Chapter No.21 includes the maternal immune system and how it fights to ward off infections.
Other chapters deal with the importance of the breast milk and its evolution and its importance during the time of pregnancy. Genetic diseases and stem cell development specific to human embryo and its development, their implications, 87 total number of human embryonic stem cell lines are derived til date, screening of 137 normal human embryonic stem cell lines , role of chemokine receptors like CCR5 are all described in details.

Further questions pertaining to how stem cells are formed and developed during the embryonic stage are explained. The mechanism and their potency in regeneration abilities and capacities. Specific organ development, maturation and function with increase in their gestational age are all discussed in details in this book at both molecular , physiological and biochemical level in details.

==References==
{{Reflist}}

==See also==
* [[Medicine]]
* [[Biology]]

==External Links==
http://link.springer.com/book/10.1007%2F978-3-319-14874-8

[[Category:Medicine]]
[[Category:Immunology]]</text>
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    <title>Parabola</title>
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      <text bytes="37953" sha1="myxkf5p09ddlfnt26egidt8hrogbmai" xml:space="preserve">[[File:20170525 Parabola y = (x^2)-(4q) 00.png|thumb|300px|'''
Figure 1: The Parabola &lt;math&gt;y = \frac{x^2}{4q}&lt;/math&gt;'''&lt;/br&gt;
Focus at point &lt;math&gt;F\ (0,q)&lt;/math&gt;&lt;/br&gt;
Vertex at origin &lt;math&gt;(0,0)&lt;/math&gt;&lt;/br&gt;
Directrix is line &lt;math&gt;y = -q&lt;/math&gt;&lt;/br&gt;
By definition &lt;math&gt;P_1F = P_1D_1,\ P_2F = P_2D_2,\ P_4F = P_4D_4.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;VF = VD_3 = q.&lt;/math&gt;&lt;/br&gt;
In Figure 1 &lt;math&gt;q = 1&lt;/math&gt;]]
In Cartesian geometry in two dimensions the &lt;math&gt;parabola&lt;/math&gt; is the locus of a point that moves so that it is always equidistant from a fixed point and a fixed line.
The fixed point is called the &lt;math&gt;focus&lt;/math&gt; and the fixed line is called the &lt;math&gt;directrix&lt;/math&gt;. Distance from &lt;math&gt;focus&lt;/math&gt; to &lt;math&gt;directrix&lt;/math&gt;
is non-zero.

See '''Figure 1.''' 

The focus is point &lt;math&gt;F\ (0,q)&lt;/math&gt; and the directrix is line &lt;math&gt;D_1D_4&lt;/math&gt;&lt;math&gt;:\ y = -q.&lt;/math&gt; The &lt;math&gt;vertex&lt;/math&gt;, point &lt;math&gt;V&lt;/math&gt;&lt;math&gt;:\ (0,0)&lt;/math&gt;, is half-way between 
focus and directrix. A &lt;math&gt;chord&lt;/math&gt; is the segment of a line joining any two distinct points of the parabola. The line segment &lt;math&gt;P_2FP_4&lt;/math&gt;
is a chord. Because chord &lt;math&gt;P_2FP_4&lt;/math&gt; passes through the focus &lt;math&gt;F&lt;/math&gt;, it is called a &lt;math&gt;focal\ chord.&lt;/math&gt;

The focal chord parallel to the directrix is called the &lt;math&gt;latus\ rectum.&lt;/math&gt;

The line through the focus and perpendicular to the directrix is the &lt;math&gt;axis&lt;/math&gt;, sometimes called &lt;math&gt;axis\ of\ symmetry&lt;/math&gt;.


Let an arbitrary point on the curve be &lt;math&gt;(x,y)&lt;/math&gt;.


By definition, &lt;math&gt;\sqrt{(x-0)^2 + (y-q)^2} = y + q&lt;/math&gt;. This expression expanded gives:

:&lt;math&gt;x^2 - 4qy = 0;\ y = \frac{x^2}{4q}&lt;/math&gt;.


If the equation of the curve is expressed as: &lt;math&gt;y = Kx^2&lt;/math&gt;, then &lt;math&gt;K=\frac{1}{4q};\ 4Kq=1;\ q = \frac{1}{4K}&lt;/math&gt; where the &lt;math&gt;focus&lt;/math&gt;
has coordinates &lt;math&gt;(0,q),&lt;/math&gt; and &lt;math&gt;q&lt;/math&gt; is the distance form vertex to focus.


If the directrix is parallel to the &lt;math&gt;X&lt;/math&gt; axis, then the parabola is the same as the familiar quadratic function.


The general parabola allows for a directrix anywhere with any orientation.


== The General Parabola ==
&lt;/br&gt;

Let the directrix be &lt;math&gt;ax + by + c = 0&lt;/math&gt; where at least one of &lt;math&gt;a,b&lt;/math&gt; is non-zero.

Let the focus be &lt;math&gt;(p,q)&lt;/math&gt;.

Let &lt;math&gt;(x,y)&lt;/math&gt; be any point on the curve.


Distance from point &lt;math&gt;(x,y)&lt;/math&gt; to focus &lt;math&gt;(p,q)&lt;/math&gt; = &lt;math&gt;\sqrt{(x-p)^2 + (y-q)^2}&lt;/math&gt;.

Distance from point &lt;math&gt;(x,y)&lt;/math&gt; to directrix (&lt;math&gt;ax + by + c = 0&lt;/math&gt;) 

= &lt;math&gt;\frac{ax + by + c}{\sqrt{R}}&lt;/math&gt; where &lt;math&gt;R = a^2 + b^2&lt;/math&gt;.


By definition these two lengths are equal:

&lt;math&gt;\sqrt{(x-p)^2 + (y-q)^2} = \frac{ax + by + c}{\sqrt{R}}&lt;/math&gt;.

&lt;math&gt;\therefore\ \sqrt{R}\sqrt{(x-p)^2 + (y-q)^2} = ax + by + c&lt;/math&gt;.

Square both sides:

&lt;math&gt;R((x-p)^2 + (y-q)^2) = (ax + by + c)^2&lt;/math&gt;.

&lt;math&gt;R((x-p)^2 + (y-q)^2) - (ax + by + c)^2 = 0&lt;/math&gt;.


Expand and the result is:

&lt;math&gt;b^2x^2 -2abxy + a^2y^2 - 2(ac+pR)x - 2(bc+qR)y  +R(p^2+q^2)-c^2 = 0\ \dots\ (1)&lt;/math&gt;.


&lt;math&gt;(1)&lt;/math&gt; has the form of the equation of the conic section &lt;math&gt;Ax^2 + Bxy + Cy^2  + Dx + Ey + F = 0&lt;/math&gt; where


&lt;math&gt;\begin{align}
A&amp; = b^2\\
B&amp; = -2ab\\
C&amp;= a^2\\
D&amp;= -2(ac+pR)\\
E&amp;= -2(bc+qR)\\
F&amp; = R(p^2+q^2)-c^2\\
\\
B&amp;^2 -4AC = 0\\
R&amp; = a^2 + b^2
\end{align}&lt;/math&gt;


&lt;math&gt;B^2 = 4AC&lt;/math&gt; because this curve is a parabola.


== An Example ==
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[[File:20170525 General parabola 00.png|thumb|300px|'''
Figure 2: The Parabola &lt;math&gt;16x^2 + 24xy + 9y^2 - 20x -140y + 100 = 0&lt;/math&gt;'''&lt;/br&gt;
Green line is &lt;math&gt;directrix:\ 3x - 4y - 5 = 0&lt;/math&gt;&lt;/br&gt;
Blue line is &lt;math&gt;axis:\ 4x + 3y - 10 = 0&lt;/math&gt;&lt;/br&gt;
Focus at point &lt;math&gt;F:\ (1,2)&lt;/math&gt;&lt;/br&gt;
Vertex at point &lt;math&gt;V:\ (1.6, 1.2)&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;VF = 1.&lt;/math&gt; Shape of curve is: &lt;math&gt;y = \frac{x^2}{4}.&lt;/math&gt;
]]

See Figure 2.


&lt;math&gt;(a,b,c) = (3,-4,-5)&lt;/math&gt;

&lt;math&gt;(p,q) = (1,2)&lt;/math&gt;


The equation of the parabola is derived as follows:


&lt;math&gt;\begin{align}
&amp;A = b^2 = (-4)^2 = 16\\
&amp;B = -2ab = -2(3)(-4) = 24\\
&amp;C = a^2 = (3)^2 = 9\\
&amp;R = a^2 + b^2 = 25\\
&amp;D = -2(ac + pR) = -2((3)(-5) + (1)(25)) = -2(-15+25) = -2(10) = -20\\
&amp;E = -2(bc + qR) = -2((-4)(-5) + (2)(25)) = -2(20 + 50) = -2(70) = -140\\
&amp;F = R(p^2 + q^2) - c^2 = 25(1 + 4) - 25 = 100
\end{align}&lt;/math&gt;


The equation of the parabola in Figure 2 is: &lt;math&gt;16x^2 + 24xy + 9y^2 -20x -140y + 100 = 0.&lt;/math&gt;


Equation of directrix in normal form: &lt;math&gt;\frac{3}{5}x - \frac{4}{5}y - 1 = 0.&lt;/math&gt;

Distance from &lt;math&gt;focus&lt;/math&gt; to &lt;math&gt;directrix = \frac{3}{5}(1) - \frac{4}{5}(2) - 1 = -2.&lt;/math&gt;

Distance from vertex to focus &lt;math&gt;= 1 = \frac{1}{4K}&lt;/math&gt;.

Therefore, curve has shape of &lt;math&gt;y = Kx^2&lt;/math&gt; where &lt;math&gt;K = \frac{1}{4}&lt;/math&gt;.
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Caution: An interesting situation occurs if the focus is on the directrix. Consider the directrix:

&lt;math&gt;4x - 3y + 15 = 0&lt;/math&gt; and the focus &lt;math&gt;(3,9)&lt;/math&gt; which is on the directrix.

&lt;math&gt;a = 4,\ b =-3,\ c =15,\ p=3,\ q=9&lt;/math&gt;


In this case the &quot;parabola&quot; has equation: &lt;math&gt;9xx + 24xy + 16yy  - 270x - 360y + 2025 = 0&lt;/math&gt;.

This seems to be the equation of a parabola because &lt;math&gt;B^2 - 4AC = 0&lt;/math&gt;, but look closely.

&lt;math&gt;9xx + 24xy + 16yy - 270x - 360y + 2025 = (3x+4y-45)^2&lt;/math&gt;.

The result is a line through the focus and normal to the directrix.


If you solve for &lt;math&gt;p, q, c&lt;/math&gt; using the algebraic solutions, you will produce the values &lt;math&gt;3, 9, 15&lt;/math&gt; as above.

However, the distance between focus and directrix = &lt;math&gt;\frac{4}{5}x + \frac{-3}{5}y + 3&lt;/math&gt; 

where 
&lt;math&gt;x = p;\ y = q;&lt;/math&gt;
distance &lt;math&gt;= \frac{4}{5}(3) + \frac{-3}{5}(9) + 3 = 0.&lt;/math&gt;
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== Reverse-Engineering the Parabola ==
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[[File:20170526 Parabola and 2 tangents 00.png|thumb|300px|
'''Figure 3: Parabola with 2 tangents parallel to axes.'''&lt;/br&gt;
Tangent &lt;math&gt;ABC: y = \frac{16}{3}&lt;/math&gt;.&lt;/br&gt;
Tangent &lt;math&gt;ADE: x = -0.25&lt;/math&gt;.&lt;/br&gt;
Point &lt;math&gt;A&lt;/math&gt; on directrix, oblique, thin, black line.&lt;math&gt;&lt;/math&gt;&lt;/br&gt;
Line &lt;math&gt;AFG&lt;/math&gt; perpendicular to focal chord &lt;math&gt;BFD.&lt;/math&gt;&lt;/br&gt;
Focus at &lt;math&gt;F: (1,7)&lt;/math&gt;.]]


Given a parabola in form &lt;math&gt;Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0&lt;/math&gt; the aim is to produce the directrix and the focus.


We will solve the example shown in Figure 3: &lt;math&gt;9x^2 - 24xy + 16y^2 + 70x - 260y + 1025 = 0&lt;/math&gt;,


where:

&lt;math&gt;\begin{align}
A&amp;=9\\
B&amp;=-24\\
C&amp;=16\\
D&amp;=70\\
E&amp;=-260\\
F&amp;=1025
\end{align}&lt;/math&gt;


&lt;math&gt;a = \sqrt{C} = 4;\ b = \frac{-B}{2a} = \frac{-(-24)}{8} = 3&lt;/math&gt;.


===Method 1. By analytical geometry===
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Find two tangents that intersect at a right angle. The simplest to find are those that are parallel to the axes.
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Put the equation of the parabola in the form of a quadratic in &lt;math&gt;x&lt;/math&gt;.

&lt;math&gt;Ax^2 + Bxy + Dx  + Cy^2 + Ey + F = 0&lt;/math&gt;

&lt;math&gt;Ax^2 + (By + D)x  + (Cy^2 + Ey + F) = 0&lt;/math&gt;

At the tangent there is exactly one value of &lt;math&gt;x&lt;/math&gt;. Therefore the discriminant must be &lt;math&gt;0&lt;/math&gt;.

&lt;math&gt;  (By + D)^2 - 4(A)(Cy^2 + Ey + F) = 0 &lt;/math&gt;

&lt;math&gt;BByy + 2BDy + DD -4ACyy - 4AEy -4AF = 0&lt;/math&gt;

&lt;math&gt;(BB-4AC)yy + (2BD-4AE)y + (DD-4AF) = 0&lt;/math&gt;

In the general parabola &lt;math&gt;B^2-4AC = 0&lt;/math&gt; therefore &lt;math&gt;y=\frac{4AF-DD}{2BD-4AE}&lt;/math&gt;.

In this example &lt;math&gt;y=\frac{16}{3};\ x=\frac{-(By+D)}{2A}=\frac{29}{9}&lt;/math&gt;.

Point &lt;math&gt;B (x_1, y_1)&lt;/math&gt; has coordinates &lt;math&gt;(\frac{29}{9},\ \frac{16}{3})&lt;/math&gt;.

The line &lt;math&gt;ABC&lt;/math&gt; is tangent to the curve at &lt;math&gt;B&lt;/math&gt; and has equation: &lt;math&gt;y=\frac{16}{3}&lt;/math&gt;.
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Put the equation of the parabola in the form of a quadratic in &lt;math&gt;y&lt;/math&gt;:

&lt;math&gt;Cy^2 + (Bx+ E)y + (Ax^2 + Dx + F) = 0&lt;/math&gt;.

By using calculations similar to the above, &lt;math&gt;x = \frac{4CF-EE}{2BE-4CD} = -0.25&lt;/math&gt; and 
&lt;math&gt;y = \frac{-(Bx+E)}{2C} = 7.9375&lt;/math&gt;. 

Point &lt;math&gt;D(x_2,y_2)&lt;/math&gt; has coordinates &lt;math&gt;(-0.25,\ 7.9375)&lt;/math&gt;.

The line &lt;math&gt;ADE&lt;/math&gt; is tangent to the curve at &lt;math&gt;D&lt;/math&gt; and has equation: &lt;math&gt;x=-0.25&lt;/math&gt;.
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Point &lt;math&gt;A&lt;/math&gt; at the intersection of the two tangents has coordinates &lt;math&gt;(x_2,y_1)=(-0.25,\ \frac{16}{3})&lt;/math&gt;, 
and point &lt;math&gt;A&lt;/math&gt; is on the directrix, the equation of which is: &lt;math&gt;ax+by+c=0&lt;/math&gt;.

Put known values into the equation of the directrix: &lt;math&gt;(4)(-0.25) + (3)\frac{16}{3}+c=0&lt;/math&gt;.

Therefore &lt;math&gt;c = -15&lt;/math&gt; and the equation of the directrix is: &lt;math&gt;4x+3y-15=0&lt;/math&gt;.
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The coordinates of points &lt;math&gt;B,D&lt;/math&gt; are known. Therefore chord &lt;math&gt;BD&lt;/math&gt; is defined 
as: &lt;math&gt;\frac{3}{5}x+\frac{4}{5}y-6.2=0&lt;/math&gt;.

Draw the line &lt;math&gt;AG&lt;/math&gt; perpendicular to &lt;math&gt;BD&lt;/math&gt;. The line &lt;math&gt;AG&lt;/math&gt; is 
defined as: &lt;math&gt;\frac{4}{5}x - \frac{3}{5}y+3.4 = 0&lt;/math&gt;. 

Point &lt;math&gt;F&lt;/math&gt; at the intersection of lines &lt;math&gt;BD, AG&lt;/math&gt; is the focus with coordinates &lt;math&gt;(1,7)&lt;/math&gt;.
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===Method 2. By algebra===
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:&lt;math&gt;\begin{align}
A&amp;=b^{2}\\
B&amp;=-2ab\\
C&amp;=a^{2}\\
D&amp;=-2(ac+pR)\\
E&amp;=-2(bc+qR)\\
F&amp;=R(p^{2}+q^{2})-c^{2}\\
\\
B&amp;^{2}-4AC=0\\
R&amp;= a^2 + b^2
\end{align}&lt;/math&gt;


After rearranging the above values, there are three equations to be solved for three unknowns: &lt;math&gt;p, q, c&lt;/math&gt;:

:&lt;math&gt;\begin{align}

D + 2ac + 2pR = 0\\
E + 2bc + 2qR = 0\\
F - Rpp - Rqq + cc = 0

\end{align}&lt;/math&gt;


The solutions are:


&lt;math&gt;c = \frac{   4FR - (DD + EE )  }{  4Da + 4Eb    }&lt;/math&gt;


&lt;math&gt;p = \frac{   -(D+2ac)    }{      2R    }&lt;/math&gt;


&lt;math&gt;q = \frac{      -(E+2bc)    }{     2R    }&lt;/math&gt;

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If &lt;math&gt;b&lt;/math&gt; is &lt;math&gt;0,\ A = B = 0,\ R = a^2 = C,&lt;/math&gt; the parabola becomes the quadratic: &lt;math&gt;-Dx = Cy^2 + Ey + F&lt;/math&gt; and:

:&lt;math&gt;\begin{align}
p&amp; = \frac{E^2 - D^2 -4FC}{4CD}\\
q&amp; = \frac{-E}{2C}\\
c&amp; = \frac{   4FC - (DD + EE )  }{  4Da   }
\end{align}&lt;/math&gt;

The directrix has equation: &lt;math&gt;ax + c = 0;\ ax = -c;\ x = \frac{DD+EE - 4FC}{4CD}&lt;/math&gt;.


If &lt;math&gt;D&lt;/math&gt; is &lt;math&gt;-1&lt;/math&gt;, then:

:&lt;math&gt;\begin{align}
x&amp; = Cy^2 + Ey + F\\
p&amp; = \frac{E^2 - 1 -4FC}{4C(-1)} = \frac{1 - (E^2 - 4CF)}{4C}\\
q&amp; = \frac{-E}{2C}
\end{align}&lt;/math&gt;

The directrix has equation: &lt;math&gt;x = \frac{-1-(E^2-4CF)}{4C}&lt;/math&gt;.
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If &lt;math&gt;a&lt;/math&gt; is &lt;math&gt;0,\ B = C = 0,\ R = b^2 = A,&lt;/math&gt; the parabola becomes the quadratic: &lt;math&gt;-Ey = Ax^2 + Dx + F&lt;/math&gt; and:

:&lt;math&gt;\begin{align}
p&amp; = \frac{-D}{2A}\\
q&amp; = \frac{D^2 - E^2 - 4FA}{4EA}\\
c&amp; = \frac{   4FA - (DD + EE )  }{  4Eb    }
\end{align}&lt;/math&gt;

The directrix has equation: &lt;math&gt;by + c = 0;\ by = -c;\ y = \frac{ DD + EE - 4FA  }{ 4EA  }&lt;/math&gt;.

[[File:Quadratic function graph key values.svg|thumb|Graph of quadratic function&lt;/br&gt;
&lt;math&gt;y = x^2 - 2x - 3&lt;/math&gt; showing :&lt;/br&gt;
* X and Y intercepts in red,&lt;/br&gt;
* vertex and axis of symmetry in blue,&lt;/br&gt;
* focus and directrix in pink.]]


If &lt;math&gt;E&lt;/math&gt; is &lt;math&gt;-1&lt;/math&gt;, then:

:&lt;math&gt;\begin{align}
y&amp; = Ax^2 + Dx + F\\
p&amp; = \frac{-D}{2A}\\
q&amp; = \frac{D^2 - 1 - 4FA}{4(-1)A} = \frac{1-(D^2 - 4AF)}{4A}
\end{align}&lt;/math&gt;

The directrix has equation: &lt;math&gt;y = \frac{-1-(D^2-4AF)}{4A}&lt;/math&gt;.


These values agree with the corresponding values in the graph of &lt;math&gt;y = x^2 - 2x - 3&lt;/math&gt; to the right.
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== Slope of the Parabola ==
&lt;/br&gt;

Consider parabola &lt;math&gt;Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0&lt;/math&gt; and line &lt;math&gt;y = mx + c.&lt;/math&gt;

Let point &lt;math&gt;(X,Y)&lt;/math&gt; be any point on the line.
Therefore &lt;math&gt;Y = mX + c;\ c = Y - mX;\ y = mx + (Y - mX).&lt;/math&gt;

Let the line intersect the parabola.
Substitute the above value of &lt;math&gt;y&lt;/math&gt; into the equation of the parabola and expand:


:&lt;math&gt;\begin{align}
(+ A + Bm + Cmm)&amp;xx+\\
(- BXm + BY - 2CXmm + 2CYm + D + Em)&amp;x+\\
(+ CXXmm - 2CXYm + CYY - EXm + EY + F)&amp; = 0
\end{align}&lt;/math&gt;


We want the line to be tangent to the curve. Therefore &lt;math&gt;x&lt;/math&gt; must have exactly one value and the discriminant is &lt;math&gt;0.&lt;/math&gt;

Discriminant = 

:&lt;math&gt;\begin{align}
(- BXm + BY - 2CXmm + 2CYm + D + Em)(- BXm + BY - 2CXmm + 2CYm + D + Em)&amp;\\
 - 4(+ A + Bm + Cmm)(+ CXXmm - 2CXYm + CYY - EXm + EY + F)&amp;  = 0    
\end{align}&lt;/math&gt;


The above discriminant is a quadratic in &lt;math&gt;m&lt;/math&gt;:

:&lt;math&gt;\begin{align}
(- 4ACXX + BBXX + 2BEX - 4CDX - 4CF + EE)&amp;mm+\\
(+ 8ACXY + 4AEX - 2BBXY - 2BDX - 2BEY - 4BF + 4CDY + 2DE)&amp;m+\\
(- 4ACYY - 4AEY - 4AF + BBYY + 2BDY + DD)&amp; = 0
\end{align}&lt;/math&gt;


&lt;math&gt;m = \frac{   -(+ 8ACXY + 4AEX - 2BBXY - 2BDX - 2BEY - 4BF + 4CDY + 2DE) \pm \sqrt{R}        }{       2  (- 4ACXX + BBXX + 2BEX - 4CDX - 4CF + EE)          }&lt;/math&gt;


where:

:&lt;math&gt;\begin{align}
R =&amp;\  16 (AXX + BXY + CYY + DX + EY + F) (-4ACF+AEE+BBF-BDE+CDD)
\end{align}&lt;/math&gt;


If the point &lt;math&gt;(X,Y)&lt;/math&gt; is on the curve, then the line touches the curve at &lt;math&gt;(X,Y)&lt;/math&gt; and:


:&lt;math&gt;\begin{align}
(AX&amp;X + BXY + CYY + DX + EY + F) = 0;\ R = 0\\
\\
m =&amp;\ \frac{   -(+ 8ACXY + 4AEX - 2BBXY - 2BDX - 2BEY - 4BF + 4CDY + 2DE)   }{       2  (- 4ACXX + BBXX + 2BEX - 4CDX - 4CF + EE)     }\\
\\
  =&amp;\ \frac{  2BBXY - 8ACXY + 2BDX - 4AEX + 2BEY - 4CDY + 4BF  - 2DE   }{       2  (BBXX - 4ACXX  + 2BEX - 4CDX + EE - 4CF)     }\\
\\
=&amp;\ \frac{  (BB - 4AC)XY + (BD - 2AE)X + (BE - 2CD)Y + 2BF  - DE   }{      (BB - 4AC)XX  + (2BE - 4CD)X + EE - 4CF     }\\
\\
=&amp;\ \frac{  (BD - 2AE)X + (BE - 2CD)Y + 2BF  - DE   }{    (2BE - 4CD)X + EE - 4CF     }
\end{align}&lt;/math&gt;


because &lt;math&gt;B^2 -4AC = 0&lt;/math&gt; for a parabola.


When slope is displayed in this format, we see that slope is vertical if &lt;math&gt;  (2BE - 4CD)X + EE - 4CF  = 0.   &lt;/math&gt;


The line &lt;math&gt;x = \frac{4CF-EE}{2BE-4CD}&lt;/math&gt; is tangent to the curve.
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Let the equation of a line be: &lt;math&gt;x = My + c&lt;/math&gt; in which case &lt;math&gt;M = \frac{1}{m}.&lt;/math&gt;

By using calculations similar to the above it can be shown that:


&lt;math&gt;M = \frac{ (BD - 2AE)X + (BE - 2CD)Y + 2BF - DE             }{    (2BD - 4AE)Y + DD - 4AF      }&lt;/math&gt;.


&lt;math&gt;m = \frac{1}{M}&lt;/math&gt; therefore:


&lt;math&gt;m= \frac {    (2BD - 4AE)Y + DD - 4AF             }{    (BD - 2AE)X + (BE - 2CD)Y + 2BF - DE             }&lt;/math&gt;


When slope is displayed in this format, we see that slope is zero if  &lt;math&gt;     (2BD - 4AE)Y + DD - 4AF   = 0    &lt;/math&gt;.


The line &lt;math&gt;y = \frac{4AF-DD}{2BD-4AE}&lt;/math&gt; is tangent to the curve.
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This examination of the parabola has produced two expressions for slope of the parabola:


&lt;math&gt;m = \frac { (2BD - 4AE)y + DD - 4AF } { (BD - 2AE)x + (BE - 2CD)y + 2BF - DE } = \frac{ (BD - 2AE)x + (BE - 2CD)y + 2BF  - DE } { (2BE - 4CD)x + EE - 4CF }  &lt;/math&gt;.


where the point &lt;math&gt;(x, y)&lt;/math&gt; is any arbitrary point on the curve.


Therefore &lt;math&gt;m = \pm\sqrt{ \frac{ (2BD - 4AE)y + DD - 4AF } { (2BE - 4CD)x + EE - 4CF } }&lt;/math&gt;. This formula for &lt;math&gt;m&lt;/math&gt;
contains both tangents parallel to the axes and is derived without calculus. 
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The formula from calculus below is simpler and unambiguous concerning sign.


:&lt;math&gt;\begin{align}

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\\
\\
\frac{d}{dx}(Ax^2 + Bxy + Cy^2 + Dx + Ey + F) = 0\\
\\
A(2x) + B(x\frac{dy}{dx} + y \frac{dx}{dx}  ) + C(2y\frac{dy}{dx}) + D + E(\frac{dy}{dx}) = 0\\
\\
A(2x) + B( x\frac{dy}{dx} + y ) + C(2y\frac{dy}{dx}) + D + E(\frac{dy}{dx}) = 0\\
\\
2Ax + Bx\frac{dy}{dx} + By + 2Cy\frac{dy}{dx} + D + E\frac{dy}{dx} = 0\\
\\
\frac{dy}{dx}(Bx + 2Cy + E) = -(2Ax + By + D)\\
\\
m = \frac{dy}{dx} = \frac{-(2Ax + By + D)}{Bx + 2Cy + E}

\end{align}&lt;/math&gt;
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The slope of the parabola is &lt;math&gt;0&lt;/math&gt; where &lt;math&gt;(2BD - 4AE)y + DD - 4AF = 0;\ 2Ax + By + D = 0;&lt;/math&gt; or:

&lt;math&gt;y = \frac{4AF-DD}{2BD-4AE};\ x = \frac{-(By+D)}{2A}.&lt;/math&gt;


The slope of the parabola is vertical where &lt;math&gt;(2BE - 4CD)x + EE - 4CF  = 0;\ Bx + 2Cy + E = 0;&lt;/math&gt; or:

&lt;math&gt;x = \frac{4CF - EE}{2BE-4CD};\ y = \frac{-(Bx+E)}{2C}.&lt;/math&gt;
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Caution: 

If the curve is &lt;math&gt;y = Kx^2&lt;/math&gt;, the slope can never be vertical.

If the curve is &lt;math&gt;x = Ky^2&lt;/math&gt;, the slope can never be &lt;math&gt;0&lt;/math&gt;.
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If &lt;math&gt;B=C=0&lt;/math&gt; and &lt;math&gt;E=-1&lt;/math&gt;, the equation of the parabola becomes: &lt;math&gt;y = Ax^2 + Dx + F&lt;/math&gt; and:


:&lt;math&gt;\begin{align}
m =&amp;\ \frac { (2BD - 4AE)y + DD - 4AF } { (BD - 2AE)x + (BE - 2CD)y + 2BF - DE }\\
\\
=&amp;\ \frac { (- 4A(-1))y + DD - 4AF } { (- 2A(-1))x  - D(-1) } = \frac { 4Ay + DD - 4AF } {  2Ax + D }\\
\\ 
=&amp;\ \frac { 4A(Ax^2+Dx+F) + DD - 4AF } {  2Ax + D } = \frac { 4A^2x^2+4ADx+4AF + DD - 4AF } {  2Ax + D }\\
\\
=&amp;\ \frac { 4A^2x^2+4ADx + DD } {  2Ax + D }\\
\\
=&amp;\ 2Ax + D\\
\\
m =&amp;\ \frac{ (BD - 2AE)x + (BE - 2CD)y + 2BF  - DE } { (2BE - 4CD)x + EE - 4CF }\\
\\
=&amp;\ \frac{ ((0)D - 2A(-1))x + ((0)E - 2(0)D)y + 2(0)F  - D(-1) } { (2(0)E - 4(0)D)x + (-1)(-1) - 4(0)F }\\
\\
=&amp;\ \frac{ ( - 2A(-1))x    - D(-1) } {  (-1)(-1)  }\\
\\
=&amp;\ 2Ax + D\\
\\
m =&amp;\ \frac{-(2Ax + By + D)}{Bx + 2Cy + E}\\
\\
=&amp;\ \frac{-(2Ax + (0)y + D)}{(0)x + 2(0)y + (-1)}\\
\\
=&amp;\ 2Ax + D
\end{align}&lt;/math&gt;
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===Point at given slope===
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Given parabola defined by &lt;math&gt;A, B, C, D, E, F&lt;/math&gt; and slope &lt;math&gt;m = \frac{yvalue}{xvalue}&lt;/math&gt; where at least one of 
&lt;math&gt;yvalue, xvalue&lt;/math&gt; is non-zero, calculate point at which the slope is &lt;math&gt;m.&lt;/math&gt;


Let &lt;math&gt;m = \frac{-(2Ax + By + D)}{Bx + 2Cy + E} = \frac{s}{t} = \frac{yvalue}{xvalue}&lt;/math&gt;


Then &lt;math&gt;s(Bx + 2Cy + E) + t(2Ax + By + D) = 0.&lt;/math&gt;


Let &lt;math&gt;G = (Bs + 2At);\ H = (2Cs + Bt);\ I = (Es + Dt).&lt;/math&gt;


Then &lt;math&gt;Gx + Hy + I = 0\ \dots\ (1)&lt;/math&gt;

Substitute in the equation of the parabola and 
&lt;math&gt;y = \frac{-(AII - DGI + FGG)}{(2AHI - BGI - DGH + EGG)}\ \dots\ (2)&lt;/math&gt;

As shown below, with a little manipulation of the data, the same formula can be used to calculate &lt;math&gt;x.&lt;/math&gt;
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Equation &lt;math&gt;(1)&lt;/math&gt; above is the equation of a straight line with slope &lt;math&gt;\frac{-G}{H}.&lt;/math&gt;

Substitute for &lt;math&gt;G, H&lt;/math&gt; and the slope of &lt;math&gt;(1)&lt;/math&gt; becomes &lt;math&gt;\frac{b}{a}.&lt;/math&gt;

Equation &lt;math&gt;(1)&lt;/math&gt; is that of a line parallel to the axis of symmetry of the parabola.

It is possible for both both &lt;math&gt;G, H&lt;/math&gt; to equal &lt;math&gt;0&lt;/math&gt; in which case the calculation of 
&lt;math&gt;y, (2)&lt;/math&gt; above fails as an attempt to divide by &lt;math&gt;0.&lt;/math&gt; See caution under
[[Parabola#Slope_of_the_Parabola | &quot;Slope of the Parabola&quot;]] above.
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====Implementation====
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&lt;syntaxhighlight lang=python&gt;
# python code
def pointAtGivenSlope(parabola, tangent) :
    s,t = tangent
    if s == t == 0 :
        print ('pointAtGivenSlope(): both s,t can not be 0.')
      	return None
    def calculate_y (parabola, tangent)  :
        A,B,C,D,E,F = parabola
        s,t = tangent
      	G = B*s + 2*A*t	; H = 2*C*s + B*t ; I =	E*s + D*t
      	return -(A*I*I - D*G*I + F*G*G) / (2*A*H*I - B*G*I - D*G*H + E*G*G)
    y = calculate_y (parabola, tangent)
    A,B,C,D,E,F = parabola
    x = calculate_y ((C,B,A,E,D,F), (t,s))
    return x,y
&lt;/syntaxhighlight&gt;
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=====Examples=====
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A parabola is defined as &lt;math&gt;9x^2 - 24xy + 16y^2 + 70x - 260y + 1025 = 0.&lt;/math&gt;

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Calculate coordinates of vertex.

At vertex tangent has same slope as directrix.
&lt;syntaxhighlight lang=python&gt;
# python code
parabola = A, B, C, D, E, F = 9, -24, 16, 70, -260, 1025
a = C**.5
b = -B/(2*a)
tangent = -a,b
result = pointAtGivenSlope(parabola, tangent)
print (result)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
(0.2, 6.4)
&lt;/syntaxhighlight&gt;
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Calculate point at which tangent is vertical.
&lt;syntaxhighlight lang=python&gt;
# python code
parabola = A, B, C, D, E, F = 9, -24, 16, 70, -260, 1025
tangent = 1,0
result = pointAtGivenSlope(parabola, tangent)
print (result)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
(-0.25, 7.9375)
&lt;/syntaxhighlight&gt;
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== Parabola and any chord ==
&lt;/br&gt;
[[File:20170418ParabolaWithChord&amp;2tangents.pdf|thumb|350px|
'''Figure 4: Parabola and any chord.'''&lt;/br&gt;
Origin &lt;math&gt;(0,0)&lt;/math&gt; at point &lt;math&gt;O;&lt;/math&gt; curve&lt;math&gt;:&lt;/math&gt; &lt;math&gt;y = Kx^2;&lt;/math&gt;   &lt;/br&gt;
chord &lt;math&gt;IJ&lt;/math&gt;&lt;math&gt;:\ y = mx + c;&lt;/math&gt; point &lt;math&gt;L&lt;/math&gt;&lt;math&gt;:\ (0,c);&lt;/math&gt;&lt;/br&gt;
2 tangents&lt;math&gt;:&lt;/math&gt; &lt;math&gt;IN, JN;&lt;/math&gt; point &lt;math&gt;N&lt;/math&gt;&lt;math&gt;:\ (\frac{m}{2K}, -c)&lt;/math&gt;
]]

Refer to Figure 4.

The curve has equation: &lt;math&gt;y=Kx^2.&lt;/math&gt;

The chord &lt;math&gt;IJ&lt;/math&gt; has equation: &lt;math&gt;y=mx+c&lt;/math&gt;.

Point &lt;math&gt;L&lt;/math&gt; has coordinates &lt;math&gt;(0,c).&lt;/math&gt;

Line &lt;math&gt;IN&lt;/math&gt; is tangent to the curve at &lt;math&gt;I.&lt;/math&gt;

Line &lt;math&gt;JN&lt;/math&gt; is tangent to the curve at &lt;math&gt;J.&lt;/math&gt;

This section shows that point &lt;math&gt;N&lt;/math&gt; has coordinates &lt;math&gt;(\frac{m}{2K}, -c).&lt;/math&gt;


:&lt;math&gt;\begin{align}
y =&amp;\ Kx^2 = mx + c\\
\\
Kx^2&amp; -mx -c = 0\\
\\
x =&amp;\ \frac{m \pm \sqrt{m^2+4Kc}}{2K}\\
\\
=&amp;\ \frac{m \pm R}{2K}
\end{align}&lt;/math&gt;


where &lt;math&gt;R = \sqrt{m^2+4Kc}&lt;/math&gt;


Point &lt;math&gt;I&lt;/math&gt; has coordinates &lt;math&gt;(x_1,y_1)&lt;/math&gt; where:

&lt;math&gt;x_1 = \frac{m-R}{2K}&lt;/math&gt;,

&lt;math&gt;y_1 = Kx_1^2 = K (\frac{m-R}{2K})(\frac{m-R}{2K}) = \frac{m^2-2mR+R^2}{4K}  = \frac{m^2-mR+2Kc}{2K}           &lt;/math&gt;,

and slope of tangent &lt;math&gt;IN = s_1 = 2Kx_1 = m-R.&lt;/math&gt;


Point &lt;math&gt;J&lt;/math&gt; has coordinates &lt;math&gt;(x_2,y_2)&lt;/math&gt; where:

&lt;math&gt;x_2 = \frac{m+R}{2K}&lt;/math&gt;,

&lt;math&gt;y_2 =  \frac{m^2+mR+2Kc}{2K}           &lt;/math&gt;,

and slope of tangent &lt;math&gt;JN = s_2 = m+R.&lt;/math&gt;


Points &lt;math&gt;D,E&lt;/math&gt; have coordinates &lt;math&gt;(x_1,0),(x_2,0).&lt;/math&gt;


Equation of tangent &lt;math&gt;IN:&lt;/math&gt;

:&lt;math&gt;\begin{align}
y =&amp;\ s_1x+c_1\\
c_1 =&amp;\ y_1-s_1x_1 = \frac{m^2-mR+2Kc}{2K}-(m-R)(\frac{m-R}{2K}) = \frac{-(m^2-mR+2Kc)}{2K}\\
y =&amp;\ (m-R)x-\frac{m^2-mR+2Kc}{2K}
\end{align}&lt;/math&gt;


Equation of tangent &lt;math&gt;JN:&lt;/math&gt;

:&lt;math&gt;\begin{align}
y = (m+R)x-\frac{m^2+mR+2Kc}{2K}

\end{align}&lt;/math&gt;


At point of intersection &lt;math&gt;N,\ (m+R)x-\frac{m^2+mR+2Kc}{2K} =  (m-R)x-\frac{m^2-mR+2Kc}{2K};\ x= \frac{m}{2K}. &lt;/math&gt;


Review the &lt;math&gt;X&lt;/math&gt; coordinates of points &lt;math&gt;D,E&lt;/math&gt;&lt;math&gt;:\ (\frac{m-R}{2K}, \frac{m+R}{2K})&lt;/math&gt;. 

The line &lt;math&gt;NGH&lt;/math&gt; 
with equation &lt;math&gt;x=\frac{m}{2K}&lt;/math&gt; bisects the line segment &lt;math&gt;DE&lt;/math&gt; and also the chord &lt;math&gt;IJ&lt;/math&gt; at point &lt;math&gt;H&lt;/math&gt;.


Any chord parallel to &lt;math&gt;IJ&lt;/math&gt; has two tangents that intersect on the line &lt;math&gt;x= \frac{m}{2K}&lt;/math&gt;.

Any chord parallel to &lt;math&gt;IJ&lt;/math&gt; is bisected by the line &lt;math&gt;x= \frac{m}{2K}&lt;/math&gt;.


The &lt;math&gt;Y&lt;/math&gt; coordinate of point &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;

:&lt;math&gt;\begin{align}
y =&amp;\ s_1(\frac{m}{2K}) + c_1\\
=&amp;\ (m-R)(\frac{m}{2K}) - \frac{m^2-mR+2Kc}{2K}\\
=&amp;\ \frac{m^2-mR}{2K} - \frac{m^2-mR+2Kc}{2K}\\
=&amp;\ \frac{-2Kc}{2K}\\
=&amp;\ -c
\end{align}&lt;/math&gt;


Any chord that passes through the point &lt;math&gt;L\ (0,c)&lt;/math&gt; has two tangents that intersect on the line &lt;math&gt;y=-c&lt;/math&gt;.


'''Angle &lt;math&gt;INJ&lt;/math&gt;'''
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Using:

:&lt;math&gt;\begin{align}
\tan(A-B) =&amp;\ \frac{\tan(A) - \tan(B)}{1+ \tan(A)\tan(B)}\\
\\
\tan(\angle INJ) =&amp;\ \frac{(m-R)-(m+R)}{1+(m-R)(m+R)}\\
\\
=&amp;\ \frac{-2R}{1+(m^2-R^2)}\\
\\
=&amp;\ \frac{-2R}{1+m^2-(m^2+4Kc)}\\
\\
=&amp;\ \frac{-2R}{1-4Kc}\\
\\
=&amp;\ \frac{2\sqrt{m^2+4Kc}} {4Kc-1}
\end{align}&lt;/math&gt;


If &lt;math&gt;4Kc &gt; 1&lt;/math&gt;, point &lt;math&gt;L&lt;/math&gt; is above the &lt;math&gt;focus,\ \tan(\angle INJ)&lt;/math&gt; is positive 
and &lt;math&gt;0&lt;/math&gt;° &lt;math&gt;&lt; \angle INJ &lt; 90&lt;/math&gt;°.

&lt;math&gt;\angle INJ&lt;/math&gt; is acute and, as &lt;math&gt;m&lt;/math&gt; increases, &lt;math&gt;\angle INJ&lt;/math&gt; increases, approaching &lt;math&gt;90&lt;/math&gt;°.


If &lt;math&gt;4Kc == 1&lt;/math&gt;, point &lt;math&gt;L&lt;/math&gt; is on the &lt;math&gt;focus,\ \tan(\angle INJ) = \frac{2\sqrt{m^2+1}} {0},\ \angle INJ = 90&lt;/math&gt;°
and the line &lt;math&gt;y = -c&lt;/math&gt; is the &lt;math&gt;directrix&lt;/math&gt;.


If &lt;math&gt;4Kc &lt; 1&lt;/math&gt;, point &lt;math&gt;L&lt;/math&gt; is below the &lt;math&gt;focus,\ \tan(\angle INJ)&lt;/math&gt; is negative 
and &lt;math&gt;90&lt;/math&gt;° &lt;math&gt;&lt; \angle INJ &lt; 180&lt;/math&gt;°.

&lt;math&gt;\angle INJ&lt;/math&gt; is obtuse and, as &lt;math&gt;m&lt;/math&gt; increases, &lt;math&gt;\angle INJ&lt;/math&gt; decreases, approaching &lt;math&gt;90&lt;/math&gt;°.
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==Parabola and two tangents==
&lt;/br&gt;
[[File:20170418ParabolaWithChord&amp;2tangents.pdf|thumb|350px|
'''Figure 5: Parabola and two tangents.'''&lt;/br&gt;
Origin &lt;math&gt;(0,0)&lt;/math&gt; at point &lt;math&gt;O;&lt;/math&gt; curve&lt;math&gt;:&lt;/math&gt; &lt;math&gt;y = Kx^2;&lt;/math&gt;   &lt;/br&gt;
point &lt;math&gt;N&lt;/math&gt;&lt;math&gt;:\ (h, -c);&lt;/math&gt; 2 tangents&lt;math&gt;:&lt;/math&gt; &lt;math&gt;NI, NJ;&lt;/math&gt;&lt;/br&gt; 
chord &lt;math&gt;IJ&lt;/math&gt;&lt;math&gt;:\ y = 2Khx + c;&lt;/math&gt; point &lt;math&gt;L&lt;/math&gt;&lt;math&gt;:\ (0,c);&lt;/math&gt;
]]

Refer to Figure 5.

The curve has equation: &lt;math&gt;y=Kx^2.&lt;/math&gt;

Point &lt;math&gt;N&lt;/math&gt; with coordinates &lt;math&gt;(h,-c)&lt;/math&gt; is any point on the line &lt;math&gt;y=-c.&lt;/math&gt;

Line &lt;math&gt;NI&lt;/math&gt; is tangent to the curve at point &lt;math&gt;I\ (x_1,y_1)&lt;/math&gt;.

Line &lt;math&gt;NJ&lt;/math&gt; is tangent to the curve at point &lt;math&gt;J\ (x_2,y_2)&lt;/math&gt;.

This section shows that the chord &lt;math&gt;IJ&lt;/math&gt; passes through the point &lt;math&gt;(0,c).&lt;/math&gt;


Equation of any line through point &lt;math&gt;N:\ y=mx-c-mh&lt;/math&gt;


Let this line intersect the curve:

&lt;math&gt;y = Kx^2 = mx-c-mh&lt;/math&gt;

&lt;math&gt;Kx^2 -mx +c+mh = 0&lt;/math&gt;

&lt;math&gt;x = \frac{m \pm \sqrt{m^2-4K(mh+c)}}{2K} = \frac{m \pm \sqrt{m^2-4Kmh-4Kc}}{2K}&lt;/math&gt;


We want this line to be a tangent to the curve, therefore &lt;math&gt;x&lt;/math&gt; has exactly one value and the discriminant is &lt;math&gt;0&lt;/math&gt;:


:&lt;math&gt;\begin{align}
m^2 -&amp; 4Kmh - 4Kc = 0\\
\\
m =&amp;\ \frac{4Kh \pm \sqrt{(4Kh)^2 - 4(1)(-4Kc)}} {2}\\
\\
=&amp;\ \frac{4Kh \pm \sqrt{16K^2h^2 + 16Kc}}{2}\\
\\
=&amp;\ 2Kh \pm 2R
\end{align}&lt;/math&gt;


where &lt;math&gt;R=\sqrt{K^2h^2+Kc}&lt;/math&gt;


&lt;math&gt;m_1=2Kh-2R=&lt;/math&gt; slope of tangent &lt;math&gt;NI&lt;/math&gt;.

&lt;math&gt;m_2=2Kh+2R =&lt;/math&gt; slope of tangent &lt;math&gt;NJ&lt;/math&gt;.


:&lt;math&gt;\begin{align}
x =&amp;\ \frac{m}{2K}\\
\\
x_1 =&amp;\ \frac{m_1}{2K} = \frac{2Kh-2R}{2K} = \frac{Kh-R}{K}\\
\\
y_1 =&amp;\ Kx_1^2 = K(\frac{Kh-R}{K})(\frac{Kh-R}{K}) = \frac{(Kh-R)(Kh-R)}{K}\\
\\ 
x_2 =&amp;\ \frac{Kh+R}{K}\\
\\
y_2 =&amp;\ \frac{(Kh+R)(Kh+R)}{K}
\end{align}&lt;/math&gt;


Slope of chord &lt;math&gt;IJ&lt;/math&gt;

:&lt;math&gt;\begin{align}
=&amp;\ \frac{y_2-y_1}{x_2-x_1}\\
\\
=&amp;\ (      \frac{(Kh+R)(Kh+R)}{K} -           \frac{(Kh-R)(Kh-R)} {K}     )/(     \frac{Kh+R}{K} -      \frac{Kh-R}{K}   )\\
\\
=&amp;\ (      \frac{KKhh + 2KhR + RR -           (KKhh-2KhR+RR)}{K}     )/(     \frac{2R}{K}   )\\
\\
=&amp;\ (   \frac{4KhR}{K}   )( \frac{K}{2R} )\\
\\
=&amp;\ 2Kh
\end{align}&lt;/math&gt;


Intercept of chord &lt;math&gt;IJ&lt;/math&gt; on the &lt;math&gt;Y&lt;/math&gt; axis

:&lt;math&gt;\begin{align}
=&amp;\ y_1 - 2Khx_1\\
\\
=&amp;\ \frac{(Kh-R)(Kh-R)}{K} - 2Kh \frac{Kh-R}{K}\\
\\
=&amp;\ \frac{KKhh - 2KhR + RR}{K} -  \frac{2Kh(Kh-R)}{K}\\
\\
=&amp;\ \frac{KKhh - 2KhR + RR - 2KhKh+2KhR}{K}\\
\\
=&amp;\ \frac{KKhh + RR - 2KhKh}{K}\\
\\
=&amp;\ \frac{-KKhh + KKhh+Kc }{K}\\
\\
=&amp;\ \frac{+Kc }{K}\\
\\
=&amp;\ c
\end{align}&lt;/math&gt;


Angle &lt;math&gt;INJ&lt;/math&gt;
----------------------


If &lt;math&gt;\angle INJ == 90&lt;/math&gt;°

:&lt;math&gt;\begin{align}
&amp;(m_1)(m_2) = -1\\
\\
&amp;(2Kh-2R)(2Kh+2R) = -1\\
\\
&amp;4(KKhh-RR) = -1\\
\\
&amp;4(KKhh-(KKhh+Kc)) = -1\\
\\
&amp;4(-Kc) = -1\\
\\
&amp;4Kc =1
\end{align}&lt;/math&gt;

In the basic parabola &lt;math&gt;y = \frac{x^2}{4q}&lt;/math&gt; where the &lt;math&gt;focus&lt;/math&gt; has coordinates &lt;math&gt;(0,q)&lt;/math&gt;.

&lt;math&gt;y=Kx^2 \therefore K=\frac{1}{4q}&lt;/math&gt; or &lt;math&gt;4Kq = 1.&lt;/math&gt;

If &lt;math&gt;4Kc == 1,&lt;/math&gt; then &lt;math&gt;(0,c)&lt;/math&gt; and &lt;math&gt;(0,q)&lt;/math&gt; are the same point, the chord &lt;math&gt;IJ&lt;/math&gt; passes through the &lt;math&gt;focus&lt;/math&gt;
and the line &lt;math&gt;y = -c&lt;/math&gt; is the &lt;math&gt;directrix&lt;/math&gt;.


== Area enclosed between parabola and chord ==

===Introduction===
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[[File:20170526 Parabola and 2 chords 00.png|thumb|300px|'''
Figure 6: The Parabola: &lt;math&gt;y = x^2&lt;/math&gt;'''&lt;/br&gt;
Chord &lt;math&gt;DC&lt;/math&gt;, parallel tangent &lt;math&gt;AOB&lt;/math&gt; and area &lt;math&gt;DOCD.&lt;/math&gt;&lt;/br&gt;
      &lt;math&gt;\ \ \ \ \ \ base = CD = 2.\ height = H_1T_1 = 1.&lt;/math&gt;&lt;/br&gt;
Chord &lt;math&gt;OC&lt;/math&gt;, parallel tangent &lt;math&gt;GHI&lt;/math&gt; and area &lt;math&gt;OHCO&lt;/math&gt;.&lt;/br&gt;
      &lt;math&gt;\ \ \ \ \ \ base = OC = \sqrt{2}.\ height = H_2T_2 = \frac{\sqrt{2}}{8}.&lt;/math&gt;
]]

See Figure 6. The curve is: &lt;math&gt;y = x^2&lt;/math&gt;. Integral is: &lt;math&gt;\frac{x^3}{3}&lt;/math&gt;.


Area under curve &lt;math&gt;(OBC)&lt;/math&gt;

:&lt;math&gt;\begin{align}
x =&amp; 1\\
=\ \ \ \ \ &amp;[\frac{x^3}{3}] = \frac{1}{3}\\
x =&amp; 0
\end{align}&lt;/math&gt;

Area under curve &lt;math&gt;(DOC) = &lt;/math&gt; area&lt;math&gt;(OAD)+&lt;/math&gt; area&lt;math&gt;(OBC) = \frac{2}{3}&lt;/math&gt;

Area between chord &lt;math&gt;DC&lt;/math&gt; and curve &lt;math&gt;DOC = 2 - \frac{2}{3} = \frac{4}{3}&lt;/math&gt;.


Consider the chord &lt;math&gt;CD&lt;/math&gt;. Call this the &lt;math&gt;base&lt;/math&gt; with value &lt;math&gt;2&lt;/math&gt;.
The tangent &lt;math&gt;AOB&lt;/math&gt; through the origin is parallel to &lt;math&gt;base\ (DC)&lt;/math&gt;, and the perpendicular distance 
between &lt;math&gt;AB, DC\ (H_1T_1)&lt;/math&gt; is &lt;math&gt;1&lt;/math&gt;. Call this distance the &lt;math&gt;height&lt;/math&gt; with value &lt;math&gt;1&lt;/math&gt;.

In this case the area enclosed between chord &lt;math&gt;DC&lt;/math&gt; and curve 
&lt;math&gt;DOC = \frac{2}{3}(base)(height) = \frac{2}{3}(2)(1)=\frac{4}{3},&lt;/math&gt; the same as that calculated earlier.


Consider the chord &lt;math&gt;OC&lt;/math&gt; and curve &lt;math&gt;OHC.&lt;/math&gt; By inspection the area between 
chord &lt;math&gt;OC&lt;/math&gt; and curve &lt;math&gt;OHC = \frac{1}{2} - \frac{1}{3} = \frac{1}{6}.&lt;/math&gt;


Chord &lt;math&gt;OC&lt;/math&gt; has equation &lt;math&gt;y=x;\ x-y = 0;\ \frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}} = 0&lt;/math&gt; in normal form.

The line &lt;math&gt;GHI&lt;/math&gt; is parallel to &lt;math&gt;base\ OC&lt;/math&gt; and touches the curve at &lt;math&gt;H(\frac{1}{2},\ \frac{1}{4}).&lt;/math&gt;

Distance from &lt;math&gt;H&lt;/math&gt; to chord &lt;math&gt;OC = H_2T_2 = \frac{1/2}{\sqrt{2}} - \frac{1/4}{\sqrt{2}} = \frac{1}{4\sqrt{2}} = \frac{\sqrt{2}}{8} = height.&lt;/math&gt;

Length of &lt;math&gt;OC = \sqrt{2} = base.&lt;/math&gt;

Area between chord &lt;math&gt;OC&lt;/math&gt; and curve 
&lt;math&gt;OHC = \frac{2}{3}(base)(height) = \frac{2}{3}(\sqrt{2})(\frac{\sqrt{2}}{  8   }) = \frac{2}{3}(\frac{1}{4}) = \frac{1}{6},&lt;/math&gt; the same
as that calculated earlier.


These observations suggest that the area enclosed between chord and curve &lt;math&gt;= \frac{2}{3}(base)(height).&lt;/math&gt;
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===Proof===
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[[File:20170527 Parabola &amp; area under chord 00.png|thumb|300px|'''
Figure 7: The Parabola: &lt;math&gt;y = Kx^2&lt;/math&gt;'''&lt;/br&gt;
Origin at point &lt;math&gt;O: (0,0)&lt;/math&gt;&lt;/br&gt;
Points &lt;math&gt;D,\ I: (p,0), (p, Kp^2)&lt;/math&gt;&lt;/br&gt;
Points &lt;math&gt;E,\ J: (q,0), (q, Kq^2)&lt;/math&gt;&lt;/br&gt;
Chord &lt;math&gt;IJ&lt;/math&gt;, parallel tangent &lt;math&gt;FG&lt;/math&gt; and area &lt;math&gt;IOJI&lt;/math&gt;, 
the area enclosed between chord &lt;math&gt;IJ&lt;/math&gt; and curve.&lt;/br&gt;
Length &lt;math&gt;IJ = base.&lt;/math&gt; Length &lt;math&gt;HT = height.&lt;/math&gt;
]]

We prove this identity for the general case. See Figure 7.

Slope of chord &lt;math&gt;IJ = \frac{Kqq-Kpp}{q-p} = \frac{K((q+p)(q-p))}{q-p} = K(q+p).&lt;/math&gt;

Find equation of chord &lt;math&gt;IJ.&lt;/math&gt;
&lt;math&gt;y = K(p+q)x + c;\ \therefore c = y - K(p+q)x = Kqq - K(p+q)q = -Kpq&lt;/math&gt;

Equation of chord &lt;math&gt;IJ:&lt;/math&gt;
&lt;math&gt;y = K(p+q)x - Kpq.&lt;/math&gt;


Find equation of tangent &lt;math&gt;FG.&lt;/math&gt;

:&lt;math&gt;\begin{align}
&amp;y = Kx^2\\
&amp;y = K(p+q)x+c\\
\therefore\ &amp;Kx^2 = K(p+q)x + c\\
&amp;Kx^2 - K(p+q)x - c = 0
\end{align}&lt;/math&gt;

We choose a value of &lt;math&gt;c&lt;/math&gt; that gives &lt;math&gt;x&lt;/math&gt; exactly one value.

Therefore discriminant &lt;math&gt;K^2(p+q)^2 + 4Kc = 0;\ c = \frac{-K(p+q)^2}{4}.&lt;/math&gt;

&lt;math&gt;y = K(p+q)x - \frac{K(p+q)^2}{4};\ K(p+q)x - y - \frac{K(p+q)^2}{4} = 0;&lt;/math&gt;

Equation of tangent &lt;math&gt;FG&lt;/math&gt; in normal form: &lt;math&gt;\frac{K(p+q)x - y - \frac{K(p+q)^2}{4}}{\sqrt{K^2(p+q)^2 + 1}} = 0.&lt;/math&gt;


Equation of chord &lt;math&gt;IJ&lt;/math&gt; in normal form: &lt;math&gt;\frac{ K(p+q)x - y - Kpq  }{ \sqrt{K^2(p+q)^2 + 1} } = 0.&lt;/math&gt;

Therefore distance between chord &lt;math&gt;IJ&lt;/math&gt; and tangent &lt;math&gt;FG&lt;/math&gt;

&lt;math&gt; = height = \frac{          -Kpq - (-\frac{K(p+q)^2}{4})        }{R} = \frac{K(p+q)^2 - 4Kpq}{4R} = \frac{K(p-q)^2}{4R}&lt;/math&gt; 
where &lt;math&gt;R = \sqrt{K^2(p+q)^2 + 1}.&lt;/math&gt;


Length of chord &lt;math&gt;IJ = base = L = \sqrt{(Kqq-Kpp)^2 + (q-p)^2}.&lt;/math&gt;


Area under chord &lt;math&gt;IJ = (q-p)\frac{Kqq+Kpp}{2} = \frac{Kqqq+Kppq - Kqqp - Kppp}{2}&lt;/math&gt;


Area under curve &lt;math&gt;IOJ&lt;/math&gt;

:&lt;math&gt;\begin{align}
x =&amp; q\\
=\ \ \ \ \ &amp;[\frac{Kx^3}{3}] = \frac{Kqqq-Kppp}{3}\\
x =&amp; p
\end{align}&lt;/math&gt;


Area between chord &lt;math&gt;IJ&lt;/math&gt; and curve &lt;math&gt;IOJ&lt;/math&gt;

&lt;math&gt; =       \frac{Kqqq+Kppq - Kqqp - Kppp}{2} -      \frac{Kqqq-Kppp}{3}       = \frac{Kqqq+3Kppq-3Kpqq-Kppp}{6} &lt;/math&gt;

&lt;math&gt; =       \frac{K(q-p)^3}{6}  =\frac{KS}{6}. &lt;/math&gt;


The aim is to prove that:

&lt;math&gt;\frac{2}{3}(base)(height) = \frac{KS}{6}&lt;/math&gt; or 

&lt;math&gt;\frac{2}{3}(L)(\frac{K(p-q)^2}{4R}) = \frac{KS}{6}&lt;/math&gt; or

&lt;math&gt;\frac{2L(p-q)^2}{12R} = \frac{S}{6}&lt;/math&gt; or

&lt;math&gt;L(p-q)^2 = R(q-p)^3&lt;/math&gt; or

&lt;math&gt;L = R(q-p)&lt;/math&gt;


where:

&lt;math&gt; L = \sqrt{(Kqq-Kpp)^2 + (q-p)^2} = \sqrt{    (q-p)^2(K^2(q+p)^2 + 1)   } = (q-p)\sqrt{    K^2(q+p)^2 + 1  }&lt;/math&gt;

&lt;math&gt;R = \sqrt{K^2(p+q)^2 + 1}&lt;/math&gt;

&lt;math&gt;RHS = (q-p)R = (q-p)\sqrt{K^2(p+q)^2 + 1} = L.&lt;/math&gt;


Therefore &lt;math&gt;L = R(q-p)&lt;/math&gt; and area enclosed between curve and chord =&lt;math&gt;\frac{2}{3}(base)(height)&lt;/math&gt;

where &lt;math&gt;base&lt;/math&gt; is the length of the chord, and &lt;math&gt;height&lt;/math&gt; is the perpendicular distance between chord and tangent parallel to chord.
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===A worked example===

Consider parabola: &lt;math&gt;16x^2 - 24xy + 9y^2 + 20x -140y + 600 = 0&lt;/math&gt;


and chord: &lt;math&gt;4x + 3y - 96 = 0.&lt;/math&gt;


The aim is to calculate area between chord and curve.


Calculate the points at which chord and parabola intersect: &lt;math&gt;(5\frac{7}{16}, 24\frac{3}{4}),\ (15\frac{1}{3}, 11\frac{5}{9}).&lt;/math&gt;


====Method 1. By chord and parallel tangent====
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[[File:20170526 Parabola and Chord 00.png|thumb|300px|'''
Figure 8: The Parabola: &lt;math&gt;16x^2 - 24xy + 9y^2 + 20x - 140y + 600 = 0&lt;/math&gt;'''&lt;/br&gt;
Chord &lt;math&gt;AD: 4x + 3y - 96 = 0.&lt;/math&gt; &lt;/br&gt;
Length &lt;math&gt;AD = base = \frac{2375}{144}.&lt;/math&gt;&lt;/br&gt;
Parallel tangent &lt;math&gt;CFB.\ height = BE = \frac{361}{24}.&lt;/math&gt;&lt;/br&gt;
Area between chord and curve &lt;math&gt;= DEAFD.&lt;/math&gt;]]

Length of chord


:&lt;math&gt;\begin{align}
=&amp;\ \sqrt{ (15\frac{1}{3} - 5\frac{7}{16})^2 + (11\frac{5}{9} - 24\frac{3}{4})^2 }\\
\\
=&amp;\ \sqrt{ (\frac{46}{3} - \frac{87}{16})^2 + (\frac{99}{4} - \frac{104}{9})^2 } \\
\\
=&amp;\ \sqrt{ (\frac{475}{48})^2 + (\frac{475}{36})^2 }
=\ \sqrt{ (\frac{475(3)}{48(3)})^2 + (\frac{475(4)}{36(4)})^2 } \\
\\
=&amp;\ \sqrt{ (\frac{475(3)}{144})^2 + (\frac{475(4)}{144})^2 }
=\ \frac{475(5)}{144} \\
\\
=&amp;\ \frac{2375}{144} = base.
\end{align}&lt;/math&gt;


Equation of chord in normal form: &lt;math&gt;\frac{4}{5}x + \frac{3}{5}y - 19.2 = 0.&lt;/math&gt;


Equation of parallel tangent in normal form: &lt;math&gt;\frac{4}{5}x + \frac{3}{5}y + g = 0,&lt;/math&gt;


where &lt;math&gt;g = \frac{       4AFee - 4BFde + 4CFdd - DDee + 2DEde - EEdd      }{     4AEe - 2BDe - 2BEd + 4CDd     }&lt;/math&gt;


and &lt;math&gt;d = \frac{4}{5},\ e = \frac{3}{5}&lt;/math&gt;


and &lt;math&gt;A = 16,\ B = -24,\ C = 9,\ D = 20,\ E = -140,\ F = 600.  &lt;/math&gt;


&lt;math&gt;g = -\frac{499}{120}.&lt;/math&gt;


Equation of chord in normal form: &lt;math&gt;\frac{4}{5}x + \frac{3}{5}y - 19.2 = 0.&lt;/math&gt;


Equation of parallel tangent in normal form: &lt;math&gt;\frac{4}{5}x + \frac{3}{5}y - \frac{499}{120} = 0.&lt;/math&gt;


Distance between chord and parallel tangent &lt;math&gt;= -\frac{499}{120} - (-19.2) = \frac{361}{24} = height.&lt;/math&gt;


Area enclosed between chord and curve &lt;math&gt;= \frac{2}{3}(base)(height) 
= \frac{2}{3}     (\frac{2375}{144})   (\frac{361}{24})
=\frac{(2375)(361)}{3(12^3)}.&lt;/math&gt;
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====Method 2. By identifying the basic parabola.====
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[[File:20170526 Determine basic parabola 00.png|thumb|300px|'''
Figure 9: The Parabola: &lt;math&gt;16x^2 - 24xy + 9y^2 + 20x - 140y + 600 = 0&lt;/math&gt;'''&lt;/br&gt;
Chord &lt;math&gt;AD: 4x + 3y - 96 = 0.&lt;/math&gt; &lt;/br&gt;
&lt;math&gt;axis&lt;/math&gt; is line &lt;math&gt;FS_1S_2.\ directrix&lt;/math&gt; is line &lt;math&gt;RT.&lt;/math&gt;&lt;/br&gt;

&lt;math&gt;focus&lt;/math&gt; is point &lt;math&gt;F: (2,6).&lt;/math&gt;&lt;/br&gt;

Line &lt;math&gt;AS_2 = p = -8\frac{1}{2}.&lt;/math&gt;

Line &lt;math&gt;DS_1 = q = 7\frac{1}{3}&lt;/math&gt;
]]

See Figure 9. Calculate directrix, focus and axis.


Focus is distance &lt;math&gt;2&lt;/math&gt; from directrix. Curve has the shape of 
&lt;math&gt;y = Kx^2&lt;/math&gt; where &lt;math&gt;K = \frac{1}{4}&lt;/math&gt;.


Axis of symmetry has equation: &lt;math&gt;\frac{4}{5}x - \frac{3}{5}y + 2 = 0.&lt;/math&gt;


Distance from point &lt;math&gt;(5\frac{7}{16}, 24\frac{3}{4} )&lt;/math&gt; to axis of symmetry &lt;math&gt; = -8\frac{1}{2} = p.&lt;/math&gt;


Distance from point &lt;math&gt;(15\frac{1}{3}, 11\frac{5}{9})&lt;/math&gt; to axis of symmetry &lt;math&gt; = 7\frac{1}{3} = q.&lt;/math&gt;


&lt;math&gt;q-p = 7\frac{1}{3} - (- 8\frac{1}{2}) = 15\frac{5}{6} = \frac{95}{6}.&lt;/math&gt;


Area between chord and curve 


:&lt;math&gt;\begin{align}
=&amp;\ \frac{K(q-p)^3}{6} \\
\\
=&amp;\ \frac{1}{24}(\frac{95}{6})      (\frac{95}{6})        (\frac{95}{6})\\
\\
=&amp;\ \frac{(2375)(361)}{3(12^3)}.

\end{align}&lt;/math&gt;

or:


&lt;math&gt;height = \frac{K(p-q)^2}{4R}&lt;/math&gt; where &lt;math&gt;R = \sqrt{K^2(p+q)^2 + 1}&lt;/math&gt;

&lt;math&gt;(p-q)^2 = \frac{95(95)}{36}&lt;/math&gt;

&lt;math&gt;(p+q)^2 = \frac{49}{36}&lt;/math&gt;

&lt;math&gt;R  =  \sqrt{ \frac{49}{16(36)} + 1 } = \sqrt{ \frac {7^2} {24^2} + \frac {24^2} {24^2} } = \sqrt{ \frac {25^2} {24^2} } = \frac {25} {24} &lt;/math&gt;

&lt;math&gt;height = \frac{   \frac{95(95)}{(4)36}       }{      4  ( \frac{25}{24} )    } 
= \frac{ \frac{95(95)}{(4)36}  }{  \frac{25}{6}  } 
= (\frac{95(95)}{(4)36})( \frac{6}{25}) 
= \frac{19(19)}{24} 
= \frac{361}{24}.&lt;/math&gt;


Calculate &lt;math&gt;base&lt;/math&gt; as above and area enclosed between chord and curve 
&lt;math&gt;= \frac{2}{3}(base)(height) = \frac{2}{3} (\frac{2375}{144}) (\frac{361}{24}) = \frac{(2375)(361)}{3(12^3)}&lt;/math&gt;.
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[[Category:Geometry]]</text>
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    <title>Metagenomics</title>
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      <comment>cleanup</comment>
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      <text bytes="6794" sha1="ajuo2dudbj7or6oos9rqpghxu0yutll" xml:space="preserve">{{uncategorized}}
{{cleanup|does this belong to a bigger project?}}
Historically, microbial studies have concentrated on pure laboratory cultures. By contrast, metagenomics is defined as the direct analysis of genomes contained in an environmental sample, in order to dillucidate the genomic composition of the entire microbial community &lt;ref&gt;Eisen, J. A. (2007). Environmental Shotgun Sequencing: Its Potential and Challenges for Studying the Hidden World of Microbes. ''PLoS Biology'', ''5''(3), e82. http://doi.org/10.1371/journal.pbio.0050082&lt;/ref&gt;. Consequently, the descriptions obtained from these kind of studies are more comprehensive than those provided for traditional phylogenetic studies, based on small-subunit ribosomal RNA loci (16S) &lt;ref&gt;Thomas, T., Gilbert, J., &amp; Meyer, F. (2012). Metagenomics - a guide from sampling to data analysis. ''Microbial Informatics and Experimentation'', ''2'', 3. http://doi.org/10.1186/2042-5783-2-3&lt;/ref&gt;.

Besides, shotgun metagenomics provides information about new enzymatic pathways and evolutionary relationships among non-culturable organisms &lt;ref&gt;Tyson G. W., Chapman J., Hugenholtz P., Allen E. E., Ram R. J., Richardson P. M., et al. . (2004). Community structure and metabolism through reconstruction of microbial genomes from the environment. Nature 428, 37–43. 10.1038/nature02340&lt;/ref&gt;. They can be complemented with metatranscriptomic and metaproteomic analyses to determine expression profiles &lt;ref&gt;Wilmes, P., Bond P. L. Metaproteomics: studying functional gene expression in microbial ecosystems.Volume 14, Issue 2, p92–97, February 2006. http://dx.doi.org/10.1016/j.tim.2005.12.006&lt;/ref&gt;&lt;ref&gt;Gilbert, J. A., Field, D., Huang, Y., Edwards, R., Li, W., Gilna, P., &amp; Joint, I. (2008). Detection of Large Numbers of Novel Sequences in the Metatranscriptomes of Complex Marine Microbial Communities. PLoS ONE, 3(8), e3042. http://doi.org/10.1371/journal.pone.0003042&lt;/ref&gt;. 

In this manner, environments so diverse as skin and guts of animals &lt;ref&gt;Hess, M., Sczyrba, A., Egan, R., Kim, T., Chokhawala, H., Schroth, G., Luo, S., Clark, D. S., Chen, F., Zhang, T., Mackie, R. I., Pennacchio, I. A., Tringe, S. G., Visel, A., Woyke, T., Wang, Z. &amp; Rubin, E. M. Metagenomic Discovery of Biomass-Degrading Genes and Genomes from Cow Rumen. Science: 463-467&lt;/ref&gt;&lt;ref&gt;Qin, J., Li, R., Raes, J., Arumugam, M., Burgdorf, K. S., Manichanh, C., … Wang, J. (2010). A human gut microbial gene catalog established by metagenomic sequencing.Nature,464(7285), 59–65. http://doi.org/10.1038/nature08821&lt;/ref&gt;, marine sediments &lt;ref&gt;Stein, J. L., Marsh, T. L., Wu, K. Y., Shizuya, H., &amp; DeLong, E. F. (1996). Characterization of uncultivated prokaryotes: isolation and analysis of a 40-kilobase-pair genome fragment from a planktonic marine archaeon. Journal of Bacteriology, 178(3), 591–599.&lt;/ref&gt;, rhizosphere &lt;ref&gt;Hanin Alzubaidy, Magbubah Essack, Tareq B. Malas, Ameerah Bokhari, Olaa Motwalli, Frederick Kinyua Kamanu, Suhaiza Ahmad Jamhor, Noor Azlin Mokhtar, André Antunes, Marta Filipa Simões, Intikhab Alam, Salim Bougouffa, Feras F. Lafi, Vladimir B. Bajic, John A.C. Archer, Rhizosphere microbiome metagenomics of gray mangroves (Avicennia marina) in the Red Sea, Gene, Volume 576, Issue 2, Part 1, 1 February 2016, Pages 626-636, ISSN 0378-1119, https://doi.org/10.1016/j.gene.2015.10.032.&lt;/ref&gt; and acid mine runoff &lt;ref&gt;Méndez-García, C., Peláez, A. I., Mesa, V., Sánchez, J., Golyshina, O. V., &amp; Ferrer, M. (2015). Microbial diversity and metabolic networks in acid mine drainage habitats. Frontiers in Microbiology, 6, 475. http://doi.org/10.3389/fmicb.2015.00475&lt;/ref&gt; have been studied.

=== '''Next Generation Sequencing''' ===
In the last 10 years, metagenomic studies have been impulsed by the development of next generation sequencing (NGS) platforms. Although Sanger sequencing has the lowest error rate and produces longer reads, it has been overcome for NGS technologies, because of its simplicity and low costs &lt;ref&gt;Behjati, S., &amp; Tarpey, P. S. (2013). What is next generation sequencing? Archives of Disease in Childhood. Education and Practice Edition, 98(6), 236–238. http://doi.org/10.1136/archdischild-2013-304340&lt;/ref&gt;.

The most used NGS platform for metagenomics studies is 454/Roche &lt;ref&gt;Wommack, K. E., Bhavsar, J., &amp; Ravel, J. (2008). Metagenomics: Read Length Matters. Applied and Environmental Microbiology, 74(5), 1453–1463. http://doi.org/10.1128/AEM.02181-07&lt;/ref&gt;&lt;ref&gt;Mardis ER. Next-generation DNA sequencing methods. Annu Rev Genomics Hum Genet. 2008;9:387–402. doi: 10.1146/annurev.genom.9.081307.164359.&lt;/ref&gt;[10,11]. This system amplifies fragments of DNA adhered to microspheres through a polymerase chain reaction in emulsion. Each microsphere is set in a well and submitted to individual and parallel pyrosequencing, which consist in the sequential addition of the four deoxinucleotide triphosphates. These are incorporated to the coding strand, if they correspond to the sequence, by a DNA polymerase. The subsequent reaction liberates one pyrophosphate, which is consumed in two enzimatic reactions to produce light. Light levels of 1.2 million parallel reactions are detected by a camera and processed to obtain the sequence of the fragments. The reads produced by 454/Roche platform have a mean length of 600 bases, which is ideal for metagenomic studies &lt;ref&gt;Wommack, K. E., Bhavsar, J., &amp; Ravel, J. (2008). Metagenomics: Read Length Matters. Applied and Environmental Microbiology, 74(5), 1453–1463. http://doi.org/10.1128/AEM.02181-07&lt;/ref&gt;.

=== '''Bioinformatic analysis''' ===
The enormous amounts of data generated by NGS platforms are subsequently processed with bioinformatic software, in order to assess the taxonomical and functional identity of the DNA sequenced. This step is called binning and it is generally done by sequence similarity &lt;ref&gt;Mande, Sharmila S.; Monzoorul Haque Mohammed; Tarini Shankar Ghosh (2012). &quot;Classification of metagenomic sequences: methods and challenges.&quot;.Briefings in Bioinformatics. 13(6): 669–81.&lt;/ref&gt;. Although there are several tools to perform a metagenomic analysis, the most widely used  are the MG-RAST server &lt;ref&gt;Meyer, F., Paarmann, D., D’Souza, M., Olson, R., Glass, E., Kubal, M., … Edwards, R. (2008). The metagenomics RAST server – a public resource for the automatic phylogenetic and functional analysis of metagenomes. BMC Bioinformatics,9, 386. http://doi.org/10.1186/1471-2105-9-386.&lt;/ref&gt; and metAMOS &lt;ref&gt;Treangen, T. J., Koren, S., Sommer, D. D., Liu, B., Astrovskaya, I., Ondov, B., … Pop, M. (2013). MetAMOS: a modular and open source metagenomic assembly and analysis pipeline. Genome Biology, 14(1), R2. http://doi.org/10.1186/gb-2013-14-1-r2&lt;/ref&gt;.

=== '''References''' ===
{{Reflist}}</text>
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      <text bytes="4875" sha1="iilf7mgu1u3zololvu0hv6rxqhxk0zn" xml:space="preserve">The &quot;economy&quot; as defined by practice and operating dogma throughout the world counts on much private individual misfortune to achieve &quot;profits&quot; which may show up in public view as a stock market price rise or other &quot;favorable&quot; event.  This article will seek to describe the process in detail with examples.
== Forced move to smaller quarters ==
Individuals and families finding themselves faced with this disaster typically make the unhappy decision to relinquish some of their possessions to the garbage dumpster.  This may be partly due to the fact that they habitually suffer from Social Anxiety Disorder and can not muster the courage to try to sell their things or give things away, preventing waste of the belongings.  After completing the move, and a period of time to rebuild their lives, they may buy over again some of the same kinds of things they previously had owned and gave up.  This adds an inadequately researched percentage to the profits of manufacturers and marketers who may in turn &quot;sense&quot; a need to support government policy and laws which increase the frequency of such forced moves, and to support the candidacy of legislators who, once elected, would support such policy and laws.
== Deportation ==
An individual captured by this fate may not have time or option to do anything about protecting the majority of their possessions which are often discarded by an apartment building owner or succeeding occupant, who is often unlikely to be interested in retaining any or much of the property.
== Imprisonment ==
Anger and prejudice directed at the allegedly guilty person may lead those remaining behind, even family members, to throw away his or her possessions in a punitive spirit of cleansing the household of disgrace or contagion.  Words like &quot;dirty&quot; and &quot;bad&quot; abound in the culture for excusing such trashing behavior.  At some future time the punishee may again have the funding to buy replacements, feeding profits. 
== Remedies ==
Ideally, at the risk of accusations of &quot;socialism&quot;, there ought to be a more extended system for sharing goods that anyone for whatever reason cannot hold onto.  An example would be recycling and creative-reuse collection centers to which things can be donated, which should be present in greater abundance especially near public housing projects where much waste of clothing, toys, furniture etc. is observed on a regular basis as vulnerable persons undergo psychological impacts and lose their grip.
=== Creative reuse workshops ===
In every neighborhood there should be a center to which orphaned belongings can be donated, where they may be shelved and exhibited and put up for sale-- or, as needed, worked on, adapted, repaired, rebuilt into a new product.  Past efforts to establish such an institution have often failed due to not getting beyond the first idea, simply exhibiting for resale, good though that is.  Often the failure resulted from not sorting out the materials by type, size, etc. as employees are trained to do at any big bucks store.  
==== Shelving====
A key missing ingredient is enough shelving of size and type to organize the stock on-- so that an obligatory aspect of this enterprise would be to have an attached or adjacent woodworking shop where foundling boards and bars are made into shelving.  By one estimate 13% of all contents of landfill are lumber products, which could have been saved, trimmed, sanded, made into transitional &quot;housing&quot; for goods which will need to be mounted in such a way that they are visible and accessible to reworking staff, shoppers, reusers.  Making the shelving would be a highest priority item in the education part of the &quot;recycling plus education&quot; paradigm-- training shelfmakers can make this idea exportable from an initial exemplary start to other neighborhoods.
A high percentage of all the goods is likely to be small enough that they can be stacked loose or in boxes on shelving which has spaces of roughly a foot height and depth and a yard or so width.  The 3/4&quot; boards used to make the shelves would in this case be about a foot wide and a yard long.  A portable stackable shelving set would have three boards enclosing two spaces, and four such units stacked against a wall would provide the shelving needed in a room of average ceiling height.  Four boards up to two feet long and six inches wide could be used as the standers left and right, and pre-drilled bars about 2 x 12 inches nailed or screwed to the stander boards to hold the stander boards together and support the shelfboards. One or two further wood pieces may be used as bracing behind the shelves, and also as protection against objects falling off in the rear.
_________________________________________________________________

In the next days further ideas will be added to this article, plus hopefully an instructive diagram related to how to make the shelving.</text>
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    <title>Preventive Health Science</title>
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[[File:Clinica Einstein, Via Argentina, Panama City.JPG|thumb|300px|Clinica Einstein, Founded 1971, Via Argentina, Panama City where the Editorial office is hosted]]

==Introduction==

The development of science includes training in research, teaching based on research and the establishment of research departments and scientific journals. It is recommended for all health professionals to include orientation in  scientific journals as part of the continuing education (Hippocrates). This &quot;school science journal&quot; should help with this. Reading of scientific articles is the basis for evidence-based medical practice, teaching and research [https://es.wikipedia.org/wiki/Medicina_basada_en_hechos (EBM/MBH)]. The Journal of &quot;Preventive Health Science&quot;,  is an electronic publication for free. The general objective is to serve students and health professionals in their continuing education. The use of everyday scientific literature is a key part of the scientific education. In other words, the aim is to contribute to create a culture of health risk prevention based on scientific evidence and critical thinking. The objective is to raise awareness about the factors that improve or damage the environment, in order to preserve the quality of life and contribute to social welfare. Another objective is to be familiar with the [https://en.wikipedia.org/wiki/IMRAD IMRAD] [https://www.slideshare.net/darwinarmijosguillen/metodo-cientifico1-84485841%20IMRYD metodo-cientifico IMRYD ]structure in scientific works. The publication plan: When a new relevant article /summary is ready, it is published quickly. The philosophy is that it is most convenient to be orientated in one subject in a few minutes, instead of many articles in a traditional scientific journal. One important objective is to bring study abstracts from other countries even years ago that is relevant to be repeated in our country as subject for a thesis alone or in a group work. So far the epidemiological studies in Public Health from Panama have focused on infectious diseases and diseases related to diet, lack of activity, smoking and alcohol, i.e. cardiovascular diseases, diabetes and cancer. We want to inspire students and professionals to do research in occupational and environmental health in a wider scope [https://en.wikipedia.org/wiki/Occupational_medicine (Occupational Medicine)]. The abstracts in this journal intend to encourage the students to use scientific literature in their thesis work and for solving daily health problems. Further, we offer research training courses and training in writing academic papers for students and professionals. Legal Rights: The texts are under the Creative Commons License. This means that the works are free of known restrictions of authors' rights. The Public Domain Label allows the work to be easily discovered, and provides valuable information about the work. Application for an ISSN number has been submitted. 

 [[File:Ccl logo.png |right|100px|]]

== Continuing education ==
Continuing education, is a core issue for all health professionals consisting of all types of health preventive practices, conferences, education and scientific articles.To remember one of the sentences in the Hippocratic Oaths: &quot;That I will recognize the limits of my knowledge and pursue lifelong learning to better care for the sick and to prevent illness&quot;

==Publication Strategy==
With the aim to create interest for scientific work. Due to the sparse original publications from Panama, we start to reprint translated abstracts from international studies, that are of relevance also for Panama. We  search globally to find scientific articles every month or more frequent within occupational-, public- and environmental health. Especially subjects of interest for ongoing research studies, like the planned study on PTSD (Post traumatic stress disease) in train drivers after episodes of sudden suicide in front of the train and the “Acoso Laboral” study project. The orginal title of the citing artcle is kept while the editors write a ''subheading'' for a quick orientation of the content. All are invited to propose new abstracts for translation and reprint and to help with the editorial work. Scientific work e.g. students thesis, are very welcome to be published in full text by following the guidelines for authors and after peer review. The PDF files are downsized to facilitate the reading in one of the available online Programs e.g. [https://www.pdf2go.com/compress-pdf ''Compress-pdf for free'']

==[[/Abstracts and PPTs from conferences /]]==

==[[/Editorial meetings 8 Aug 2017 to Dec 31 2019/]]==


[[File:The Spanish international journal in maritime medicine with approval from the Editor Dr. ML Canals.jpg|200px|left|thumb|  ]]
[[File:Sociedad Española de Medicina Marítima.jpg|thumb|300px|right|Spanish Society of Maritime Medicine]]

==[https://www.dropbox.com/sh/zvumb7j8qj42hij/AABVQowxMPYBy8ylrVVIydXqa?dl=0 Medicina Maritima PDF]==

==Rules of good conduct==
# Members of the editorial committee are active and able to edit issues of the journal
# We agree to comply with the international medical ethical principles 
# Commercial interests are not accepted
#

==Guidelines for publication of Abstracts  ==
*[https://www.dropbox.com/s/iqnh4e6cmz3xp67/TEMPLATE%20NOT%20TO%20DELETE%20LAYOUT%2028%20DEC%202018%20.docx?dl=0 Open TEMPLATE here]

==Guidelines for original contributions==
All texts should be as short as possible, systematic, precise and easy to read with: Title, names of authors, email, telephone and institutions, type of contribution, a summary, text and references, three lines with the main messages and a photo. The preparation of the original manuscripts  follow [http://www.equator-network.org/ the Equator-Network standards ]. The main manuscript has an extension of 1000-2500 words + summary + figures and tables (separated pages) +  bibliography. For correspondence, e-mail and telephone. An original text will consist of the following sections (you can add acknowledgments): IMRAD [https://en.wikipedia.org/wiki/IMRAD ''Explanation to open'' ]
# Introduction
# Material and methods
# Results
# Discussion
# Bibliography
# Bibliographic citations 
* To be presented by the use of Zotero  or similar program - often in Vancouver style. 
* In the text will appear the numbering of the bibliographic citations in Arabic numerals flown. 
* Tables and figures are on separate pages of the text, always a table or a figure by sheet
* Acronyms or abbreviations be defined in the foot of the table or chart 
* The structured summary, should not exceed 200 words and preferably consist of: Objectives, Methodology, Results, Conclusions and 4-6 Keywords 
* Structured summaries of the thesis (for masters): (200-300 words) consist of: Title, Objectives, Methodology, Results and Conclusions . 4-8 keywords 
* Send your contribution to ocj@health.sdu.dk in Word

==Peer review process==
The peer review process is a way of ensuring that the information is verifiable and of a good quality. Any research paper is forwarded to the editorial group who assess quality, accuracy and relevance. The chairman of the group will assess whether the manuscript will comply with the guidelines, advice the authors and take the final decision whether it should be published or not.

==The Journal Content==

# ''Abstracts from international studies of relevance for the Panamenean population''
# Comments: opinion, on current issues
# Originals: Epidemiological and clinical research works (-2500)
# Protocols for scientific studies
# Standardized questionnaires: with references where they have been used
# Structured summaries of the theses made for masters
# International window: Articles presented in international forums
# Informative: About activities of the Scientific Associations
# Visual documentation: Photos that show the areas of studies
# Permanent education: Materials for learning
# Share knowledge of conferences: power points, articles, etc
# Meetings for editors, authors and subscribers
# General advice on preventive health care
# Current topic

==Editors==
* Olaf Jensen ocj@health.sdu.dk 
* Agnes Flores agnesflores230572@yahoo.com
* Christian Munoz cmunoz@metrodepanama.com.pa 
* Aruxi Hidalgi

==[[/Subscribers/]]==

*If you do not wish to receive Preventive Health Science or have received it in error, you may unsubscribe here cienciaspreventivas@gmail.com 
*Thank you very much

==Group Email==
* cienciaspreventivas@gmail.com

==Subpages==
{{Subpages/List}}

[[Category:Journals]]


[[File:Tissue necrosis following bite from Bothrops asper PLoS Medicine.jpg|thumb|Tissue necrosis following bite from Bothrops asper PLoS Medicine]]
[[File:Bothrops asper on the trail (Panama).jpg|thumb|Bothrops asper on the trail (Panama)]]</text>
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    <title>AP Environmental Science/Soil and Biomes</title>
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      <text bytes="18668" sha1="hm455vgiq8abszu7bf4s8q8ze4u6zne" xml:space="preserve">==Desert==
;What causes deserts?
-Rain Shadow effect&lt;br&gt;
-Convection currents (sinking air)&lt;br&gt;
;Where do deserts commonly occur geographically?
-Around 30N and 30S latitude&lt;br&gt;
-Interior continental areas&lt;br&gt;
-Leeward side of mountains
;What climate zones have deserts?
-Tropical: Hot regions year round&lt;br&gt;
-Temperate: Cooler winters, some more precipitation&lt;br&gt;
-Polar: Cold, winter
;How do plants and animals survive?
====Plants====
*Fast growing/blooming annuals
*Thick, waxy cuticle
*Thin spine

====Animals====
*Highly efficient kidney
*Nocturnal/Burrowers
*Thin and linkey; disperses heat
;Human Impactes
*Large cities
*Soil destruction by vehicles
*Depletion of groundwater
*Land disturbance/pollution from mineral extraction

==Grasslands==
[[File:Tallgrass prairie flora Andropogon gerardii.jpg|thumb|right|Grasslands have a rich, thick A layer due to the hummus from the decaying grassland plants every year]]
A '''[[w:grassland|grassland]]''' is a &quot;fire-maintained&quot; ecosystem, thus frequent fires are good. It returns nutrients to the soil, accommodating in productivity. Grazers, animals that eat grass, are common in grasslands as they maintain the grass to keep it, so to speak, &quot;grassy&quot;. Animals in the American prairies consist of elks, bisons, while an example of a browser (an animal that feeds on trees and buds) is a deer. In a grassland, it is better to have small, time-time fires than one, huge inferno.
;Human impacts
*Agriculture (foods: grains, breads, wheat)
*Fossil fuels
*Overgrazing by livestock
*Oil production and off-road vehicles in arctic tundra

Grasslands have enough precipitation to support its grasses (and more precipitation to be different from a desert and less precipitation to be different from a forest) but not enough to support large acres of trees. Grasslands are found in tropical, temperate, and polar regions and are most common in the interiors of continents (North America).
===Savanna===
[[File:1632x1224 sertaoe 2 rio grande do norte landscape panorama brasil.jpg|thumb|right|A savanna usually has warm temperatures year-round and changes between dry and wet seasons]]
A '''[[w:savanna|savanna]]''' is a tropical grassland. Scattered along with it are scattered groups of trees (acacia, for example), which naturally contain thorns to keep herbivores away. A savanna usually has warm temperatures year-round and changes between dry and wet seasons. 

During the dry season, droughts are pretty common. During the rainy seasons, since savannas are &quot;fire-maintained&quot;, fires time-time take place during the beginning of this wet season. Intense grazing by grazers and browsers prevent the growth of trees and bushes, as do the dry and fire-full seasons as well. Although the radically different seasons, the savanna plants have evolved to adapt to these circumstances they face. These plants have deep roots that can tap into groundwater. 

Herbivores in the savanna have attained astounding eating habits that keep competition to a minimum. Giraffes like to eat leaves from the tops of trees while the elephant eats leaves farther down. 

In some savannas in Africa, overgrazing by cattle and the use of trees for firewood (deforestation) have converted savannas into deserts.
===Fertile Soils===
[[File:Prairie near Brooks.JPG|thumb|left|The work of continuous wind-blow and rapid evaporation causing fires, which both the wind and fire help maintain the grassland]]
'''Temperate grasslands''' once covered a good majority of the Earth, but their fertile soil was exploited. Its soil was used to grow crops, raise cattle and build cities. Although rigorously abused, there are still some temperate grasslands we're allowed to enjoy.

In temperate grasslands, winters are terribly cold and summers are radically hot and dry. Precipitation is a guess, as they fall unevenly throughout the year. What keeps the trees and bushes from growing (except in the case of the trees and bushes '''in rivers''')? Drought, time-time fires, and constant grazing. 

Due to the death of above-ground parts of the majority of the grass... [causing] decomposition every year, organic matter from the dead grasses accumulates to produce a deep, fertile soil. This soil is held tightly in place by the works of a network of stocky, intertwined roots of drought-tolerant grasses. This is the case with soil unless the topsoil is plowed up, causing it to be blown away by prolonged periods of exposure. These grasses are not only drought-tolerant but also fire-tolerant, as the fires burn the plants above the ground but do no damage to the roots below the ground, which is the cause of new plant-life.  

The combination of continuous wind-blow and rapid evaporation causing fires, which both the wind and fire help keep the grassland a grassland!

===Tundra===
[[File:Valle de Mifafí 3.jpg|thumb|right|A limiting factor for the arctic tundra is '''temperature and light''', while a limiting factor for the alpine tundra (another type of tundra where there is more sunlight and NO permafrost layer) is '''temperature''' (during the summer, the alpine tundra can have beautiful flowers for display)]]
A '''tundra''' (Russian for &quot;marshy plain&quot;) is a grassland covered with ice and snow except during the summer. Some ecologists consider the tundra as a very cold desert due to the low levels of the precipitation and the unavailability of the water (which is frozen and not able to support life).

The winters in the tundra are long and dark, and usually extremely snowful. Under this snow, there is a squishy carpet of low-growing plants, mostly grasses, lichens, mosses, and dwarf shrubs. Trees/tall plants cannot survive in the cold and windy tundra due to these chilling circumstances. The period for growing for these tundra plants takes place during the 6-8 week summer when the sun shines constantly. As a result of the short growing season, the soil and vegetation recover from injuries VERY slowly. 

'''Permafrost''' is an underground soil in which water stays frozen for a few years. Sometimes, even the soil freezes due to the long and cold winters.

So, what happens during the brief summer? The permafrost layer prevents melted snow and ice from being absorbed into the ground. As a result, the permafrost layer creates bands of water bodies (lakes, marshes, ponds), which attract insects such as mosquitos. These insects attract the migratory birds, such as waterfowl. Animals in the tundra adapt to its circumstances with thick coats of fur (arctic wolf/fox), feathers (snowy owl), or taking shelter underground.  

Global warming plays an effect on the tundra: Global warming causes permafrost to melt, releasing methane in the process. Methane is a greenhouse gas that can increase global warming, thus increasing the rate of which the permafrost melts. 

Humans also negatively affect the tundra with their oil drilling sites and military bases.

A limiting factor for the arctic tundra is '''temperature and light''', while a limiting factor for the alpine tundra (another type of tundra where there is more sunlight and NO permafrost layer) is '''temperature''' (during the summer, the alpine tundra can have beautiful flowers for display).

==Chapparal==
[[File:Del Puerto Canyon, California.jpg|thumb|left|Fires are beneficial to this climate-ecosystem since seeds sprout out only by hot fires and fires release nutrients which are used by the new shrubs that grow (when the first rain comes along)]]
A '''[[w:chapparal|chapparal]]''' (temperate shrublands) is a Mediterranean climate-ecosystem. It is also a scrub-shrub system. Dry, warm summers and cool, rainy winters. Found in Southern California (LA, San Diego). Its shrubs are subject to periodic fires. Its relatively close location to the sea gives longer winter rainy seasons than nearby deserts; the fogs that are common during the spring and fall season and occasional small trees with leathery leaves reduce evaporation. The soil of chaparrals is thin and not very fertile.

During the rainless (dry) and warm summers, chaparral vegetation becomes extremely dry and highly prone to fires. These fires are beneficial to the climate-ecosystem: 
*Several of the shrubs maintain food hosted in their roots. Hot fires are the only cause of seeds sprouting out.
*When the first rain of the summer season comes by, annual grasses spring up and use the nutrients released by the fire. New shrubs grow as a result. 

Due to the favorable circumstances here (dry, warm summers; cool, rainy winters), humans have moved to chapparals, such as in central Chile and southern Australia, and considerably altered the environment. One of the downsides of living in a chaparral is the constant fires, which pose a serious threat to human life, and mudslides during the rainy seasons.

==Forest==
[[File:Zall Dajti.jpg|thumb|right|Forest in Albania]]
[[File:Adirondacks in May 2008.jpg|thumb|left|Forest in New York]]
A '''[[w:forest|forest]]''' requires moderate-high annual precipitations which support trees. A forest contains several different species of trees and smaller forms of vegetation.
;Tropical, temperate and polar regions of forests
-Tropical&lt;br&gt;
-Temperate&lt;br&gt;
-Boreal/Taiga (Arctic)&lt;br&gt;


;Human Impact
*Agriculture
*Harvesting for timber and paper
*Mineral mining
*Air pollution
*Tree plantations
*Pollution of forest streams
===Tropical Rainforests===
[[File:Rio Madre de Dios, Peru.JPG|thumb|right|Light is a limiting factor since plants on the ground-level cannot get light due to the huge, stocky trees towering over them. This is also why tropical rainforests have very little vegetation.]]
'''Tropical rainforests''' are found relatively close to the equator, where the hot, moist air rises and dumps its moisture onto the surrounding area. These forests have year-round warm temperatures, high humidity, and heavy rainfall (monsoons). The tropical rainforests usually consist of redwood and sequoia trees, and they are found north of San Francisco to British Columbia (in the US).

Tropical rainforests usually house huge trees with wide bases, which block out sunlight for the plants on ground-level. This blocking of sunlight is why tropical rainforests have very little vegetation. Many of the small plants on ground-level have huge leaves in order to capture what little sunlight they might get. A limiting factor for tropical rainforests is '''light'''. 

Although the severe lack of light, tropical rainforests tend to have high nets of productivity due to the precipitation rate; they also have high biodiversity. 

Due to the little wind in the forests spreading seeds/pollen (due to the dense vegetation), most rain-forest plant species depend on animals (bats, butterflies, bees, etc.) to pollinate their flowers and to spread speeds all around. The Rafflesia smells like rotten meat in order to attract flies and beetles to pollinate its flower. 
[[File:Rain Forest Daintree Australia.jpg|thumb|left|The competition in the tropical rainforest leads to a thin, acidic, and nutrient-poor soil]]
It seems the tropical rainforest has a huge, thick, fertile soil... correct? Nope! The soil of a tropical rainforest is usually acidic and low in nutrients due to the terribly-fast competition. Dropped leaves and dead animals are usually decomposed at a very fast rate due to the warm, moist conditions and scores of decomposers. Most mineral nutrients released by decomposition are taken up by trees, vines, and other plants. Because of this, '''tropical rainforest soils contain very few plant nutrients'''.

This is why rain forests are not good places to clear and grow crops/graze cattle on a regular basis. The nutrient-poor soil only has a limited time to support crops (about 1-2 years). Although this factor, rainforests are still commonly cleared or degraded for deforestation, growing crops and grazing cattle. This is a serious issue: If the destruction of rainforests continues, then global warming will accelerate. Trees that are used to remove carbon dioxide will no longer exist/be in plentiful, so carbon dioxide (a greenhouse gas) will accelerate global warming.
===Temperate Deciduous Forest===
[[File:Deciduous forest (4843082944).jpg|thumb|right|Temperature is a limiting factor since trees drop their leaves in order to become dormant]]
'''Temperate Deciduous Forests''' grow in moderately avg. temperatures that have significant changes every season. Long, warm summers with cold winters. Precipitation is evenly spread and prevalent throughout the year. 

Trees like oak, maple, ash, and gum drop their leaves in the fall to become dormant. Every spring after the fall, these trees grow new leaves. This is why temperature is a limiting factor to a temperate deciduous forest.

Temperate deciduous forests have fewer trees than the tropical rainforests, but more sunlight means more diversity of plant life at ground level. Slow decomposition results in a thick layer of slowly decomposing leaves that serve as a storehouse of nutrients. 

This biome is the most disturbed biome as these biomes were once home to several species, such as bears, wolves and foxes, but they have been misplaced/killed and have been replaced by squirrels and rabbits. Humans came over to this biome and industrialized and urbanized it. See the Eastern USA and western Europe as examples.  
;Prevalent geneses
#Oak
#Hickory
#Beech
#Maple
#Ash
#Gum
#Much more diverse; diversity increases from the poles to the equator
===Taiga===
[[File:Jack London Lake by bartosh.jpg|thumb|right|Lack of decomposition due to the low temperatures and acidity of the coniferous needles; significant O layer]]
'''Taigas''' are found south of the arctic tundra in the northern regions across Asia and North America. Winters are long, dry and cold. Summers are short, with cool-warm temperatures. The availability of the sun varies, with it shining only from 6-8 hours a day in the winter while it shining 19 hours a day during the summer. 

The needles of the evergreen/coniferous are kept all year round. These small needles have a thick, waxy coding on it, which prevents them from succumbing to the cold, harsh winters and drying out (as winter = cold air, and cold air = less moisture). When summertime comes about, they are ready to take the advantages that summer has to offer (starting photosynthesis earlier).

Plant diversity is low due to the harsh temperatures.

The soil is nutrient-poor and thin due to the low temperatures, waxy coating of the coniferous needles (which leads to acid; the soil is acidic). Lack of decomposition takes place.

Despite the low plant diversity, the taiga contains a wide variety of wildlife: Year-round residents include the wolves, moose, and bears while insects are attracted to the waterlogged soils, forming acidic bogs (muskegs). Insect-eating birds, such as the warblers, are attracted to these acidic bogs.

==Mountains==
[[File:EverestfromKalarPatarcrop.JPG|thumb|right|Slowly releasing melting ice, snow, and water maintained in the soils and vegetation of mountainsides to small streams (helps in the hydrologic cycle)]]
'''[[w:Mountains|Mountains]]''' are diverse ecosystems, not only elevation but N-S orientation. They usually have snow-covered tops with high albedo, which reflect solar radiation. Mountains cover 1/4 of the earth's land surface. Huge changes in altitude, climate, soil, and vegetation take place in mountains. 

Due to the steep slopes, mountain soils are vulnerable to erosion when the vegetation keeping them in place is removed by natural perturbations (landslides, avalanches) or anthropogenic factors (timber cutting, agriculture). 

Mountains do many ecological roles that benefit the communities they're in:
*Majority of the world's forests are in mountains.
*Habitats for species found nowhere else in the world.  
*New habitats for animal species driven away from their homelands.
*75% of the world's freshwater is found in glacial ice, mostly found in mountains.
*Mountaintops with ice (highest albedo) reflects solar radiation back into space.
*Affects sea level based on glacial ice.
*Slowly releasing melting ice, snow, and water kept in the soils and vegetation of mountainsides over to small streams.
;Human Impacts
*Timber and mineral mining
*Hydroelectric dams
*Recreation
*Air pollution
*Increase tourism
====Agriculture==== 
*Forests are cut down so that timber is harvested for wood and paper
====Mineral mining====
*Coal
*Mountaintop renewal: Southwestern VA
*Strip mining 
====Tree plantation====
*Harvested for wood and paper (timber)

==Limiting Factors==
*'''Desert''': Precipitation
*'''Arctic tundra''': Temperature/Light
*'''Alpine tundra''': Temperature
*'''Tropical rain-forest floor''': Light
*'''Temperate deciduous forest''': Temperature (trees lose leaves)
*'''Grasslands''': Precipitation
==Wind==
Wind plays an important factor in biomes:
*Promote sustainability by helping distribute solar energy.
*Promote sustainability by helping distribute earth's nutrients.

^Supports life-sustaining biodiversity of deserts, grassland, and forests.&lt;br&gt;
^Supports the diversity of species whose interactions in these ecosystems help control population sizes.

==Soil==
To put it basic, soil is &quot;organic stuff&quot;. 
#O layer (Humus)
#A layer (Topsoil)
#B layer (Mineral, Clay, Sand, Silt)
#Parent layer (Bedrock; Granite in VA)

'''Decomposition''' (from O layer to A layer) requires a warm and moist environment, bacteria and fungi (decomposers), neutral pH at about 6-5 to 8. Acidity can come from the minerals in the soil/acid rain/leaves from the falling trees.
===Soils in Dif. Biomes===
''See also: [[Soil Formation]], including [[Soil_Formation#Soil_and_Climate|Soil Formation#Soil and Climate]]''
;Desert
*A lot of heat, low precipitation
*Low productivity (lack of organic matter)
*No rich O layer or A layer
*Mostly mineral B layer
*Alcaline: High pH (basic)
;Grasslands
*Humus is created from the dying grassland plants (every year)
*Rich, thickest layer: A layer
;Temperate deciduous forests
*A layer: Significant
*O layer: Significant (from the leaves from the trees)
*B Layer: Clay; naturally acidic
;Coniferous forest/Maritime Forest
*O layer: Very significant
*Needles exclude trees from growing due to their acidity
*Not big of an A layer due to lack of decomposition. 
;Tropical Rainforest
*Not much of an O layer due to competition for nutrients. So much competition that the nutrients are used up very fast.
*Little A layer
*Mineral B layer

'''SIDENOTE''': Cutting down a rainforest for crops is a bad thing due to the limitations.
==See also==
*https://quizlet.com/30727010/apes-ch7-flash-cards/

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      <text bytes="1056693" sha1="0eo70o2o9h2y2f1vbl2vvqhx11ymhab" xml:space="preserve">== First Message Posting ==

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* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2020-12-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2020-12-09|en}}. It will be on all wikis from {{#time:j xg|2020-12-10|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* You can vote on proposals in the [[m:Special:MyLanguage/Community Wishlist Survey 2021|Community Wishlist Survey]] between 8 December and 21 December. The survey decides what the [[m:Community Tech|Community Tech team]] will work on.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/50|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2020-W50&quot;/&gt; 16:15, 7 December 2020 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2020/51|Tech News: 2020-51]] ==

&lt;section begin=&quot;technews-2020-W51&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2020/51|Translations]] are available.

'''Recent changes'''
* There is a [[mw:Wikipedia for KaiOS|Wikipedia app]] for [[:w:en:KaiOS|KaiOS]] phones. It was released in India in September. It can now be downloaded in other countries too. [https://diff.wikimedia.org/2020/12/10/growing-wikipedias-reach-with-an-app-for-kaios-feature-phones/]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2020-12-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2020-12-16|en}}. It will be on all wikis from {{#time:j xg|2020-12-17|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/51|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2020-W51&quot;/&gt; 21:34, 14 December 2020 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2020/52|Tech News: 2020-52]] ==

&lt;section begin=&quot;technews-2020-W52&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2020/52|Translations]] are available.

'''Tech News'''
* Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 11 January 2021.

'''Recent changes'''
* The &lt;code&gt;&lt;nowiki&gt;{{citation needed}}&lt;/nowiki&gt;&lt;/code&gt; template shows when a statement in a Wikipedia article needs a source. If you click on it when you edit with the visual editor there is a popup that explains this. Now it can also show the reason and when it was added. [https://phabricator.wikimedia.org/T270107]

'''Changes later this week'''
* There is no new MediaWiki version this week or next week.

'''Future changes'''
* You can [[m:WMDE Technical Wishes/Geoinformation/Ideas|propose and discuss]] what technical improvements should be done for geographic information. This could be coordinates, maps or other related things.
* Some wikis use [[mw:Writing systems/LanguageConverter|LanguageConverter]] to switch between writing systems or variants of a language. This can only be done for the entire page. There will be a &lt;code&gt;&lt;nowiki&gt;&lt;langconvert&gt;&lt;/nowiki&gt;&lt;/code&gt; tag that can convert a piece of text on a page. [https://phabricator.wikimedia.org/T263082]
*  Oversighters and stewards can hide entries in [[Special:AbuseLog|Special:AbuseLog]]. They can soon hide multiple entries at once using checkboxes. This works like hiding normal edits. It will happen in early January. [https://phabricator.wikimedia.org/T260904]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/52|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2020-W52&quot;/&gt; 20:54, 21 December 2020 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=20833836 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/02|Tech News: 2021-02]] ==

&lt;section begin=&quot;technews-2021-W02&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/02|Translations]] are available.

'''Recent changes'''
* You can choose to be reminded when you have not added an edit summary. This can be done in your preferences. This could conflict with the [[:w:en:CAPTCHA|CAPTCHA]]. This has now been fixed. [https://phabricator.wikimedia.org/T12729]
* You can link to specific log entries. You can get these links for example by clicking the timestamps in the log. Until now, such links to private log entries showed no entry even if you had permission to view private log entries. The links now show the entry. [https://phabricator.wikimedia.org/T269761]
* Admins can use the [[:mw:Special:MyLanguage/Extension:AbuseFilter|abuse filter tool]] to automatically prevent bad edits. Three changes happened last week:
** The filter editing interface now shows syntax errors while you type. This is similar to JavaScript pages. It also shows a warning for regular expressions that match the empty string. New warnings will be added later. [https://phabricator.wikimedia.org/T187686]
** [[m:Special:MyLanguage/Meta:Oversighters|Oversighters]] can now hide multiple filter log entries at once using checkboxes on [[Special:AbuseLog]]. This is how the usual revision deletion works. [https://phabricator.wikimedia.org/T260904]
** When a filter matches too many actions after it has been changed it is &quot;throttled&quot;. The most powerful actions are disabled. This is to avoid many editors getting blocked when an administrator made a mistake. The administrator will now get a notification about this &quot;throttle&quot;.
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] There is a new tool to [https://skins.wmflabs.org/?#/add build new skins]. You can also [https://skins.wmflabs.org/?#/ see] existing [[mw:Special:MyLanguage/Manual:Skins|skins]]. You can [[mw:User talk:Jdlrobson|give feedback]]. [https://lists.wikimedia.org/pipermail/wikitech-l/2020-December/094130.html]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Bots using the API no longer watch pages automatically based on account preferences. Setting the &lt;code&gt;watchlist&lt;/code&gt; to &lt;code&gt;watch&lt;/code&gt; will still work. This is to reduce the size of the watchlist data in the database. [https://phabricator.wikimedia.org/T258108]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[mw:Special:MyLanguage/Extension:Scribunto|Scribunto's]] [[:mw:Extension:Scribunto/Lua reference manual#File metadata|file metadata]] now includes length. [https://phabricator.wikimedia.org/T209679]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:w:en:CSS|CSS]] and [[:w:en:JavaScript|JavaScript]] code pages now have link anchors to [https://patchdemo.wmflabs.org/wikis/40e4795d4448b55a6d8c46ff414bcf78/w/index.php/MediaWiki:En.js#L-125 line numbers]. You can use wikilinks like [[:w:en:MediaWiki:Common.js#L-50]]. [https://phabricator.wikimedia.org/T29531]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] There was a [[mw:MediaWiki 1.36/wmf.25|new version]] of MediaWiki last week. You can read [[mw:MediaWiki 1.36/wmf.25/Changelog|a detailed log]] of all 763 changes. Most of them are very small and will not affect you.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-13|en}}. It will be on all wikis from {{#time:j xg|2021-01-14|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/02|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W02&quot;/&gt; 15:42, 11 January 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/03|Tech News: 2021-03]] ==

&lt;section begin=&quot;technews-2021-W03&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/03|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-20|en}}. It will be on all wikis from {{#time:j xg|2021-01-21|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* The [[mw:Special:MyLanguage/Growth|Growth team]] plans to add features to [[mw:Special:MyLanguage/Growth/Personalized first day/Newcomer tasks/Experiment analysis, November 2020|get more visitors to edit]] to more Wikipedias. You can help [https://translatewiki.net/w/i.php?title=Special:Translate&amp;group=ext-growthexperiments&amp;language=&amp;filter=&amp;action=translate translating the interface].
* You will be able to read but not to edit Wikimedia Commons for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210126T07 {{#time:j xg|2021-01-26|en}} at 07:00 (UTC)]. [https://phabricator.wikimedia.org/T271791]
* [[m:Special:MyLanguage/MassMessage|MassMessage]] posts could be automatically timestamped in the future. This is because MassMessage senders can now send pages using MassMessage. Pages are more difficult to sign. If there are times when a MassMessage post should not be timestamped you can [[phab:T270435|let the developers know]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/03|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W03&quot;/&gt; 16:10, 18 January 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=20974628 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/04|Tech News: 2021-04]] ==

&lt;section begin=&quot;technews-2021-W04&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/04|Translations]] are available.

'''Problems'''
* You will be able to read but not to edit Wikimedia Commons for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210126T07 {{#time:j xg|2021-01-26|en}} at 07:00 (UTC)]. You will not be able to read or edit [[:wikitech:Main Page|Wikitech]] for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210128T09 {{#time:j xg|2021-01-28|en}} at 09:00 (UTC)]. [https://phabricator.wikimedia.org/T271791][https://phabricator.wikimedia.org/T272388]

'''Changes later this week'''
* [[m:WMDE Technical Wishes/Bracket Matching|Bracket matching]] will be added to the [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] syntax highlighter on the first wikis. The first wikis are German and Catalan Wikipedia and maybe other Wikimedia wikis. This will happen on 27 January. [https://phabricator.wikimedia.org/T270238]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-27|en}}. It will be on all wikis from {{#time:j xg|2021-01-28|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/04|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W04&quot;/&gt; 18:31, 25 January 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/05|Tech News: 2021-05]] ==

&lt;section begin=&quot;technews-2021-W05&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/05|Translations]] are available.

'''Problems'''
* [[:w:en:IPv6|IPv6 addresses]] were written in lowercase letters in diffs. This caused dead links since [[Special:Contributions|Special:Contributions]] only accepted uppercase letters for the IPs. This has been fixed. [https://phabricator.wikimedia.org/T272225]

'''Changes later this week'''
* You can soon use Wikidata to link to pages on the multilingual Wikisource. [https://phabricator.wikimedia.org/T138332]
* Often editors use a &quot;non-breaking space&quot; to make a gap between two items when reading but still show them together. This can be used to avoid a line break. You will now be able to add new ones via the special character tool in the 2010, 2017, and visual editors. The character will be shown in the visual editor as a space with a grey background. [https://phabricator.wikimedia.org/T70429][https://phabricator.wikimedia.org/T96666]
* [[File:Octicons-tools.svg|15px|link=| Advanced item]] Wikis use [[mw:Special:MyLanguage/Extension:AbuseFilter|abuse filters]] to stop bad edits being made. Filter maintainers can now use syntax like &lt;code&gt;1.2.3.4 - 1.2.3.55&lt;/code&gt; as well as the &lt;code&gt;1.2.3.4/27&lt;/code&gt; syntax for IP ranges. [https://phabricator.wikimedia.org/T218074]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.29|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-03|en}}. It will be on all wikis from {{#time:j xg|2021-02-04|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* [[mw:Skin:Minerva Neue|Minerva]] is the skin Wikimedia wikis use for mobile traffic. When a page is protected and you can't edit it you can normally read the source wikicode. This doesn't work on Minerva on mobile devices. This is being fixed. Some text might overlap. This is because your community needs to update [[MediaWiki:Protectedpagetext|MediaWiki:Protectedpagetext]] to work on mobile. You can [[phab:T208827|read more]]. [https://www.mediawiki.org/wiki/Recommendations_for_mobile_friendly_articles_on_Wikimedia_wikis#Inline_styles_should_not_use_properties_that_impact_sizing_and_positioning][https://www.mediawiki.org/wiki/Recommendations_for_mobile_friendly_articles_on_Wikimedia_wikis#Avoid_tables_for_anything_except_data]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:wikitech:Portal:Cloud VPS|Cloud VPS]] and [[:wikitech:Portal:Toolforge|Toolforge]] will change the IP address they use to contact the wikis. The new IP address will be &lt;code&gt;185.15.56.1&lt;/code&gt;. This will happen on February 8. You can [[:wikitech:News/CloudVPS NAT wikis|read more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/05|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W05&quot;/&gt; 22:38, 1 February 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/06|Tech News: 2021-06]] ==

&lt;section begin=&quot;technews-2021-W06&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/06|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/Wikimedia Apps|Wikipedia app]] for Android now has watchlists and talk pages in the app. [https://play.google.com/store/apps/details?id=org.wikipedia]

'''Changes later this week'''
* You can see edits to chosen pages on [[Special:Watchlist|Special:Watchlist]]. You can add pages to your watchlist on every wiki you like. The [[:mw:Special:MyLanguage/Extension:GlobalWatchlist|GlobalWatchlist]] extension will come to Meta on 11 February. There you can see entries on watched pages on different wikis on the same page. The new watchlist will be found on [[m:Special:GlobalWatchlist|Special:GlobalWatchlist]] on Meta. You can choose which wikis to watch and other preferences on [[m:Special:GlobalWatchlistSettings|Special:GlobalWatchlistSettings]] on Meta. You can watch up to five wikis. [https://phabricator.wikimedia.org/T260862]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.30|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-10|en}}. It will be on all wikis from {{#time:j xg|2021-02-11|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* When admins [[mw:Special:MyLanguage/Help:Protecting and unprotecting pages|protect]] pages the form will use the [[mw:UX standardization|OOUI look]]. [[Special:Import|Special:Import]] will also get the new look. This will make them easier to use on mobile phones. [https://phabricator.wikimedia.org/T235424][https://phabricator.wikimedia.org/T108792]
* Some services will not work for a short period of time from 07:00 UTC on 17 February. There might be problems with new [[m:Special:MyLanguage/Wikimedia URL Shortener|short links]], new translations, new notifications, adding new items to your [[mw:Reading/Reading Lists|reading lists]] or recording [[:w:en:Email#Tracking of sent mail|email bounces]]. This is because of database maintenance. [https://phabricator.wikimedia.org/T273758]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[m:Tech/News/2021/05|Last week]] Tech News reported that the IP address [[:wikitech:Portal:Cloud VPS|Cloud VPS]] and [[:wikitech:Portal:Toolforge|Toolforge]] use to contact the wikis will change on 8 February. This is delayed. It will happen later instead. [https://wikitech.wikimedia.org/wiki/News/CloudVPS_NAT_wikis]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/06|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W06&quot;/&gt; 17:42, 8 February 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21082948 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/07|Tech News: 2021-07]] ==

&lt;section begin=&quot;technews-2021-W07&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/07|Translations]] are available.

'''Problems'''
* There were problems with recent versions of MediaWiki.  Because the updates caused problems the developers rolled back to an earlier version. Some updates and new functions will come later than planned. [https://lists.wikimedia.org/pipermail/wikitech-l/2021-February/094255.html][https://lists.wikimedia.org/pipermail/wikitech-l/2021-February/094271.html]
* Some services will not work for a short period of time from 07:00 UTC on 17 February. There might be problems with new [[m:Special:MyLanguage/Wikimedia URL Shortener|short links]], new translations, new notifications, adding new items to your [[mw:Reading/Reading Lists|reading lists]] or recording [[:w:en:Email#Tracking of sent mail|email bounces]]. This is because of database maintenance. [https://phabricator.wikimedia.org/T273758]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.31|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-17|en}}. It will be on all wikis from {{#time:j xg|2021-02-18|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/07|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W07&quot;/&gt; 17:56, 15 February 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21105437 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/08|Tech News: 2021-08]] ==

&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/08|Translations]] are available.

'''Recent changes'''
* The visual editor will now use [[:c:Commons:Structured data/Media search|MediaSearch]] to find images. You can search for images on Commons in the visual editor when you are looking for illustrations. This is to help editors find better images. [https://phabricator.wikimedia.org/T259896]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlighter]] now works with more languages: [[:w:en:Futhark (programming language)|Futhark]], [[:w:en:Graphviz|Graphviz]]/[[:w:en:DOT (graph description language)|DOT]], CDDL and AMDGPU. [https://phabricator.wikimedia.org/T274741]

'''Problems'''
* Editing a [[mw:Special:MyLanguage/Extension:EasyTimeline|timeline]] might have removed all text from it. This was because of a bug and has been fixed. You might need to edit the timeline again for it to show properly. [https://phabricator.wikimedia.org/T274822]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.32|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-24|en}}. It will be on all wikis from {{#time:j xg|2021-02-25|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] There is a [[:m:Wikimedia Rust developers user group|user group]] for developers and users interested in working on Wikimedia wikis with the [[:w:en:Rust (programming language)|Rust programming language]]. You can join or tell others who want to make your wiki better in the future.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;

----

00:17, 23 February 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21134058 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/09|Tech News: 2021-09]] ==

&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/09|Translations]] are available.

'''Recent changes'''
*  Wikis using the [[mw:Special:MyLanguage/Growth/Feature summary|Growth team tools]] can now show the name of a newcomer's mentor anywhere [[mw:Special:MyLanguage/Help:Growth/Mentorship/Integrating_mentorship|through a magic word]]. This can be used for welcome messages or userboxes.
* A new version of the [[c:Special:MyLanguage/Commons:VideoCutTool|VideoCutTool]] is now available. It enables cropping, trimming, audio disabling, and rotating video content. It is being created as part of the developer outreach programs.

'''Problems'''
* There was a problem with the [[mw:Special:MyLanguage/Manual:Job queue|job queue]]. This meant some functions did not save changes and mass messages were delayed. This did not affect wiki edits. [https://phabricator.wikimedia.org/T275437]
* Some editors may not be logged in to their accounts automatically in the latest versions of Firefox and Safari. [https://phabricator.wikimedia.org/T226797]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.33|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-03|en}}. It will be on all wikis from {{#time:j xg|2021-03-04|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;

----

19:08, 1 March 2021 (UTC)
&lt;!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21161722 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/10|Tech News: 2021-10]] ==

&lt;section begin=&quot;technews-2021-W10&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/10|Translations]] are available.

'''Recent changes'''
* [[mw:Special:MyLanguage/Content translation/Section translation|Section translation]] now works on Bengali Wikipedia. It helps mobile editors translate sections of articles. It will come to more wikis later. The first focus is active wikis with a smaller number of articles. You can [https://sx.wmflabs.org/index.php/Main_Page test it] and [[mw:Talk:Content translation/Section translation|leave feedback]].
* [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs|Flagged revisions]] now give admins the review right. [https://phabricator.wikimedia.org/T275293]
* When someone links to a Wikipedia article on Twitter this will now show a preview of the article. [https://phabricator.wikimedia.org/T276185]

'''Problems'''
* Many graphs have [[:w:en:JavaScript|JavaScript]] errors. Graph editors can check their graphs in their browser's developer console after editing. [https://phabricator.wikimedia.org/T275833]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.34|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-10|en}}. It will be on all wikis from {{#time:j xg|2021-03-11|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).
* The [[mw:Talk pages project/New discussion|New Discussion]] tool will soon be a new [[mw:Special:MyLanguage/Extension:DiscussionTools|discussion tools]] beta feature for on most Wikipedias. The goal is to make it easier to start new discussions. [https://phabricator.wikimedia.org/T275257]

'''Future changes'''
* There will be a number of changes to make it easier to work with templates. Some will come to the first wikis in March. Other changes will come to the first wikis in June. This is both for those who use templates and those who create or maintain them. You can [[:m:WMDE Technical Wishes/Templates|read more]].
* [[m:WMDE Technical Wishes/ReferencePreviews|Reference Previews]] will become a default feature on some wikis on 17 March. They will share a setting with [[mw:Page Previews|Page Previews]]. If you prefer the Reference Tooltips or Navigation-Popups gadget you can keep using them. If so Reference Previews won't be shown. [https://phabricator.wikimedia.org/T271206][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/ReferencePreviews]
* New JavaScript-based functions will not work in [[:w:en:Internet Explorer 11|Internet Explorer 11]]. This is because Internet Explorer is an old browser that doesn't work with how JavaScript is written today. Everything that works in Internet Explorer 11 today will continue working in Internet Explorer for now. You can [[mw:Compatibility/IE11|read more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/10|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W10&quot;/&gt; 17:51, 8 March 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21175593 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/11|Tech News: 2021-11]] ==

&lt;section begin=&quot;technews-2021-W11&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/11|Translations]] are available.

'''Recent changes'''
* Wikis that are part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|desktop improvements]] project can now use a new [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Search|search function]]. The desktop improvements and the new search will come to more wikis later. You can also [[mw:Reading/Web/Desktop Improvements#Deployment plan and timeline|test it early]].
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Editors who put up banners or change site-wide [[:w:en:JavaScript|JavaScript]] code should use the [https://grafana.wikimedia.org/d/000000566/overview?viewPanel=16&amp;orgId=1 client error graph] to see that their changes has not caused problems. You can [https://diff.wikimedia.org/2021/03/08/sailing-steady%e2%80%8a-%e2%80%8ahow-you-can-help-keep-wikimedia-sites-error-free read more]. [https://phabricator.wikimedia.org/T276296]

'''Problems'''
* Due to [[phab:T276968|database issues]] the [https://meta.wikimedia.beta.wmflabs.org Wikimedia Beta Cluster] was read-only for over a day.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.34|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-17|en}}. It will be on all wikis from {{#time:j xg|2021-03-18|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* You can add a [[:w:en:Newline|newline]] or [[:w:en:Carriage return|carriage return]] character to a custom signature if you use a template. There is a proposal to not allow them in the future. This is because they can cause formatting problems. [https://www.mediawiki.org/wiki/New_requirements_for_user_signatures#Additional_proposal_(2021)][https://phabricator.wikimedia.org/T272322]
* You will be able to read but not edit [[phab:T276899|12 wikis]] for a short period of time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210323T06 {{#time:j xg|2021-03-23|en}} at 06:00 (UTC)]. This could take 30 minutes but will probably be much faster.
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] You can use [https://quarry.wmflabs.org/ Quarry] for [[:w:en:SQL|SQL]] queries to the [[wikitech:Wiki replicas|Wiki Replicas]]. Cross-database &lt;code&gt;JOINS&lt;/code&gt; will no longer work from 23 March. There will be a new field to specify the database to connect to. If you think this affects you and you need help you can [[phab:T268498|post on Phabricator]] or on [[wikitech:Talk:News/Wiki Replicas 2020 Redesign|Wikitech]]. [https://wikitech.wikimedia.org/wiki/PAWS PAWS] and other ways to do [[:w:en:SQL|SQL]] queries to the Wiki Replicas will be affected later. [https://wikitech.wikimedia.org/wiki/News/Wiki_Replicas_2020_Redesign]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/11|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W11&quot;/&gt; 23:22, 15 March 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21226057 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/12|Tech News: 2021-12]] ==

&lt;section begin=&quot;technews-2021-W12&quot;/&gt;&lt;div class=&quot;plainlinks mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/12|Translations]] are available.

'''Recent changes'''
* There is a [[mw:Wikipedia for KaiOS|Wikipedia app]] for [[:w:en:KaiOS|KaiOS]] phones. They don't have a touch screen so readers navigate with the phone keys. There is now a [https://wikimedia.github.io/wikipedia-kaios/sim.html simulator] so you can see what it looks like.
* The [[mw:Special:MyLanguage/Talk pages project/Replying|reply tool]] and [[mw:Special:MyLanguage/Talk pages project/New discussion|new discussion tool]] are now available as the &quot;{{int:discussiontools-preference-label}}&quot; [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] in almost all wikis except German Wikipedia.

'''Problems'''
* You will be able to read but not edit [[phab:T276899|twelve wikis]] for a short period of time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210323T06 {{#time:j xg|2021-03-23|{{PAGELANGUAGE}}}} at 06:00 (UTC)]. This can also affect password changes, logging in to new wikis, global renames and changing or confirming emails. This could take 30 minutes but will probably be much faster.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.36|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-24|en}}. It will be on all wikis from {{#time:j xg|2021-03-25|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).
* [[:w:en:Syntax highlighting|Syntax highlighting]] colours will change to be easier to read. This will soon come to the [[phab:T276346|first wikis]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Improved_Color_Scheme_of_Syntax_Highlighting]

'''Future changes'''
* [[mw:Special:MyLanguage/Extension:FlaggedRevs|Flagged revisions]] will no longer have multiple tags like &quot;tone&quot; or &quot;depth&quot;. It will also only have one tier. This was changed because very few wikis used these features and they make the tool difficult to maintain. [https://phabricator.wikimedia.org/T185664][https://phabricator.wikimedia.org/T277883]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets and user scripts can access variables about the current page in JavaScript. In 2015 this was moved from &lt;code dir=ltr&gt;wg*&lt;/code&gt; to &lt;code dir=ltr&gt;mw.config&lt;/code&gt;. &lt;code dir=ltr&gt;wg*&lt;/code&gt; will soon no longer work. [https://phabricator.wikimedia.org/T72470]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/12|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;/div&gt; &lt;section end=&quot;technews-2021-W12&quot;/&gt; 16:53, 22 March 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21244806 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/13|Tech News: 2021-13]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/13|Translations]] are available.

'''Recent changes'''
* Some very old [[:w:en:Web browser|web browsers]] [[:mw:Special:MyLanguage/Compatibility|don’t work]] well with the Wikimedia wikis. Some old code for browsers that used to be supported is being removed. This could cause issues in those browsers. [https://phabricator.wikimedia.org/T277803]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:m:IRC/Channels#Raw_feeds|IRC recent changes feeds]] have been moved to a new server. Make sure all tools automatically reconnect to &lt;code&gt;irc.wikimedia.org&lt;/code&gt; and not to the name of any specific server. Users should also consider switching to the more modern [[:wikitech:Event Platform/EventStreams|EventStreams]]. [https://phabricator.wikimedia.org/T224579]

'''Problems'''
* When you move a page that many editors have on their watchlist the history can be split. It might also not be possible to move it again for a while. This is because of a [[:w:en:Job queue|job queue]] problem. [https://phabricator.wikimedia.org/T278350]
* Some translatable pages on Meta could not be edited. This was because of a bug in the translation tool. The new MediaWiki version was delayed because of problems like this. [https://phabricator.wikimedia.org/T278429][https://phabricator.wikimedia.org/T274940]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.37|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-31|en}}. It will be on all wikis from {{#time:j xg|2021-04-01|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

17:30, 29 March 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21267131 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/14|Tech News: 2021-14]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/14|Translations]] are available.

'''Recent changes'''
* Editors can collapse part of an article so you have to click on it to see it. When you click a link to a section inside collapsed content it will now expand to show the section. The browser will scroll down to the section. Previously such links didn't work unless you manually expanded the content first. [https://phabricator.wikimedia.org/T276741]

'''Changes later this week'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:Special:MyLanguage/Citoid|citoid]] [[:w:en:API|API]] will use for example &lt;code&gt;2010-12-XX&lt;/code&gt; instead of &lt;code&gt;2010-12&lt;/code&gt; for dates with a month but no days. This is because &lt;code&gt;2010-12&lt;/code&gt; could be confused with &lt;code&gt;2010-2012&lt;/code&gt; instead of &lt;code&gt;December 2010&lt;/code&gt;. This is called level 1 instead of level 0 in the [https://www.loc.gov/standards/datetime/ Extended Date/Time Format]. [https://phabricator.wikimedia.org/T132308]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.38|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-04-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-04-07|en}}. It will be on all wikis from {{#time:j xg|2021-04-08|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:wikitech:PAWS|PAWS]] can now connect to the new [[:wikitech:Wiki Replicas|Wiki Replicas]]. Cross-database &lt;code&gt;JOINS&lt;/code&gt; will no longer work from 28 April. There is [[:wikitech:News/Wiki Replicas 2020 Redesign#How should I connect to databases in PAWS?|a new way to connect]] to the databases. Until 28 April both ways to connect to the databases will work. If you think this affects you and you need help you can post [[phab:T268498|on Phabricator]] or on [[wikitech:Talk:News/Wiki Replicas 2020 Redesign|Wikitech]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

19:41, 5 April 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/16|Tech News: 2021-16]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/16|Translations]] are available.

'''Recent changes'''
* Email to the Wikimedia wikis are handled by groups of Wikimedia editors. These volunteer response teams now use [https://github.com/znuny/Znuny Znuny] instead of [[m:Special:MyLanguage/OTRS|OTRS]]. The functions and interface remain the same. The volunteer administrators will give more details about the next steps soon. [https://phabricator.wikimedia.org/T279303][https://phabricator.wikimedia.org/T275294]
* If you use [[Mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighting]], you can see line numbers in the 2010 and 2017 wikitext editors when editing templates. This is to make it easier to see line breaks or talk about specific lines. Line numbers will soon come to all namespaces. [https://phabricator.wikimedia.org/T267911][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Line_Numbering][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/Line_Numbering]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Because of a technical change there could be problems with gadgets and scripts that have an edit summary area that looks [https://phab.wmfusercontent.org/file/data/llvdqqnb5zpsfzylbqcg/PHID-FILE-25vs4qowibmtysl7cbml/Screen_Shot_2021-04-06_at_2.34.04_PM.png similar to this one]. If they look strange they should use &lt;code&gt;mw.loader.using('mediawiki.action.edit.styles')&lt;/code&gt; to go back to how they looked before. [https://phabricator.wikimedia.org/T278898]
* The [[mw:MediaWiki 1.37/wmf.1|latest version]] of MediaWiki came to the Wikimedia wikis last week. There was no Tech News issue last week.

'''Changes later this week'''
*  There is no new MediaWiki version this week.

'''Future changes'''
* The user group &lt;code&gt;oversight&lt;/code&gt; will be renamed &lt;code&gt;suppress&lt;/code&gt;. This is for [[phab:T109327|technical reasons]]. This is the technical name. It doesn't affect what you call the editors with this user right on your wiki. This is planned to happen in two weeks. You can comment [[phab:T112147|in Phabricator]] if you have objections.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

16:48, 19 April 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/17|Tech News: 2021-17]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/17|Translations]] are available.

'''Recent changes'''
* Templates have parameters that can have specific values. It is possible to suggest values for editors with [[mw:Special:MyLanguage/Extension:TemplateData|TemplateData]]. You can soon see them as a drop-down list in the visual editor. This is to help template users find the right values faster. [https://phabricator.wikimedia.org/T273857][https://meta.wikimedia.org/wiki/Special:MyLanguage/WMDE_Technical_Wishes/Suggested_values_for_template_parameters][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/Suggested_values_for_template_parameters]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-04-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-04-28|en}}. It will be on all wikis from {{#time:j xg|2021-04-29|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

21:24, 26 April 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/18|Tech News: 2021-18]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/18|Translations]] are available.

'''Recent changes'''
* [[w:en:Wikipedia:Twinkle|Twinkle]] is a gadget on English Wikipedia. It can help with maintenance and patrolling. It can [[m:Grants:Project/Rapid/SD0001/Twinkle localisation/Report|now be used on other wikis]]. You can get Twinkle on your wiki using the [https://github.com/wikimedia-gadgets/twinkle-starter twinkle-starter] GitHub repository.

'''Problems'''
* The [[mw:Special:MyLanguage/Content translation|content translation tool]] did not work for many articles for a little while. This was because of a bug. [https://phabricator.wikimedia.org/T281346]
* Some things will not work for about a minute on 5 May. This will happen [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210505T0600 around 06:00 UTC]. This will affect the content translation tool and notifications among other things. This is because of an upgrade to avoid crashes. [https://phabricator.wikimedia.org/T281212]

'''Changes later this week'''
* [[mw:Special:MyLanguage/Help:Reference Previews|Reference Previews]] will become a default feature on a number of wikis on 5 May. This is later than planned because of some changes. You can use it without using [[mw:Special:MyLanguage/Page Previews|Page Previews]] if you want to. The earlier plan was to have the preference to use both or none. [https://phabricator.wikimedia.org/T271206][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/ReferencePreviews]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-05|en}}. It will be on all wikis from {{#time:j xg|2021-05-06|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[:w:en:CSS|CSS]] classes &lt;code dir=ltr&gt;.error&lt;/code&gt;, &lt;code dir=ltr&gt;.warning&lt;/code&gt; and &lt;code dir=ltr&gt;.success&lt;/code&gt; do not work for mobile readers if they have not been specifically defined on your wiki. From June they will not work for desktop readers. This can affect gadgets and templates. The classes can be defined in [[MediaWiki:Common.css]] or template styles instead. [https://phabricator.wikimedia.org/T280766]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:43, 3 May 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21418010 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/19|Tech News: 2021-19]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/19|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-12|en}}. It will be on all wikis from {{#time:j xg|2021-05-13|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* You can see what participants plan to work on at the online [[mw:Wikimedia Hackathon 2021|Wikimedia hackathon]] 22–23 May.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:10, 10 May 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21428676 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/20|Tech News: 2021-20]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/20|Translations]] are available.

'''Recent changes'''
* There is a new toolbar in [[mw:Talk pages project/Replying|the Reply tool]]. It works in the wikitext source mode. You can enable it in [[Special:Preferences#mw-htmlform-discussion|your preferences]]. [https://phabricator.wikimedia.org/T276608] [https://www.mediawiki.org/wiki/Talk_pages_project/Replying#13_May_2021] [https://www.mediawiki.org/wiki/Talk_pages_project/New_discussion#13_May_2021]
* Wikimedia [https://lists.wikimedia.org/mailman/listinfo mailing lists] are being moved to [[:w:en:GNU Mailman|Mailman 3]]. This is a newer version. For the [[:w:en:Character encoding|character encoding]] to work it will change from &lt;code&gt;[[:w:en:UTF-8|UTF-8]]&lt;/code&gt; to &lt;code&gt;utf8mb3&lt;/code&gt;. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IEYQ2HS3LZF2P3DAYMNZYQDGHWPVMTPY/][https://phabricator.wikimedia.org/T282621]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] An [[m:Special:MyLanguage/Tech/News/2021/14|earlier issue]] of Tech News said that the  [[mw:Special:MyLanguage/Citoid|citoid]] [[:w:en:API|API]] would handle dates with a month but no days in a new way. This has been reverted for now. There needs to be more discussion of how it affects different wikis first. [https://phabricator.wikimedia.org/T132308]

'''Changes later this week'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] &lt;code&gt;MediaWiki:Pageimages-blacklist&lt;/code&gt; will be renamed &lt;code&gt;MediaWiki:Pageimages-denylist&lt;/code&gt;. The list can be copied to the new name. It will happen on 19 May for some wikis and 20 May for some wikis. Most wikis don't use it. It lists images that should never be used as thumbnails for articles. [https://phabricator.wikimedia.org/T282626]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-19|en}}. It will be on all wikis from {{#time:j xg|2021-05-20|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

13:49, 17 May 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/21|Tech News: 2021-21]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/21|Translations]] are available.

'''Recent changes'''
* The Wikimedia movement has been using [[:m:Special:MyLanguage/IRC|IRC]] on a network called [[:w:en:Freenode|Freenode]]. There have been changes around who is in control of the network. The [[m:Special:MyLanguage/IRC/Group_Contacts|Wikimedia IRC Group Contacts]] have [[m:Special:Diff/21476411|decided]] to move to the new [[:w:en:Libera Chat|Libera Chat]] network instead. This is not a formal decision for the movement to move all channels but most Wikimedia IRC channels will probably leave Freenode. There is a [[:m:IRC/Migrating_to_Libera_Chat|migration guide]] and ongoing Wikimedia [[m:Wikimedia Forum#Freenode (IRC)|discussions about this]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-26|en}}. It will be on all wikis from {{#time:j xg|2021-05-27|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

17:07, 24 May 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/22|Tech News: 2021-22]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/22|Translations]] are available.

'''Problems'''
* There was an issue on the Vector skin with the text size of categories and notices under the page title. It was fixed last Monday. [https://phabricator.wikimedia.org/T283206]

'''Changes later this week'''
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/22|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

17:05, 31 May 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/23|Tech News: 2021-23]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/23|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-09|en}}. It will be on all wikis from {{#time:j xg|2021-06-10|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* The Wikimedia movement uses [[:mw:Special:MyLanguage/Phabricator|Phabricator]] for technical tasks. This is where we collect technical suggestions, bugs and what developers are working on. The company behind Phabricator will stop working on it. This will not change anything for the Wikimedia movement now. It could lead to changes in the future. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/YAXOD46INJLAODYYIJUVQWOZFIV54VUI/][https://admin.phacility.com/phame/post/view/11/phacility_is_winding_down_operations/][https://phabricator.wikimedia.org/T283980]
* Searching on Wikipedia will find more results in some languages. This is mainly true for when those who search do not use the correct [[:w:en:Diacritic|diacritics]] because they are not seen as necessary in that language. For example searching for &lt;code&gt;Bedusz&lt;/code&gt; doesn't find &lt;code&gt;Będusz&lt;/code&gt; on German Wikipedia. The character &lt;code&gt;ę&lt;/code&gt; isn't used in German so many would write &lt;code&gt;e&lt;/code&gt; instead. This will work better in the future in some languages. [https://phabricator.wikimedia.org/T219550]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[:w:en:Cross-site request forgery|CSRF token parameters]] in the [[:mw:Special:MyLanguage/API:Main page|action API]] were changed in 2014. The old parameters from before 2014 will stop working soon. This can affect bots, gadgets and user scripts that still use the old parameters. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IMP43BNCI32C524O5YCUWMQYP4WVBQ2B/][https://phabricator.wikimedia.org/T280806]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/23|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

20:02, 7 June 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21551759 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/24|Tech News: 2021-24]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/24|Translations]] are available.

'''Recent changes'''
* Logged-in users on the mobile web can choose to use the [[:mw:Special:MyLanguage/Reading/Web/Advanced mobile contributions|advanced mobile mode]]. They now see categories in a similar way as users on desktop do. This means that some gadgets that have just been for desktop users could work for users of the mobile site too. If your wiki has such gadgets you could decide to turn them on for the mobile site too. Some gadgets probably need to be fixed to look good on mobile. [https://phabricator.wikimedia.org/T284763]
* Language links on Wikidata now works for [[:oldwikisource:Main Page|multilingual Wikisource]]. [https://phabricator.wikimedia.org/T275958]

'''Changes later this week'''
* There is no new MediaWiki version this week.

'''Future changes'''
* In the future we [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation|can't show the IP]] of unregistered editors to everyone. This is because privacy regulations and norms have changed. There is now a rough draft of how [[m:IP Editing: Privacy Enhancement and Abuse Mitigation#Updates|showing the IP to those who need to see it]] could work.
* German Wikipedia, English Wikivoyage and 29 smaller wikis will be read-only for a few minutes on 22 June. This is planned between 5:00 and 5:30 UTC. [https://phabricator.wikimedia.org/T284530]
* All wikis will be read-only for a few minutes in the week of 28 June. More information will be published in Tech News later. It will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T281515][https://phabricator.wikimedia.org/T281209]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/24|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

20:26, 14 June 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21587625 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/25|Tech News: 2021-25]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/25|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The &lt;code&gt;otrs-member&lt;/code&gt; group name is now &lt;code&gt;vrt-permissions&lt;/code&gt;. This could affect abuse filters. [https://phabricator.wikimedia.org/T280615]

'''Problems'''
* You will be able to read but not edit German Wikipedia, English Wikivoyage and 29 smaller wikis for a few minutes on 22 June. This is planned between [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210623T0500 5:00 and 5:30 UTC]. [https://phabricator.wikimedia.org/T284530]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-23|en}}. It will be on all wikis from {{#time:j xg|2021-06-24|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/25|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:49, 21 June 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21593987 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/26|Tech News: 2021-26]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/26|Translations]] are available.

'''Recent changes'''
* Wikis with the [[mw:Special:MyLanguage/Growth|Growth features]] now can [[mw:Special:MyLanguage/Growth/Community configuration|configure Growth features directly on their wiki]]. This uses the new special page &lt;code&gt;Special:EditGrowthConfig&lt;/code&gt;. [https://phabricator.wikimedia.org/T285423]
* Wikisources have a new [[m:Special:MyLanguage/Community Tech/OCR Improvements|OCR tool]]. If you don't want to see the &quot;extract text&quot; button on Wikisource you can add &lt;code&gt;.ext-wikisource-ExtractTextWidget { display: none; }&lt;/code&gt; to your [[Special:MyPage/common.css|common.css page]]. [https://phabricator.wikimedia.org/T285311]

'''Problems'''
*You will be able to read but not edit the Wikimedia wikis for a few minutes on 29 June. This is planned at [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210629T1400 14:00 UTC]. [https://phabricator.wikimedia.org/T281515][https://phabricator.wikimedia.org/T281209]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-30|en}}. It will be on all wikis from {{#time:j xg|2021-07-01|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* &lt;code&gt;Threshold for stub link formatting&lt;/code&gt;, &lt;code&gt;thumbnail size&lt;/code&gt; and &lt;code&gt;auto-number headings&lt;/code&gt; can be set in preferences. They are expensive to maintain and few editors use them. The developers are planning to remove them. Removing them will make pages load faster. You can [[mw:Special:MyLanguage/User:SKim (WMF)/Performance Dependent User Preferences|read more and give feedback]].
* A toolbar will be added to the [[mw:Talk pages project/Replying|Reply tool]]'s wikitext source mode. This will make it easier to link to pages and to ping other users. [https://phabricator.wikimedia.org/T276609][https://www.mediawiki.org/wiki/Talk_pages_project/Replying#Status_updates]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/26|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

16:32, 28 June 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/27|Tech News: 2021-27]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/27|Translations]] are available.

'''Tech News'''
* The next issue of Tech News will be sent out on 19 July.

'''Recent changes'''
* [[:wikidata:Q4063270|AutoWikiBrowser]] is a tool to make repetitive tasks easier. It now uses [[:w:en:JSON|JSON]]. &lt;code&gt;Wikipedia:AutoWikiBrowser/CheckPage&lt;/code&gt; has moved to &lt;code&gt;Wikipedia:AutoWikiBrowser/CheckPageJSON&lt;/code&gt; and &lt;code&gt;Wikipedia:AutoWikiBrowser/Config&lt;/code&gt;. &lt;code&gt;Wikipedia:AutoWikiBrowser/CheckPage/Version&lt;/code&gt; has moved to &lt;code&gt;Wikipedia:AutoWikiBrowser/CheckPage/VersionJSON&lt;/code&gt;. The tool will eventually be configured on the wiki so that you don't have to wait until the new version to add templates or regular expression fixes. [https://phabricator.wikimedia.org/T241196]

'''Problems'''
* [[m:Special:MyLanguage/InternetArchiveBot|InternetArchiveBot]] helps saving online sources on some wikis. It adds them to [[:w:en:Wayback Machine|Wayback Machine]] and links to them there. This is so they don't disappear if the page that was linked to is removed. It currently has a problem with linking to the wrong date when it moves pages from &lt;code&gt;archive.is&lt;/code&gt; to &lt;code&gt;web.archive.org&lt;/code&gt;. [https://phabricator.wikimedia.org/T283432]

'''Changes later this week'''
* The tool to [[m:WMDE Technical Wishes/Finding and inserting templates|find, add and remove templates]] will be updated. This is to make it easier to find and use the right templates. It will come to the first wikis on 7 July. It will come to more wikis later this year. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Removing_a_template_from_a_page_using_the_VisualEditor][https://phabricator.wikimedia.org/T284553]
* There is no new MediaWiki version this week.

'''Future changes'''
* Some Wikimedia wikis use [[m:Special:MyLanguage/Flagged Revisions|Flagged Revisions]] or pending changes. It hides edits from new and unregistered accounts for readers until they have been patrolled. The auto review action in Flagged Revisions will no longer be logged. All old logs of auto-review will be removed. This is because it creates a lot of logs that are not very useful. [https://phabricator.wikimedia.org/T285608]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/27|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

17:33, 5 July 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21694636 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/29|Tech News: 2021-29]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/29|Translations]] are available.

'''Recent changes'''
* The tool to [[m:WMDE Technical Wishes/Finding and inserting templates|find, add and remove templates]] was updated. This is to make it easier to find and use the right templates. It was supposed to come to the first wikis on 7 July. It was delayed to 12 July instead. It will come to more wikis later this year. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Removing_a_template_from_a_page_using_the_VisualEditor][https://phabricator.wikimedia.org/T284553]
* [[Special:UnconnectedPages|Special:UnconnectedPages]] lists pages that are not connected to Wikidata. This helps you find pages that can be connected to Wikidata items. Some pages should not be connected to Wikidata. You can use the magic word &lt;code&gt;&lt;nowiki&gt;__EXPECTED_UNCONNECTED_PAGE__&lt;/nowiki&gt;&lt;/code&gt; on pages that should not be listed on the special page. [https://phabricator.wikimedia.org/T97577]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-07-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-07-21|en}}. It will be on all wikis from {{#time:j xg|2021-07-22|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] How media is structured in the [[:w:en:Parsing|parser's]] HTML output will soon change. This can affect bots, gadgets, user scripts and extensions. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/L2UQJRHTFK5YG3IOZEC7JSLH2ZQNZRVU/ read more]. You can test it on [[:testwiki:Main Page|Testwiki]] or [[:test2wiki:Main Page|Testwiki 2]].
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The parameters for how you obtain [[mw:API:Tokens|tokens]] in the MediaWiki API were changed in 2014. The old way will no longer work from 1 September. Scripts, bots and tools that use the parameters from before the 2014 change need to be updated. You can [[phab:T280806#7215377|read more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/29|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:31, 19 July 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21755027 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/30|Tech News: 2021-30]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/30|Translations]] are available.

'''Recent changes'''
* A [[mw:MediaWiki 1.37/wmf.14|new version]] of MediaWiki came to the Wikimedia wikis the week before last week. This was not in Tech News because there was no newsletter that week. 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-07-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-07-28|en}}. It will be on all wikis from {{#time:j xg|2021-07-29|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* If you use the [[mw:Special:MyLanguage/Skin:MonoBook|Monobook skin]] you can choose to switch off [[:w:en:Responsive web design|responsive design]] on mobile. This will now work for more skins. If &lt;code&gt;{{int:monobook-responsive-label}}&lt;/code&gt; is unticked you need to also untick the new [[Special:Preferences#mw-prefsection-rendering|preference]] &lt;code&gt;{{int:prefs-skin-responsive}}&lt;/code&gt;. Otherwise it will stop working. Interface admins can automate this process on your wiki. You can [[phab:T285991|read more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/30|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

21:11, 26 July 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/31|Tech News: 2021-31]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/31|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] If your wiki uses markup like &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-content-ltr&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-content-rtl&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; without the required &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;dir&lt;/code&gt;&lt;/bdi&gt; attribute, then these will no longer work in 2 weeks. There is a short-term fix that can be added to your local wiki's Common.css page, which is explained at [[phab:T287701|T287701]]. From now on, all usages should include the full attributes, for example: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-content-ltr&quot; dir=&quot;ltr&quot; lang=&quot;en&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;mw-content-rtl&quot; dir=&quot;rtl&quot; lang=&quot;he&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. This also applies to some other HTML tags, such as &lt;code&gt;span&lt;/code&gt; or &lt;code&gt;code&lt;/code&gt;. You can find existing examples on your wiki that need to be updated, using the instructions at [[phab:T287701|T287701]].
* Reminder: Wikimedia has [[m:Special:MyLanguage/IRC/Migrating to Libera Chat|migrated to the Libera Chat IRC network]], from the old Freenode network. Local documentation should be updated.

'''Problems'''
* Last week, all wikis had slow access or no access for 30 minutes. There was a problem with generating dynamic lists of articles on the Russian Wikinews, due to the bulk import of 200,000+ new articles over 3 days, which led to database problems. The problematic feature has been disabled on that wiki and developers are discussing if it can be fixed properly. [https://phabricator.wikimedia.org/T287380][https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-07-26_ruwikinews_DynamicPageList]

'''Changes later this week'''
* When adding links to a page using [[mw:VisualEditor|VisualEditor]] or the [[mw:Special:MyLanguage/2017 wikitext editor|2017 wikitext editor]], [[mw:Special:MyLanguage/Extension:Disambiguator|disambiguation pages]] will now only appear at the bottom of search results. This is because users do not often want to link to disambiguation pages. [https://phabricator.wikimedia.org/T285510]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-04|en}}. It will be on all wikis from {{#time:j xg|2021-08-05|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* The [[mw:Wikimedia Apps/Team/Android|team of the Wikipedia app for Android]] is working on communication in the app. The developers are working on how to talk to other editors and get notifications. You can [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication|read more]]. They are looking for users who want to [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication/UsertestingJuly2021|test the plans]]. Any editor who has an Android phone and is willing to download the app can do this.
* The [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] for {{int:discussiontools-preference-label}} will be updated in the coming weeks.  You will be able to [[mw:Talk pages project/Notifications|subscribe to individual sections]] on a talk page at more wikis.  You can test this now by adding &lt;code&gt;?dtenable=1&lt;/code&gt; to the end of the talk page's URL ([https://meta.wikimedia.org/wiki/Meta_talk:Sandbox?dtenable=1 example]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/31|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

20:47, 2 August 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21818289 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/32|Tech News: 2021-32]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/32|Translations]] are available.

'''Problems'''
* You can read but not edit 17 wikis for a few minutes on 10 August. This is planned at [https://zonestamp.toolforge.org/1628571650 05:00 UTC]. This is because of work on the database. [https://phabricator.wikimedia.org/T287449]

'''Changes later this week'''
* The [[wmania:Special:MyLanguage/2021:Hackathon|Wikimania Hackathon]] will take place remotely on 13 August, starting at 5:00 UTC, for 24 hours. You can participate in many ways. You can still propose projects and sessions.
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-11|en}}. It will be on all wikis from {{#time:j xg|2021-08-12|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The old CSS &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div class=&quot;visualClear&quot;&gt;&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; will not be supported after 12 August. Instead, templates and pages should use &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;div style=&quot;clear:both;&quot;&gt;&lt;/div&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. Please help to replace any existing uses on your wiki. There are global-search links available at [[phab:T287962|T287962]].

'''Future changes'''
* [[m:Special:MyLanguage/The Wikipedia Library|The Wikipedia Library]] is a place for Wikipedia editors to get access to sources. There is an [[mw:Special:MyLanguage/Extension:TheWikipediaLibrary|extension]] which has a new function to tell users when they can take part in it. It will use notifications. It will start pinging the first users in September. It will ping more users later. [https://phabricator.wikimedia.org/T288070]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[w:en:Vue.js|Vue.js]] will be the [[w:en:JavaScript|JavaScript]] framework for MediaWiki in the future. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/SOZREBYR36PUNFZXMIUBVAIOQI4N7PDU/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/32|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

16:21, 9 August 2021 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=21856726 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/33|Tech News: 2021-33]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/33|Translations]] are available.

'''Recent changes'''
* You can add language links in the sidebar in the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|new Vector skin]] again. You do this by connecting the page to a Wikidata item. The new Vector skin has moved the language links but the new language selector cannot add language links yet. [https://phabricator.wikimedia.org/T287206]

'''Problems'''
* There was a problem on wikis which use the Translate extension. Translations were not updated or were replaced with the English text. The problems have been fixed. [https://phabricator.wikimedia.org/T288700][https://phabricator.wikimedia.org/T288683][https://phabricator.wikimedia.org/T288719]

'''Changes later this week'''
* A [[mw:Help:Tags|revision tag]] will soon be added to edits that add links to [[mw:Special:MyLanguage/Extension:Disambiguator|disambiguation pages]]. This is because these links are usually added by accident. The tag will allow editors to easily find the broken links and fix them. If your wiki does not like this feature, it can be [[mw:Help:Tags#Deleting a tag added by the software|hidden]]. [https://phabricator.wikimedia.org/T287549]
*Would you like to help improve the information about tools? Would you like to attend or help organize a small virtual meetup for your community to discuss the list of tools? Please get in touch on the [[m:Toolhub/The Quality Signal Sessions|Toolhub Quality Signal Sessions]] talk page. We are also looking for feedback [[m:Talk:Toolhub/The Quality Signal Sessions#Discussion topic for &quot;Quality Signal Sessions: The Tool Maintainers edition&quot;|from tool maintainers]] on some specific questions.
* In the past, edits to any page in your user talk space ignored your [[mw:Special:MyLanguage/Help:Notifications#mute|mute list]], e.g. sub-pages. Starting this week, this is only true for edits to your talk page. [https://phabricator.wikimedia.org/T288112]
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-18|en}}. It will be on all wikis from {{#time:j xg|2021-08-19|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/33|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

19:27, 16 August 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/34|Tech News: 2021-34]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/34|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/Extension:Score|Score]] extension (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;score&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; notation) has been re-enabled on public wikis and upgraded to a newer version. Some musical score functionality may no longer work because the extension is only enabled in &quot;safe mode&quot;. The security issue has been fixed and an [[mw:Special:MyLanguage/Extension:Score/2021 security advisory|advisory published]].

'''Problems'''
* You will be able to read but not edit [[phab:T289130|some wikis]] for a few minutes on {{#time:j xg|2021-08-25|en}}. This will happen around [https://zonestamp.toolforge.org/1629871217 06:00 UTC]. This is for database maintenance. During this time, operations on the CentralAuth will also not be possible.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-25|en}}. It will be on all wikis from {{#time:j xg|2021-08-26|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/34|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

21:58, 23 August 2021 (UTC)
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== Read-only reminder ==

&lt;section begin=&quot;MassMessage&quot;/&gt;
A maintenance operation will be performed on [https://zonestamp.toolforge.org/1629871231 {{#time: l F d H:i e|2021-08-25T06:00|en}}]. It should only last for a few minutes.

This will affect your wiki as well as 11 other wikis. During this time, publishing edits will not be possible. 

Also during this time, operations on the CentralAuth will not be possible (GlobalRenames, changing/confirming e-mail addresses, logging into new wikis, password changes).

For more details about the operation and on all impacted services, please check [[phab:T289130|on Phabricator]].

A banner will be displayed 30 minutes before the operation.

Please help your community to be aware of this maintenance operation. {{Int:Feedback-thanks-title}}&lt;section end=&quot;MassMessage&quot;/&gt;

20:35, 24 August 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/35|Tech News: 2021-35]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/35|Translations]] are available.

'''Recent changes'''
* Some musical score syntax no longer works and may needed to be updated, you can check [[:Category:{{MediaWiki:score-error-category}}]] on your wiki for a list of pages with errors.

'''Problems'''
* Musical scores were unable to render lyrics in some languages because of missing fonts. This has been fixed now. If your language would prefer a different font, please file a request in Phabricator. [https://phabricator.wikimedia.org/T289554]

'''Changes later this week'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The parameters for how you obtain [[mw:API:Tokens|tokens]] in the MediaWiki API were changed in 2014. The old way will no longer work from 1 September. Scripts, bots and tools that use the parameters from before the 2014 change need to be updated. You can [[phab:T280806#7215377|read more]] about this.
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-01|en}}. It will be on all wikis from {{#time:j xg|2021-09-02|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).

'''Future changes'''
* You will be able to read but not edit [[phab:T289660|Commons]] for a few minutes on {{#time:j xg|2021-09-06|en}}. This will happen around [https://zonestamp.toolforge.org/1630818058 05:00 UTC]. This is for database maintenance.
* All wikis will be read-only for a few minutes in the week of 13 September. More information will be published in Tech News later. It will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T287539]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/35|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

16:01, 30 August 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/36|Tech News: 2021-36]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/36|Translations]] are available.

'''Recent changes'''
* The wikis that have [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] deployed have been part of A/B testing since deployment, in which some newcomers did not receive the new features. Now, all of the newcomers on 21 of the smallest of those wikis will be receiving the features. [https://phabricator.wikimedia.org/T289786]

'''Changes later this week'''
* There is no new MediaWiki version this week.

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] In 2017, the provided jQuery library was upgraded from version 1 to 3, with a compatibility layer. The migration will soon finish, to make the site load faster for everyone. If you maintain a gadget or user script, check if you have any JQMIGRATE errors and fix them, or they will break. [https://phabricator.wikimedia.org/T280944][https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/6Z2BVLOBBEC2QP4VV4KOOVQVE52P3HOP/]
* Last year, the Portuguese Wikipedia community embarked on an experiment to make log-in compulsory for editing.  The [[m:IP Editing: Privacy Enhancement and Abuse Mitigation/Impact report for Login Required Experiment on Portuguese Wikipedia|impact report of this trial]] is ready. Moving forward, the Anti-Harassment Tools team is looking for projects that are willing to experiment with restricting IP editing on their wiki for a short-term experiment. [[m:IP Editing: Privacy Enhancement and Abuse Mitigation/Login Required Experiment|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/36|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:20, 6 September 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/37|Tech News: 2021-37]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/37|Translations]] are available.

'''Recent changes'''
* 45 new Wikipedias now have access to the [[mw:Special:MyLanguage/Growth/Feature summary|Growth features]]. [https://phabricator.wikimedia.org/T289680]
* [[mw:Special:MyLanguage/Growth/Deployment table|A majority of Wikipedias]] now have access to the Growth features. The Growth team [[mw:Special:MyLanguage/Growth/FAQ|has published an FAQ page]] about the features. This translatable FAQ covers the description of the features, how to use them, how to change the configuration, and more.

'''Problems'''
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on 14 September. This is planned at [https://zonestamp.toolforge.org/1631628002 14:00 UTC]. [https://phabricator.wikimedia.org/T287539]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-15|en}}. It will be on all wikis from {{#time:j xg|2021-09-16|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]).
* Starting this week, Wikipedia in Italian will receive weekly software updates on Wednesdays. It used to receive the updates on Thursdays. Due to this change, bugs will be noticed and fixed sooner. [https://phabricator.wikimedia.org/T286664]
* You can add language links in the sidebar in [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|the new Vector skin]] again. You do this by connecting the page to a Wikidata item. The new Vector skin has moved the language links but the new language selector cannot add language links yet. [https://phabricator.wikimedia.org/T287206]
* The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlight]] tool marks up code with different colours. It now can highlight 23 new code languages. Additionally, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;golang&lt;/code&gt;&lt;/bdi&gt; can now be used as an alias for the [[d:Q37227|Go programming language]], and a special &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;output&lt;/code&gt;&lt;/bdi&gt; mode has been added to show a program's output. [https://phabricator.wikimedia.org/T280117][https://gerrit.wikimedia.org/r/c/mediawiki/extensions/SyntaxHighlight_GeSHi/+/715277/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/37|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

15:35, 13 September 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/38|Tech News: 2021-38]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/38|Translations]] are available.

'''Recent changes'''
* Growth features are now deployed to almost all Wikipedias. [[phab:T290582|For the majority of small Wikipedias]], the features are only available for experienced users, to [[mw:Special:MyLanguage/Growth/FAQ#enable|test the features]] and [[mw:Special:MyLanguage/Growth/FAQ#config|configure them]]. Features will be available for newcomers starting on 20 September 2021.
* MediaWiki had a feature that would highlight local links to short articles in a different style. Each user could pick the size at which &quot;stubs&quot; would be highlighted. This feature was very bad for performance, and following a consultation, has been removed. [https://phabricator.wikimedia.org/T284917]
* A technical change was made to the MonoBook skin to allow for easier maintenance and upkeep. This has resulted in some minor changes to HTML that make MonoBook's HTML consistent with other skins. Efforts have been made to minimize the impact on editors, but please ping [[m:User:Jon (WMF)|Jon (WMF)]] on wiki or in [[phab:T290888|phabricator]] if any problems are reported.

'''Problems'''
* There was a problem with search last week. Many search requests did not work for 2 hours because of an accidental restart of the search servers. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-09-13_cirrussearch_restart]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-22|en}}. It will be on all wikis from {{#time:j xg|2021-09-23|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[s:Special:ApiHelp/query+proofreadinfo|meta=proofreadpage API]] has changed. The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;piprop&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; parameter has been renamed to &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;prpiprop&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. API users should update their code to avoid unrecognized parameter warnings. Pywikibot users should upgrade to 6.6.0. [https://phabricator.wikimedia.org/T290585]

'''Future changes'''
* The [[mw:Special:MyLanguage/Help:DiscussionTools#Replying|Reply tool]] will be deployed to the remaining wikis in the coming weeks.  It is currently part of &quot;{{int:discussiontools-preference-label}}&quot; in [[Special:Preferences#mw-prefsection-betafeatures|Beta features]] at most wikis. You will be able to turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|Editing Preferences]]. [https://phabricator.wikimedia.org/T262331]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:MediaWiki_1.37/Deprecation_of_legacy_API_token_parameters|previously announced]] change to how you obtain tokens from the API has been delayed to September 21 because of an incompatibility with Pywikibot. Bot operators using Pywikibot can follow [[phab:T291202|T291202]] for progress on a fix, and should plan to upgrade to 6.6.1 when it is released.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/38|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

18:32, 20 September 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/39|Tech News: 2021-39]] ==

&lt;section begin=&quot;technews-2021-W39&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/39|Translations]] are available.

'''Recent changes'''
* [[w:en:IOS|iOS 15]] has a new function called [https://support.apple.com/en-us/HT212614 Private Relay] (Apple website). This can hide the user's IP when they use [[w:en:Safari (software)|Safari]] browser. This is like using a [[w:en:Virtual private network|VPN]] in that we see another IP address instead. It is opt-in and only for those who pay extra for [[w:en:ICloud|iCloud]]. It will come to Safari users on [[:w:en:OSX|OSX]] later. There is a [[phab:T289795|technical discussion]] about what this means for the Wikimedia wikis.

'''Problems'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Some gadgets and user-scripts add items to the [[m:Customization:Explaining_skins#Portlets|portlets]] (article tools) part of the skin. A recent change to the HTML may have made those links a different font-size. This can be fixed by adding the CSS class &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.vector-menu-dropdown-noicon&lt;/code&gt;&lt;/bdi&gt;. [https://phabricator.wikimedia.org/T291438]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-29|en}}. It will be on all wikis from {{#time:j xg|2021-09-30|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* The [[mw:Special:MyLanguage/Onboarding_new_Wikipedians#New_experience|GettingStarted extension]] was built in 2013, and provides an onboarding process for new account holders in a few versions of Wikipedia. However, the recently developed [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] provide a better onboarding experience. Since the vast majority of Wikipedias now have access to the Growth features, GettingStarted will be deactivated starting on 4 October. [https://phabricator.wikimedia.org/T235752]
* A small number of users will not be able to connect to the Wikimedia wikis after 30 September. This is because an old [[:w:en:root certificate|root certificate]] will no longer work. They will also have problems with many other websites. Users who have updated their software in the last five years are unlikely to have problems. Users in Europe, Africa and Asia are less likely to have immediate problems even if their software is too old. You can [[m:Special:MyLanguage/HTTPS/2021 Let's Encrypt root expiry|read more]].
* You can [[mw:Special:MyLanguage/Help:Notifications|receive notifications]] when someone leaves a comment on user talk page or mentions you in a talk page comment. Clicking the notification link will now bring you to the comment and highlight it. Previously, doing so brought you to the top of the section that contained the comment. You can find [[phab:T282029|more information in T282029.]]

'''Future changes'''
* The [[mw:Special:MyLanguage/Help:DiscussionTools#Replying|Reply tool]] will be deployed to the remaining wikis in the coming weeks. It is currently part of &quot;{{int:discussiontools-preference-label}}&quot; in [[Special:Preferences#mw-prefsection-betafeatures|Beta features]] at most wikis. You will be able to turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|Editing Preferences]]. [[phab:T288485|See the list of wikis.]] [https://phabricator.wikimedia.org/T262331]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/39|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W39&quot;/&gt;

22:23, 27 September 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/40|Tech News: 2021-40]] ==

&lt;section begin=&quot;tech-newsletter-content&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/40|Translations]] are available.

'''Recent changes'''
* A more efficient way of sending changes from Wikidata to Wikimedia wikis that show them has been enabled for the following 10 wikis: mediawiki.org, the Italian, Catalan, Hebrew and Vietnamese Wikipedias, French Wikisource, and English Wikivoygage, Wikibooks, Wiktionary and Wikinews. If you notice anything strange about how changes from Wikidata appear in recent changes or your watchlist on those wikis you can [[phab:T48643|let the developers know]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-06|en}}. It will be on all wikis from {{#time:j xg|2021-10-07|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Some gadgets and bots that use the API to read the AbuseFilter log might break. The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;hidden&lt;/code&gt;&lt;/bdi&gt; property will no longer say an entry is &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;implicit&lt;/code&gt;&lt;/bdi&gt; for unsuppressed log entries about suppressed edits. If your bot needs to know this, do a separate revision query. Additionally, the property will have the value &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;false&lt;/code&gt;&lt;/bdi&gt; for visible entries; previously, it wasn't included in the response. [https://phabricator.wikimedia.org/T291718]
* A more efficient way of sending changes from Wikidata to Wikimedia wikis that show them will be enabled for ''all production wikis''. If you notice anything strange about how changes from Wikidata appear in recent changes or your watchlist you can [[phab:T48643|let the developers know]].

'''Future changes'''
* You can soon get cross-wiki notifications in the [[mw:Wikimedia Apps/Team/iOS|iOS Wikipedia app]]. You can also get notifications as push notifications. More notification updates will follow in later versions. [https://www.mediawiki.org/wiki/Wikimedia_Apps/Team/iOS/Notifications#September_2021_update]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The JavaScript variables &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgExtraSignatureNamespaces&lt;/code&gt;&lt;/bdi&gt;, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgLegalTitleChars&lt;/code&gt;&lt;/bdi&gt;, and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgIllegalFileChars&lt;/code&gt;&lt;/bdi&gt; will soon be removed from &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:Special:MyLanguage/Manual:Interface/JavaScript#mw.config|mw.config]]&lt;/code&gt;&lt;/bdi&gt;. These are not part of the &quot;stable&quot; variables available for use in wiki JavaScript. [https://phabricator.wikimedia.org/T292011] 
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The JavaScript variables &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgCookiePrefix&lt;/code&gt;&lt;/bdi&gt;, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgCookieDomain&lt;/code&gt;&lt;/bdi&gt;, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgCookiePath&lt;/code&gt;&lt;/bdi&gt;, and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wgCookieExpiration&lt;/code&gt;&lt;/bdi&gt; will soon be removed from mw.config. Scripts should instead use &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw.cookie&lt;/code&gt;&lt;/bdi&gt; from the &quot;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;[[mw:ResourceLoader/Core_modules#mediawiki.cookie|mediawiki.cookie]]&lt;/bdi&gt;&quot; module. [https://phabricator.wikimedia.org/T291760]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/40|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;tech-newsletter-content&quot;/&gt;

16:32, 4 October 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/41|Tech News: 2021-41]] ==

&lt;section begin=&quot;technews-2021-W41&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/41|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-13|en}}. It will be on all wikis from {{#time:j xg|2021-10-14|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

* The [[mw:Manual:Table_of_contents#Auto-numbering|&quot;auto-number headings&quot; preference]] is being removed. You can read [[phab:T284921]] for the reasons and discussion. This change was [[m:Tech/News/2021/26|previously]] announced. [[mw:Snippets/Auto-number_headings|A JavaScript snippet]] is available which can be used to create a Gadget on wikis that still want to support auto-numbering.

'''Meetings'''
* You can join a meeting about the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]]. A demonstration version of the [[mw:Reading/Web/Desktop Improvements/Features/Sticky Header|newest feature]] will be shown. The event will take place on Tuesday, 12 October at 16:00 UTC. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web/12-10-2021|See how to join]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/41|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W41&quot;/&gt;

15:30, 11 October 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/42|Tech News: 2021-42]] ==

&lt;section begin=&quot;technews-2021-W42&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/42|Translations]] are available.

'''Recent changes'''
*[[m:Toolhub|Toolhub]] is a catalogue to make it easier to find software tools that can be used for working on the Wikimedia projects. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/LF4SSR4QRCKV6NPRFGUAQWUFQISVIPTS/ read more].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-20|en}}. It will be on all wikis from {{#time:j xg|2021-10-21|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Future changes'''
* The developers of the [[mw:Wikimedia Apps/Team/Android|Wikipedia Android app]] are working on [[mw:Wikimedia Apps/Team/Android/Communication|communication in the app]]. You can now answer questions in [[mw:Wikimedia Apps/Team/Android/Communication/UsertestingOctober2021|survey]] to help the development.
* 3–5% of editors may be blocked in the next few months. This is because of a new service in Safari, which is similar to a [[w:en:Proxy server|proxy]] or a [[w:en:VPN|VPN]]. It is called iCloud Private Relay. There is a [[m:Special:MyLanguage/Apple iCloud Private Relay|discussion about this]] on Meta. The goal is to learn what iCloud Private Relay could mean for the communities.
* [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] is a new [[w:en:API|API]] for those who use a lot of information from the Wikimedia projects on other sites. It is a way to get big commercial users to pay for the data. There will soon be a copy of the Wikimedia Enterprise dataset. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-ambassadors@lists.wikimedia.org/message/B2AX6PWH5MBKB4L63NFZY3ADBQG7MSBA/ read more]. You can also ask the team questions [https://wikimedia.zoom.us/j/88994018553 on Zoom] on [https://www.timeanddate.com/worldclock/fixedtime.html?hour=15&amp;min=00&amp;sec=0&amp;day=22&amp;month=10&amp;year=2021 22 October 15:00 UTC].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/42|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W42&quot;/&gt;

20:53, 18 October 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22176877 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/43|Tech News: 2021-43]] ==

&lt;section begin=&quot;technews-2021-W43&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/43|Translations]] are available.

'''Recent changes'''
* The [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award 2021]] is looking for nominations. You can recommend tools until 27 October.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-27|en}}. It will be on all wikis from {{#time:j xg|2021-10-28|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Future changes'''
*[[m:Special:MyLanguage/Help:Diff|Diff pages]] will have an improved copy and pasting experience. [[m:Special:MyLanguage/Community Wishlist Survey 2021/Copy paste diffs|The changes]] will allow the text in the diff for before and after to be treated as separate columns and will remove any unwanted syntax. [https://phabricator.wikimedia.org/T192526]
* The version of the [[w:en:Liberation fonts|Liberation fonts]] used in SVG files will be upgraded. Only new thumbnails will be affected. Liberation Sans Narrow will not change. [https://phabricator.wikimedia.org/T253600]

'''Meetings'''
* You can join a meeting about the [[m:Special:MyLanguage/Community Wishlist Survey|Community Wishlist Survey]]. News about the [[m:Special:MyLanguage/Community Wishlist Survey 2021/Warn when linking to disambiguation pages|disambiguation]] and the [[m:Special:MyLanguage/Community Wishlist Survey 2021/Real Time Preview for Wikitext|real-time preview]] wishes will be shown. The event will take place on Wednesday, 27 October at 14:30 UTC. [[m:Special:MyLanguage/Community Wishlist Survey/Updates/Talk to Us|See how to join]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/43|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W43&quot;/&gt;

20:08, 25 October 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22232718 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/44|Tech News: 2021-44]] ==

&lt;section begin=&quot;technews-2021-W44&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/44|Translations]] are available.

'''Recent changes'''
* There is a limit on the amount of emails a user can send each day. This limit is now global instead of per-wiki. This change is to prevent abuse. [https://phabricator.wikimedia.org/T293866]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-11-03|en}}. It will be on all wikis from {{#time:j xg|2021-11-04|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/44|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W44&quot;/&gt;

20:28, 1 November 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22269406 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/45|Tech News: 2021-45]] ==

&lt;section begin=&quot;technews-2021-W45&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/45|Translations]] are available.

'''Recent changes'''
* Mobile IP editors are now able to receive warning notices indicating they have a talk page message on the mobile website (similar to the orange banners available on desktop). These notices will be displayed on every page outside of the main namespace and every time the user attempts to edit. The notice on desktop now has a slightly different colour. [https://phabricator.wikimedia.org/T284642][https://phabricator.wikimedia.org/T278105]

'''Changes later this week'''
* [[phab:T294321|Wikidata will be read-only]] for a few minutes on 11 November. This will happen around [https://zonestamp.toolforge.org/1636610400 06:00 UTC]. This is for database maintenance. [https://phabricator.wikimedia.org/T294321]
* There is no new MediaWiki version this week.

'''Future changes'''
* In the future, unregistered editors will be given an identity that is not their [[:w:en:IP address|IP address]]. This is for legal reasons. A new user right will let editors who need to know the IPs of unregistered accounts to fight vandalism, spam, and harassment, see the IP. You can read the [[m:IP Editing: Privacy Enhancement and Abuse Mitigation#IP Masking Implementation Approaches (FAQ)|suggestions for how that identity could work]] and [[m:Talk:IP Editing: Privacy Enhancement and Abuse Mitigation|discuss on the talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/45|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W45&quot;/&gt;

20:36, 8 November 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22311003 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/46|Tech News: 2021-46]] ==

&lt;section begin=&quot;technews-2021-W46&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/46|Translations]] are available.

'''Recent changes'''
* Most [[c:Special:MyLanguage/Commons:Maximum_file_size#MAXTHUMB|large file uploads]] errors that had messages like &quot;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;stashfailed&lt;/code&gt;&lt;/bdi&gt;&quot; or &quot;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;DBQueryError&lt;/code&gt;&lt;/bdi&gt;&quot; have now been fixed. An [[wikitech:Incident documentation/2021-11-04 large file upload timeouts|incident report]] is available.

'''Problems'''
* Sometimes, edits made on iOS using the visual editor save groups of numbers as telephone number links, because of a feature in the operating system. This problem is under investigation. [https://phabricator.wikimedia.org/T116525]
* There was a problem with search last week. Many search requests did not work for 2 hours because of a configuration error. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-11-10_cirrussearch_commonsfile_outage]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-11-17|en}}. It will be on all wikis from {{#time:j xg|2021-11-18|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/46|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W46&quot;/&gt;

22:06, 15 November 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22338097 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/47|Tech News: 2021-47]] ==

&lt;section begin=&quot;technews-2021-W47&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/47|Translations]] are available.

'''Changes later this week'''
* There is no new MediaWiki version this week.
*The template dialog in VisualEditor and in the [[Special:Preferences#mw-prefsection-betafeatures|new wikitext mode]] Beta feature will be [[m:WMDE Technical Wishes/VisualEditor template dialog improvements|heavily improved]] on [[phab:T286992|a few wikis]]. Your [[m:Talk:WMDE Technical Wishes/VisualEditor template dialog improvements|feedback is welcome]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/47|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W47&quot;/&gt;

20:02, 22 November 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22366010 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/48|Tech News: 2021-48]] ==

&lt;section begin=&quot;technews-2021-W48&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/48|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-01|en}}. It will be on all wikis from {{#time:j xg|2021-12-02|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/48|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W48&quot;/&gt;

21:15, 29 November 2021 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22375666 --&gt;

== [[m:Special:MyLanguage/Tech/News/2021/49|Tech News: 2021-49]] ==

&lt;section begin=&quot;technews-2021-W49&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/49|Translations]] are available.

'''Problems'''
* MediaWiki 1.38-wmf.11 was scheduled to be deployed on some wikis last week. The deployment was delayed because of unexpected problems.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-12-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-08|en}}. It will be on all wikis from {{#time:j xg|2021-12-09|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* At all Wikipedias, a Mentor Dashboard is now available at &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;Special:MentorDashboard&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. It allows registered mentors, who take care of newcomers' first steps, to monitor their assigned newcomers' activity. It is part of the [[mw:Special:MyLanguage/Growth/Feature summary|Growth features]]. You can learn more about [[mw:Special:MyLanguage/Growth/Communities/How_to_configure_the_mentors%27_list|activating the mentor list]] on your wiki and about [[mw:Special:MyLanguage/Growth/Mentor dashboard|the mentor dashboard project]].
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The predecessor to the current [[mw:API|MediaWiki Action API]] (which was created in 2008), &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;action=ajax&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, will be removed this week. Any scripts or bots using it will need to switch to the corresponding API module. [https://phabricator.wikimedia.org/T42786]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] An old ResourceLoader module, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;jquery.jStorage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, which was deprecated in 2016, will be removed this week. Any scripts or bots using it will need to switch to &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;mediawiki.storage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; instead. [https://phabricator.wikimedia.org/T143034]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/49|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W49&quot;/&gt;

21:59, 6 December 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/50|Tech News: 2021-50]] ==

&lt;section begin=&quot;technews-2021-W50&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/50|Translations]] are available.

'''Recent changes'''
* There are now default [[m:Special:MyLanguage/Help:Namespace#Other_namespace_aliases|short aliases]] for the &quot;Project:&quot; namespace on most wikis. E.g. On Wikibooks wikis, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;[[WB:]]&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; will go to the local language default for the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;[[Project:]]&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; namespace. This change is intended to help the smaller communities have easy access to this feature. Additional local aliases can still be requested via [[m:Special:MyLanguage/Requesting wiki configuration changes|the usual process]]. [https://phabricator.wikimedia.org/T293839]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-12-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-15|en}}. It will be on all wikis from {{#time:j xg|2021-12-16|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/50|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W50&quot;/&gt;

22:27, 13 December 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2021/51|Tech News: 2021-51]] ==

&lt;section begin=&quot;technews-2021-W51&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/51|Translations]] are available.

'''Tech News'''
* Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 10 January 2022.

'''Recent changes'''
* Queries made by the DynamicPageList extension (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;DynamicPageList&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;) are now only allowed to run for 10 seconds and error if they take longer. This is in response to multiple outages where long-running queries caused an outage on all wikis. [https://phabricator.wikimedia.org/T287380#7575719]

'''Changes later this week'''
* There is no new MediaWiki version this week or next week.

'''Future changes'''
* The developers of the Wikipedia iOS app are looking for testers who edit in multiple languages. You can [[mw:Wikimedia Apps/Team/iOS/202112 testing|read more and let them know if you are interested]].
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] The Wikimedia [[wikitech:Portal:Cloud VPS|Cloud VPS]] hosts technical projects for the Wikimedia movement. Developers need to [[wikitech:News/Cloud VPS 2021 Purge|claim projects]] they use. This is because old and unused projects are removed once a year. Unclaimed projects can be shut down from February. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/2B7KYL5VLQNHGQQHMYLW7KTUKXKAYY3T/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2021/51|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2021-W51&quot;/&gt;

22:05, 20 December 2021 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/02|Tech News: 2022-02]] ==

&lt;section begin=&quot;technews-2022-W02&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/02|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] A &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;oauth_consumer&lt;/code&gt;&lt;/bdi&gt; variable has been added to the [[mw:Special:MyLanguage/AbuseFilter|AbuseFilter]] to enable identifying changes made by specific tools. [https://phabricator.wikimedia.org/T298281]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets are [[mw:Special:MyLanguage/ResourceLoader/Migration_guide_(users)#Package_Gadgets|now able to directly include JSON pages]]. This means some gadgets can now be configured by administrators without needing the interface administrator permission, such as with the Geonotice gadget. [https://phabricator.wikimedia.org/T198758]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets [[mw:Extension:Gadgets#Options|can now specify page actions]] on which they are available. For example, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;|actions=edit,history&lt;/code&gt;&lt;/bdi&gt; will load a gadget only while editing and on history pages. [https://phabricator.wikimedia.org/T63007]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets can now be loaded on demand with the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;withgadget&lt;/code&gt;&lt;/bdi&gt; URL parameter. This can be used to replace [[mw:Special:MyLanguage/Snippets/Load JS and CSS by URL|an earlier snippet]] that typically looks like &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;withJS&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;withCSS&lt;/code&gt;&lt;/bdi&gt;. [https://phabricator.wikimedia.org/T29766]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] At wikis where [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list|the Mentorship system is configured]], you can now use the Action API to get a list of a [[mw:Special:MyLanguage/Growth/Mentor_dashboard|mentor's]] mentees. [https://phabricator.wikimedia.org/T291966]
* The heading on the main page can now be configured using &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Mainpage-title-loggedin]]&lt;/span&gt; for logged-in users and &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Mainpage-title]]&lt;/span&gt; for logged-out users. Any CSS that was previously used to hide the heading should be removed. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Small_wiki_toolkits/Starter_kit/Main_page_customization#hide-heading] [https://phabricator.wikimedia.org/T298715]
* Four special pages (and their API counterparts) now have a maximum database query execution time of 30 seconds. These special pages are: RecentChanges, Watchlist, Contributions, and Log. This change will help with site performance and stability. You can read [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IPJNO75HYAQWIGTHI5LJHTDVLVOC4LJP/ more details about this change] including some possible solutions if this affects your workflows. [https://phabricator.wikimedia.org/T297708]
* The [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Sticky Header|sticky header]] has been deployed for 50% of logged-in users on [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Frequently asked questions#pilot-wikis|more than 10 wikis]]. This is part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]]. See [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Participate|how to take part in the project]]. 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-12|en}}. It will be on all wikis from {{#time:j xg|2022-01-13|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Events'''
* [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey 2022]] begins. All contributors to the Wikimedia projects can propose for tools and platform improvements. The proposal phase takes place from {{#time:j xg|2022-01-10|en}} 18:00 UTC to {{#time:j xg|2022-01-23|en}} 18:00 UTC. [[m:Special:MyLanguage/Community_Wishlist_Survey/FAQ|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/02|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W02&quot;/&gt;

01:23, 11 January 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/03|Tech News: 2022-03]] ==

&lt;section begin=&quot;technews-2022-W03&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/03|Translations]] are available.

'''Recent changes'''
* When using [[mw:Special:MyLanguage/Extension:WikiEditor|WikiEditor]] (also known as the 2010 wikitext editor), people will now see a warning if they link to disambiguation pages.  If you click &quot;{{int:Disambiguator-review-link}}&quot; in the warning, it will ask you to correct the link to a more specific term. You can [[m:Community Wishlist Survey 2021/Warn when linking to disambiguation pages#Jan 12, 2021: Turning on the changes for all Wikis|read more information]] about this completed 2021 Community Wishlist item.
* You can [[mw:Special:MyLanguage/Help:DiscussionTools#subscribe|automatically subscribe to all of the talk page discussions]] that you start or comment in using [[mw:Special:MyLanguage/Talk pages project/Feature summary|DiscussionTools]].  You will receive [[mw:Special:MyLanguage/Notifications|notifications]] when another editor replies.  This is available at most wikis.  Go to your [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]] and turn on &quot;{{int:discussiontools-preference-autotopicsub}}&quot;. [https://phabricator.wikimedia.org/T263819]
* When asked to create a new page or talk page section, input fields can be [[mw:Special:MyLanguage/Manual:Creating_pages_with_preloaded_text|&quot;preloaded&quot; with some text]]. This feature is now limited to wikitext pages. This is so users can't be tricked into making malicious edits. There is a discussion about [[phab:T297725|if this feature should be re-enabled]] for some content types.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-19|en}}. It will be on all wikis from {{#time:j xg|2022-01-20|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Events'''
* [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey 2022]] continues. All contributors to the Wikimedia projects can propose for tools and platform improvements. The proposal phase takes place from {{#time:j xg|2022-01-10|en}} 18:00 UTC to {{#time:j xg|2022-01-23|en}} 18:00 UTC. [[m:Special:MyLanguage/Community_Wishlist_Survey/FAQ|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/03|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W03&quot;/&gt;

19:55, 17 January 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/04|Tech News: 2022-04]] ==

&lt;section begin=&quot;technews-2022-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/04|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-26|en}}. It will be on all wikis from {{#time:j xg|2022-01-27|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* The following languages can now be used with [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlighting]]: BDD, Elpi, LilyPond, Maxima, Rita, Savi, Sed, Sophia, Spice, .SRCINFO.
* You can now access your watchlist from outside of the user menu in the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|new Vector skin]]. The watchlist link appears next to the notification icons if you are at the top of the page. [https://phabricator.wikimedia.org/T289619]

'''Events'''
* You can see the results of the [[m:Special:MyLanguage/Coolest Tool Award|Coolest Tool Award 2021]] and learn more about 14 tools which were selected this year.
* You can [[m:Special:MyLanguage/Community_Wishlist_Survey/Help_us|translate, promote]], or comment on [[m:Special:MyLanguage/Community Wishlist Survey 2022/Proposals|the proposals]] in the Community Wishlist Survey. Voting will begin on {{#time:j xg|2022-01-28|en}}.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W04&quot;/&gt;

21:38, 24 January 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/05|Tech News: 2022-05]] ==

&lt;section begin=&quot;technews-2022-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/05|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] If a gadget should support the new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;?withgadget&lt;/code&gt;&lt;/bdi&gt; URL parameter that was [[m:Special:MyLanguage/Tech/News/2022/02|announced]] 3 weeks ago, then it must now also specify &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;supportsUrlLoad&lt;/code&gt;&lt;/bdi&gt; in the gadget definition ([[mw:Special:MyLanguage/Extension:Gadgets#supportsUrlLoad|documentation]]). [https://phabricator.wikimedia.org/T29766]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-02|en}}. It will be on all wikis from {{#time:j xg|2022-02-03|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Future changes'''
* A change that was [[m:Special:MyLanguage/Tech/News/2021/16|announced]] last year was delayed. It is now ready to move ahead:
** The user group &lt;code&gt;oversight&lt;/code&gt; will be renamed &lt;code&gt;suppress&lt;/code&gt;. This is for [[phab:T109327|technical reasons]]. This is the technical name. It doesn't affect what you call the editors with this user right on your wiki. This is planned to happen in three weeks. You can comment [[phab:T112147|in Phabricator]] if you have objections. As usual, these labels can be translated on translatewiki ([[phab:T112147|direct links are available]]) or by administrators on your wiki.

'''Events'''
* You can vote on proposals in the [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey]] between 28 January and 11 February. The survey decides what the [[m:Special:MyLanguage/Community Tech|Community Tech team]] will work on.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W05&quot;/&gt;

17:42, 31 January 2022 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=22721804 --&gt;

== [[m:Special:MyLanguage/Tech/News/2022/06|Tech News: 2022-06]] ==

&lt;section begin=&quot;technews-2022-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/06|Translations]] are available.

'''Recent changes'''
* English Wikipedia recently set up a gadget for dark mode. You can enable it there, or request help from an [[m:Special:MyLanguage/Interface administrators|interface administrator]] to set it up on your wiki ([[w:en:Wikipedia:Dark mode (gadget)|instructions and screenshot]]).
* Category counts are sometimes wrong. They will now be completely recounted at the beginning of every month. [https://phabricator.wikimedia.org/T299823]

'''Problems'''
* A code-change last week to fix a bug with [[mw:Special:MyLanguage/Manual:Live preview|Live Preview]] may have caused problems with some local gadgets and user-scripts. Any code with skin-specific behaviour for &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;vector&lt;/code&gt;&lt;/bdi&gt; should be updated to also check for &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;vector-2022&lt;/code&gt;&lt;/bdi&gt;. [[phab:T300987|A code-snippet, global search, and example are available]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-09|en}}. It will be on all wikis from {{#time:j xg|2022-02-10|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W06&quot;/&gt;

21:15, 7 February 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/07|Tech News: 2022-07]] ==

&lt;section begin=&quot;technews-2022-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/07|Translations]] are available.

'''Recent changes'''
* [[mw:Special:MyLanguage/Manual:Purge|Purging]] a category page with fewer than 5,000 members will now recount it completely. This will allow editors to fix incorrect counts when it is wrong. [https://phabricator.wikimedia.org/T85696]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-16|en}}. It will be on all wikis from {{#time:j xg|2022-02-17|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|Advanced item]] In the [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] extension, the &lt;code dir=ltr&gt;rmspecials()&lt;/code&gt; function has been updated so that it does not remove the &quot;space&quot; character. Wikis are advised to wrap all the uses of &lt;code dir=ltr&gt;rmspecials()&lt;/code&gt; with &lt;code dir=ltr&gt;rmwhitespace()&lt;/code&gt; wherever necessary to keep filters' behavior unchanged. You can use the search function on [[Special:AbuseFilter]] to locate its usage. [https://phabricator.wikimedia.org/T263024]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W07&quot;/&gt;

19:18, 14 February 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/08|Tech News: 2022-08]] ==

&lt;section begin=&quot;technews-2022-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/08|Translations]] are available.

'''Recent changes'''
* [[Special:Nuke|Special:Nuke]] will now provide the standard deletion reasons (editable at &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Deletereason-dropdown]]&lt;/bdi&gt;) to use when mass-deleting pages. This was [[m:Community Wishlist Survey 2022/Admins and patrollers/Mass-delete to offer drop-down of standard reasons, or templated reasons.|a request in the 2022 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T25020]
* At Wikipedias, all new accounts now get the [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] by default when creating an account. Communities are encouraged to [[mw:Special:MyLanguage/Help:Growth/Tools/Account_creation|update their help resources]]. Previously, only 80% of new accounts would get the Growth features. A few Wikipedias remain unaffected by this change. [https://phabricator.wikimedia.org/T301820]
* You can now prevent specific images that are used in a page from appearing in other locations, such as within PagePreviews or Search results. This is done with the markup &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;class=notpageimage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. For example, &lt;code&gt;&lt;nowiki&gt;[[File:Example.png|class=notpageimage]]&lt;/nowiki&gt;&lt;/code&gt;. [https://phabricator.wikimedia.org/T301588]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] There has been a change to the HTML of Special:Contributions, Special:MergeHistory, and History pages, to support the grouping of changes by date in [[mw:Special:MyLanguage/Skin:Minerva_Neue|the mobile skin]]. While unlikely, this may affect gadgets and user scripts. A [[phab:T298638|list of all the HTML changes]] is on Phabricator.

'''Events'''
* [[m:Special:MyLanguage/Community Wishlist Survey 2022/Results|Community Wishlist Survey results]] have been published. The [[m:Special:MyLanguage/Community Wishlist Survey/Updates/2022 results#leaderboard|ranking of prioritized proposals]] is also available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-23|en}}. It will be on all wikis from {{#time:j xg|2022-02-24|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Future changes'''
* The software to play videos and audio files on pages will change soon on all wikis. The old player will be removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Toolforge's underlying operating system is being updated. If you maintain any tools there, there are two options for migrating your tools into the new system.  There are [[wikitech:News/Toolforge Stretch deprecation|details, deadlines, and instructions]] on Wikitech. [https://lists.wikimedia.org/hyperkitty/list/cloud-announce@lists.wikimedia.org/thread/EPJFISC52T7OOEFH5YYMZNL57O4VGSPR/]
* Administrators will soon have [[m:Special:MyLanguage/Community Wishlist Survey 2021/(Un)delete associated talk page|the option to delete/undelete]] the associated &quot;talk&quot; page when they are deleting a given page. An API endpoint with this option will also be available. This was [[m:Community Wishlist Survey 2021/Admins and patrollers/(Un)delete associated talk page|a request from the 2021 Wishlist Survey]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W08&quot;/&gt;

19:12, 21 February 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/09|Tech News: 2022-09]] ==

&lt;section begin=&quot;technews-2022-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/09|Translations]] are available.

'''Recent changes'''
* When searching for edits by [[mw:Special:MyLanguage/Help:Tags|change tags]], e.g. in page history or user contributions, there is now a dropdown list of possible tags. This was [[m:Community Wishlist Survey 2022/Miscellaneous/Improve plain-text change tag selector|a request in the 2022 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T27909]
* Mentors using the [[mw:Special:MyLanguage/Growth/Mentor_dashboard|Growth Mentor dashboard]] will now see newcomers assigned to them who have made at least one edit, up to 200 edits. Previously, all newcomers assigned to the mentor were visible on the dashboard, even ones without any edit or ones who made hundred of edits. Mentors can still change these values using the filters on their dashboard. Also, the last choice of filters will now be saved. [https://phabricator.wikimedia.org/T301268][https://phabricator.wikimedia.org/T294460]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The user group &lt;code&gt;oversight&lt;/code&gt; was renamed &lt;code&gt;suppress&lt;/code&gt;. This is for [[phab:T109327|technical reasons]]. You may need to update any local references to the old name, e.g. gadgets, links to Special:Listusers, or uses of [[mw:Special:MyLanguage/Help:Magic_words|NUMBERINGROUP]].

'''Problems'''
* The recent change to the HTML of [[mw:Special:MyLanguage/Help:Tracking changes|tracking changes]] pages caused some problems for screenreaders. This is being fixed. [https://phabricator.wikimedia.org/T298638]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-02|en}}. It will be on all wikis from {{#time:j xg|2022-03-03|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''Future changes'''
* Working with templates will become easier. [[m:WMDE_Technical_Wishes/Templates|Several improvements]] are planned for March 9 on most wikis and on March 16 on English Wikipedia. The improvements include: Bracket matching, syntax highlighting colors, finding and inserting templates, and related visual editor features.
* If you are a template developer or an interface administrator, and you are intentionally overriding or using the default CSS styles of user feedback boxes (the classes: &lt;code dir=ltr&gt;successbox, messagebox, errorbox, warningbox&lt;/code&gt;), please note that these classes and associated CSS will soon be removed from MediaWiki core. This is to prevent problems when the same class-names are also used on a wiki. Please let us know by commenting at [[phab:T300314]] if you think you might be affected.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W09&quot;/&gt;

22:59, 28 February 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/10|Tech News: 2022-10]] ==

&lt;section begin=&quot;technews-2022-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/10|Translations]] are available.

'''Problems'''
* There was a problem with some interface labels last week. It will be fixed this week. This change was part of ongoing work to simplify the support for skins which do not have active maintainers. [https://phabricator.wikimedia.org/T301203]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-09|en}}. It will be on all wikis from {{#time:j xg|2022-03-10|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W10&quot;/&gt;

21:16, 7 March 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/11|Tech News: 2022-11]] ==

&lt;section begin=&quot;technews-2022-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/11|Translations]] are available.

'''Recent changes'''
* In the Wikipedia Android app [[mw:Special:MyLanguage/Wikimedia_Apps/Team/Android/Communication#Updates|it is now possible]] to change the toolbar at the bottom so the tools you use more often are easier to click on. The app now also has a focused reading mode. [https://phabricator.wikimedia.org/T296753][https://phabricator.wikimedia.org/T254771]

'''Problems'''
* There was a problem with the collection of some page-view data from June 2021 to January 2022 on all wikis. This means the statistics are incomplete. To help calculate which projects and regions were most affected, relevant datasets are being retained for 30 extra days. You can [[m:Talk:Data_retention_guidelines#Added_exception_for_page_views_investigation|read more on Meta-wiki]].
* There was a problem with the databases on March 10. All wikis were unreachable for logged-in users for 12 minutes. Logged-out users could read pages but could not edit or access uncached content then. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2022-03-10_MediaWiki_availability]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-16|en}}. It will be on all wikis from {{#time:j xg|2022-03-17|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]).
* When [[mw:Special:MyLanguage/Help:System_message#Finding_messages_and_documentation|using &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;uselang=qqx&lt;/code&gt;&lt;/bdi&gt; to find localisation messages]], it will now show all possible message keys for navigation tabs such as &quot;{{int:vector-view-history}}&quot;. [https://phabricator.wikimedia.org/T300069]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Access to [[{{#special:RevisionDelete}}]] has been expanded to include users who have &lt;code dir=ltr&gt;deletelogentry&lt;/code&gt; and &lt;code dir=ltr&gt;deletedhistory&lt;/code&gt; rights through their group memberships. Before, only those with the &lt;code dir=ltr&gt;deleterevision&lt;/code&gt; right could access this special page. [https://phabricator.wikimedia.org/T301928]
* On the [[{{#special:Undelete}}]] pages for diffs and revisions, there will be a link back to the main Undelete page with the list of revisions. [https://phabricator.wikimedia.org/T284114]

'''Future changes'''
*  The Wikimedia Foundation has announced the IP Masking implementation strategy and next steps. The [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation#feb25|announcement can be read here]].
* The [[mw:Special:MyLanguage/Wikimedia Apps/Android FAQ|Wikipedia Android app]] developers are working on [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication|new functions]] for user talk pages and article talk pages. [https://phabricator.wikimedia.org/T297617]

'''Events'''
* The [[mw:Wikimedia Hackathon 2022|Wikimedia Hackathon 2022]] will take place as a hybrid event on 20-22 May 2022. The Hackathon will be held online and there are grants available to support local in-person meetups around the world. Grants can be requested until 20 March.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W11&quot;/&gt;

22:07, 14 March 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/12|Tech News: 2022-12]] ==

&lt;section begin=&quot;technews-2022-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/12|Translations]] are available.

'''New code release schedule for this week'''
* There will be four MediaWiki releases this week, instead of just one. This is an experiment which should lead to fewer problems and to faster feature updates. The releases will be on all wikis, at different times, on Monday, Tuesday, and Wednesday. You can [[mw:Special:MyLanguage/Wikimedia Release Engineering Team/Trainsperiment week|read more about this project]].

'''Recent changes'''
* You can now set how many search results to show by default in [[Special:Preferences#mw-prefsection-searchoptions|your Preferences]]. This was the 12th most popular wish in the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Results|Community Wishlist Survey 2022]]. [https://phabricator.wikimedia.org/T215716]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The Jupyter notebooks tool [[wikitech:PAWS|PAWS]] has been updated to a new interface. [https://phabricator.wikimedia.org/T295043]

'''Future changes'''
* Interactive maps via [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] will soon work on wikis using the [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevisions]] extension. [https://wikimedia.sslsurvey.de/Kartographer-Workflows-EN/ Please tell us] which improvements you want to see in Kartographer. You can take this survey in simple English. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W12&quot;/&gt;

16:01, 21 March 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/13|Tech News: 2022-13]] ==

&lt;section begin=&quot;technews-2022-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/13|Translations]] are available.

'''Recent changes'''
* There is a simple new Wikimedia Commons upload tool available for macOS users, [[c:Commons:Sunflower|Sunflower]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-30|en}}. It will be on all wikis from {{#time:j xg|2022-03-31|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* Some wikis will be in read-only for a few minutes because of regular database maintenance. It will be performed on {{#time:j xg|2022-03-29|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]) and on {{#time:j xg|2022-03-31|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]). [https://phabricator.wikimedia.org/T301850][https://phabricator.wikimedia.org/T303798]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W13&quot;/&gt;

19:54, 28 March 2022 (UTC)
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== [[m:Special:MyLanguage/Tech/News/2022/14|Tech News: 2022-14]] ==

&lt;section begin=&quot;technews-2022-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/14|Translations]] are available.

'''Problems'''
* For a few days last week, edits that were suggested to newcomers were not tagged in the [[{{#special:recentchanges}}]] feed. This bug has been fixed. [https://phabricator.wikimedia.org/T304747]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-06|en}}. It will be on all wikis from {{#time:j xg|2022-04-07|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-07|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]).

'''Future changes'''
* Starting next week, Tech News' title will be translatable. When the newsletter is distributed, its title may not be &lt;code dir=ltr&gt;Tech News: 2022-14&lt;/code&gt; anymore. It may affect some filters that have been set up by some communities. [https://phabricator.wikimedia.org/T302920]
* Over the next few months, the &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; Growth feature [[phab:T304110|will become available to more Wikipedias]]. Each week, a few wikis will get the feature. You can test this tool at [[mw:Special:MyLanguage/Growth#deploymentstable|a few wikis where &quot;Link recommendation&quot; is already available]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W14&quot;/&gt;

21:01, 4 April 2022 (UTC)
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== Tech News: 2022-15 ==

&lt;section begin=&quot;technews-2022-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/15|Translations]] are available.

'''Recent changes'''
* There is a new public status page at &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikimediastatus.net/ www.wikimediastatus.net]&lt;/span&gt;. This site shows five automated high-level metrics where you can see the overall health and performance of our wikis' technical environment. It also contains manually-written updates for widespread incidents, which are written as quickly as the engineers are able to do so while also fixing the actual problem. The site is separated from our production infrastructure and hosted by an external service, so that it can be accessed even if the wikis are briefly unavailable. You can [https://diff.wikimedia.org/2022/03/31/announcing-www-wikimediastatus-net/ read more about this project].
* On Wiktionary wikis, the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-13|en}}. It will be on all wikis from {{#time:j xg|2022-04-14|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W15&quot;/&gt;

19:44, 11 April 2022 (UTC)
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== Tech News: 2022-16 ==

&lt;section begin=&quot;technews-2022-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/16|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-20|en}}. It will be on all wikis from {{#time:j xg|2022-04-21|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-19|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]) and on {{#time:j xg|2022-04-21|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s8.dblist targeted wikis]).
* Administrators will now have [[m:Community Wishlist Survey 2021/(Un)delete associated talk page|the option to delete/undelete the associated &quot;Talk&quot; page]] when they are deleting a given page. An API endpoint with this option is also available. This concludes the [[m:Community Wishlist Survey 2021/Admins and patrollers/(Un)delete associated talk page|11th wish of the 2021 Community Wishlist Survey]].
* On [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#test-wikis|selected wikis]], 50% of logged-in users will see the new [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Table of contents|table of contents]]. When scrolling up and down the page, the table of contents will stay in the same place on the screen. This is part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]] project. [https://phabricator.wikimedia.org/T304169]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Message boxes produced by MediaWiki code will no longer have these CSS classes: &lt;code dir=ltr&gt;successbox&lt;/code&gt;, &lt;code dir=ltr&gt;errorbox&lt;/code&gt;, &lt;code dir=ltr&gt;warningbox&lt;/code&gt;. The styles for those classes and &lt;code dir=ltr&gt;messagebox&lt;/code&gt; will be removed from MediaWiki core. This only affects wikis that use these classes in wikitext, or change their appearance within site-wide CSS. Please review any local usage and definitions for these classes you may have. This was previously announced in the [[m:Special:MyLanguage/Tech/News/2022/09|28 February issue of Tech News]].

'''Future changes'''
* [[mw:Special:MyLanguage/Extension:Kartographer|Kartographer]] will become compatible with [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevisions page stabilization]]. Kartographer maps will also work on pages with [[mw:Special:MyLanguage/Help:Pending changes|pending changes]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Project_descriptions] The Kartographer documentation has been thoroughly updated. [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:Kartographer/Getting_started] [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:VisualEditor/Maps] [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:Kartographer]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W16&quot;/&gt;

23:11, 18 April 2022 (UTC)
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== Tech News: 2022-17 ==

&lt;section begin=&quot;technews-2022-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/17|Translations]] are available.

'''Recent changes'''
*  On [https://noc.wikimedia.org/conf/dblists/group1.dblist many wikis] (group 1), the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-27|en}}. It will be on all wikis from {{#time:j xg|2022-04-28|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-26|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]).
* Some very old browsers and operating systems are no longer supported. Some things on the wikis might look weird or not work in very old browsers like Internet Explorer 9 or 10, Android 4, or Firefox 38 or older. [https://phabricator.wikimedia.org/T306486]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W17&quot;/&gt;

22:56, 25 April 2022 (UTC)
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== Tech News: 2022-18 ==

&lt;section begin=&quot;technews-2022-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/18|Translations]] are available.

'''Recent changes'''
* On [https://noc.wikimedia.org/conf/dblists/group2.dblist all remaining wikis] (group 2), the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-04|en}}. It will be on all wikis from {{#time:j xg|2022-05-05|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).

'''Future changes'''
* The developers are working on talk pages in the [[mw:Wikimedia Apps/Team/iOS|Wikipedia app for iOS]]. You can [https://wikimedia.qualtrics.com/jfe/form/SV_9GBcHczQGLbQWTY give feedback]. You can take the survey in English, German, Hebrew or Chinese.
* [[m:WMDE_Technical_Wishes/VisualEditor_template_dialog_improvements#Status_and_next_steps|Most wikis]] will receive an [[m:WMDE_Technical_Wishes/VisualEditor_template_dialog_improvements|improved template dialog]] in VisualEditor and New Wikitext mode. [https://phabricator.wikimedia.org/T296759] [https://phabricator.wikimedia.org/T306967]
* If you use syntax highlighting while editing wikitext, you can soon activate a [[m:WMDE_Technical_Wishes/Improved_Color_Scheme_of_Syntax_Highlighting#Color-blind_mode|colorblind-friendly color scheme]]. [https://phabricator.wikimedia.org/T306867]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Several CSS IDs related to MediaWiki interface messages will be removed. Technical editors should please [[phab:T304363|review the list of IDs and links to their existing uses]]. These include &lt;code dir=ltr&gt;#mw-anon-edit-warning&lt;/code&gt;, &lt;code dir=ltr&gt;#mw-undelete-revision&lt;/code&gt; and 3 others.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W18&quot;/&gt;

19:33, 2 May 2022 (UTC)
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== Tech News: 2022-19 ==

&lt;section begin=&quot;technews-2022-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/19|Translations]] are available.

'''Recent changes'''
* You can now see categories in the [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android|Wikipedia app for Android]]. [https://phabricator.wikimedia.org/T73966]

'''Problems'''
* Last week, there was a problem with Wikidata's search autocomplete. This has now been fixed. [https://phabricator.wikimedia.org/T307586]
* Last week, all wikis had slow access or no access for 20 minutes, for logged-in users and non-cached pages. This was caused by a problem with a database change. [https://phabricator.wikimedia.org/T307647]

'''Changes later this week'''
* There is no new MediaWiki version this week. [https://phabricator.wikimedia.org/T305217#7894966]
*  [[m:WMDE Technical Wishes/Geoinformation#Current issues|Incompatibility issues]] with [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] and the [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs|FlaggedRevs extension]] will be fixed: Deployment is planned for May 10 on all wikis. Kartographer will then be enabled on the [[phab:T307348|five wikis which have not yet enabled the extension]] on May 24.
* The [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector (2022)]] skin will be set as the default on several more wikis, including Arabic and Catalan Wikipedias. Logged-in users will be able to switch back to the old Vector (2010). See the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2022-04 for the largest wikis|latest update]] about Vector (2022).

'''Future meetings'''
* The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place on 17 May. The following meetings are currently planned for: 7 June, 21 June, 5 July, 19 July.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W19&quot;/&gt;

15:22, 9 May 2022 (UTC)
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== Tech News: 2022-20 ==

&lt;section begin=&quot;technews-2022-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/20|Translations]] are available.

'''Changes later this week'''
* Some wikis can soon use the [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|add a link]] feature. This will start on Wednesday. The wikis are {{int:project-localized-name-cawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-simplewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-svwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}. This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304542]
* The [[mw:Special:MyLanguage/Wikimedia Hackathon 2022|Wikimedia Hackathon 2022]] will take place online on May 20–22. It will be in English. There are also local [[mw:Special:MyLanguage/Wikimedia Hackathon 2022/Meetups|hackathon meetups]] in Germany, Ghana, Greece, India, Nigeria and the United States. Technically interested Wikimedians can work on software projects and learn new skills. You can also host a session or post a project you want to work on.
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-18|en}}. It will be on all wikis from {{#time:j xg|2022-05-19|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).

'''Future changes'''
* You can soon edit translatable pages in the visual editor. Translatable pages exist on for examples Meta and Commons. [https://diff.wikimedia.org/2022/05/12/mediawiki-1-38-brings-support-for-editing-translatable-pages-with-the-visual-editor/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W20&quot;/&gt;

18:58, 16 May 2022 (UTC)
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== Tech News: 2022-21 ==

&lt;section begin=&quot;technews-2022-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/21|Translations]] are available.

'''Recent changes'''
* Administrators using the mobile web interface can now access Special:Block directly from user pages. [https://phabricator.wikimedia.org/T307341]
* The &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wiktionary.org/ www.wiktionary.org]&lt;/span&gt; portal page now uses an automated update system. Other [[m:Project_portals|project portals]] will be updated over the next few months. [https://phabricator.wikimedia.org/T304629]

'''Problems'''
* The Growth team maintains a mentorship program for newcomers. Previously, newcomers weren't able to opt out from the program. Starting May 19, 2022, newcomers are able to fully opt out from Growth mentorship, in case they do not wish to have any mentor at all. [https://phabricator.wikimedia.org/T287915]
* Some editors cannot access the content translation tool if they load it by clicking from the contributions menu. This problem is being worked on. It should still work properly if accessed directly via Special:ContentTranslation. [https://phabricator.wikimedia.org/T308802]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-25|en}}. It will be on all wikis from {{#time:j xg|2022-05-26|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Gadget and user scripts developers are invited to give feedback on a [[mw:User:Jdlrobson/Extension:Gadget/Policy|proposed technical policy]] aiming to improve support from MediaWiki developers. [https://phabricator.wikimedia.org/T308686]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W21&quot;/&gt;

00:21, 24 May 2022 (UTC)
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== Tech News: 2022-22 ==

&lt;section begin=&quot;technews-2022-W22&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/22|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|Advanced item]]  In the [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] extension, an &lt;code dir=ltr&gt;ip_in_ranges()&lt;/code&gt; function has been introduced to check if an IP is in any of the ranges. Wikis are advised to combine multiple &lt;code dir=ltr&gt;ip_in_range()&lt;/code&gt; expressions joined by &lt;code&gt;|&lt;/code&gt; into a single expression for better performance. You can use the search function on [[Special:AbuseFilter|Special:AbuseFilter]] to locate its usage. [https://phabricator.wikimedia.org/T305017]
* The [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature|IP Info feature]] which helps abuse fighters access information about IPs, [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#May 24, 2022|has been deployed]] to all wikis as a beta feature. This comes after weeks of beta testing on test.wikipedia.org.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-01|en}}. It will be on all wikis from {{#time:j xg|2022-06-02|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-05-31|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]).
* The [[mw:Special:MyLanguage/Help:DiscussionTools#New topic tool|New Topic Tool]] will be deployed for all editors at most wikis soon. You will be able to opt out from within the tool and in [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/New_discussion][https://phabricator.wikimedia.org/T287804]
* [[File:Octicons-tools.svg|15px|link=|Advanced item]]  The [[:mw:Special:ApiHelp/query+usercontribs|list=usercontribs API]] will support fetching contributions from an [[mw:Special:MyLanguage/Help:Range blocks#Non-technical explanation|IP range]] soon. API users can set the &lt;code&gt;uciprange&lt;/code&gt; parameter to get contributions from any IP range within [[:mw:Manual:$wgRangeContributionsCIDRLimit|the limit]]. [https://phabricator.wikimedia.org/T177150]
* A new parser function will be introduced: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;{{=}}&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. It will replace existing templates named &quot;=&quot;. It will insert an [[w:en:Equals sign|equal sign]]. This can be used to escape the equal sign in the parameter values of templates. [https://phabricator.wikimedia.org/T91154]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/22|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W22&quot;/&gt;

20:28, 30 May 2022 (UTC)
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== Tech News: 2022-23 ==

&lt;section begin=&quot;technews-2022-W23&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/23|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-08|en}}. It will be on all wikis from {{#time:j xg|2022-06-09|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;str_replace_regexp()&lt;/code&gt;&lt;/bdi&gt; function can be used in [[Special:AbuseFilter|abuse filters]] to replace parts of text using a [[w:en:Regular expression|regular expression]]. [https://phabricator.wikimedia.org/T285468]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/23|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W23&quot;/&gt;

02:46, 7 June 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23366979 --&gt;

== Tech News: 2022-24 ==

&lt;section begin=&quot;technews-2022-W24&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/24|Translations]] are available.

'''Recent changes'''
* All wikis can now use [[mw:Special:MyLanguage/Extension:Kartographer|Kartographer]] maps. Kartographer maps now also work on pages with [[mw:Special:MyLanguage/Help:Pending changes|pending changes]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Project_descriptions][https://phabricator.wikimedia.org/T307348]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-15|en}}. It will be on all wikis from {{#time:j xg|2022-06-16|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-14|en}} at 06:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]). [https://phabricator.wikimedia.org/T300471]
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-abwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-acewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-adywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-afwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-akwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-alswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-amwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-anwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-angwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-arcwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-arzwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-astwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-atjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-avwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-aywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-azbwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304548]
* The [[mw:Special:MyLanguage/Help:DiscussionTools#New topic tool|New Topic Tool]] will be deployed for all editors at Commons, Wikidata, and some other wikis soon. You will be able to opt out from within the tool and in [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/New_discussion][https://phabricator.wikimedia.org/T287804]

'''Future meetings'''
* The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place today (13 June). The following meetings will take place on: 28 June, 12 July, 26 July.

'''Future changes'''
* By the end of July, the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022]] skin should be ready to become the default across all wikis. Discussions on how to adjust it to the communities' needs will begin in the next weeks. It will always be possible to revert to the previous version on an individual basis. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2022-04 for the largest wikis|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/24|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W24&quot;/&gt;

16:58, 13 June 2022 (UTC)
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== Tech News: 2022-25 ==

&lt;section begin=&quot;technews-2022-W25&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/25|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android|Wikipedia App for Android]] now has an option for editing the whole page at once, located in the overflow menu (three-dots menu [[File:Ic more vert 36px.svg|15px|link=|alt=]]). [https://phabricator.wikimedia.org/T103622]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Some recent database changes may affect queries using the [[m:Research:Quarry|Quarry tool]]. Queries for &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;site_stats&lt;/code&gt;&lt;/bdi&gt; at English Wikipedia, Commons, and Wikidata will need to be updated. [[phab:T306589|Read more]].
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;user_global_editcount&lt;/code&gt;&lt;/bdi&gt; variable can be used in [[Special:AbuseFilter|abuse filters]] to avoid affecting globally active users. [https://phabricator.wikimedia.org/T130439]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-22|en}}. It will be on all wikis from {{#time:j xg|2022-06-23|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* Users of non-responsive skins (e.g. MonoBook or Vector) on mobile devices may notice a slight change in the default zoom level. This is intended to optimize zooming and ensure all interface elements are present on the page (for example the table of contents on Vector 2022). In the unlikely event this causes any problems with how you use the site, we'd love to understand better, please ping &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[m:User:Jon (WMF)|Jon (WMF)]]&lt;/span&gt; to any on-wiki conversations. [https://phabricator.wikimedia.org/T306910]

'''Future changes'''
* The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July.  Discussions will look different.  You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]].
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Parsoid's HTML output will soon stop annotating file links with different &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;typeof&lt;/code&gt;&lt;/bdi&gt; attribute values, and instead use &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw:File&lt;/code&gt;&lt;/bdi&gt; for all types. Tool authors should adjust any code that expects: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw:Image&lt;/code&gt;&lt;/bdi&gt;, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw:Audio&lt;/code&gt;&lt;/bdi&gt;, or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw:Video&lt;/code&gt;&lt;/bdi&gt;. [https://phabricator.wikimedia.org/T273505]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/25|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W25&quot;/&gt;

20:18, 20 June 2022 (UTC)
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== Tech News: 2022-26 ==

&lt;section begin=&quot;technews-2022-W26&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/26|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] API service now has self-service accounts with free on-demand requests and monthly snapshots ([https://enterprise.wikimedia.com/docs/ API documentation]). Community access [[m:Special:MyLanguage/Wikimedia Enterprise/FAQ#community-access|via database dumps &amp; Wikimedia Cloud Services]] continues.
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[d:Special:MyLanguage/Wikidata:Wiktionary#lua|All Wikimedia wikis can now use Wikidata Lexemes in Lua]] after creating local modules and templates. Discussions are welcome [[d:Wikidata_talk:Lexicographical_data#You_can_now_reuse_Wikidata_Lexemes_on_all_wikis|on the project talk page]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-29|en}}. It will be on all wikis from {{#time:j xg|2022-06-30|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-28|en}} at 06:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). [https://phabricator.wikimedia.org/T311033]
*  Some global and cross-wiki services will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-30|en}} at 06:00 UTC. This will impact ContentTranslation, Echo, StructuredDiscussions, Growth experiments and a few more services. [https://phabricator.wikimedia.org/T300472]
* Users will be able to sort columns within sortable tables in the mobile skin. [https://phabricator.wikimedia.org/T233340]

'''Future meetings'''
* The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place tomorrow (28 June). The following meetings will take place on 12 July and 26 July.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/26|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W26&quot;/&gt;

20:02, 27 June 2022 (UTC)
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== Tech News: 2022-27 ==

&lt;section begin=&quot;technews-2022-W27&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/27|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-06|en}}. It will be on all wikis from {{#time:j xg|2022-07-07|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-07-05|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]) and on {{#time:j xg|2022-07-07|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]).
* The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July.  Discussions will look different.  You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]].
* [[File:Octicons-tools.svg|15px|link=|alt=| Advanced item]] This change only affects pages in the main namespace in Wikisource. The Javascript config variable &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;proofreadpage_source_href&lt;/code&gt;&lt;/bdi&gt; will be removed from &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:Special:MyLanguage/Manual:Interface/JavaScript#mw.config|mw.config]]&lt;/code&gt;&lt;/bdi&gt; and be replaced with the variable &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;prpSourceIndexPage&lt;/code&gt;&lt;/bdi&gt;.  [https://phabricator.wikimedia.org/T309490]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/27|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W27&quot;/&gt;

19:32, 4 July 2022 (UTC)
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== Tech News: 2022-28 ==

&lt;section begin=&quot;technews-2022-W28&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/28|Translations]] are available.

'''Recent changes'''
* In the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022 skin]], the page title is now displayed above the tabs such as Discussion, Read, Edit, View history, or More. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates#Page title/tabs switch|Learn more]]. [https://phabricator.wikimedia.org/T303549]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] It is now possible to easily view most of the configuration settings that apply to just one wiki, and to compare settings between two wikis if those settings are different. For example: [https://noc.wikimedia.org/wiki.php?wiki=jawiktionary Japanese Wiktionary settings], or [https://noc.wikimedia.org/wiki.php?wiki=eswiki&amp;compare=eowiki settings that are different between the Spanish and Esperanto Wikipedias]. Local communities may want to [[m:Special:MyLanguage/Requesting_wiki_configuration_changes|discuss and propose changes]] to their local settings. Details about each of the named settings can be found by [[mw:Special:Search|searching MediaWiki.org]]. [https://phabricator.wikimedia.org/T308932]
*The Anti-Harassment Tools team [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#May|recently deployed]] the IP Info Feature as a [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature at all wikis]]. This feature allows abuse fighters to access information about IP addresses. Please check our update on [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#April|how to find and use the tool]]. Please share your feedback using a link you will be given within the tool itself.

'''Changes later this week'''
* There is no new MediaWiki version this week.
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-07-12|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]).

'''Future changes'''
* The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July.  Discussions will look different.  You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/28|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W28&quot;/&gt;

19:24, 11 July 2022 (UTC)
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== Tech News: 2022-29 ==

&lt;section begin=&quot;technews-2022-W29&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/29|Translations]] are available.

'''Problems'''
* The feature on mobile web for [[mw:Special:MyLanguage/Extension:NearbyPages|Nearby Pages]] was missing last week. It will be fixed this week. [https://phabricator.wikimedia.org/T312864]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-20|en}}. It will be on all wikis from {{#time:j xg|2022-07-21|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).

'''Future changes'''
* The [[mw:Technical_decision_making/Forum|Technical Decision Forum]] is seeking [[mw:Technical_decision_making/Community_representation|community representatives]]. You can apply on wiki or by emailing &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;TDFSupport@wikimedia.org&lt;/span&gt; before 12 August.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/29|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W29&quot;/&gt;

22:59, 18 July 2022 (UTC)
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== Tech News: 2022-30 ==

&lt;section begin=&quot;technews-2022-W30&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/30|Translations]] are available.

'''Recent changes'''
* The &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikibooks.org/ www.wikibooks.org]&lt;/span&gt; and &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikiquote.org/ www.wikiquote.org]&lt;/span&gt; portal pages now use an automated update system. Other [[m:Project_portals|project portals]] will be updated over the next few months. [https://phabricator.wikimedia.org/T273179]

'''Problems'''
*  Last week, some wikis were in read-only mode for a few minutes because of an emergency switch of their main database ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). [https://phabricator.wikimedia.org/T313383]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-27|en}}. It will be on all wikis from {{#time:j xg|2022-07-28|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* The external link icon will change slightly in the skins Vector legacy and Vector 2022. The new icon uses simpler shapes to be more recognizable on low-fidelity screens. [https://phabricator.wikimedia.org/T261391]
* Administrators will now see buttons on user pages for &quot;{{int:changeblockip}}&quot; and &quot;{{int:unblockip}}&quot; instead of just &quot;{{int:blockip}}&quot; if the user is already blocked. [https://phabricator.wikimedia.org/T308570]

'''Future meetings'''
* The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place tomorrow (26 July).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/30|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W30&quot;/&gt;

19:27, 25 July 2022 (UTC)
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== Tech News: 2022-31 ==

&lt;section begin=&quot;technews-2022-W31&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/31|Translations]] are available.

'''Recent changes'''
* Improved [[m:Special:MyLanguage/Help:Displaying_a_formula#Phantom|LaTeX capabilities for math rendering]] are now available in the wikis thanks to supporting &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Phantom&lt;/code&gt;&lt;/bdi&gt; tags. This completes part of [[m:Community_Wishlist_Survey_2022/Editing/Missing_LaTeX_capabilities_for_math_rendering|the #59 wish]] of the 2022 Community Wishlist Survey.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-03|en}}. It will be on all wikis from {{#time:j xg|2022-08-04|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] will be available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup0.dblist Group 0]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]].

'''Future changes'''
* The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout August.  Discussions will look different.  You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]].

'''Future meetings'''
* This week, three meetings about [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector (2022)]] with live interpretation will take place. On Tuesday, interpretation in Russian will be provided. On Thursday, meetings for Arabic and Spanish speakers will take place. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|See how to join]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/31|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W31&quot;/&gt;

21:21, 1 August 2022 (UTC)
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== Tech News: 2022-32 ==

&lt;section begin=&quot;technews-2022-W32&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/32|Translations]] are available.

'''Recent changes'''
* [[:m:Special:MyLanguage/Meta:GUS2Wiki/Script|GUS2Wiki]] copies the information from [[{{#special:GadgetUsage}}]] to an on-wiki page so you can review its history. If your project isn't already listed on the [[d:Q113143828|Wikidata entry for Project:GUS2Wiki]] you can either run GUS2Wiki yourself or [[:m:Special:MyLanguage/Meta:GUS2Wiki/Script#Opting|make a request to receive updates]]. [https://phabricator.wikimedia.org/T121049]

'''Changes later this week'''
* There is no new MediaWiki version this week.
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-09|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2022-08-11|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]).

'''Future meetings'''
* The [[wmania:Special:MyLanguage/Hackathon|Wikimania Hackathon]] will take place online from August 12–14. Don't miss [[wmania:Special:MyLanguage/Hackathon/Schedule|the pre-hacking showcase]] to learn about projects and find collaborators. Anyone can [[phab:/project/board/6030/|propose a project]] or [[wmania:Special:MyLanguage/Hackathon/Schedule|host a session]]. [[wmania:Special:MyLanguage/Hackathon/Newcomers|Newcomers are welcome]]!

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/32|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W32&quot;/&gt;

19:50, 8 August 2022 (UTC)
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== Tech News: 2022-33 ==

&lt;section begin=&quot;technews-2022-W33&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/33|Translations]] are available.

'''Recent changes'''
* The Persian (Farsi) Wikipedia community decided to block IP editing from October 2021 to April 2022. The Wikimedia Foundation's Product Analytics team tracked the impact of this change. [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Editing Restriction Study/Farsi Wikipedia|An impact report]] is now available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-17|en}}. It will be on all wikis from {{#time:j xg|2022-08-18|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-16|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]) and on {{#time:j xg|2022-08-18|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s8.dblist targeted wikis]).
* The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] will be available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup1.dblist Group 1]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]].

'''Future changes'''
* The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout August.  Discussions will look different.  You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. [https://www.mediawiki.org/wiki/Talk_pages_project/Usability#4_August_2022][https://www.mediawiki.org/wiki/Talk_pages_project/Usability#Phase_1:_Topic_containers][https://phabricator.wikimedia.org/T312672]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/33|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W33&quot;/&gt;

21:08, 15 August 2022 (UTC)
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== Tech News: 2022-34 ==

&lt;section begin=&quot;technews-2022-W34&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/34|Translations]] are available.

'''Recent changes'''
* Two problems with [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps have been fixed. Maps are no longer shown as empty when a geoline was created via VisualEditor. Geolines consisting of points with QIDs (e.g., subway lines) are no longer shown with pushpins. [https://phabricator.wikimedia.org/T292613][https://phabricator.wikimedia.org/T308560]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-24|en}}. It will be on all wikis from {{#time:j xg|2022-08-25|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-25|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]).
* The colours of links and visited links will change. This is to make the difference between links and other text more clear. [https://phabricator.wikimedia.org/T213778]

'''Future changes'''
* The new [{{int:discussiontools-topicsubscription-button-subscribe}}] button [[mw:Talk pages project/Notifications#12 August 2022|helps newcomers get answers]].  The Editing team is enabling this tool everywhere.  You can turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|your preferences]]. [https://phabricator.wikimedia.org/T284489]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/34|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W34&quot;/&gt;

00:12, 23 August 2022 (UTC)
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== Tech News: 2022-35 ==

&lt;section begin=&quot;technews-2022-W35&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/35|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] is available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup2.dblist Group 2]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]]. Please note that when this Beta feature is enabled, it may cause conflicts with some wiki-specific Gadgets.

'''Problems'''
* In recent months, there have been inaccurate numbers shown for various [[{{#special:statistics}}]] at Commons, Wikidata, and English Wikipedia. This has now been fixed. [https://phabricator.wikimedia.org/T315693]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-31|en}}. It will be on all wikis from {{#time:j xg|2022-09-01|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-30|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]) and on {{#time:j xg|2022-09-01|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]).

'''Future changes'''
* The Wikimedia Foundation wants to improve how Wikimedia communities report harmful incidents by building the [[m:Special:MyLanguage/Private Incident Reporting System|Private Incident Reporting System (PIRS)]] to make it easy and safe for users to make reports. You can leave comments on the talk page, by answering the [[m:Special:MyLanguage/Private Incident Reporting System#Phase 1|questions provided]].  If you have ever faced a harmful situation that you wanted to report/reported, join a PIRS interview to share your experience. To sign up [[m:Special:EmailUser/MAna_(WMF)|please email]] &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[m:User:MAna (WMF)|Madalina Ana]]&lt;/span&gt;.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/35|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W35&quot;/&gt;

23:05, 29 August 2022 (UTC)
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== Tech News: 2022-36 ==

&lt;section begin=&quot;technews-2022-W36&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/36|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-07|en}}. It will be on all wikis from {{#time:j xg|2022-09-08|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-09-06|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]) and on {{#time:j xg|2022-09-08|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]).
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] On Special pages that only have one tab, the tab-bar's row will be hidden in the Vector-2022 skin to save space. The row will still show if Gadgets use it. Gadgets that currently append directly to the CSS id of &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;#p-namespaces&lt;/code&gt;&lt;/bdi&gt; should be updated to use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:ResourceLoader/Core_modules#addPortletLink|mw.util.addPortletLink]]&lt;/code&gt;&lt;/bdi&gt; function instead. Gadgets that style this id should consider also targeting &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;#p-associated-pages&lt;/code&gt;&lt;/bdi&gt;, the new id for this row. [[phab:T316908|Examples are available]]. [https://phabricator.wikimedia.org/T316908][https://phabricator.wikimedia.org/T313409]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/36|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W36&quot;/&gt;

23:22, 5 September 2022 (UTC)
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== Tech News: 2022-37 ==

&lt;section begin=&quot;technews-2022-W37&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/37|Translations]] are available.

'''Recent changes'''
* The search servers have been upgraded to a new major version. If you notice any issues with searching, please report them on [[phab:project/view/1849/|Phabricator]]. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/XPCTYYTN67FVFKN6XOHULJVGUO44J662]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-14|en}}. It will be on all wikis from {{#time:j xg|2022-09-15|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[mw:Special:MyLanguage/Extension:SyntaxHighlight|Syntax highlighting]] is now tracked as an [[mw:Special:MyLanguage/Manual:$wgExpensiveParserFunctionLimit|expensive parser function]]. Only 500 expensive function calls can be used on a single page. Pages that exceed the limit are added to a [[:Category:{{MediaWiki:expensive-parserfunction-category}}|tracking category]]. [https://phabricator.wikimedia.org/T316858]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/37|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W37&quot;/&gt;

01:50, 13 September 2022 (UTC)
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== Tech News: 2022-38 ==

&lt;section begin=&quot;technews-2022-W38&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/38|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Two database fields in the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;templatelinks&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; table are now being dropped: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;tl_namespace&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;tl_title&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. Any queries that rely on these fields need to be changed to use the new normalization field called &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;tl_target_id&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. See &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[phab:T299417|T299417]]&lt;/span&gt; for more information. This is part of [[w:Database normalization|normalization]] of links tables. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/U2U6TXIBABU3KDCVUOITIGI5OJ4COBSW/][https://www.mediawiki.org/wiki/User:ASarabadani_(WMF)/Database_for_devs_toolkit/Concepts/Normalization]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-21|en}}. It will be on all wikis from {{#time:j xg|2022-09-22|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* In [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps, you can use icons on markers for common points of interest. On Tuesday, the [[mw:Special:MyLanguage/Help:Extension:Kartographer/Icons|previous icon set]] will be updated to [https://de.wikipedia.beta.wmflabs.org/wiki/Hilfe:Extension:Kartographer/Icons version maki 7.2]. That means, around 100 new icons will be available.  Additionally, all existing icons were updated for clarity and to make them work better in international contexts. [https://phabricator.wikimedia.org/T302861][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Update_maki_icons]

'''Future changes'''
* In a [[m:Content_Partnerships_Hub/Software/Volunteer_developers_discussion_at_Wikimania_2022|group discussion at Wikimania]], more than 30 people talked about how to make content partnership software in the Wikimedia movement more sustainable. What kind of support is acceptable for volunteer developers? Read the summary and [[m:Talk:Content Partnerships Hub/Software/Volunteer developers discussion at Wikimania 2022|leave your feedback]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/38|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W38&quot;/&gt;

&lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/span&gt; 22:16, 19 September 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23826293 --&gt;

== Tech News: 2022-39 ==

&lt;section begin=&quot;technews-2022-W39&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/39|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Parsoid clients should be updated to allow for space-separated multi-values in the &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;rel&lt;/code&gt;&lt;/bdi&gt; attribute of links. Further details are in &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[phab:T315209|T315209]]&lt;/bdi&gt;.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-28|en}}. It will be on all wikis from {{#time:j xg|2022-09-29|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[mw:Special:MyLanguage/VisualEditor/Diffs|Visual diffs]] will become available to all users, except at the Wiktionaries and Wikipedias. [https://phabricator.wikimedia.org/T314588]
* [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|Talk pages on the mobile site]] will change at the Arabic, Bangla, Chinese, French, Haitian Creole, Hebrew, Korean, and Vietnamese Wikipedias.  They should be easier to use and provide more information. [https://phabricator.wikimedia.org/T318302] [https://www.mediawiki.org/wiki/Talk_pages_project/Mobile]
* In the [[mw:Lua/Scripting|{{ns:828}}]] namespace, pages ending with &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.json&lt;/code&gt;&lt;/bdi&gt; will be treated as JSON, just like they already are in the {{ns:2}} and {{ns:8}} namespaces. [https://phabricator.wikimedia.org/T144475]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/39|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W39&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:30, 27 September 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23860085 --&gt;

== Tech News: 2022-40 ==

&lt;section begin=&quot;technews-2022-W40&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/40|Translations]] are available.

'''Recent changes'''
* [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps can now show geopoints from Wikidata, via QID or SPARQL query. Previously, this was only possible for geoshapes and geolines. [https://phabricator.wikimedia.org/T307695] [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Geopoints_via_QID]
* The [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award 2022]] is looking for nominations. You can recommend tools until 12 October.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-05|en}}. It will be on all wikis from {{#time:j xg|2022-10-06|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|Talk pages on the mobile site]] will change at the Arabic, Bangla, Chinese, French, Haitian Creole, Hebrew, Korean, and Vietnamese Wikipedias.  They should be easier to use and provide more information. (Last week's release was delayed) [https://phabricator.wikimedia.org/T318302] [https://www.mediawiki.org/wiki/Talk_pages_project/Mobile]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;scribunto-console&lt;/code&gt;&lt;/bdi&gt; API module will require a [[mw:Special:MyLanguage/API:Tokens|CSRF token]]. This module is documented as internal and use of it is not supported. [[phab:T212071|[5]]] 
* The Vector 2022 skin will become the default across the smallest Wikimedia projects. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#Deployment_plan_and_timeline|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/40|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W40&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:23, 4 October 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23885489 --&gt;

== Tech News: 2022-41 ==

&lt;section begin=&quot;technews-2022-W41&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/41|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-12|en}}. It will be on all wikis from {{#time:j xg|2022-10-13|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* On some wikis, [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps in full size view will be able to display nearby articles. After a feedback period, more wikis will follow. [https://phabricator.wikimedia.org/T316782][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Nearby_articles]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/41|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W41&quot;/&gt;

14:08, 10 October 2022 (UTC)
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== Tech News: 2022-42 ==

&lt;section begin=&quot;technews-2022-W42&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/42|Translations]] are available.

'''Recent changes'''
* The recently implemented feature of [[phab:T306883|article thumbnails in Special:Search]] will be limited to Wikipedia projects only. Further details are in [[phab:T320510|T320510]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Structured_Data_Across_Wikimedia/Search_Improvements]
* A bug that caused problems in loading article thumbnails in Special:Search has been fixed. Further details are in [[phab:T320406|T320406]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-19|en}}. It will be on all wikis from {{#time:j xg|2022-10-20|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Lua module authors can use &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:Special:MyLanguage/Extension:Scribunto/Lua_reference_manual#mw.loadJsonData|mw.loadJsonData()]]&lt;/code&gt;&lt;/bdi&gt; to load data from JSON pages. [https://phabricator.wikimedia.org/T217500]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Lua module authors can enable &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:Special:MyLanguage/Extension:Scribunto/Lua_reference_manual#Strict_library|require( &quot;strict&quot; )]]&lt;/code&gt;&lt;/bdi&gt; to add errors for some possible code problems. This replaces &quot;[[wikidata:Q16748603|Module:No globals]]&quot; on most wikis. [https://phabricator.wikimedia.org/T209310]

'''Future changes'''
* The [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated at most wikis. The &quot;{{int:discussiontools-replylink}}&quot; button will look different after this change. [https://phabricator.wikimedia.org/T320683]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/42|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W42&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:46, 17 October 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23943992 --&gt;

== Tech News: 2022-43 ==

&lt;section begin=&quot;technews-2022-W43&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/43|Translations]] are available.

'''Recent changes'''
* There have been some minor visual fixes in Special:Search, regarding audio player alignment and image placeholder height. Further details are in [[phab:T319230|T319230]].
* On Wikipedias, a new [[Special:Preferences#mw-prefsection-searchoptions|preference]] has been added to hide article thumbnails in Special:Search. Full details are in [[phab:T320337|T320337]].

'''Problems'''
* Last week, three wikis ({{int:project-localized-name-frwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ruwiki/en}}) had read-only access for 25 minutes. This was caused by a hardware problem. [https://phabricator.wikimedia.org/T320990]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-26|en}}. It will be on all wikis from {{#time:j xg|2022-10-27|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-10-25|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2022-10-27|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-aswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-banwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-barwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bat smgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bclwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-be x oldwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-biwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bjnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bpywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-brwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bugwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bxrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304549] 
* Starting on Wednesday October 26, 2022, the list of mentors will be upgraded [[d:Q14339834 | at wikis where Growth mentorship is available]]. The mentorship system will continue to work as it does now. The signup process [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list#add|will be replaced]], and a new management option will be provided. Also, this change simplifies [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list#create|the creation of mentorship systems at Wikipedias]]. [https://phabricator.wikimedia.org/T314858][https://phabricator.wikimedia.org/T310905][https://www.mediawiki.org/wiki/Special:MyLanguage/Growth/Structured_mentor_list]
* Pages with titles that start with a lower-case letter according to Unicode 11 will be renamed or deleted. There is a list of affected pages at &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[m:Unicode 11 case map migration]]&lt;/bdi&gt;. More information can be found at [[phab:T292552|T292552]].
* The Vector 2022 skin will become the default across the smallest Wikipedias. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#smallest-1|Learn more]].

'''Future changes'''
* The [[mw:Special:MyLanguage/Talk pages project/Replying|Reply tool]] and [[mw:Special:MyLanguage/Talk pages project/New discussion|New Topic tool]] will soon get a [[mw:Special:MyLanguage/VisualEditor/Special characters|special characters menu]]. [https://phabricator.wikimedia.org/T249072]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/43|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W43&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:22, 24 October 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23975411 --&gt;

== Tech News: 2022-44 ==

&lt;section begin=&quot;technews-2022-W44&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/44|Translations]] are available.

'''Recent changes'''
* When using keyboard navigation on a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map, the focus will become more visible. [https://phabricator.wikimedia.org/T315997]
* In {{#special:RecentChanges}}, you can now hide the log entries for new user creations with the filter for &quot;{{int:rcfilters-filter-newuserlogactions-label}}&quot;. [https://phabricator.wikimedia.org/T321155]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-02|en}}. It will be on all wikis from {{#time:j xg|2022-11-03|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* The [[mw:Special:MyLanguage/Help:Extension:Kartographer|maps dialog]] in VisualEditor now has some help texts. [https://phabricator.wikimedia.org/T318818]
* It is now possible to select the language of a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor via a dropdown menu. [https://phabricator.wikimedia.org/T318817]
* It is now possible to add a caption to a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor. [https://phabricator.wikimedia.org/T318815]
* It is now possible to hide the frame of a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor. [https://phabricator.wikimedia.org/T318813]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/44|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W44&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:15, 31 October 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=23977539 --&gt;

== Tech News: 2022-45 ==

&lt;section begin=&quot;technews-2022-W45&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/45|Translations]] are available.

'''Recent changes'''
* An updated version of the [[m:Special:MyLanguage/EventCenter/Registration|Event Registration]] tool is now available for testing at [[testwiki:|testwiki]] and [[test2wiki:| test2wiki]]. The tool provides features for event organizers and participants. Your feedback is welcome at our [[m:Talk:Campaigns/Foundation Product Team/Registration|project talkpage]]. More information about [[m:Campaigns/Foundation Product Team/Registration|the project]] is available. [https://phabricator.wikimedia.org/T318592]

'''Problems'''
* Twice last week, for about 45 minutes, some files and thumbnails failed to load and uploads failed, mostly for logged-in users. The cause is being investigated and an incident report will be available soon.

'''Changes later this week'''
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/45|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W45&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:32, 8 November 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24001035 --&gt;

== Tech News: 2022-46 ==

&lt;section begin=&quot;technews-2022-W46&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/46|Translations]] are available.

'''Recent changes'''
* At Wikidata, an interwiki link can now point to a redirect page if certain conditions are met. This new feature is called [[wikidata:Special:MyLanguage/Wikidata:Sitelinks_to_redirects|sitelinks to redirects]]. It is needed when one wiki uses one page to cover multiple concepts but another wiki uses more pages to cover the same concepts. Your [[wikidata:Special:MyLanguage/Wikidata talk:Sitelinks to redirects|feedback on the talkpage]] of the new proposed guideline is welcome. [https://phabricator.wikimedia.org/T278962]
* The &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikinews.org/ www.wikinews.org]&lt;/span&gt;, &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikiversity.org/ www.wikiversity.org]&lt;/span&gt;, and &lt;span class=&quot;mw-content-ltr&quot; lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikivoyage.org/ www.wikivoyage.org]&lt;/span&gt; portal pages now use an automated update system. [https://phabricator.wikimedia.org/T273179]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-16|en}}. It will be on all wikis from {{#time:j xg|2022-11-17|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* There will be a new link to directly &quot;Edit template data&quot; on Template pages. [https://phabricator.wikimedia.org/T316759]

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Wikis where mobile [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] are enabled ([[mw:Special:MyLanguage/Talk pages project/Deployment Status|these ones]]) will soon use full CSS styling to display any templates that are placed at the top of talk pages. To adapt these “talk page boxes” for narrow mobile devices you can use media queries, such as in [https://en.wikipedia.org/w/index.php?title=Module:Message_box/tmbox.css&amp;oldid=1097618699#L-69 this example]. [https://phabricator.wikimedia.org/T312309]
* Starting in January 2023, [[m:Special:MyLanguage/Community Tech|Community Tech]] will be [[m:Special:MyLanguage/Community Wishlist Survey/Updates/2023 Changes Update|running the Community Wishlist Survey (CWS) every two years]]. This means that in 2024, there will be no new proposals or voting.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/46|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W46&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:54, 14 November 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24071290 --&gt;

== Tech News: 2022-47 ==

&lt;section begin=&quot;technews-2022-W47&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/47|Translations]] are available.

'''Recent changes'''
* The display of non-free media in the search bar and for article thumbnails in Special:Search has been deactivated. Further details are in [[phab:T320661|T320661]].

'''Changes later this week'''
* There is no new MediaWiki version this week.
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-11-22|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]) and on {{#time:j xg|2022-11-24|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/47|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W47&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:22, 21 November 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24071290 --&gt;

== Tech News: 2022-48 ==

&lt;section begin=&quot;technews-2022-W48&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/48|Translations]] are available.

'''Recent changes'''
* A new preference, “Enable limited width mode”, has been added to the [[Special:Preferences#mw-prefsection-rendering|Vector 2022 skin]]. The preference is also available as a toggle on every page if your monitor is 1600 pixels or wider. It allows for increasing the width of the page for logged-out and logged-in users. [https://phabricator.wikimedia.org/T319449]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-30|en}}. It will be on all wikis from {{#time:j xg|2022-12-01|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-11-29|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]) and on {{#time:j xg|2022-12-01|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]).
* Mathematical formulas shown in SVG image format will no longer have PNG fall-backs for browsers that don't support them. This is part of work to modernise the generation system. Showing only PNG versions was the default option until in February 2018. [https://lists.wikimedia.org/hyperkitty/list/wikimedia-l@lists.wikimedia.org/message/3BGOKWJIZGL4TC4HJ22ICRU2SEPWGCR4/][https://phabricator.wikimedia.org/T311620][https://phabricator.wikimedia.org/T186327]
* On [[phab:P40224|some wikis]] that use flagged revisions, [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs#Special:Contributions|a new checkbox will be added]] to Special:Contributions that enables you to see only the [[mw:Special:MyLanguage/Help:Pending changes|pending changes]] by a user. [https://phabricator.wikimedia.org/T321445]

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] How media is structured in the parser's HTML output will change early next week at [https://wikitech.wikimedia.org/wiki/Deployments/Train#Wednesday group1 wikis] (but not Wikimedia Commons or Meta-Wiki). This change improves the accessibility of content, and makes it easier to write related CSS. You may need to update your site-CSS, or userscripts and gadgets. There are [[mw:Special:MyLanguage/Parsoid/Parser_Unification/Media_structure/FAQ|details on what code to check, how to update the code, and where to report any related problems]]. [https://phabricator.wikimedia.org/T314318]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/48|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W48&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:03, 28 November 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24114342 --&gt;

== Tech News: 2022-49 ==

&lt;section begin=&quot;technews-2022-W49&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/49|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The Wikisources use a tool called ProofreadPage. ProofreadPage uses OpenSeadragon which is an open source tool. The OpenSeadragon JavaScript API has been significantly re-written to support dynamically loading images. The functionality provided by the older version of the API should still work but it is no longer supported. User scripts and gadgets should migrate over to the newer version of the API. The functionality provided by the newer version of the API is [[mw:Extension:Proofread_Page/Page_viewer#JS_API|documented on MediaWiki]]. [https://phabricator.wikimedia.org/T308098][https://www.mediawiki.org/wiki/Extension:Proofread_Page/Edit-in-Sequence]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-12-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-12-07|en}}. It will be on all wikis from {{#time:j xg|2022-12-08|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/49|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W49&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:41, 6 December 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24151590 --&gt;

== Tech News: 2022-50 ==

&lt;section begin=&quot;technews-2022-W50&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/50|Translations]] are available.

'''Recent changes'''
* An [[mw:Special:MyLanguage/Talk pages project/Mobile|A/B test has begun]] at 15 Wikipedias for [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|DiscussionTools on mobile]].  Half of the editors on the [[mw:Reading/Web/Mobile|mobile web site]] will have access to the {{int:discussiontools-replybutton}} tool and other features. [https://phabricator.wikimedia.org/T321961]
* The character &lt;code&gt;=&lt;/code&gt; cannot be used in new usernames, to make usernames work better with templates. Existing usernames are not affected. [https://phabricator.wikimedia.org/T254045]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-12-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-12-14|en}}. It will be on all wikis from {{#time:j xg|2022-12-15|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The HTML markup used by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] to [[mw:Special:MyLanguage/Talk_pages_project/Usability#Phase_1:_Topic_containers|show discussion metadata below section headings]] will be inserted after these headings, not inside of them. This change improves the accessibility of discussion pages for screen reader software. [https://phabricator.wikimedia.org/T314714]

'''Events'''
* The fourth edition of the [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award]] will happen online on [https://zonestamp.toolforge.org/1671210002 Friday 16 December 2022 at 17:00 UTC]! The event will be live-streamed on YouTube in the [https://www.youtube.com/user/watchmediawiki MediaWiki channel] and added to Commons afterwards.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/50|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W50&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:34, 12 December 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24216570 --&gt;

== Tech News: 2022-51 ==

&lt;section begin=&quot;technews-2022-W51&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/51|Translations]] are available.

'''Tech News'''
* Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 9 January 2023.

'''Recent changes'''
* On a user's contributions page, you can filter it for edits with a tag like 'reverted'. Now, you can also filter for all edits that are not tagged like that. This was part of a Community Wishlist 2022 request. [https://phabricator.wikimedia.org/T119072]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new function has been used for gadget developers to add content underneath the title on article pages. This is considered a stable API that should work across all skins. [[mw:Special:MyLanguage/ResourceLoader/Core_modules#addSubtitle|Documentation is available]]. [https://phabricator.wikimedia.org/T316830]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[test2wiki:|One of our test wikis]] is now being served from a new infrastructure powered by [[w:Kubernetes|Kubernetes]] ([[wikitech:MediaWiki On Kubernetes|read more]]). More Wikis will switch to this new infrastructure in early 2023. Please test and let us know of any issues. [https://phabricator.wikimedia.org/T290536]

'''Problems'''
* Last week, all wikis had no edit access for 9 minutes. This was caused by a database problem. [https://wikitech.wikimedia.org/wiki/Incidents/2022-12-13_sessionstore]

'''Changes later this week'''
* There is no new MediaWiki version this week or next week.
* The word &quot;{{int:discussiontools-replybutton}}&quot; is very short in some languages, such as Arabic (&quot;&lt;bdi lang=&quot;ar&quot;&gt;ردّ&lt;/bdi&gt;&quot;). This makes the {{int:discussiontools-preference-label}} button on talk pages difficult to use. An arrow icon will be added to those languages. This will only be visible to editors who have the [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] turned on. [https://www.mediawiki.org/wiki/Talk_pages_project/Usability#Status] [https://phabricator.wikimedia.org/T323537]

'''Future changes'''
* Edits can be automatically &quot;tagged&quot; by the system software or the {{int:Abusefilter}} system. Those tags link to a help page about the tags. Soon they will also link to Recent Changes to let you see other edits tagged this way. This was a Community Wishlist 2022 request. [https://phabricator.wikimedia.org/T301063]
* The Trust &amp; Safety tools team [[m:Special:MyLanguage/Private Incident Reporting System/Timeline and Updates|have shared new plans]] for building the Private Incident Reporting System. The system will make it easier for editors to ask for help if they are harassed or abused. 
* [[m:Special:MyLanguage/Community Wishlist Survey 2021/Real Time Preview for Wikitext|Realtime Preview for Wikitext]] is coming out of beta as an enabled feature for every user of the 2010 Wikitext [[mw:Special:MyLanguage/Editor|editor]] in the week of January 9, 2023. It will be available to use via the toolbar in the 2010 Wikitext editor. The feature was the 4th most popular wish of the Community Wishlist Survey 2021.

'''Events'''
* You can now [[mw:Special:MyLanguage/Wikimedia Hackathon 2023/Participate|register for the Wikimedia Hackathon 2023]], taking place on May 19–21 in Athens, Greece. You can also apply for a scholarship until January 14th.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2022/51|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2022-W51&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:00, 20 December 2022 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24258101 --&gt;

== Tech News: 2023-02 ==

&lt;section begin=&quot;technews-2023-W02&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/02|Translations]] are available.

'''Recent changes'''
* You can use tags to filter edits in the recent changes feed or on your watchlist. You can now use tags to filter out edits you don't want to see. Previously you could only use tags to focus on the edits with those tags. [https://phabricator.wikimedia.org/T174349]
* [[Special:WhatLinksHere|Special:WhatLinksHere]] shows all pages that link to a specific page. There is now a [https://wlh.toolforge.org prototype] for how to sort those pages alphabetically. You can see the discussion in the [[phab:T4306|Phabricator ticket]].
* You can now use the [[mw:Special:MyLanguage/Extension:Thanks|thanks]] function on your watchlist and the user contribution page. [https://phabricator.wikimedia.org/T51541]
* A wiki page can be moved to give it a new name. You can now get a dropdown menu with common reasons when you move a page. This is so you don't have to write the explanation every time. [https://phabricator.wikimedia.org/T325257]
* [[m:Special:MyLanguage/Matrix.org|Matrix]] is a chat tool. You can now use &lt;code&gt;matrix:&lt;/code&gt; to create Matrix links on wiki pages. [https://phabricator.wikimedia.org/T326021]
* You can filter out translations when you look at the recent changes on multilingual wikis. This didn't hide translation pages. You can now also hide subpages which are translation pages. [https://phabricator.wikimedia.org/T233493]

'''Changes later this week'''
* [[m:Special:MyLanguage/Real Time Preview for Wikitext|Realtime preview for wikitext]] is a tool which lets editors preview the page when they edit wikitext. It will be enabled for all users of the 2010 wikitext editor. You will find it in the editor toolbar.
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2023-01-10|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2023-01-12|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]).
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-11|en}}. It will be on all wikis from {{#time:j xg|2023-01-12|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/02|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W02&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:07, 10 January 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24342971 --&gt;

== Tech News: 2023-03 ==

&lt;section begin=&quot;technews-2023-W03&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/03|Translations]] are available.

'''Problems'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The URLs in &quot;{{int:last}}&quot; links on page history now contain &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;diff=prev&amp;oldid=[revision ID]&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; in place of &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;diff=[revision ID]&amp;oldid=[revision ID]&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. This is to fix a problem with links pointing to incorrect diffs when history was filtered by a tag. Some user scripts may break as a result of this change. [https://phabricator.wikimedia.org/T243569]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-18|en}}. It will be on all wikis from {{#time:j xg|2023-01-19|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* Some [[mw:Special:MyLanguage/Talk pages project/Usability|changes to the appearance of talk pages]] have only been available on &lt;code&gt;{{ns:1}}:&lt;/code&gt; and &lt;code&gt;{{ns:3}}:&lt;/code&gt; namespaces.  These will be extended to other talk namespaces, such as &lt;code&gt;{{ns:5}}:&lt;/code&gt;.  They will continue to be unavailable in non-talk namespaces, including &lt;code&gt;{{ns:4}}:&lt;/code&gt; pages (e.g., at the Village Pump).  You can [[Special:Preferences#mw-prefsection-editing-discussion|change your preferences]] ([[Special:Preferences#mw-prefsection-betafeatures|beta feature]]). [https://phabricator.wikimedia.org/T325417]
*On Wikisources, when an image is zoomed or panned in the Page: namespace, the same zoom and pan settings will be remembered for all Page: namespace pages that are linked to a particular Index: namespace page. [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/ProofreadPage/+/868841]
* The Vector 2022 skin will become the default for the English Wikipedia desktop users. The change will take place on January 18 at 15:00 UTC. [[:en:w:Wikipedia:Vector 2022|Learn more]].

'''Future changes'''
* The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]], which invites contributors to make technical proposals and vote for tools and improvements, starts next week on 23 January 2023 at 18:00 UTC. You can start drafting your proposals in [[m:Community Wishlist Survey/Sandbox|the CWS sandbox]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/03|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W03&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:10, 17 January 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24381020 --&gt;

== Tech News: 2023-04 ==

&lt;section begin=&quot;technews-2023-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/04|Translations]] are available.

'''Problems'''
* Last week, for ~15 minutes, all wikis were unreachable for logged-in users and non-cached pages. This was caused by a timing issue. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-17_MediaWiki]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-25|en}}. It will be on all wikis from {{#time:j xg|2023-01-26|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* If you have the Beta Feature for [[mw:Special:MyLanguage/Talk pages project|DiscussionTools]] enabled, the appearance of talk pages will add more information about discussion activity. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/Usability#Status][https://phabricator.wikimedia.org/T317907]
* The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]] (CWS), which invites contributors to make technical proposals and vote for tools and improvements, starts on Monday 23 January 2023 at [https://zonestamp.toolforge.org/1674496814 18:00 UTC]. 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W04&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:46, 23 January 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24418874 --&gt;

== Tech News: 2023-05 ==

&lt;section begin=&quot;technews-2023-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/05|Translations]] are available.

'''Problems'''
* Last week, for ~15 minutes, some users were unable to log in or edit pages. This was caused by a problem with session storage. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-24_sessionstore_quorum_issues]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-01|en}}. It will be on all wikis from {{#time:j xg|2023-02-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Wikis that use localized numbering schemes for references need to add new CSS. This will help to show citation numbers the same way in all reading and editing modes. If your wiki would prefer to do it yourselves, please see the [[mw:Special:MyLanguage/Parsoid/Parser Unification/Cite CSS|details and example CSS to copy from]], and also add your wiki to the list. Otherwise, the developers will directly help out starting the week of February 5.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W05&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:05, 31 January 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24455949 --&gt;

== Tech News: 2023-06 ==

&lt;section begin=&quot;technews-2023-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/06|Translations]] are available.

'''Recent changes'''
* In the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022 skin]], logged-out users using the full-width toggle will be able to see the setting of their choice even after refreshing pages or opening new ones. This only applies to wikis where Vector 2022 is the default. [https://phabricator.wikimedia.org/T321498]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-08|en}}. It will be on all wikis from {{#time:j xg|2023-02-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* Previously, we announced when some wikis would be in read-only for a few minutes because of a switch of their main database. These switches will not be announced any more, as the read-only time has become non-significant. Switches will continue to happen at 7AM UTC on Tuesdays and Thursdays. [https://phabricator.wikimedia.org/T292543#8568433]
* Across all the wikis, in the Vector 2022 skin, logged-in users will see the page-related links such as &quot;What links here&quot; in a [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Features/Page_tools|new side menu]]. It will be displayed on the other side of the screen. This change had previously been made on Czech, English, and Vietnamese Wikipedias. [https://phabricator.wikimedia.org/T328692]
*[[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] will stop receiving new proposals on [https://zonestamp.toolforge.org/1675706431 Monday, 6 February 2023, at 18:00 UTC]. Proposers should complete any edits by then, to give time for [[m:Special:MyLanguage/Community_Wishlist_Survey/Help_us|translations]] and review. Voting will begin on Friday, 10 February.

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Gadgets and user scripts will be changing to load on desktop and mobile sites. Previously they would only load on the desktop site. It is recommended that wiki administrators audit the [[MediaWiki:Gadgets-definition|gadget definitions]] prior to this change, and add &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;skins=…&lt;/code&gt;&lt;/bdi&gt; for any gadgets which should not load on mobile. [https://phabricator.wikimedia.org/T328610 More details are available].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W06&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 10:21, 6 February 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24491749 --&gt;

== Tech News: 2023-07 ==

&lt;section begin=&quot;technews-2023-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/07|Translations]] are available.

'''Problems'''
* On wikis where patrolled edits are enabled, changes made to the [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list|mentor list]] by autopatrolled mentors are not correctly marked as patrolled. It will be fixed later this week. [https://phabricator.wikimedia.org/T328444]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-15|en}}. It will be on all wikis from {{#time:j xg|2023-02-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* The Reply tool and other parts of [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|DiscussionTools]] will be deployed for all editors using the mobile site.  You can [[mw:Special:MyLanguage/Talk_pages_project/Mobile#Status_Updates|read more about this decision]]. [https://phabricator.wikimedia.org/T298060]

'''Future changes'''
* All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W07&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:48, 14 February 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24540832 --&gt;

== Tech News: 2023-08 ==

&lt;section begin=&quot;technews-2023-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/08|Translations]] are available.

'''Problems'''
* Last week, during planned maintenance of Cloud Services, unforeseen complications forced the team to turn off all tools for 2–3 hours to prevent data corruption. Work is ongoing to prevent similar problems in the future. [https://phabricator.wikimedia.org/T329535] 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-22|en}}. It will be on all wikis from {{#time:j xg|2023-02-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
*The voting phase for the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] ends on [https://zonestamp.toolforge.org/1677261621 24 February at 18:00 UTC]. The results of the survey will be announced on 28 February.

'''Future changes'''
* All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W08&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:57, 21 February 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24570514 --&gt;

== Tech News: 2023-09 ==

&lt;section begin=&quot;technews-2023-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/09|Translations]] are available.

'''Problems'''
* Last week, in some areas of the world, there were problems with loading pages for 20 minutes and saving edits for 55 minutes. These issues were caused by a problem with our caching servers due to unforseen events during a routine maintenance task. [https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_wiki_outage][https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_read_only] 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-01|en}}. It will be on all wikis from {{#time:j xg|2023-03-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W09&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:47, 27 February 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24634242 --&gt;

== Tech News: 2023-10 ==

&lt;section begin=&quot;technews-2023-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/10|Translations]] are available.

'''Recent changes'''
* The Community Wishlist Survey 2023 edition has been concluded. Community Tech has [[m:Special:MyLanguage/Community Wishlist Survey 2023/Results|published the results]] of the survey and will provide an update on what is next in April 2023.
* On wikis which use [[mw:Special:MyLanguage/Writing_systems|LanguageConverter]] to handle multiple writing systems, articles which used custom conversion rules in the wikitext (primarily on Chinese Wikipedia) would have these rules applied inconsistently in the table of contents, especially in the Vector 2022 skin. This has now been fixed. [https://phabricator.wikimedia.org/T306862]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-08|en}}. It will be on all wikis from {{#time:j xg|2023-03-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* A search system has been added to the [[Special:Preferences|Preferences screen]]. This will let you find different options more easily. Making it work on mobile devices will happen soon. [https://phabricator.wikimedia.org/T313804]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W10&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:49, 6 March 2023 (UTC)
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== Tech News: 2023-11 ==

&lt;section begin=&quot;technews-2023-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/11|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-15|en}}. It will be on all wikis from {{#time:j xg|2023-03-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-cbk_zamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cdowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cebwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ckbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-csbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-itwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304542][https://phabricator.wikimedia.org/T304550] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W11&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:20, 13 March 2023 (UTC)
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== Tech News: 2023-12 ==

&lt;section begin=&quot;technews-2023-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/12|Translations]] are available.

'''Problems'''
* Last week, some users experienced issues loading image thumbnails. This was due to incorrectly cached images. [https://phabricator.wikimedia.org/T331820]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-22|en}}. It will be on all wikis from {{#time:j xg|2023-03-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A link to the user's [[{{#special:CentralAuth}}]] page will appear on [[{{#special:Contributions}}]] — some user scripts which previously added this link may cause conflicts. This feature request was [[:m:Community Wishlist Survey 2023/Admins and patrollers/Add link to CentralAuth on Special:Contributions|voted #17 in the 2023 Community Wishlist Survey]].
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[{{#special:AbuseFilter}}]] edit window will be resizable and larger by default. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Make the AbuseFilter edit window resizable and larger by default|voted #80 in the 2023 Community Wishlist Survey]].
* There will be a new option for Administrators when they are unblocking a user, to add the unblocked user’s user page to their watchlist. This will work both via [[{{#special:Unblock}}]] and via the API. [https://phabricator.wikimedia.org/T257662]

'''Meetings'''
* You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1679677204 24 March at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia Apps/Office Hours|details and how to join]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W12&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:25, 21 March 2023 (UTC)
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== Tech News: 2023-13 ==

&lt;section begin=&quot;technews-2023-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/13|Translations]] are available.

'''Recent changes'''
* The [[:mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] condition limit was increased from 1000 to 2000. [https://phabricator.wikimedia.org/T309609]
* [[:m:Special:MyLanguage/Global AbuseFilter#Locally disabled actions|Some Global AbuseFilter]] actions will no longer apply to local projects. [https://phabricator.wikimedia.org/T332521]
* Desktop users are now able to subscribe to talk pages by clicking on the {{int:discussiontools-newtopicssubscription-button-subscribe-label}} link in the {{int:toolbox}} menu. If you subscribe to a talk page, you receive [[mw:Special:MyLanguage/Notifications|notifications]] when new topics are started on that talk page. This is separate from putting the page on your watchlist or subscribing to a single discussion. [https://phabricator.wikimedia.org/T263821]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-29|en}}. It will be on all wikis from {{#time:j xg|2023-03-30|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]).

'''Future changes'''
* You will be able to choose [[mw:Special:MyLanguage/VisualEditor/Diffs|visual diffs]] on all [[m:Special:MyLanguage/Help:Page history|history pages]] at the Wiktionaries and Wikipedias. [https://phabricator.wikimedia.org/T314588]
* [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The legacy [[mw:Mobile Content Service|Mobile Content Service]] is going away in July 2023. Developers are encouraged to switch to Parsoid or another API before then to ensure service continuity. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/4MVQQTONJT7FJAXNVOFV3WWVVMCHRINE/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W13&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:13, 28 March 2023 (UTC)
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== Tech News: 2023-14 ==

&lt;section begin=&quot;technews-2023-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/14|Translations]] are available.

'''Recent changes'''
* The system for automatically creating categories for the [[mw:Special:MyLanguage/Extension:Babel|Babel]] extension has had several important changes and fixes. One of them allows you to insert templates for automatic category descriptions on creation, allowing you to categorize the new categories. [https://phabricator.wikimedia.org/T211665][https://phabricator.wikimedia.org/T64714][https://phabricator.wikimedia.org/T170654][https://phabricator.wikimedia.org/T184941][https://phabricator.wikimedia.org/T33074]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-05|en}}. It will be on all wikis from {{#time:j xg|2023-04-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Some older [[w:en:Web browser|Web browsers]] will stop being able to use [[w:en:JavaScript|JavaScript]] on Wikimedia wikis from this week. This mainly affects users of Internet Explorer 11. If you have an old web browser on your computer you can try to upgrade to a newer version. [https://phabricator.wikimedia.org/T178356]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The deprecated &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;jquery.hoverIntent&lt;/code&gt;&lt;/bdi&gt; module has been removed. This module could be used by gadgets and user scripts, to create an artificial delay in how JavaScript responds to a hover event. Gadgets and user scripts should now use jQuery &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;hover()&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;on()&lt;/code&gt;&lt;/bdi&gt; instead. Examples can be found in the [[mw:Special:MyLanguage/ResourceLoader/Migration_guide_(users)#jquery.hoverIntent|migration guide]]. [https://phabricator.wikimedia.org/T311194]
* Some of the links in [[{{#special:SpecialPages}}]] will be re-arranged. There will be a clearer separation between links that relate to all users, and links related to your own user account. [https://phabricator.wikimedia.org/T333242]
* You will be able to hide the [[mw:Special:MyLanguage/Talk pages project/Replying|Reply button]] in archived discussion pages with a new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;__ARCHIVEDTALK__&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; magic word.  There will also be a new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.mw-archivedtalk&lt;/code&gt;&lt;/bdi&gt; CSS class for hiding the Reply button in individual sections on a page. [https://phabricator.wikimedia.org/T249293][https://phabricator.wikimedia.org/T295553][https://gerrit.wikimedia.org/r/c/mediawiki/extensions/DiscussionTools/+/738221]

'''Future changes'''
* The Vega software that creates data visualizations in pages, such as graphs, will be upgraded to the newest version in the future. Graphs that still use the very old version 1.5 syntax may stop working properly. Most existing uses have been found and updated, but you can help to check, and to update any local documentation. [[phab:T260542|Examples of how to find and fix these graphs are available]]. 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W14&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:39, 3 April 2023 (UTC)
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== Tech News: 2023-15 ==

&lt;section begin=&quot;technews-2023-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/15|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] In the visual editor, it is now possible to edit captions of images in galleries without opening the gallery dialog. This feature request was [[:m:Community Wishlist Survey 2023/Editing/Editable gallery captions in Visual Editor|voted #61 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T190224]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] You can now receive notifications when another user edits your user page. See the &quot;{{int:Echo-category-title-edit-user-page}}&quot; option in [[Special:Preferences#mw-prefsection-echo|your Preferences]]. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Notifications for user page edits|voted #3 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T3876]

'''Problems'''
* There was a problem with all types of CentralNotice banners still being shown to logged-in users even if they had [[Special:Preferences#mw-prefsection-centralnotice-banners|turned off]] specific banner types. This has now been fixed. [https://phabricator.wikimedia.org/T331671]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-12|en}}. It will be on all wikis from {{#time:j xg|2023-04-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-arywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dinwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-elwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-emlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-etwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-euwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-extwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tumwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ffwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiu_vrowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-furwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gcrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gomwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gotwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-guwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304551][https://phabricator.wikimedia.org/T308133]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W15&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:05, 10 April 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=24851886 --&gt;

== Tech News: 2023-16 ==

&lt;section begin=&quot;technews-2023-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/16|Translations]] are available.

'''Recent changes'''
* You can now see [[mw:Special:MyLanguage/Help:Extension:Kartographer#Show_nearby_articles|nearby articles on a Kartographer map]] with the button for the new feature &quot;{{int:Kartographer-sidebar-nearbybutton}}&quot;. Six wikis have been testing this feature since October. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Nearby_articles#Implementation][https://phabricator.wikimedia.org/T334079]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[m:Special:GlobalWatchlist|Special:GlobalWatchlist]] page now has links for &quot;{{int:globalwatchlist-markpageseen}}&quot; for each entry. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Button to mark a single change as read in the global watch list|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334246]

'''Problems'''
* At Wikimedia Commons, some thumbnails have not been getting replaced correctly after a new version of the image is uploaded. This should be fixed later this week. [https://phabricator.wikimedia.org/T331138][https://phabricator.wikimedia.org/T333042]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] For the last few weeks, some external tools had inconsistent problems with logging-in with OAuth. This has now been fixed. [https://phabricator.wikimedia.org/T332650]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-19|en}}. It will be on all wikis from {{#time:j xg|2023-04-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W16&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:54, 18 April 2023 (UTC)
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== Tech News: 2023-17 ==

&lt;section begin=&quot;technews-2023-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/17|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The date-selection menu on pages such as [[{{#special:Contributions}}]] will now show year-ranges that are in the current and past decade, instead of the current and future decade. This feature request was [[m:Community Wishlist Survey 2023/Miscellaneous/Change year range shown in date selection popup|voted #145 in the 2023 Community Wishlist Survey]].  [https://phabricator.wikimedia.org/T334316]

'''Problems'''
* Due to security issues with the [[mw:Special:MyLanguage/Extension:Graph|Graph extension]], graphs have been disabled in all Wikimedia projects. Wikimedia Foundation teams are working to respond to these vulnerabilities. [https://phabricator.wikimedia.org/T334940]
* For a few days, it was not possible to save some kinds of edits on the mobile version of a wiki. This has been fixed. [https://phabricator.wikimedia.org/T334797][https://phabricator.wikimedia.org/T334799][https://phabricator.wikimedia.org/T334794]

'''Changes later this week'''
* All wikis will be read-only for a few minutes on April 26. This is planned for [https://zonestamp.toolforge.org/1682517653 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch]
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-26|en}}. It will be on all wikis from {{#time:j xg|2023-04-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''Future changes'''
* The Editing team plans an A/B test for [[mw:Special:MyLanguage/Talk pages project/Usability|a usability analysis of the Talk page project]]. The [[mw:Special:MyLanguage/Talk pages project/Usability/Analysis|planned measurements are available]]. Your wiki [[phab:T332946|may be invited to participate]]. Please suggest improvements to the measurement plan at [[mw:Talk:Talk pages project/Usability|the discussion page]].
* [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2023-2024|The Wikimedia Foundation annual plan 2023-2024 draft is open for comment and input]] until May 19. The final plan will be published in July 2023 on Meta-wiki.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W17&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:03, 24 April 2023 (UTC)
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== Tech News: 2023-18 ==

&lt;section begin=&quot;technews-2023-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/18|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the French and Italian Wikipedias. More languages will be added in the near future. This is part of the [[m:Community Wishlist Survey 2023/Reading/Extend &quot;Who Wrote That?&quot; tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T243711][https://phabricator.wikimedia.org/T270490][https://phabricator.wikimedia.org/T334891]
* The [[:commons:Special:MyLanguage/Commons:Video2commons|Video2commons]] tool has been updated. This fixed several bugs related to YouTube uploads. [https://github.com/toolforge/video2commons/pull/162/commits]
* The [[{{#special:Preferences}}]] page has been redesigned on mobile web. The new design makes it easier to browse the different categories and settings at low screen widths. You can also now access the page via a link in the Settings menu in the mobile web sidebar. [https://www.mediawiki.org/wiki/Moderator_Tools/Content_moderation_on_mobile_web/Preferences]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-03|en}}. It will be on all wikis from {{#time:j xg|2023-05-04|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W18&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:45, 2 May 2023 (UTC)
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== Tech News: 2023-19 ==

&lt;section begin=&quot;technews-2023-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/19|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] Last week, Community Tech released the first update for providing [[m:Special:MyLanguage/Community Wishlist Survey 2022/Better diff handling of paragraph splits|better diffs]], the #1 request in the 2022 Community Wishlist Survey. [[phab:T324759|This update]] adds legends and tooltips to inline diffs so that users unfamiliar with the blue and yellow highlights can better understand the type of edits made.
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] When you close an image that is displayed via MediaViewer, it will now return to the wiki page instead of going back in your browser history. This feature request was [[m:Community Wishlist Survey 2023/Reading/Return to the article when closing the MediaViewer|voted #65 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T236591]
* The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|SyntaxHighlight]] extension now supports &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;wikitext&lt;/code&gt;&lt;/bdi&gt; as a selected language. Old alternatives that were used to highlight wikitext, such as &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;html5&lt;/code&gt;&lt;/bdi&gt;, &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;moin&lt;/code&gt;&lt;/bdi&gt;, and &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;html+handlebars&lt;/code&gt;&lt;/bdi&gt;, can now be replaced. [https://phabricator.wikimedia.org/T29828]
* [[mw:Special:MyLanguage/Manual:Creating pages with preloaded text|Preloading text to new pages/sections]] now supports preloading from localized MediaWiki interface messages. [https://cs.wikipedia.org/wiki/User_talk:Martin_Urbanec_(WMF)?action=edit&amp;section=new&amp;preload=MediaWiki:July Here is an example] at the {{int:project-localized-name-cswiki/en}} that uses &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;preload=MediaWiki:July&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. [https://phabricator.wikimedia.org/T330337]

'''Problems'''
* Graph Extension update: Foundation developers have completed upgrading the visualization software to Vega5. Existing community graphs based on Vega2 are no longer compatible. Communities need to update local graphs and templates, and shared lua modules like &lt;bdi lang=&quot;de&quot; dir=&quot;ltr&quot;&gt;[[:de:Modul:Graph]]&lt;/bdi&gt;. The [https://vega.github.io/vega/docs/porting-guide/ Vega Porting guide] provides the most comprehensive detail on migration from Vega2 and [https://www.mediawiki.org/w/index.php?title=Template:Graph:PageViews&amp;action=history here is an example migration]. Vega5 has currently just been enabled on mediawiki.org to provide a test environment for communities. [https://phabricator.wikimedia.org/T334940#8813922]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-10|en}}. It will be on all wikis from {{#time:j xg|2023-05-11|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Until now, all new OAuth apps went through manual review. Starting this week, apps using identification-only or basic authorizations will not require review. [https://phabricator.wikimedia.org/T67750]

'''Future changes'''
* During the next year, MediaWiki will stop using IP addresses to identify logged-out users, and will start automatically assigning unique temporary usernames. Read more at [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates|IP Editing: Privacy Enhancement and Abuse Mitigation/Updates]]. You can [[m:Talk:IP Editing: Privacy Enhancement and Abuse Mitigation#What should it look like?|join the discussion]] about the [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates#What will temporary usernames look like?|format of the temporary usernames]]. [https://phabricator.wikimedia.org/T332805]
* There will be an [[:w:en:A/B testing|A/B test]] on 10 Wikipedias where the Vector 2022 skin is the default skin. Half of logged-in desktop users will see an interface where the different parts of the page are more clearly separated. You can [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2023-05 Zebra9 A/B test|read more]]. [https://phabricator.wikimedia.org/T333180][https://phabricator.wikimedia.org/T335972]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] &lt;code&gt;jquery.tipsy&lt;/code&gt; will be removed from the MediaWiki core. This will affect some user scripts. Many lines with &lt;code&gt;.tipsy(&lt;/code&gt; can be commented out. &lt;code&gt;OO.ui.PopupWidget&lt;/code&gt; can be used to keep things working like they are now. You can [[phab:T336019|read more]] and [[:mw:Help:Locating broken scripts|read about how to find broken scripts]]. [https://phabricator.wikimedia.org/T336019]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W19&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:36, 9 May 2023 (UTC)
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== Tech News: 2023-20 ==

&lt;section begin=&quot;technews-2023-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/20|Translations]] are available.

'''Problems'''
* Citations that are automatically generated based on [[d:Q33057|ISBN]] are currently broken. This affects citations made with the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]], and the use of the citoid API in gadgets and user scripts. Work is ongoing to restore this feature. [https://phabricator.wikimedia.org/T336298] 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-17|en}}. It will be on all wikis from {{#time:j xg|2023-05-18|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-gorwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hakwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hifwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-htwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-igwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ilowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-inhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308134] 

'''Future changes'''
* There is a recently formed team at the Wikimedia Foundation which will be focusing on experimenting with new tools. Currently they are building [[m:Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI|a prototype ChatGPT plugin that allows information generated by ChatGPT to be properly attributed]] to the Wikimedia projects.
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget and userscript developers should replace &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;jquery.cookie&lt;/code&gt;&lt;/bdi&gt; with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mediawiki.cookie&lt;/code&gt;&lt;/bdi&gt;. The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;jquery.cookie&lt;/code&gt;&lt;/bdi&gt; library will be removed in ~1 month, and staff developers will run a script to replace any remaining uses at that time. [https://phabricator.wikimedia.org/T336018]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W20&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:45, 15 May 2023 (UTC)
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== Tech News: 2023-21 ==

&lt;section begin=&quot;technews-2023-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/21|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The &quot;recent edits&quot; time period for page watchers is now 30 days. It used to be 180 days. This was a [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Change information about the number of watchers on a page|Community Wishlist Survey proposal]]. [https://phabricator.wikimedia.org/T336250]

'''Changes later this week'''
* An [[mw:special:MyLanguage/Growth/Positive reinforcement#Impact|improved impact module]] will be available at Wikipedias. The impact module is a feature available to newcomers [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer homepage|at their personal homepage]]. It will show their number of edits, how many readers their edited pages have, how many thanks they have received and similar things. It is also accessible by accessing Special:Impact. [https://phabricator.wikimedia.org/T336203]
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-24|en}}. It will be on all wikis from {{#time:j xg|2023-05-25|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W21&quot;/&gt;

16:55, 22 May 2023 (UTC)
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== Tech News: 2023-22 ==

&lt;section begin=&quot;technews-2023-W22&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/22|Translations]] are available.

'''Recent changes'''
* Citations can once again be added automatically from ISBNs, thanks to Zotero's ISBN searches. The current data sources are the Library of Congress (United States), the Bibliothèque nationale de France (French National Library), and K10plus ISBN (German repository). Additional data source searches can be [[mw:Citoid/Creating Zotero translators|proposed to Zotero]]. The ISBN labels in the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]] will reappear later this week. [https://phabricator.wikimedia.org/T336298#8859917]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The page [[{{#special:EditWatchlist}}]] now has &quot;{{int:watchlistedit-normal-check-all}}&quot; options to select all the pages within a namespace. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Watchlist edit - &quot;check all&quot; checkbox|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334252]	

'''Problems'''
* For a few days earlier this month, the &quot;Add interlanguage link&quot; item in the Tools menu did not work properly. This has now been fixed. [https://phabricator.wikimedia.org/T337081]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-31|en}}. It will be on all wikis from {{#time:j xg|2023-06-01|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* VisualEditor will be switched to a new backend on [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/small.dblist small] and [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/medium.dblist medium] wikis this week. Large wikis will follow in the coming weeks. This is part of the effort to move Parsoid into MediaWiki core. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/22|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W22&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:03, 29 May 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25079963 --&gt;

== Tech News: 2023-23 ==

&lt;section begin=&quot;technews-2023-W23&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/23|Translations]] are available.

'''Recent changes'''
* The [[:mw:Special:MyLanguage/Help:Extension:RealMe|RealMe]] extension allows you to mark URLs on your user page as verified for Mastodon and similar software.
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] Citation and footnote editing can now be started from the reference list when using the visual editor. This feature request was [[m:Community Wishlist Survey 2023/Citations/Allow citations to be edited in the references section with VisualEditor|voted #2 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T54750]
* Previously, clicking on someone else's link to Recent Changes with filters applied within the URL could unintentionally change your preference for &quot;{{int:Rcfilters-group-results-by-page}}&quot;. This has now been fixed. [https://phabricator.wikimedia.org/T202916#8874081]

'''Problems'''
* For a few days last week, some tools and bots returned outdated information due to database replication problems, and may have been down entirely while it was being fixed. These issues have now been fixed. [https://phabricator.wikimedia.org/T337446]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-07|en}}. It will be on all wikis from {{#time:j xg|2023-06-08|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Bots will no longer be prevented from making edits because of URLs that match the [[mw:Special:MyLanguage/Extension:SpamBlacklist|spam blacklist]]. [https://phabricator.wikimedia.org/T313107]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/23|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W23&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:52, 5 June 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25114640 --&gt;

== Tech News: 2023-24 ==

&lt;section begin=&quot;technews-2023-W24&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/24|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the Dutch, German, Hungarian, Indonesian, Japanese, Polish and Portuguese Wikipedias. This was the [[m:Community Wishlist Survey 2023/Reading/Extend &quot;Who Wrote That?&quot; tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334891]
* The [[mw:Special:MyLanguage/Structured Data Across Wikimedia/Search Improvements#Search Preview panel|Search Preview panel]] has been deployed on four Wikipedias (Catalan, Dutch, Hungarian and Norwegian). The panel will show an image related to the article (if existing), the top sections of the article, related images (coming from MediaSearch on Commons), and eventually the sister projects associated with the article. [https://phabricator.wikimedia.org/T306341]
* The [[:mw:Special:MyLanguage/Help:Extension:RealMe#Verifying_a_link_on_non-user_pages|RealMe]] extension now allows administrators to verify URLs for any page, for Mastodon and similar software. [https://phabricator.wikimedia.org/T324937]
* The default project license [https://lists.wikimedia.org/hyperkitty/list/wikimediaannounce-l@lists.wikimedia.org/thread/7G6XPWZPQFLZ2JANN3ZX6RT4DVUI3HZQ/ has been officially upgraded] to CC BY-SA 4.0. The software interface messages have been updated. Communities should feel free to start updating any mentions of the old CC BY-SA 3.0 licensing within policies and related documentation pages. [https://phabricator.wikimedia.org/T319064]

'''Problems'''
* For three days last month, some Wikipedia pages edited with VisualEditor or DiscussionTools had an unintended &lt;code&gt;&lt;nowiki&gt;__TOC__&lt;/nowiki&gt;&lt;/code&gt; (or its localized form) added during an edit. There is [[mw:Parsoid/Deployments/T336101_followup|a listing of affected pages sorted by wiki]], that may still need to be fixed. [https://phabricator.wikimedia.org/T336101]
* Currently, the &quot;{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}&quot; feature in VisualEditor is broken. Existing &lt;code&gt;&lt;nowiki&gt;{{DEFAULTSORT:...}}&lt;/nowiki&gt;&lt;/code&gt; keywords incorrectly appear as missing templates in VisualEditor. Developers are exploring how to fix this. In the meantime, those wishing to edit the default sortkey of a page are advised to switch to source editing. [https://phabricator.wikimedia.org/T337398]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Last week, an update to the delete form may have broken some gadgets or user scripts. If you need to manipulate (empty) the reason field, replace &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;#wpReason&lt;/code&gt;&lt;/bdi&gt; with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot; style=&quot;white-space: nowrap;&quot;&gt;&lt;code&gt;#wpReason &gt; input&lt;/code&gt;&lt;/bdi&gt;. See [https://cs.wikipedia.org/w/index.php?title=MediaWiki%3AGadget-CleanDeleteReasons.js&amp;diff=22859956&amp;oldid=12794189 an example fix]. [https://phabricator.wikimedia.org/T337809]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-14|en}}. It will be on all wikis from {{#time:j xg|2023-06-15|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* VisualEditor will be switched to a new backend on English Wikipedia on Monday, and all other [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/large.dblist large] wikis on Thursday. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529]

'''Future changes'''
* From 5 June to 17 July, the Foundation's [[:mw:Wikimedia Security Team|Security team]] is holding a consultation with contributors regarding a draft policy to govern the use of third-party resources in volunteer-developed gadgets and scripts. Feedback and suggestions are warmly welcome at [[m:Special:MyLanguage/Third-party resources policy|Third-party resources policy]] on meta-wiki.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/24|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W24&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 14:51, 12 June 2023 (UTC)
&lt;!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25133779 --&gt;

== Tech News: 2023-25 ==

&lt;section begin=&quot;technews-2023-W25&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/25|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Flame graphs are now available in WikimediaDebug. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/JXNQD3EHG5V5QW5UXFDPSHQG4MJ3FWJQ/][https://techblog.wikimedia.org/2023/06/08/flame-graphs-arrive-in-wikimediadebug/]

'''Changes later this week'''
* There is no new MediaWiki version this week.
* There is now a toolbar search popup in the visual editor. You can trigger it by typing &lt;code&gt;\&lt;/code&gt; or pressing &lt;code&gt;ctrl + shift + p&lt;/code&gt;. It can help you quickly access most tools in the editor. [https://commons.wikimedia.org/wiki/File:Visual_editor_toolbar_search_feature.png][https://phabricator.wikimedia.org/T66905]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/25|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W25&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:08, 19 June 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25159510 --&gt;

== Tech News: 2023-26 ==

&lt;section begin=&quot;technews-2023-W26&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/26|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Action API modules and Special:LinkSearch will now add a trailing &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;/&lt;/code&gt;&lt;/bdi&gt; to all &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;prop=extlinks&lt;/code&gt;&lt;/bdi&gt; responses for bare domains. This is part of the work to remove duplication in the &lt;code&gt;externallinks&lt;/code&gt; database table. [https://phabricator.wikimedia.org/T337994]

'''Problems'''
* Last week, search was broken on Commons and Wikidata for 23 hours. [https://phabricator.wikimedia.org/T339810][https://wikitech.wikimedia.org/wiki/Incidents/2023-06-18_search_broken_on_wikidata_and_commons]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-28|en}}. It will be on all wikis from {{#time:j xg|2023-06-29|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Minerva skin now applies more predefined styles to the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.mbox-text&lt;/code&gt;&lt;/bdi&gt; CSS class. This enables support for mbox templates that use divs instead of tables. Please make sure that the new styles won't affect other templates in your wiki. [https://gerrit.wikimedia.org/r/c/mediawiki/skins/MinervaNeue/+/930901/][https://phabricator.wikimedia.org/T339040]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadgets will now load on both desktop and mobile by default. Previously, gadgets loaded only on desktop by default. Changing this default using the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;|targets=&lt;/code&gt;&lt;/bdi&gt; parameter is also deprecated and should not be used. You should make gadgets work on mobile or disable them based on the skin (with the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;|skins=&lt;/code&gt;&lt;/bdi&gt; parameter in &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;MediaWiki:Gadgets-definition&lt;/bdi&gt;) rather than whether the user uses the mobile or the desktop website. Popular gadgets that create errors on mobile will be disabled by developers on the Minerva skin as a temporary solution. [https://phabricator.wikimedia.org/T127268]
* All namespace tabs now have the same browser [[m:Special:MyLanguage/Help:Keyboard_shortcuts|access key]] by default. Previously, custom and extension-defined namespaces would have to have their access keys set manually on-wiki, but that is no longer necessary. [https://phabricator.wikimedia.org/T22126]
* The review form of the Flagged Revisions extension now uses the standardized [[mw:Special:MyLanguage/Codex|user interface components]]. [https://phabricator.wikimedia.org/T191156]

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] How media is structured in the parser's HTML output will change in the coming weeks at [[:wikitech:Deployments/Train#Thursday|group2 wikis]]. This change improves the accessibility of content. You may need to update your site-CSS, or userscripts and gadgets. There are [[mw:Special:MyLanguage/Parsoid/Parser_Unification/Media_structure/FAQ|details on what code to check, how to update the code, and where to report any related problems]]. [https://phabricator.wikimedia.org/T314318]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/26|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W26&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:18, 26 June 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25202311 --&gt;

== Tech News: 2023-27 ==

&lt;section begin=&quot;technews-2023-W27&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/27|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the rolling out of the [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|audio links that play on click]] wishlist proposal, [https://noc.wikimedia.org/conf/highlight.php?file=dblists/small.dblist small wikis] will now be able to use the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline audio player mode|inline audio player]] that is implemented by the [[mw:Extension:Phonos|Phonos]] extension. [https://phabricator.wikimedia.org/T336763]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] From this week all gadgets automatically load on mobile and desktop sites. If you see any problems with gadgets on your wikis, please adjust the [[mw:Special:MyLanguage/Extension:Gadgets#Options|gadget options]] in your gadget definitions file. [https://phabricator.wikimedia.org/T328610]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-05|en}}. It will be on all wikis from {{#time:j xg|2023-07-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/27|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W27&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:51, 3 July 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25231546 --&gt;

== Tech News: 2023-28 ==

&lt;section begin=&quot;technews-2023-W28&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/28|Translations]] are available.

'''Recent changes'''
* The [[:mw:Special:MyLanguage/Structured Data Across Wikimedia/Section-level Image Suggestions|Section-level Image Suggestions feature]] has been deployed on seven Wikipedias (Portuguese, Russian, Indonesian, Catalan, Hungarian, Finnish and Norwegian Bokmål). The feature recommends images for articles on contributors' watchlists that are a good match for individual sections of those articles.
* [[:m:Special:MyLanguage/Global AbuseFilter|Global abuse filters]] have been enabled on all Wikimedia projects, except English and Japanese Wikipedias (who opted out). This change was made following a [[:m:Requests for comment/Make global abuse filters opt-out|global request for comments]]. [https://phabricator.wikimedia.org/T341159]
* [[{{#special:BlockedExternalDomains}}]] is a new tool for administrators to help fight spam. It provides a clearer interface for blocking plain domains (and their subdomains), is more easily searchable, and is faster for the software to process for each edit on the wiki. It does not support regex (for complex cases), nor URL path-matching, nor the [[MediaWiki:Spam-whitelist|MediaWiki:Spam-whitelist]], but otherwise it replaces most of the functionalities of the existing [[MediaWiki:Spam-blacklist|MediaWiki:Spam-blacklist]]. There is a Python script to help migrate all simple domains into this tool, and more feature details, within [[mw:Special:MyLanguage/Manual:BlockedExternalDomains|the tool's documentation]]. It is available at all wikis except for Meta-wiki, Commons, and Wikidata. [https://phabricator.wikimedia.org/T337431]
* The WikiEditor extension was updated. It includes some of the most frequently used features of wikitext editing. In the past, many of its messages could only be translated by administrators, but now all regular translators on translatewiki can translate them. Please check [https://translatewiki.net/wiki/Special:MessageGroupStats?group=ext-wikieditor&amp;messages=&amp;x=D#sortable:0=asc the state of WikiEditor localization into your language], and if the &quot;Completion&quot; for your language shows anything less than 100%, please complete the translation. See [https://lists.wikimedia.org/hyperkitty/list/wikitech-ambassadors@lists.wikimedia.org/thread/D4YELU2DXMZ75PGELUOKXXMFF3FH45XA/ a more detailed explanation].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-12|en}}. It will be on all wikis from {{#time:j xg|2023-07-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* The default protocol of [[{{#special:LinkSearch}}]] and API counterparts has changed from http to both http and https. [https://phabricator.wikimedia.org/T14810]
* [[{{#special:LinkSearch}}]] and its API counterparts will now search for all of the URL provided in the query. It used to be only the first 60 characters. This feature was requested fifteen years ago. [https://phabricator.wikimedia.org/T17218]

'''Future changes'''
* There is an experiment with a [[:w:en:ChatGPT|ChatGPT]] plugin. This is to show users where the information is coming from when they read information from Wikipedia. It has been tested by Wikimedia Foundation staff and other Wikimedians. Soon all ChatGPT plugin users can use the Wikipedia plugin. This is the same plugin which was mentioned in [[m:Special:MyLanguage/Tech/News/2023/20|Tech News 2023/20]]. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI]
* There is an ongoing discussion on a [[m:Special:MyLanguage/Third-party resources policy|proposed Third-party resources policy]]. The proposal will impact the use of third-party resources in gadgets and userscripts. Based on the ideas received so far, policy includes some of the risks related to user scripts and gadgets loading third-party resources, some best practices and exemption requirements such as code transparency and inspectability. Your feedback and suggestions are warmly welcome until July 17, 2023 on [[m:Talk:Third-party resources policy|on the policy talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/28|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W28&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:54, 10 July 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25278797 --&gt;

== Tech News: 2023-29 ==

&lt;section begin=&quot;technews-2023-W29&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/29|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] We are now serving 1% of all global user traffic from [[w:en:Kubernetes|Kubernetes]] (you can [[wikitech:MediaWiki On Kubernetes|read more technical details]]). We are planning to increment this percentage regularly. You can [[phab:T290536|follow the progress of this work]]. 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-19|en}}. It will be on all wikis from {{#time:j xg|2023-07-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki [[mw:Special:MyLanguage/Help:System_message|system messages]] will now look for available local fallbacks, instead of always using the default fallback defined by software. This means wikis no longer need to override each language on the [[mw:Special:MyLanguage/Manual:Language#Fallback_languages|fallback chain]] separately. For example, English Wikipedia doesn't have to create &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;en-ca&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;en-gb&lt;/code&gt;&lt;/bdi&gt; subpages with a transclusion of the base pages anymore. This makes it easier to maintain local overrides. [https://phabricator.wikimedia.org/T229992]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;action=growthsetmentorstatus&lt;/code&gt;&lt;/bdi&gt; API will be deprecated with the new MediaWiki version. Bots or scripts calling that API should use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;action=growthmanagementorlist&lt;/code&gt;&lt;/bdi&gt; API now. [https://phabricator.wikimedia.org/T321503]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/29|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W29&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:08, 17 July 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25289122 --&gt;

== Tech News: 2023-30 ==

&lt;section begin=&quot;technews-2023-W30&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/30|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]]   On July 18, the Wikimedia Foundation launched a survey about the [[:mw:Technical_decision_making|technical decision making process]] for people who do technical work that relies on software that is maintained by the Foundation or affiliates. If this applies to you, [https://wikimediafoundation.limesurvey.net/885471 please take part in the survey]. The survey will be open for three weeks, until August 7. You can find more information in [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/Q7DUCFA75DXG3G2KHTO7CEWMLCYTSDB2/|the announcement e-mail on wikitech-l]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-26|en}}. It will be on all wikis from {{#time:j xg|2023-07-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/30|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W30&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 02:20, 25 July 2023 (UTC)
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== Tech News: 2023-31 ==

&lt;section begin=&quot;technews-2023-W31&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/31|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Synchronizer|Synchronizer]] tool is now available to keep Lua modules synced across Wikimedia wikis, along with [[mw:Multilingual Templates and Modules|updated documentation]] to develop global Lua modules and templates.
* The tag filter on [[{{#special:NewPages}}]] and revision history pages can now be inverted. For example, you can hide edits that were made using an automated tool. [https://phabricator.wikimedia.org/T334337][https://phabricator.wikimedia.org/T334338]
* The Wikipedia [[:w:en:ChatGPT|ChatGPT]] plugin experiment can now be used by ChatGPT users who can use plugins. You can participate in a [[:m:Talk:Wikimedia Foundation Annual Plan/2023-2024/Draft/Future Audiences#Announcing monthly Future Audiences open &quot;office hours&quot;|video call]] if you want to talk about this experiment or similar work. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI]

'''Problems'''
* It was not possible to generate a PDF for pages with non-Latin characters in the title, for the last two weeks. This has now been fixed. [https://phabricator.wikimedia.org/T342442]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-02|en}}. It will be on all wikis from {{#time:j xg|2023-08-03|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Tuesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-kawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kaawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kabwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-knwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kshwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kwwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308135] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/31|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W31&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:54, 31 July 2023 (UTC)
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== Tech News: 2023-32 ==

&lt;section begin=&quot;technews-2023-W32&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/32|Translations]] are available.

'''Recent changes'''
* Mobile Web editors can now [[mw:Special:MyLanguage/Reading/Web/Advanced_mobile_contributions#August_1,_2023_-_Full-page_editing_added_on_mobile|edit a whole page at once]]. To use this feature, turn on &quot;{{int:Mobile-frontend-mobile-option-amc}}&quot; in your settings and use the &quot;{{int:Minerva-page-actions-editfull}}&quot; button in the &quot;{{int:Minerva-page-actions-overflow}}&quot; menu. [https://phabricator.wikimedia.org/T203151]

'''Changes later this week'''
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/32|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W32&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:20, 7 August 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25420038 --&gt;

== Tech News: 2023-33 ==

&lt;section begin=&quot;technews-2023-W33&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/33|Translations]] are available.

'''Recent changes'''
* The Content translation system is no longer using Youdao's [[mw:Special:MyLanguage/Help:Content_translation/Translating/Initial_machine_translation|machine translation service]]. The service was in place for several years, but due to no usage, and availability of alternatives, it was deprecated to reduce maintenance overheads. Other services which cover the same languages are still available. [https://phabricator.wikimedia.org/T329137]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-16|en}}. It will be on all wikis from {{#time:j xg|2023-08-17|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-lawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ladwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lezwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lfnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-liwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lijwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lmowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ltgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-maiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-map_bmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mdfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kywiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308136] &lt;!-- TODO replace wiki codes --&gt;

'''Future changes'''
* A few gadgets/user scripts which add icons to the Minerva skin need to have their CSS updated. There are more details available including a [[phab:T344067|search for all existing instances and how to update them]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/33|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W33&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 05:59, 15 August 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25428668 --&gt;

== Tech News: 2023-34 ==

&lt;section begin=&quot;technews-2023-W34&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/34|Translations]] are available.

'''Recent changes'''
* The [https://gdrive-to-commons.toolforge.org/ GDrive to Commons Uploader] tool is now available. It enables [[m:Special:MyLanguage/GDrive to Commons Uploader|securely selecting and uploading files]] from your Google Drive directly to Wikimedia Commons. [https://phabricator.wikimedia.org/T267868]
* From now on, we will announce new Wikimedia wikis in Tech News, so you can update any tools or pages.
** Since the last edition, two new wikis have been created:
*** a Wiktionary in [[d:Q7121294|Pa'O]] ([[wikt:blk:|&lt;code&gt;wikt:blk:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T343540]
*** a Wikisource in [[d:Q34002|Sundanese]] ([[s:su:|&lt;code&gt;s:su:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T343539]
** To catch up, the next most recent six wikis are:
*** Wikifunctions ([[f:|&lt;code&gt;f:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T275945]
*** a Wiktionary in [[d:Q2891049|Mandailing]] ([[wikt:btm:|&lt;code&gt;wikt:btm:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T335216]
*** a Wikipedia in [[d:Q5555465|Ghanaian Pidgin]] ([[w:gpe:|&lt;code&gt;w:gpe:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T335969]
*** a Wikinews in [[d:Q3111668|Gungbe]] ([[n:guw:|&lt;code&gt;n:guw:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T334394]
*** a Wiktionary in [[d:Q33522|Kabardian]] ([[wikt:kbd:|&lt;code&gt;wikt:kbd:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T333266]
*** a Wikipedia in [[d:Q35570|Fante]] ([[w:fat:|&lt;code&gt;w:fat:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T335016]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-23|en}}. It will be on all wikis from {{#time:j xg|2023-08-24|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There is an existing [[mw:Stable interface policy|stable interface policy]] for MediaWiki backend code. There is a [[mw:User:Jdlrobson/Stable interface policy/frontend|proposed stable interface policy for frontend code]]. This is relevant for anyone who works on gadgets or Wikimedia frontend code. You can read it, discuss it, and let the proposer know if there are any problems. [https://phabricator.wikimedia.org/T344079]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/34|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W34&quot;/&gt;

15:25, 21 August 2023 (UTC)
&lt;!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25497111 --&gt;

== Tech News: 2023-35 ==

&lt;section begin=&quot;technews-2023-W35&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/35|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Community Wishlist Survey 2022/Better diff handling of paragraph splits|better diff handling of paragraph splits]], improved detection of splits is being rolled out. Over the last two weeks, we deployed this support to [[wikitech:Deployments/Train#Groups|group0]] and group1 wikis. This week it will be deployed to group2 wikis. [https://phabricator.wikimedia.org/T341754]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] All [[{{#special:Contributions}}]] pages now show the user's local edit count and the account's creation date. [https://phabricator.wikimedia.org/T324166]
* Wikisource users can now use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;prpbengalicurrency&lt;/code&gt;&lt;/bdi&gt; label to denote Bengali currency characters as page numbers inside the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;pagelist&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; tag.  [https://phabricator.wikimedia.org/T268932]
* Two preferences have been relocated. The preference &quot;{{int:visualeditor-preference-visualeditor}}&quot; is now shown on the [[Special:Preferences#mw-prefsection-editing|&quot;{{int:prefs-editing}}&quot; tab]] at all wikis. Previously it was shown on the &quot;{{int:prefs-betafeatures}}&quot; tab at some wikis. The preference &quot;{{int:visualeditor-preference-newwikitexteditor-enable}}&quot; is now also shown on the &quot;{{int:prefs-editing}}&quot; tab at all wikis, instead of the &quot;{{int:prefs-betafeatures}}&quot; tab. [https://phabricator.wikimedia.org/T335056][https://phabricator.wikimedia.org/T344158]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-30|en}}. It will be on all wikis from {{#time:j xg|2023-08-31|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] New signups for a Wikimedia developer account will start being pushed towards &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://idm.wikimedia.org/ idm.wikimedia.org]&lt;/bdi&gt;, rather than going via Wikitech. [[wikitech:IDM|Further information about the new system is available]].
* All right-to-left language wikis, plus Korean, Armenian, Ukrainian, Russian, and Bulgarian Wikipedias, will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. This feature will come to more wikis in future weeks. [https://phabricator.wikimedia.org/T267921]

'''Future changes'''
* The removal of the [[mw:Special:MyLanguage/Extension:DoubleWiki|DoubleWiki extension]] is being discussed. This extension currently allows Wikisource users to view articles from multiple language versions side by side when the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;=&gt;&lt;/code&gt;&lt;/bdi&gt; symbol next to a specific language edition is selected. Comments on this are welcomed at [[phab:T344544|the phabricator task]].
* A proposal has been made to merge the second hidden-categories list (which appears below the wikitext editing form) with the main list of categories (which is further down the page). [[phab:T340606|More information is available on Phabricator]]; feedback is welcome!

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/35|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W35&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 14:00, 28 August 2023 (UTC)
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== Tech News: 2023-36 ==

&lt;section begin=&quot;technews-2023-W36&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/36|Translations]] are available.

'''Recent changes'''
* [[m:Wikisource_EditInSequence|EditInSequence]], a feature that allows users to edit pages faster on Wikisource has been moved to a Beta Feature based on community feedback. To enable it, you can navigate to the [[Special:Preferences#mw-prefsection-betafeatures|beta features tab in Preferences]]. [https://phabricator.wikimedia.org/T308098]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Generate Audio for IPA|Generate Audio for IPA]] and [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|Audio links that play on click]] wishlist proposals, the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline_audio_player_mode|inline audio player mode]] of [[mw:Extension:Phonos|Phonos]] has been deployed to all projects. [https://phabricator.wikimedia.org/T336763]
* There is a new option for Administrators when they are changing the usergroups for a user, to add the user’s user page to their watchlist. This works both via [[{{#special:UserRights}}]] and via the API. [https://phabricator.wikimedia.org/T272294]
* One new wiki has been created:
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q34318|Talysh]] ([[w:tly:|&lt;code&gt;w:tly:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T345166]
'''Problems'''
* The [[mw:Special:MyLanguage/Extension:LoginNotify|LoginNotify extension]] was not sending notifications since January. It has now been fixed, so going forward, you may see notifications for failed login attempts, and successful login attempts from a new device. [https://phabricator.wikimedia.org/T344785]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-06|en}}. It will be on all wikis from {{#time:j xg|2023-09-07|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-mhrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-miwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-minwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mtwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mwlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-myvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mznwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-napwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ndswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nds_nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-novwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nqowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nrmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nsowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ocwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-olowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-omwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-orwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-oswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pagwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-papwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pcdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pdcwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pflwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pihwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pnbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pntwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pswiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308137][https://phabricator.wikimedia.org/T308138]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/36|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W36&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:33, 4 September 2023 (UTC)
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== Tech News: 2023-37 ==

&lt;section begin=&quot;technews-2023-W37&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/37|Translations]] are available.

'''Recent changes'''
* [[mw:Special:MyLanguage/ORES|ORES]], the revision evaluation service, is now using a new open-source infrastructure on all wikis except for English Wikipedia and Wikidata. These two will follow this week. If you notice any unusual results from the Recent Changes filters that are related to ORES (for example, &quot;{{int:ores-rcfilters-damaging-title}}&quot; and &quot;{{int:ores-rcfilters-goodfaith-title}}&quot;), please [[mw:Talk:Machine Learning|report them]]. [https://phabricator.wikimedia.org/T342115]
* When you are logged in on one Wikimedia wiki and visit a different Wikimedia wiki, the system tries to log you in there automatically. This has been unreliable for a long time. You can now visit the login page to make the system try extra hard. If you feel that made logging in better or worse than it used to be, your feedback is appreciated. [https://phabricator.wikimedia.org/T326281]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-13|en}}. It will be on all wikis from {{#time:j xg|2023-09-14|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/Technical decision making|Technical Decision-Making Forum Retrospective]] team invites anyone involved in the technical field of Wikimedia projects to signup to and join [[mw:Technical decision making/Listening Sessions|one of their listening sessions]] on 13 September. Another date will be scheduled later. The goal is to improve the technical decision-making processes.
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Better diff handling of paragraph splits|Better diff handling of paragraph splits]] wishlist proposal, the inline switch widget in diff pages is being rolled out this week to all wikis. The inline switch will allow viewers to toggle between a unified inline or two-column diff wikitext format. [https://phabricator.wikimedia.org/T336716]

'''Future changes'''
* All wikis will be read-only for a few minutes on 20 September. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T345263]
* The Enterprise API is launching a new feature called &quot;[http://breakingnews-beta.enterprise.wikimedia.com/ breaking news]&quot;. Currently in BETA, this attempts to identify likely &quot;newsworthy&quot; topics as they are currently being written about in any Wikipedia. Your help is requested to improve the accuracy of its detection model, especially on smaller language editions, by recommending templates or identifiable editing patterns. See more information at [[mw:Special:MyLanguage/Wikimedia Enterprise/Breaking news|the documentation page]] on MediaWiki or [[m:Special:MyLanguage/Wikimedia Enterprise/FAQ#What is Breaking News|the FAQ]] on Meta.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/37|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W37&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:07, 11 September 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25589064 --&gt;

== Tech News: 2023-38 ==

&lt;section begin=&quot;technews-2023-W38&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/38|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki now has a [[mw:Stable interface policy/frontend|stable interface policy for frontend code]] that more clearly defines how we deprecate MediaWiki code and wiki-based code (e.g. gadgets and user scripts). Thank you to everyone who contributed to the content and discussions. [https://phabricator.wikimedia.org/T346467][https://phabricator.wikimedia.org/T344079]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-20|en}}. It will be on all wikis from {{#time:j xg|2023-09-21|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* All wikis will be read-only for a few minutes on September 20. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] [https://phabricator.wikimedia.org/T345263]
* All wikis will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. [https://phabricator.wikimedia.org/T267921]

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The team investigating the Graph Extension posted [[mw:Extension:Graph/Plans#Proposal|a proposal for reenabling it]] and they need your input.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/38|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W38&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:19, 18 September 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25623533 --&gt;

== Tech News: 2023-39 ==

&lt;section begin=&quot;technews-2023-W39&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/39|Translations]] are available.

'''Recent changes'''
* The Vector 2022 skin will now remember the pinned/unpinned status for the Table of Contents for all logged-out users. [https://phabricator.wikimedia.org/T316060]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-27|en}}. It will be on all wikis from {{#time:j xg|2023-09-28|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The ResourceLoader &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;mediawiki.ui&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; modules are now deprecated as part of the move to Vue.js and Codex. There is a [[mw:Codex/Migrating_from_MediaWiki_UI|guide for migrating from MediaWiki UI to Codex]] for any tools that use it. More [[phab:T346468|details are available in the task]] and your questions are welcome there.
* Gadget definitions will have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new &quot;namespaces&quot; option]]. The option takes a list of namespace IDs. Gadgets that use this option will only load on pages in the given namespaces.

'''Future changes'''
* New variables will be added to [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]]: &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;global_account_groups&lt;/bdi&gt;&lt;/code&gt; and &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;global_account_editcount&lt;/bdi&gt;&lt;/code&gt;. They are available only when an account is being created. You can use them to prevent blocking automatic creation of accounts when users with many edits elsewhere visit your wiki for the first time. [https://phabricator.wikimedia.org/T345632][https://www.mediawiki.org/wiki/Special:MyLanguage/Extension:AbuseFilter/Rules_format]

'''Meetings'''
* You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1698426015 27 October at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia_Apps/Office_Hours#October_2023|details and how to join]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/39|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W39&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:51, 26 September 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25655264 --&gt;

== Tech News: 2023-40 ==

&lt;section begin=&quot;technews-2023-W40&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/40|Translations]] are available.

'''Recent changes'''
* There is a new [[Special:Preferences#mw-prefsection-rendering-advancedrendering|user preference]] for &quot;{{int:tog-forcesafemode}}&quot;. This setting will make pages load without including any on-wiki JavaScript or on-wiki stylesheet pages. It can be useful for debugging broken JavaScript gadgets. [https://phabricator.wikimedia.org/T342347]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget definitions now have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new &quot;&lt;var&gt;contentModels&lt;/var&gt;&quot; option]]. The option takes a list of page content models, like &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;wikitext&lt;/bdi&gt;&lt;/code&gt; or &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;css&lt;/bdi&gt;&lt;/code&gt;. Gadgets that use this option will only load on pages with the given content models.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.29|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-04|en}}. It will be on all wikis from {{#time:j xg|2023-10-05|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Vector 2022 skin will no longer use the custom styles and scripts of Vector legacy (2010). The change will be made later this year or in early 2024. See [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|how to adjust the CSS and JS pages on your wiki]]. [https://phabricator.wikimedia.org/T331679]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/40|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W40&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:26, 3 October 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25686930 --&gt;

== Tech News: 2023-41 ==

&lt;section begin=&quot;technews-2023-W41&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/41|Translations]] are available.

'''Recent changes'''
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q33291|Fon]] ([[w:fon:|&lt;code&gt;w:fon:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T347935]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.30|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-11|en}}. It will be on all wikis from {{#time:j xg|2023-10-12|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-swwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-warwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xalwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xmfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zeawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zh_min_nanwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zuwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308139]
* At some wikis, newcomers are suggested images from Commons to add to articles without any images. Starting on Tuesday, newcomers at these wikis will be able to add images to unillustrated article sections. The specific wikis are listed under &quot;Images recommendations&quot; [[mw:Special:MyLanguage/Growth/Deployment table|at the Growth team deployment table]]. You can [[mw:Special:MyLanguage/Help:Growth/Tools/Add an image|learn more about this feature.]] [https://phabricator.wikimedia.org/T345940]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In the mobile web skin (Minerva) the CSS ID &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;#page-actions&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; will be replaced with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;#p-views&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. This change is to make it consistent with other skins and to improve support for gadgets and extensions in the mobile skin. A few gadgets may need to be updated; there are [https://phabricator.wikimedia.org/T348267 details and search-links in the task].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/41|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W41&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 14:39, 9 October 2023 (UTC)
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== Tech News: 2023-42 ==

&lt;section begin=&quot;technews-2023-W42&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/42|Translations]] are available.

'''Recent changes'''
* The [[m:Special:MyLanguage/Help:Unified login|Unified login]] system's edge login should now be fixed for some browsers (Chrome, Edge, Opera). This means that if you visit a new sister project wiki, you should be logged in automatically without the need to click &quot;Log in&quot; or reload the page. Feedback on whether it's working for you is welcome. [https://phabricator.wikimedia.org/T347889]
* [[mw:Special:MyLanguage/Manual:Interface/Edit_notice|Edit notices]] are now available within the MobileFrontend/Minerva skin. This feature was inspired by [[w:en:Wikipedia:EditNoticesOnMobile|the gadget on English Wikipedia]]. See more details in [[phab:T316178|T316178]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-18|en}}. It will be on all wikis from {{#time:j xg|2023-10-19|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]).

'''Future changes'''
* In 3 weeks, in the Vector 2022 skin, code related to &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;addPortletLink&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;#p-namespaces&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; that was deprecated one year ago will be removed. If you notice tools that should appear next to the &quot;Discussion&quot; tab are then missing, please tell the gadget's maintainers to see [[phab:T347907|instructions in the Phabricator task]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/42|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W42&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:47, 16 October 2023 (UTC)
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== Tech News: 2023-43 ==

&lt;section begin=&quot;technews-2023-W43&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/43|Translations]] are available.

'''Recent changes'''
* There is a new [[mw:Special:MyLanguage/Wikimedia Language engineering/Newsletter/2023/October|Language and internationalization newsletter]], written quarterly. It contains updates on new feature development, improvements in various language-related technical projects, and related support work.
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Source map support has been enabled on all wikis. When you open the debugger in your browser's developer tools, you should be able to see the unminified JavaScript source code. [https://phabricator.wikimedia.org/T47514]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-25|en}}. It will be on all wikis from {{#time:j xg|2023-10-26|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/43|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W43&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:16, 23 October 2023 (UTC)
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== Tech News: 2023-44 ==

&lt;section begin=&quot;technews-2023-W44&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/44|Translations]] are available.

'''Recent changes'''
* The Structured Content team, as part of its project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]], made some UX improvements to the upload step of choosing own vs not own work ([[phab:T347590|T347590]]), as well as to the licensing step for own work ([[phab:T347756|T347756]]).
* The Design Systems team has released version 1.0.0 of [[wmdoc:codex/latest/|Codex]], the new design system for Wikimedia. See the [[mw:Special:MyLanguage/Design_Systems_Team/Announcing_Codex_1.0|full announcement about the release of Codex 1.0.0]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-01|en}}. It will be on all wikis from {{#time:j xg|2023-11-02|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]).
* Listings on category pages are sorted on each wiki for that language using a [[:w:en:International Components for Unicode|library]]. For a brief period on 2 November, changes to categories will not be sorted correctly for many languages. This is because the developers are upgrading to a new version of the library. They will then use a script to fix the existing categories. This will take a few hours or a few days depending on how big the wiki is. You can [[mw:Special:MyLanguage/Wikimedia Technical Operations/ICU announcement|read more]]. [https://phabricator.wikimedia.org/T345561][https://phabricator.wikimedia.org/T267145] 
* Starting November 1, the impact module (Special:Impact) will be upgraded by the Growth team. The new impact module shows newcomers more data regarding their impact on the wiki. It was tested by a few wikis during the last few months. [https://phabricator.wikimedia.org/T336203]

'''Future changes'''
* There is [[mw:Special:MyLanguage/Extension:Graph/Plans#Roadmap|a proposed plan]] for re-enabling the Graph Extension. You can help by reviewing this proposal and [[mw:Extension_talk:Graph/Plans#c-PPelberg_(WMF)-20231020221600-Update:_20_October|sharing what you think about it]].
* The WMF is working on making it possible for administrators to [[mw:Special:MyLanguage/Community_configuration_2.0|edit MediaWiki configuration directly]]. This is similar to previous work on Special:EditGrowthConfig. [[phab:T349757|A technical RfC is running until November 08, where you can provide feedback.]] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/44|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W44&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:21, 30 October 2023 (UTC)
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== Tech News: 2023-45 ==

&lt;section begin=&quot;technews-2023-W45&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/45|Translations]] are available.

'''Recent changes'''
* In the Vector 2022 skin, the default font-size of a number of navigational elements (tagline, tools menu, navigational links, and more) has been increased slightly to match the font size used in page content. [https://phabricator.wikimedia.org/T346062]

'''Problems'''
* Last week, there was a problem displaying some recent edits on [https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist a few wikis], for 1-6 hours. The edits were saved but not immediately shown. This was due to a database problem. [https://phabricator.wikimedia.org/T350443]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-08|en}}. It will be on all wikis from {{#time:j xg|2023-11-09|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]).
* The Growth team will reassign newcomers from former mentors to [[mw:Special:MyLanguage/Growth/Structured mentor list|the currently active mentors]]. They have also changed the notification language to be more user-friendly. [https://phabricator.wikimedia.org/T330071][https://phabricator.wikimedia.org/T327493]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/45|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W45&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:05, 6 November 2023 (UTC)
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== Tech News: 2023-46 ==

&lt;section begin=&quot;technews-2023-W46&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/46|Translations]] are available.

'''Recent changes'''
* Four new wikis have been created:
** a Wikipedia in [[d:Q7598268|Moroccan Amazigh]] ([[w:zgh:|&lt;code&gt;w:zgh:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T350216]
** a Wikipedia in [[d:Q35159|Dagaare]] ([[w:dga:|&lt;code&gt;w:dga:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T350218]
** a Wikipedia in [[d:Q33017|Toba Batak]] ([[w:bbc:|&lt;code&gt;w:bbc:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T350320]
** a Wikiquote in [[d:Q33151|Banjar]] ([[q:bjn:|&lt;code&gt;q:bjn:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T350217]

'''Problems'''
* Last week, users who previously visited Meta-Wiki or Wikimedia Commons and then became logged out on those wikis could not log in again. The problem is now resolved. [https://phabricator.wikimedia.org/T350695]
* Last week, some pop-up dialogs and menus were shown with the wrong font size. The problem is now resolved. [https://phabricator.wikimedia.org/T350544]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-15|en}}. It will be on all wikis from {{#time:j xg|2023-11-16|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]).

'''Future changes'''
* Reference Previews are coming to many wikis as a default feature. They are popups for references, similar to the [[mw:Special:MyLanguage/Page Previews|PagePreviews feature]]. [[m:WMDE Technical Wishes/ReferencePreviews#Opt-out feature|You can opt out]] of seeing them. If you are [[Special:Preferences#mw-prefsection-gadgets|using the gadgets]] Reference Tooltips or Navigation Popups, you won’t see Reference Previews. [[phab:T282999|Deployment]] is planned for November 22, 2023. 
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Canary (also known as heartbeat) events will be produced into [https://stream.wikimedia.org/?doc#/streams Wikimedia event streams] from December 11. Streams users are advised to filter out these events, by discarding all events where &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;meta.domain == &quot;canary&quot;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. Updates to [[mw:Special:MyLanguage/Manual:Pywikibot|Pywikibot]] or [https://github.com/ChlodAlejandro/wikimedia-streams wikimedia-streams] will discard these events by default. [https://phabricator.wikimedia.org/T266798]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/46|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W46&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:52, 13 November 2023 (UTC)
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== Tech News: 2023-47 ==

&lt;section begin=&quot;technews-2023-W47&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/47|Translations]] are available.

'''Changes later this week'''
* There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Starting on Wednesday, a new set of Wikipedias will get &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot; ({{int:project-localized-name-quwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_rupwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_tarawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ruewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rwwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-satwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-shwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-siwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-skwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-slwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-smwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-suwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-szlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tcywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tetwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-towiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tpiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ttwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-twwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tyvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-udmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ugwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-uzwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vecwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vepwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vlswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vowiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308141][https://phabricator.wikimedia.org/T308142][https://phabricator.wikimedia.org/T308143] 
* The Vector 2022 skin will have some minor visual changes to drop-down menus, column widths, and more. These changes were added to four Wikipedias last week. If no issues are found, these changes will proceed to all wikis this week. These changes will make it possible to add new menus for readability and dark mode. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Updates#November_2023:_Visual_changes,_more_deployments,_and_shifting_focus|Learn more]]. [https://phabricator.wikimedia.org/T347711]

'''Future changes'''
* There is [[mw:Extension talk:Graph/Plans#Update: 15 November|an update on re-enabling the Graph Extension]]. To speed up the process, Vega 2 will not be supported and only [https://phabricator.wikimedia.org/T335325 some protocols] will be available at launch. You can help by sharing what you think about the plan.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/47|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W47&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:55, 21 November 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25884616 --&gt;

== Tech News: 2023-48 ==

&lt;section begin=&quot;technews-2023-W48&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/48|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-29|en}}. It will be on all wikis from {{#time:j xg|2023-11-30|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki's JavaScript system will now allow &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;async&lt;/code&gt;/&lt;code&gt;await&lt;/code&gt;&lt;/bdi&gt; syntax in gadgets and user scripts. Gadget authors should remember that users' browsers may not support it, so it should be used appropriately. [https://phabricator.wikimedia.org/T343499]
* The deployment of &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add_a_link|Add a link]]&quot; announced [[m:Special:MyLanguage/Tech/News/2023/47|last week]] was postponed. It will resume this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/48|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W48&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:08, 27 November 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25906379 --&gt;

== Tech News: 2023-49 ==

&lt;section begin=&quot;technews-2023-W49&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/49|Translations]] are available.

'''Recent changes'''
* The spacing between paragraphs on Vector 2022 has been changed from 7px to 14px to match the size of the text. This will make it easier to distinguish paragraphs from sentences. [https://phabricator.wikimedia.org/T351754]
* The &quot;{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}&quot; feature in VisualEditor is working again. You no longer need to switch to source editing to edit &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;{{DEFAULTSORT:...}}&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; keywords. [https://phabricator.wikimedia.org/T337398]

'''Changes later this week'''
* There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* On 6 December, people who have the enabled the preference for &quot;{{int:Discussiontools-preference-visualenhancements}}&quot; will notice the [[mw:Special:MyLanguage/Talk pages project/Usability|talk page usability improvements]] appear on pages that include the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;__NEWSECTIONLINK__&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; magic word. If you notice any issues, please [[phab:T352232|share them with the team on Phabricator]].

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge [[wikitech:News/Toolforge Grid Engine deprecation|Grid Engine shutdown process]] will start on December 14. Maintainers of [[toolforge:grid-deprecation|tools that still use this old system]] should plan to migrate to Kubernetes, or tell the team your plans on Phabricator in the task about your tool, before that date. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/VIWWQKMSQO2ED3TVUR7KPPWRTOBYBVOA/]
* Communities using [[mw:Special:MyLanguage/Structured_Discussions|Structured Discussions]] are being contacted regarding [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|the upcoming deprecation of Structured Discussions]]. You can read more about this project, and share your comments, [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|on the project's page]].

'''Events'''
* Registration &amp; Scholarship applications are now open for the [[mw:Special:MyLanguage/Wikimedia Hackathon 2024|Wikimedia Hackathon 2024]] that will take place from 3–5 May in Tallinn, Estonia. Scholarship applications are open until 5 January 2024.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/49|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W49&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:50, 4 December 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25914435 --&gt;

== Tech News: 2023-50 ==

&lt;section begin=&quot;technews-2023-W50&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/50|Translations]] are available.

'''Recent changes'''
* On Wikimedia Commons, there are some minor user-interface improvements for the &quot;choosing own vs not own work&quot; step in the UploadWizard. This is part of the Structured Content team's project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]]. [https://phabricator.wikimedia.org/T352707][https://phabricator.wikimedia.org/T352709]

'''Problems'''
* There was a problem showing the [[mw:Special:MyLanguage/Growth/Personalized first day/Newcomer homepage|Newcomer homepage]] feature with the &quot;impact module&quot; and their page-view graphs, for a few days in early December. This has now been fixed. [https://phabricator.wikimedia.org/T352352][https://phabricator.wikimedia.org/T352349]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-13|en}}. It will be on all wikis from {{#time:j xg|2023-12-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
* [[File:Octicons-tools.svg|15px|link=]] The [https://wikimediafoundation.limesurvey.net/796964 2023 Developer Satisfaction Survey] is seeking the opinions of the Wikimedia developer community. Please take the survey if you have any role in developing software for the Wikimedia ecosystem. The survey is open until 5 January 2024, and has an associated [[foundation:Legal:December_2023_Developer_Satisfaction_Survey|privacy statement]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/50|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W50&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 02:12, 12 December 2023 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25945501 --&gt;

== Tech News: 2023-51 ==

&lt;section begin=&quot;technews-2023-W51&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/51|Translations]] are available.

'''Tech News'''
* The next issue of Tech News will be sent out on 8 January 2024 because of [[w:en:Christmas and holiday season|the holidays]].

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-20|en}}. It will be on all wikis from {{#time:j xg|2023-12-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Starting December 18, it won't be possible to activate Structured Discussions on a user's own talk page using the Beta feature. The Beta feature option remains available for users who want to deactivate Structured Discussions. This is part of [[mw:Structured Discussions/Deprecation|Structured Discussions' deprecation work]]. [https://phabricator.wikimedia.org/T248309] 
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There will be full support for redirects in the Module namespace. The &quot;Move Page&quot; feature will leave an appropriate redirect behind, and such redirects will be appropriately recognized by the software (e.g. hidden from [[{{#special:UnconnectedPages}}]]). There will also be support for [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Renaming or moving modules|manual redirects]]. [https://phabricator.wikimedia.org/T120794]

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The MediaWiki JavaScript documentation is moving to a new format. During the move, you can read the old docs using [https://doc.wikimedia.org/mediawiki-core/REL1_41/js/ version 1.41]. Feedback about [https://doc.wikimedia.org/mediawiki-core/master/js/ the new site] is welcome on the [[mw:Talk:JSDoc_WMF_theme|project talk page]].
* The Wishathon is a new initiative that encourages collaboration across the Wikimedia community to develop solutions for wishes collected through the [[m:Special:MyLanguage/Community Wishlist Survey|Community Wishlist Survey]]. The first community Wishathon will take place from 15–17 March. If you are interested in a project proposal as a user, developer, designer, or product lead, you can [[m:Special:MyLanguage/Event:WishathonMarch2024|register for the event and read more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2023/51|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2023-W51&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:17, 18 December 2023 (UTC)
&lt;!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=25959059 --&gt;

== Tech News: 2024-02 ==

&lt;section begin=&quot;technews-2024-W02&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/02|Translations]] are available.

'''Recent changes'''
* [https://mediawiki2latex.wmflabs.org/ mediawiki2latex] is a tool that converts wiki content into the formats of LaTeX, PDF, ODT, and EPUB. The code now runs many times faster due to recent improvements. There is also an optional Docker container you can [[b:de:Benutzer:Dirk_Hünniger/wb2pdf/install#Using_Docker|install]] on your local machine.
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The way that Random pages are selected has been updated. This will slowly reduce the problem of some pages having a lower chance of appearing. [https://phabricator.wikimedia.org/T309477]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-10|en}}. It will be on all wikis from {{#time:j xg|2024-01-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/02|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W02&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:19, 9 January 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26026251 --&gt;

== Tech News: 2024-03 ==

&lt;section begin=&quot;technews-2024-W03&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/03|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Pages that use the JSON [[mw:Special:MyLanguage/Manual:ContentHandler|contentmodel]] will now use tabs instead of spaces for auto-indentation. This will significantly reduce the page size. [https://phabricator.wikimedia.org/T326065]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] and personal user scripts may now use JavaScript syntax introduced in ES6 (also known as &quot;ES2015&quot;) and ES7 (&quot;ES2016&quot;). MediaWiki validates the source code to protect other site functionality from syntax errors, and to ensure scripts are valid in all [[mw:Special:MyLanguage/Compatibility#Browsers|supported browsers]]. Previously, Gadgets could use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;requiresES6&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; option. This option is no longer needed and will be removed in the future. [https://phabricator.wikimedia.org/T75714]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Manual:Bot passwords|Bot passwords]] and [[mw:Special:MyLanguage/OAuth/Owner-only consumers|owner-only OAuth consumers]] can now be restricted to allow editing only specific pages. [https://phabricator.wikimedia.org/T349957]
* You can now [[mw:Special:MyLanguage/Extension:Thanks|thank]] edits made by bots. [https://phabricator.wikimedia.org/T341388]
* An update on the status of the Community Wishlist Survey for 2024 [[m:Special:MyLanguage/Community Wishlist Survey/Future Of The Wishlist/January 4, 2024 Update|has been published]]. Please read and give your feedback.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-17|en}}. It will be on all wikis from {{#time:j xg|2024-01-18|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Starting on January 17, it will not be possible to login to Wikimedia wikis from some specific old versions of the Chrome browser (versions 51–66, released between 2016 and 2018). Additionally, users of iOS 12, or Safari on Mac OS 10.14, may need to login to each wiki separately. [https://phabricator.wikimedia.org/T344791]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;jquery.cookie&lt;/code&gt;&lt;/bdi&gt; module was deprecated and replaced with the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mediawiki.cookie&lt;/code&gt;&lt;/bdi&gt; module last year. A script has now been run to replace any remaining uses, and this week the temporary alias will be removed. [https://phabricator.wikimedia.org/T354966]

'''Future changes'''
* Wikimedia Deutschland is working to [[m:WMDE Technical Wishes/Reusing references|make reusing references easier]]. They are looking for people who are interested in participating in [https://wikimedia.sslsurvey.de/User-research-into-Reusing-References-Sign-up-Form-2024/en/ individual video calls for user research in January and February].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/03|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W03&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:13, 16 January 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26074460 --&gt;

== Tech News: 2024-04 ==

&lt;section begin=&quot;technews-2024-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/04|Translations]] are available.

'''Problems'''
* A bug in UploadWizard prevented linking to the userpage of the uploader when uploading. It has now been fixed. [https://phabricator.wikimedia.org/T354529]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-24|en}}. It will be on all wikis from {{#time:j xg|2024-01-25|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W04&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:03, 23 January 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26096197 --&gt;

== Tech News: 2024-05 ==

&lt;section begin=&quot;technews-2024-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/05|Translations]] are available.

'''Recent changes'''
* Starting Monday January 29, all talk pages messages' timestamps will become a link. This link is a permanent link to the comment. It allows users to find the comment they are looking for, even if this comment was moved elsewhere. This will affect all wikis except for the English Wikipedia. You can read more about this change [https://diff.wikimedia.org/2024/01/29/talk-page-permalinks-dont-lose-your-threads/ on Diff] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk_pages_permalinking|on Mediawiki.org]].&lt;!-- The Diff post will be published on Monday morning UTC--&gt; [https://phabricator.wikimedia.org/T302011]
* There are some improvements to the CAPTCHA to make it harder for spam bots and scripts to bypass it. If you have feedback on this change, please comment on [[phab:T141490|the task]]. Staff are monitoring metrics related to the CAPTCHA, as well as secondary metrics such as account creations and edit counts.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-31|en}}. It will be on all wikis from {{#time:j xg|2024-02-01|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] On February 1, a link will be added to the &quot;Tools&quot; menu to download a [[w:en:QR code|QR code]] that links to the page you are viewing. There will also be a new [[{{#special:QrCode}}]] page to create QR codes for any Wikimedia URL. This addresses the [[m:Community Wishlist Survey 2023/Mobile and apps/Add ability to share QR code for a page in any Wikimedia project|#19 most-voted wish]] from the [[m:Community Wishlist Survey 2023/Results|2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T329973]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] which only work in some skins have sometimes used the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;targets&lt;/code&gt;&lt;/bdi&gt; option to limit where you can use them. This will stop working this week. You should use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;skins&lt;/code&gt;&lt;/bdi&gt; option instead. [https://phabricator.wikimedia.org/T328497]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W05&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:31, 29 January 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26137870 --&gt;

== Tech News: 2024-06 ==

&lt;section begin=&quot;technews-2024-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/06|Translations]] are available.

'''Recent changes'''
*The mobile site history pages now use the same HTML as the desktop history pages. If you hear of any problems relating to mobile history usage please point them to [[phab:T353388|the phabricator task]].
*On most wikis, admins can now block users from making specific actions. These actions are: uploading files, creating new pages, moving (renaming) pages, and sending thanks. The goal of this feature is to allow admins to apply blocks that are adequate to the blocked users' activity. [[m:Special:MyLanguage/Community health initiative/Partial blocks#action-blocks|Learn more about &quot;action blocks&quot;]]. [https://phabricator.wikimedia.org/T242541][https://phabricator.wikimedia.org/T280531]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-07|en}}. It will be on all wikis from {{#time:j xg|2024-02-08|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Talk pages permalinks that included diacritics and non-Latin script were malfunctioning. This issue is fixed. [https://phabricator.wikimedia.org/T356199]

'''Future changes'''
* [[m:WMDE Technical Wishes/ReferencePreviews#24WPs|24 Wikipedias]] with [[mw:Special:MyLanguage/Reference_Tooltips|Reference Tooltips]] as a default gadget are encouraged to remove that default flag. This would make [[mw:Special:MyLanguage/Help:Reference_Previews|Reference Previews]] the new default for reference popups, leading to a more consistent experience across wikis. For [[m:WMDE Technical Wishes/ReferencePreviews#46WPs|46 Wikipedias]] with less than 4 interface admins, the change is already scheduled for mid-February, [[m:Talk:WMDE Technical Wishes/ReferencePreviews#Reference Previews to become the default for previewing references on more wikis.|unless there are concerns]]. The older Reference Tooltips gadget will still remain usable and will override this feature, if it is available on your wiki and you have enabled it in your settings. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/ReferencePreviews#Reference_Previews_to_become_the_default_for_previewing_references_on_more_wikis][https://phabricator.wikimedia.org/T355312]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W06&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:22, 5 February 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26180971 --&gt;

== Tech News: 2024-07 ==

&lt;section begin=&quot;technews-2024-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/07|Translations]] are available.

'''Recent changes'''
*  The [[d:Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split experiment]] is working and loaded onto 3 test servers. The team in charge is testing the split's impact and requires feedback from WDQS users through the UI or programmatically in different channels. [https://www.wikidata.org/wiki/Wikidata_talk:SPARQL_query_service/WDQS_graph_split][https://phabricator.wikimedia.org/T356773][https://www.wikidata.org/wiki/User:Sannita_(WMF)] Users' feedback will validate the impact of various use cases and workflows around the Wikidata Query service. [https://www.wikidata.org/wiki/Wikidata:SPARQL_query_service/WDQS_backend_update/October_2023_scaling_update][https://www.mediawiki.org/wiki/Wikidata_Query_Service/User_Manual#Federation]

'''Problems'''
*There was a bug that affected the appearance of visited links when using mobile device to access wiki sites. It made the links appear black; [[phab:T356928|this issue]] is fixed.  

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-14|en}}. It will be on all wikis from {{#time:j xg|2024-02-15|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] As work continues on the grid engine deprecation,[https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation] tools on the grid engine will be stopped starting on February 14th, 2024. If you have tools actively migrating you can ask for an extension so they are not stopped. [https://wikitech.wikimedia.org/wiki/Portal:Toolforge/About_Toolforge#Communication_and_support] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W07&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 05:48, 13 February 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26223994 --&gt;

== Tech News: 2024-08 ==

&lt;section begin=&quot;technews-2024-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/08|Translations]] are available.

'''Recent changes'''
* If you have the &quot;{{int:Tog-enotifwatchlistpages}}&quot; option enabled, edits by bot accounts no longer trigger notification emails. Previously, only minor edits would not trigger the notification emails. [https://phabricator.wikimedia.org/T356984]
* There are changes to how user and site scripts load for [[mw:Special:MyLanguage/Skin:Vector/2022| Vector 2022]] on specific wikis. The changes impacted the following Wikis: all projects with [[mw:Special:MyLanguage/Skin:Vector|Vector legacy]] as the default skin, Wikivoyage, and Wikibooks. Other wikis will be affected over the course of the next three months. Gadgets are not impacted. If you have been affected or want to minimize the impact on your project, see [[Phab:T357580| this ticket]]. Please coordinate and take action proactively.
*Newly auto-created accounts (the accounts you get when you visit a new wiki) now have the same local notification preferences as users who freshly register on that wiki. It is effected in four notification types listed in the [[phab:T353225|task's description]].
*The maximum file size when using [[c:Special:MyLanguage/Commons:Upload_Wizard|Upload Wizard]] is now 5 GiB. [https://phabricator.wikimedia.org/T191804]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-21|en}}. It will be on all wikis from {{#time:j xg|2024-02-22|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Selected tools on the grid engine have been [[wikitech:News/Toolforge_Grid_Engine_deprecation|stopped]] as we prepare to shut down the grid on March 14th, 2024. The tool's code and data have not been deleted. If you are a maintainer and you want your tool re-enabled reach out to the [[wikitech:Portal:Toolforge/About_Toolforge#Communication_and_support|team]]. Only tools that have asked for extension are still running on the grid.
* The CSS &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[https://developer.mozilla.org/en-US/docs/Web/CSS/filter filter]&lt;/code&gt;&lt;/bdi&gt; property can now be used in HTML &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;style&lt;/code&gt;&lt;/bdi&gt; attributes in wikitext. [https://phabricator.wikimedia.org/T308160]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W08&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:36, 19 February 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26254282 --&gt;

== Tech News: 2024-09 ==

&lt;section begin=&quot;technews-2024-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/09|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/VisualEditor_on_mobile|mobile visual editor]] is now the default editor for users who never edited before, at a small group of wikis. [[mw:Special:MyLanguage/VisualEditor_on_mobile/VE_mobile_default#A/B_test_results| Research ]] shows that users using this editor are slightly more successful publishing the edits they started, and slightly less successful publishing non-reverted edits. Users who defined the wikitext editor as their default on desktop will get the wikitext editor on mobile for their first edit on mobile as well. [https://phabricator.wikimedia.org/T352127]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/ResourceLoader/Core modules#mw.config|mw.config]] value &lt;code&gt;wgGlobalGroups&lt;/code&gt; now only contains groups that are active in the wiki. Scripts no longer have to check whether the group is active on the wiki via an API request. A code example of the above is: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;if (/globalgroupname/.test(mw.config.get(&quot;wgGlobalGroups&quot;)))&lt;/code&gt;&lt;/bdi&gt;. [https://phabricator.wikimedia.org/T356008]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-28|en}}. It will be on all wikis from {{#time:j xg|2024-02-29|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
* The right to change [[mw:Special:MyLanguage/Manual:Tags|edit tags]] (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;changetags&lt;/code&gt;&lt;/bdi&gt;) will be removed from users in Wikimedia sites, keeping it by default for admins and bots only. Your community can ask to retain the old configuration on your wiki before this change happens. Please indicate in [[phab:T355639|this ticket]] to keep it for your community before the end of March 2024.
'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W09&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:23, 26 February 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26294125 --&gt;

== Tech News: 2024-10 ==

&lt;section begin=&quot;technews-2024-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/10|Translations]] are available.

'''Recent changes'''
* The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Special:Book&lt;/code&gt;&lt;/bdi&gt; page (as well as the associated &quot;Create a book&quot; functionality) provided by the old [[mw:Special:MyLanguage/Extension:Collection|Collection extension]] has been removed from all Wikisource wikis, as it was broken. This does not affect the ability to download normal books, which is provided by the [[mw:Special:MyLanguage/Extension:Wikisource|Wikisource extension]]. [https://phabricator.wikimedia.org/T358437]
* [[m:Wikitech|Wikitech]] now uses the next-generation [[mw:Special:MyLanguage/Parsoid|Parsoid]] wikitext parser by default to generate all pages in the Talk namespace.  Report any problems on the [[mw:Talk:Parsoid/Parser_Unification/Known_Issues|Known Issues discussion page]]. You can use the [[mw:Special:MyLanguage/Extension:ParserMigration|ParserMigration]] extension to control the use of Parsoid; see the [[mw:Special:MyLanguage/Help:Extension:ParserMigration|ParserMigration help documentation]] for more details.
* Maintenance on [https://etherpad.wikimedia.org etherpad] is completed. If you encounter any issues, please indicate in [[phab:T316421|this ticket]].
* [[File:Octicons-tools.svg|12px|link=|alt=| Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] allow interface admins to create custom features with CSS and JavaScript. The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Gadget&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Gadget_definition&lt;/code&gt;&lt;/bdi&gt; namespaces and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;gadgets-definition-edit&lt;/code&gt;&lt;/bdi&gt; user right were reserved for an experiment in 2015, but were never used. These were visible on Special:Search and Special:ListGroupRights. The unused namespaces and user rights are now removed. No pages are moved, and no changes need to be made. [https://phabricator.wikimedia.org/T31272]
* A usability improvement to the &quot;Add a citation&quot; in Wikipedia workflow has been made, the insert button was moved to the popup header. [https://phabricator.wikimedia.org/T354847]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-06|en}}. It will be on all wikis from {{#time:j xg|2024-03-07|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
*  All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233]
* The HTML markup of headings and section edit links will be changed later this year to improve accessibility. See [[mw:Special:MyLanguage/Heading_HTML_changes|Heading HTML changes]] for details. The new markup will be the same as in the new Parsoid wikitext parser. You can test your gadget or stylesheet with the new markup if you add &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;?useparsoid=1&lt;/code&gt;&lt;/bdi&gt; to your URL ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Selecting_a_parser_using_a_URL_query_string|more info]]) or turn on Parsoid read views in your user options ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Enabling_via_user_preference|more info]]).
*

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W10&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:47, 4 March 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26329807 --&gt;

== Tech News: 2024-11 ==

&lt;section begin=&quot;technews-2024-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/11|Translations]] are available.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-13|en}}. It will be on all wikis from {{#time:j xg|2024-03-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* After consulting with various communities, the line height of the text on the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] will be increased to its previous value of 1.65. Different options for typography can also be set using the options in the menu, as needed. [https://phabricator.wikimedia.org/T358498]
*The active link color in [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva]] will be changed to provide more consistency with our other platforms and best practices. [https://phabricator.wikimedia.org/T358516]
* [[c:Special:MyLanguage/Commons:Structured data|Structured data on Commons]] will no longer ask whether you want to leave the page without saving. This will prevent the “information you’ve entered may not be saved” popups from appearing when no information have been entered. It will also make file pages on Commons load faster in certain cases. However, the popups will be hidden even if information has indeed been entered. If you accidentally close the page before saving the structured data you entered, that data will be lost. [https://phabricator.wikimedia.org/T312315]

'''Future changes'''
* All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W11&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:04, 11 March 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26374013 --&gt;

== Tech News: 2024-12 ==

&lt;section begin=&quot;technews-2024-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/12|Translations]] are available.

'''Recent changes'''
* The notice &quot;Language links are at the top of the page&quot; that appears in the [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]] main menu has been removed now that users have learned the new location of the Language switcher. [https://phabricator.wikimedia.org/T353619]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/IP_Editing:_Privacy_Enhancement_and_Abuse_Mitigation/IP_Info_feature|IP info feature]] displays data from Spur, an IP addresses database. Previously, the only data source for this feature was MaxMind. Now, IP info is more useful for patrollers. [https://phabricator.wikimedia.org/T341395]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge Grid Engine services have been shut down after the final migration process from Grid Engine to Kubernetes. [https://wikitech.wikimedia.org/wiki/Obsolete:Toolforge/Grid][https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation][https://techblog.wikimedia.org/2022/03/14/toolforge-and-grid-engine/]
* Communities can now customize the default reasons for undeleting a page by creating [[MediaWiki:Undelete-comment-dropdown]]. [https://phabricator.wikimedia.org/T326746]

'''Problems'''
* [[m:Special:MyLanguage/WMDE_Technical_Wishes/RevisionSlider|RevisionSlider]] is an interface to interactively browse a page's history. Users in [[mw:Special:MyLanguage/Extension:RevisionSlider/Developing_a_RTL-accessible_feature_in_MediaWiki_-_what_we%27ve_learned_while_creating_the_RevisionSlider|right-to-left]] languages reported RevisionSlider reacting wrong to mouse clicks. This should be fixed now. [https://phabricator.wikimedia.org/T352169]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-20|en}}. It will be on all wikis from {{#time:j xg|2024-03-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* All wikis will be read-only for a few minutes on March 20. This is planned at [https://zonestamp.toolforge.org/1710943200 14:00 UTC]. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W12&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:39, 18 March 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26410165 --&gt;

== Tech News: 2024-13 ==

&lt;section begin=&quot;technews-2024-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/13|Translations]] are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] An update was made on March 18th 2024 to how various projects load site, user JavaScript and CSS in [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]]. A [[phab:T360384|checklist]] is provided for site admins to follow.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-27|en}}. It will be on all wikis from {{#time:j xg|2024-03-28|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W13&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:56, 25 March 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26446209 --&gt;

== Tech News: 2024-14 ==

&lt;section begin=&quot;technews-2024-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/14|Translations]] are available.

'''Recent changes'''
* Users of the [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading|reading accessibility]] beta feature will notice that the default line height for the standard and large text options has changed. [https://phabricator.wikimedia.org/T359030]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-03|en}}. It will be on all wikis from {{#time:j xg|2024-04-04|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
* The Wikimedia Foundation has an annual plan. The annual plan decides what the Wikimedia Foundation will work on. You can now read [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product &amp; Technology OKRs#Draft Key Results|the draft key results]] for the Product and Technology department. They are suggestions for what results the Foundation wants from big technical changes from July 2024 to June 2025. You can [[m:Talk:Wikimedia Foundation Annual Plan/2024-2025/Product &amp; Technology OKRs|comment on the talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W14&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 03:36, 2 April 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26462933 --&gt;

== Tech News: 2024-15 ==

&lt;section begin=&quot;technews-2024-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/15|Translations]] are available.

'''Recent changes'''
* Web browsers can use tools called [[:w:en:Browser extension|extensions]]. There is now a Chrome extension called [[m:Future Audiences/Experiment:Citation Needed|Citation Needed]] which you can use to see if an online statement is supported by a Wikipedia article. This is a small experiment to see if Wikipedia can be used this way. Because it is a small experiment, it can only be used in Chrome in English.
* [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A new [[mw:Special:MyLanguage/Help:Edit Recovery|Edit Recovery]] feature has been added to all wikis, available as a [[Special:Preferences#mw-prefsection-editing|user preference]]. Once you enable it, your in-progress edits will be stored in your web browser, and if you accidentally close an editing window or your browser or computer crashes, you will be prompted to recover the unpublished text. Please leave any feedback on the [[m:Special:MyLanguage/Talk:Community Wishlist Survey 2023/Edit-recovery feature|project talk page]]. This was the #8 wish in the 2023 Community Wishlist Survey.
* Initial results of [[mw:Special:MyLanguage/Edit check|Edit check]] experiments [[mw:Special:MyLanguage/Edit_check#4_April_2024|have been published]]. Edit Check is now deployed as a default feature at [[phab:T342930#9538364|the wikis that tested it]]. [[mw:Talk:Edit check|Let us know]] if you want your wiki to be part of the next deployment of Edit check. [https://phabricator.wikimedia.org/T342930][https://phabricator.wikimedia.org/T361727]
* Readers using the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] on mobile will notice there has been an improvement in the line height across all typography settings. [https://phabricator.wikimedia.org/T359029]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-10|en}}. It will be on all wikis from {{#time:j xg|2024-04-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* New accounts and logged-out users will get the [[mw:Special:MyLanguage/VisualEditor|visual editor]] as their default editor on mobile. This deployment is made at all wikis except for the English Wikipedia. [https://phabricator.wikimedia.org/T361134]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W15&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:37, 8 April 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26564838 --&gt;

== Tech News: 2024-16 ==

&lt;section begin=&quot;technews-2024-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/16|Translations]] are available.

'''Problems'''
* Between 2 April and 8 April, on wikis using [[mw:Special:MyLanguage/Extension:FlaggedRevs|Flagged Revisions]], the &quot;{{Int:tag-mw-reverted}}&quot; tag was not applied to undone edits. In addition, page moves, protections and imports were not autoreviewed. This problem is now fixed. [https://phabricator.wikimedia.org/T361918][https://phabricator.wikimedia.org/T361940]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-17|en}}. It will be on all wikis from {{#time:j xg|2024-04-18|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[mw:Special:MyLanguage/Help:Magic words#DEFAULTSORT|Default category sort keys]] will now affect categories added by templates placed in [[mw:Special:MyLanguage/Help:Cite|footnotes]]. Previously footnotes used the page title as the default sort key even if a different default sort key was specified (category-specific sort keys already worked). [https://phabricator.wikimedia.org/T40435]
* A new variable &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;page_last_edit_age&lt;/code&gt;&lt;/bdi&gt; will be added to [[Special:AbuseFilter|abuse filters]]. It tells how many seconds ago the last edit to a page was made. [https://phabricator.wikimedia.org/T269769]

'''Future changes'''
* Volunteer developers are kindly asked to update the code of their tools and features to handle [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]]. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]].
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Four database fields will be removed from database replicas (including [[quarry:|Quarry]]). This affects only the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;abuse_filter&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;abuse_filter_history&lt;/code&gt;&lt;/bdi&gt; tables. Some queries might need to be updated. [https://phabricator.wikimedia.org/T361996]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W16&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:29, 15 April 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26564838 --&gt;

== Tech News: 2024-17 ==

&lt;section begin=&quot;technews-2024-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/17|Translations]] are available.

'''Recent changes'''
* Starting this week, newcomers editing Wikipedia [[mw:Special:MyLanguage/Growth/Positive reinforcement#Leveling up 3|will be encouraged]] to try structured tasks. [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer tasks|Structured tasks]] have been shown to [[mw:Special:MyLanguage/Growth/Personalized first day/Structured tasks/Add a link/Experiment analysis, December 2021|improve newcomer activation and retention]]. [https://phabricator.wikimedia.org/T348086]
* You can [[m:Special:MyLanguage/Coolest Tool Award|nominate your favorite tools]] for the fifth edition of the Coolest Tool Award. Nominations will be open until May 10. 

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-24|en}}. It will be on all wikis from {{#time:j xg|2024-04-25|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
* This is the last warning that by the end of May 2024 the Vector 2022 skin will no longer share site and user scripts/styles with old Vector. For user-scripts that you want to keep using on Vector 2022, copy the contents of [[{{#special:MyPage}}/vector.js]] to [[{{#special:MyPage}}/vector-2022.js]]. There are [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|more technical details]] available. Interface administrators who foresee this leading to lots of technical support questions may wish to send a mass message to your community, as was done on French Wikipedia. [https://phabricator.wikimedia.org/T362701]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W17&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:28, 22 April 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26647188 --&gt;

== Tech News: 2024-18 ==

&lt;section begin=&quot;technews-2024-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/18|Translations]] are available.

'''Recent changes'''

[[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]]
* The appearance of talk pages changed for the following wikis: {{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-viwiki/en}}. These wikis participated to a test, where 50% of users got the new design, for one year. As this test [[Mw:Special:MyLanguage/Talk pages project/Usability/Analysis|gave positive results]], the new design is deployed on these wikis as the default design. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] (&quot;{{int:discussiontools-preference-visualenhancements}}&quot;). The deployment will happen at all wikis in the coming weeks. [https://phabricator.wikimedia.org/T341491]
* Seven new wikis have been created: 
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q33014|Betawi]] ([[w:bew:|&lt;code&gt;w:bew:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T357866]
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35708|Kusaal]] ([[w:kus:|&lt;code&gt;w:kus:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T359757]
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35513|Igala]] ([[w:igl:|&lt;code&gt;w:igl:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T361644]
** a {{int:project-localized-name-group-wiktionary}} in [[d:Q33541|Karakalpak]] ([[wikt:kaa:|&lt;code&gt;wikt:kaa:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T362135]
** a {{int:project-localized-name-group-wikisource}} in [[d:Q9228|Burmese]] ([[s:my:|&lt;code&gt;s:my:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T361085]
** a {{int:project-localized-name-group-wikisource}} in [[d:Q9237|Malay]] ([[s:ms:|&lt;code&gt;s:ms:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T363039]
** a {{int:project-localized-name-group-wikisource}} in [[d:Q8108|Georgian]] ([[s:ka:|&lt;code&gt;s:ka:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T363085]
* You can now [https://translatewiki.net/wiki/Support#Early_access:_Watch_Message_Groups_on_Translatewiki.net watch message groups/projects] on [[m:Special:MyLanguage/translatewiki.net|Translatewiki.net]]. Initially, this feature will notify you of added or deleted messages in these groups. [https://phabricator.wikimedia.org/T348501]
* Dark mode is now available on all wikis, on mobile web for logged-in users who opt into the [[Special:MobileOptions|advanced mode]]. This is the early release of the feature. Technical editors are invited to [https://night-mode-checker.wmcloud.org/ check for accessibility issues on wikis]. See [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-04|more detailed guidelines]].

'''Problems'''
* [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps can use an alternative visual style without labels, by using &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;mapstyle=&quot;osm&quot;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;. This wasn't working in previews, creating the wrong impression that it wasn't supported. This has now been fixed. [https://phabricator.wikimedia.org/T362531]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-01|en}}. It will be on all wikis from {{#time:j xg|2024-05-02|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W18&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 03:33, 30 April 2024 (UTC)
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== Tech News: 2024-19 ==

&lt;section begin=&quot;technews-2024-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/19|Translations]] are available.

'''Recent changes'''
[[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]]
* The appearance of talk pages changed for all wikis, except for Commons, Wikidata and most Wikipedias ([[m:Special:MyLanguage/Tech/News/2024/18|a few]] have already received this design change). You can read the detail of the changes [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|on ''Diff'']]. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] (&quot;{{int:discussiontools-preference-visualenhancements}}&quot;). The deployment will happen at remaining wikis in the coming weeks. [https://phabricator.wikimedia.org/T352087][https://phabricator.wikimedia.org/T319146]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Interface admins now have greater control over the styling of article components on mobile with the introduction of the &lt;code&gt;SiteAdminHelper&lt;/code&gt;. More information on how styles can be disabled can be found [[mw:Special:MyLanguage/Extension:WikimediaMessages#Site_admin_helper|at the extension's page]]. [https://phabricator.wikimedia.org/T363932]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] has added article body sections in JSON format and a curated short description field to the existing parsed Infobox. This expansion to the API is also available via Wikimedia Cloud Services. [https://enterprise.wikimedia.com/blog/article-sections-and-description/]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-08|en}}. It will be on all wikis from {{#time:j xg|2024-05-09|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* When you look at the Special:Log page, the first view is labelled &quot;All public logs&quot;, but it only shows some logs. This label will now say &quot;Main public logs&quot;. [https://phabricator.wikimedia.org/T237729]

'''Future changes'''
* A new service will be built to replace [[mw:Special:MyLanguage/Extension:Graph|Extension:Graph]]. Details can be found in [[mw:Special:MyLanguage/Extension:Graph/Plans|the latest update]] regarding this extension.
* Starting May 21, English Wikipedia and German Wikipedia will get the possibility to activate &quot;[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]&quot;. This is part of the [[phab:T304110|progressive deployment of this tool to all Wikipedias]]. These communities can [[mw:Special:MyLanguage/Growth/Community configuration|activate and configure the feature locally]]. [https://phabricator.wikimedia.org/T308144]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W19&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:44, 6 May 2024 (UTC)
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== Tech News: 2024-20 ==

&lt;section begin=&quot;technews-2024-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/20|Translations]] are available.

'''Recent changes'''
* On Wikisource there is a special page listing pages of works without corresponding scan images. Now you can use the new magic word &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;__EXPECTWITHOUTSCANS__&lt;/code&gt;&lt;/bdi&gt; to exclude certain pages (list of editions or translations of works) from that list. [https://phabricator.wikimedia.org/T344214]
* If you use the [[Special:Preferences#mw-prefsection-editing|user-preference]] &quot;{{int:tog-uselivepreview}}&quot;, then the template-page feature &quot;{{int:Templatesandbox-editform-legend}}&quot; will now also work without reloading the page. [https://phabricator.wikimedia.org/T136907]
* [[mw:Special:Mylanguage/Extension:Kartographer|Kartographer]] maps can now specify an alternative text via the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;alt=&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; attribute. This is identical in usage to the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;alt=&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; attribute in the [[mw:Special:MyLanguage/Help:Images#Syntax|image and gallery syntax]]. An exception for this feature is wikis like Wikivoyage where the miniature maps are interactive. [https://phabricator.wikimedia.org/T328137]
* The old [[mw:Special:MyLanguage/Extension:GuidedTour|Guided Tour]] for the &quot;[[mw:Special:MyLanguage/Edit Review Improvements/New filters for edit review|New Filters for Edit Review]]&quot; feature has been removed. It was created in 2017 to show people with older accounts how the interface had changed, and has now been seen by most of the intended people. [https://phabricator.wikimedia.org/T217451]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-15|en}}. It will be on all wikis from {{#time:j xg|2024-05-16|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[{{#special:search}}]] results page will now use CSS flex attributes, for better accessibility, instead of a table. If you have a gadget or script that adjusts search results, you should update your script to the new HTML structure. [https://phabricator.wikimedia.org/T320295]

'''Future changes'''
* In the Vector 2022 skin, main pages will be displayed at full width (like special pages). The goal is to keep the number of characters per line large enough. This is related to the coming changes to typography in Vector 2022. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates|Learn more]]. [https://phabricator.wikimedia.org/T357706]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Two columns of the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:Special:MyLanguage/Manual:pagelinks table|pagelinks]]&lt;/code&gt;&lt;/bdi&gt; database table (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;pl_namespace&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;pl_title&lt;/code&gt;&lt;/bdi&gt;) are being dropped soon. Users must use two columns of the new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;[[mw:special:MyLanguage/Manual:linktarget table|linktarget]]&lt;/code&gt;&lt;/bdi&gt; table instead (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;lt_namespace&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;lt_title&lt;/code&gt;&lt;/bdi&gt;). In your existing SQL queries:
*# Replace &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;JOIN pagelinks&lt;/code&gt;&lt;/bdi&gt; with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;JOIN linktarget&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;pl_&lt;/code&gt;&lt;/bdi&gt; with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;lt_&lt;/code&gt;&lt;/bdi&gt; in the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;ON&lt;/code&gt;&lt;/bdi&gt; statement
*# Below that add &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;JOIN pagelinks ON lt_id = pl_target_id&lt;/code&gt;&lt;/bdi&gt;
** See &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[phab:T222224]]&lt;/bdi&gt; for technical reasoning. [https://phabricator.wikimedia.org/T222224][https://phabricator.wikimedia.org/T299947]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W20&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:58, 13 May 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26762074 --&gt;

== Tech News: 2024-21 ==

&lt;section begin=&quot;technews-2024-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/21|Translations]] are available.

'''Recent changes'''
* The [[mw:Special:MyLanguage/Extension:Nuke|Nuke]] feature, which enables administrators to mass delete pages, will now correctly delete pages which were moved to another title. [https://phabricator.wikimedia.org/T43351]
* New changes have been made to the UploadWizard in Wikimedia Commons: the overall layout has been improved, by following new styling and spacing for the form and its fields; the headers and helper text for each of the fields was changed; the Caption field is now a required field, and there is an option for users to copy their caption into the media description. [https://commons.wikimedia.org/wiki/Commons:WMF_support_for_Commons/Upload_Wizard_Improvements#Changes_to_%22Describe%22_workflow][https://phabricator.wikimedia.org/T361049]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-22|en}}. It will be on all wikis from {{#time:j xg|2024-05-23|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]]  The HTML used to render all headings [[mw:Heading_HTML_changes|is being changed to improve accessibility]]. It will change on 22 May in some skins (Timeless, Modern, CologneBlue, Nostalgia, and Monobook). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in all other skins. The developers are also considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W21&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:04, 20 May 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26786311 --&gt;

== Tech News: 2024-22 ==

&lt;section begin=&quot;technews-2024-W22&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/22|Translations]] are available.

'''Recent changes'''
* Several bugs related to the latest updates to the UploadWizard on Wikimedia Commons have been fixed. For more information, see [[:phab:T365107|T365107]] and [[:phab:T365119|T365119]].
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In March 2024 a new [[mw:ResourceLoader/Core_modules#addPortlet|addPortlet]] API was added to allow gadgets to create new portlets (menus) in the skin. In certain skins this can be used to create dropdowns. Gadget developers are invited to try it and [[phab:T361661|give feedback]].
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Some CSS in the Minerva skin has been removed to enable easier community configuration. Interface editors should check the rendering on mobile devices for aspects related to the classes: &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.collapsible&lt;/code&gt;&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.multicol&lt;/code&gt;&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.reflist&lt;/code&gt;&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.coordinates&lt;/code&gt;&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;.topicon&lt;/code&gt;&lt;/bdi&gt;. [[phab:T361659|Further details are available on replacement CSS]] if it is needed.

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-29|en}}. It will be on all wikis from {{#time:j xg|2024-05-30|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* When you visit a wiki where you don't yet have a local account, local rules such as edit filters can sometimes prevent your account from being created. Starting this week, MediaWiki takes your global rights into account when evaluating whether you can override such local rules. [https://phabricator.wikimedia.org/T316303]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/22|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W22&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:15, 28 May 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26832205 --&gt;

== Tech News: 2024-23 ==

&lt;section begin=&quot;technews-2024-W23&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/23|Translations]] are available.

'''Recent changes'''
* It is now possible for local administrators to add new links to the bottom of the site Tools menu without JavaScript. [[mw:Manual:Interface/Sidebar#Add or remove toolbox sections|Documentation is available]]. [https://phabricator.wikimedia.org/T6086]
* The message name for the definition of the tracking category of WikiHiero has changed from &quot;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;MediaWiki:Wikhiero-usage-tracking-category&lt;/code&gt;&lt;/bdi&gt;&quot; to &quot;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;MediaWiki:Wikihiero-usage-tracking-category&lt;/code&gt;&lt;/bdi&gt;&quot;. [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/wikihiero/+/1035855]
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q5317225|Kadazandusun]] ([[w:dtp:|&lt;code&gt;w:dtp:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T365220]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-05|en}}. It will be on all wikis from {{#time:j xg|2024-06-06|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Future changes'''
* Next week, on wikis with the Vector 2022 skin as the default, logged-out desktop users will be able to choose between different font sizes. The default font size will also be increased for them. This is to make Wikimedia projects easier to read. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-06 deployments|Learn more]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/23|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W23&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:35, 3 June 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=26844397 --&gt;

== Tech News: 2024-24 ==

&lt;section begin=&quot;technews-2024-W24&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/24|Translations]] are available.

'''Recent changes'''
* The software used to render SVG files has been updated to a new version, fixing many longstanding bugs in SVG rendering. [https://phabricator.wikimedia.org/T265549]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML used to render all headings [[mw:Heading HTML changes|is being changed to improve accessibility]]. It was changed last week in some skins (Vector legacy and Minerva). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in Vector-2022. The developers are still considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that.
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML markup used for citations by [[mw:Special:MyLanguage/Parsoid|Parsoid]] changed last week. In places where Parsoid previously added the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw-reference-text&lt;/code&gt;&lt;/bdi&gt; class, Parsoid now also adds the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;reference-text&lt;/code&gt;&lt;/bdi&gt; class for better compatibility with the legacy parser. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1036705]

'''Problems'''
* There was a bug with the Content Translation interface that caused the tools menus to appear in the wrong location. This has now been fixed. [https://phabricator.wikimedia.org/T366374]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-12|en}}. It will be on all wikis from {{#time:j xg|2024-06-13|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The new version of MediaWiki includes another change to the HTML markup used for citations: [[mw:Special:MyLanguage/Parsoid|Parsoid]] will now generate a &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;span class=&quot;mw-cite-backlink&quot;&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; wrapper for both named and unnamed references for better compatibility with the legacy parser. Interface administrators should verify that gadgets that interact with citations are compatible with the new markup. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1035809] 
* On multilingual wikis that use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;translate&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; system, there is a feature that shows potentially-outdated translations with a pink background until they are updated or confirmed. From this week, confirming translations will be logged, and there is a new user-right that can be required for confirming translations if the community [[m:Special:MyLanguage/Requesting wiki configuration changes|requests it]]. [https://phabricator.wikimedia.org/T49177]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/24|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W24&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:20, 10 June 2024 (UTC)
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== Tech News: 2024-25 ==

&lt;section begin=&quot;technews-2024-W25&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/25|Translations]] are available.

'''Recent changes'''
* People who attempt to add an external link in the visual editor will now receive immediate feedback if they attempt to link to a domain that a project has decided to block. Please see [[mw:Special:MyLanguage/Edit_check#11_June_2024|Edit check]] for more details. [https://phabricator.wikimedia.org/T366751]
* The new [[mw:Special:MyLanguage/Extension:CommunityConfiguration|Community Configuration extension]] is available [[testwiki:Special:CommunityConfiguration|on Test Wikipedia]]. This extension allows communities to customize specific features to meet their local needs. Currently only Growth features are configurable, but the extension will support other [[mw:Special:MyLanguage/Community_configuration#Use_cases|Community Configuration use cases]] in the future. [https://phabricator.wikimedia.org/T323811][https://phabricator.wikimedia.org/T360954]
* The dark mode [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] is now available on category and help pages, as well as more special pages. There may be contrast issues. Please report bugs on the [[mw:Talk:Reading/Web/Accessibility_for_reading|project talk page]]. [https://phabricator.wikimedia.org/T366370]

'''Problems'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Cloud Services tools were not available for 25 minutes last week. This was caused by a faulty hardware cable in the data center. [https://wikitech.wikimedia.org/wiki/Incidents/2024-06-11_WMCS_Ceph]
* Last week, styling updates were made to the Vector 2022 skin. This caused unforeseen issues with templates, hatnotes, and images. Changes to templates and hatnotes were reverted. Most issues with images were fixed. If you still see any, [[phab:T367463|report them here]]. [https://phabricator.wikimedia.org/T367480]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-19|en}}. It will be on all wikis from {{#time:j xg|2024-06-20|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Starting June 18, the [[mw:Special:MyLanguage/Help:Edit check#ref|Reference Edit Check]] will be deployed to [[phab:T361843|a new set of Wikipedias]]. This feature is intended to help newcomers and to assist edit-patrollers by inviting people who are adding new content to a Wikipedia article to add a citation when they do not do so themselves. During [[mw:Special:MyLanguage/Edit_check#Reference_Check_A/B_Test|a test at 11 wikis]], the number of citations added [https://diff.wikimedia.org/?p=127553 more than doubled] when Reference Check was shown to people. Reference Check is [[mw:Special:MyLanguage/Edit check/Configuration|community configurable]]. [https://phabricator.wikimedia.org/T361843]&lt;!-- NOTE: THE DIFF BLOG WILL BE PUBLISHED ON MONDAY --&gt;
* [[m:Special:MyLanguage/Mailing_lists|Mailing lists]] will be unavailable for roughly two hours on Tuesday 10:00–12:00 UTC. This is to enable migration to a new server and upgrade its software. [https://phabricator.wikimedia.org/T367521]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/25|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W25&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:48, 17 June 2024 (UTC)
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== Tech News: 2024-26 ==

&lt;section begin=&quot;technews-2024-W26&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/26|Translations]] are available.

'''Recent changes'''
* Editors will notice that there have been some changes to the background color of text in the diff view, and the color of the byte-change numbers, last week. These changes are intended to make text more readable in both light mode and dark mode, and are part of a larger effort to increase accessibility. You can share your comments or questions [[mw:Talk:Reading/Web/Accessibility for reading|on the project talkpage]]. [https://phabricator.wikimedia.org/T361717]
* The text colors that are used for visited-links, hovered-links, and active-links, were also slightly changed last week to improve their accessibility in both light mode and dark mode. [https://phabricator.wikimedia.org/T366515]

'''Problems'''
* You can [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|copy permanent links to talk page comments]] by clicking on a comment's timestamp. [[mw:Talk pages project/Permalinks|This feature]] did not always work when the topic title was very long and the link was used as a wikitext link. This has been fixed. Thanks to Lofhi for submitting the bug. [https://phabricator.wikimedia.org/T356196]

'''Changes later this week'''
* [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-26|en}}. It will be on all wikis from {{#time:j xg|2024-06-27|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]
* Starting 26 June, all talk pages messages' timestamps will become a link at English Wikipedia, making this feature available for you to use at all wikis. This link is a permanent link to the comment. It allows users to find the comment they were linked to, even if this comment has since been moved elsewhere. You can read more about this feature [[DiffBlog:/2024/01/29/talk-page-permalinks-dont-lose-your-threads/|on Diff]] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|on Mediawiki.org]]. [https://phabricator.wikimedia.org/T365974]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/26|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W26&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:32, 24 June 2024 (UTC)
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== Tech News: 2024-27 ==

&lt;section begin=&quot;technews-2024-W27&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/27|Translations]] are available.

'''Recent changes'''
* Over the next three weeks, dark mode will become available for all users, both logged-in and logged-out, starting with the mobile web version. This fulfils one of the [[m:Special:MyLanguage/Community_Wishlist_Survey_2023/Reading/Dark_mode|top-requested community wishes]], and improves low-contrast reading and usage in low-light settings. As part of these changes, dark mode will also work on User-pages and Portals. There is more information in [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading/Updates#June_2024:_Typography_and_dark_mode_deployments,_new_global_preferences|the latest Web team update]]. [https://phabricator.wikimedia.org/T366364]
* Logged-in users can now set [[m:Special:GlobalPreferences#mw-prefsection-rendering-skin-skin-prefs|global preferences for the text-size and dark-mode]], thanks to a combined effort across Foundation teams. This allows Wikimedians using multiple wikis to set up a consistent reading experience easily, for example by switching between light and dark mode only once for all wikis. [https://phabricator.wikimedia.org/T341278] 
* If you use a very old web browser some features might not work on the Wikimedia wikis. This affects Internet Explorer 11 and versions of Chrome, Firefox and Safari older than 2016. This change makes it possible to use new [[d:Q46441|CSS]] features and to send less code to all readers. [https://phabricator.wikimedia.org/T288287][https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:How_to_make_a_MediaWiki_skin#Using_CSS_variables_for_supporting_different_themes_e.g._dark_mode]
* Wikipedia Admins can customize local wiki configuration options easily using [[mw:Special:MyLanguage/Community Configuration|Community Configuration]]. Community Configuration was created to allow communities to customize how some features work, because each language wiki has unique needs. At the moment, admins can configure [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] on their home wikis, in order to better recruit and retain new editors. More options will be provided in the coming months. [https://phabricator.wikimedia.org/T366458]
* Editors interested in language issues that are related to [[w:en:Unicode|Unicode standards]], can now discuss those topics at [[mw:Talk:WMF membership with Unicode Consortium|a new conversation space in MediaWiki.org]]. The Wikimedia Foundation is now a [[mw:Special:MyLanguage/WMF membership with Unicode Consortium|member of the Unicode Consortium]], and the coordination group can collaboratively review the issues discussed and, where appropriate, bring them to the attention of the Unicode Consortium.
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2891049|Mandailing]] ([[w:btm:|&lt;code&gt;w:btm:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T368038] 

'''Problems'''
* Editors can once again click on links within the visual editor's citation-preview, thanks to a bug fix by the Editing Team. [https://phabricator.wikimedia.org/T368119]

'''Future changes'''
* Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 2 weeks. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/27|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W27&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:59, 1 July 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27038456 --&gt;

== Tech News: 2024-28 ==

&lt;section begin=&quot;technews-2024-W28&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/28|Translations]] are available.

'''Recent changes'''
* At the Wikimedia Foundation a new task force was formed to replace the disabled Graph with [[mw:Special:MyLanguage/Extension:Chart/Project|more secure, easy to use, and extensible Chart]]. You can [[mw:Special:MyLanguage/Newsletter:Chart Project|subscribe to the newsletter]] to get notified about new project updates and other news about Chart.
* The [[m:Special:MyLanguage/CampaignEvents|CampaignEvents]] extension is now available on Meta-wiki, Igbo Wikipedia, and Swahili Wikipedia, and can be requested on your wiki. This extension helps in managing and making events more visible, giving Event organizers the ability to use tools like the Event registration tool. To learn more about the deployment status and how to request this extension for your wiki, visit the [[m:Special:MyLanguage/CampaignEvents/Deployment_status|CampaignEvents page on Meta-wiki]]. 
* Editors using the iOS Wikipedia app who have more than 50 edits can now use the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits#Add an image|Add an Image]] feature. This feature presents opportunities for small but useful contributions to Wikipedia.
* Thank you to [[mw:MediaWiki Product Insights/Contributor retention and growth/Celebration|all of the authors]] who have contributed to MediaWiki Core. As a result of these contributions, the [[mw:MediaWiki Product Insights/Contributor retention and growth|percentage of authors contributing more than 5 patches has increased by 25% since last year]], which helps ensure the sustainability of the platform for the Wikimedia projects.

'''Problems'''
* A problem with the color of the talkpage tabs always showing as blue, even for non-existent pages which should have been red, affecting the Vector 2022 skin, [[phab:T367982|has been fixed]]. 

'''Future changes'''
* The Trust and Safety Product team wants to introduce [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] with as little disruption to tools and workflows as possible. Volunteer developers, including gadget and user-script maintainers, are kindly asked to update the code of their tools and features to handle temporary accounts. The team has [[mw:Trust and Safety Product/Temporary Accounts/For developers|created documentation]] explaining how to do the update. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]].

'''Tech News survey'''
* Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 1 more week. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/28|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W28&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:31, 8 July 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27080357 --&gt;

== Tech News: 2024-29 ==

&lt;section begin=&quot;technews-2024-W29&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/29|Translations]] are available.

'''Tech News survey'''
* Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 3 more days. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available.

'''Recent changes'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Wikimedia developers can now officially continue to use both [[mw:Special:MyLanguage/Gerrit|Gerrit]] and [[mw:Special:MyLanguage/GitLab|GitLab]], due to a June 24 decision by the Wikimedia Foundation to support software development on both platforms. Gerrit and GitLab are both code repositories used by developers to write, review, and deploy the software code that supports the MediaWiki software that the wiki projects are built on, as well as the tools used by editors to create and improve content. This decision will safeguard the productivity of our developers and prevent problems in code review from affecting our users. More details are available in the [[mw:GitLab/Migration status|Migration status]] page.
* The Wikimedia Foundation seeks applicants for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product and Technology Advisory Council]] (PTAC). This group will bring technical contributors and Wikimedia Foundation together to co-define a more resilient, future-proof technological platform. Council members will evaluate and consult on the movement's product and technical activities, so that we develop multi-generational projects. We are looking for a range of technical contributors across the globe, from a variety of Wikimedia projects. [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal#Joining the PTAC as a technical volunteer|Please apply here by August 10]].
* Editors with rollback user-rights who use the Wikipedia App for Android can use the new [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Anti Vandalism|Edit Patrol]] features. These features include a new feed of Recent Changes, related links such as Undo and Rollback, and the ability to create and save a personal library of user talk messages to use while patrolling. If your wiki wants to make these features available to users who do not have rollback rights but have reached a certain edit threshold, [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android#Contact us|you can contact the team]]. You can [[diffblog:2024/07/10/ِaddressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/|read more about this project on Diff blog]].
* Editors who have access to [[m:Special:MyLanguage/The_Wikipedia_Library|The Wikipedia Library]] can once again use non-open access content in SpringerLinks, after the Foundation [[phab:T368865|contacted]] them to restore access. You can read more about [[m:Tech/News/Recently_resolved_community_tasks|this and 21 other community-submitted tasks that were completed last week]]. 

'''Changes later this week'''
* This week, [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-07 deployments|dark mode will be available on a number of Wikipedias]], both desktop and mobile, for logged-in and logged-out users. Interface admins and user script maintainers are encouraged to check gadgets and user scripts in the dark mode, to find any hard-coded colors and fix them. There are some [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations for dark mode compatibility]] to help.

'''Future changes'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Next week, functionaries, volunteers maintaining tools, and software development teams are invited to test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on testwiki. Temporary accounts is a feature that will help improve privacy on the wikis. No further temporary account deployments are scheduled yet. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]]. [https://phabricator.wikimedia.org/T348895]
* Editors who upload files cross-wiki, or teach other people how to do so, may wish to join a Wikimedia Commons discussion. The Commons community is discussing limiting who can upload files through the cross-wiki upload/Upload dialog feature to users auto-confirmed on Wikimedia Commons. This is due to the large amount of copyright violations uploaded this way. There is a short summary at [[c:Special:MyLanguage/Commons:Cross-wiki upload|Commons:Cross-wiki upload]] and [[c:Commons:Village pump/Proposals#Deactivate cross-wiki uploads for new users|discussion at Commons:Village Pump]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/29|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]].
&lt;/div&gt;&lt;section end=&quot;technews-2024-W29&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:31, 16 July 2024 (UTC)
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== Tech News: 2024-30 ==

&lt;section begin=&quot;technews-2024-W30&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/30|Translations]] are available.

'''Feature News'''
* Stewards can now [[:m:Special:MyLanguage/Global_blocks|globally block]] accounts. Before [[phab:T17294|the change]] only IP addresses and IP ranges could be blocked globally. Global account blocks are useful when the blocked user should not be logged out. [[:m:Special:MyLanguage/Global_locks|Global locks]] (a similar tool logging the user out of their account) are unaffected by this change. The new global account block feature is related to the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project, which is a new type of user account that replaces IP addresses of unregistered editors that are no longer made public.
* Later this week, Wikimedia site users will notice that the Interface of [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as &quot;Pending Changes&quot;) is improved and consistent with the rest of the MediaWiki interface and [[mw:Special:MyLanguage/Codex|Wikimedia's design system]]. The FlaggedRevs interface experience on mobile and [[mw:Special:MyLanguage/Skin:MinervaNeue|Minerva skin]] was inconsistent before it was fixed and ported to [[mw:Special:MyLanguage/Codex|Codex]] by the WMF Growth team and some volunteers. [https://phabricator.wikimedia.org/T191156]
*  Wikimedia site users can now submit account vanishing requests via [[m:Special:GlobalVanishRequest|GlobalVanishRequest]]. This feature is used when a contributor wishes to stop editing forever. It helps you hide your past association and edit to protect your privacy. Once processed, the account will be locked and renamed. [https://phabricator.wikimedia.org/T367329]
* Have you tried monitoring and addressing vandalism in Wikipedia using your phone? [https://diff.wikimedia.org/2024/07/10/%d9%90addressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/ A Diff blog post on Patrolling features in the Mobile App] highlights some of the new capabilities of the feature, including swiping through a feed of recent changes and a personal library of user talk messages for use when patrolling from your phone. 
* Wikimedia contributors and GLAM (galleries, libraries, archives, and museums) organisations can now learn and measure the impact Wikimedia Commons is having towards creating quality encyclopedic content using the [https://doc.wikimedia.org/generated-data-platform/aqs/analytics-api/reference/commons.html Commons Impact Metrics] analytics dashboard. The dashboard offers organizations analytics on things like monthly edits in a category, the most viewed files, and which Wikimedia articles are using Commons images. As a result of these new data dumps, GLAM organisation can more reliably measure their return on investment for programs bringing content into the digital Commons. [https://diff.wikimedia.org/2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/]

'''Project Updates'''
*  Come share your ideas for improving the wikis on the newly reopened [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]]. The Community Wishlist is Wikimedia’s forum for volunteers to share ideas (called wishes) to improve how the wikis work. The new version of the wishlist is always open, works with both wikitext and Visual Editor, and allows wishes in any language.

'''Learn more'''
* Have you ever wondered how Wikimedia software works across over 300 languages? This is 253 languages more than the Google Chrome interface, and it's no accident. The Language and Product Localization Team at the Wikimedia Foundation supports your work by adapting all the tools and interfaces in the MediaWiki software so that contributors in our movement who translate pages and strings can translate them and have the sites in all languages. Read more about the team and their upcoming work on [https://diff.wikimedia.org/2024/07/17/building-towards-a-robust-multilingual-knowledge-ecosystem-for-the-wikimedia-movement/ Diff]. 
* How can Wikimedia build innovative and experimental products while maintaining such heavily used websites? A recent [https://diff.wikimedia.org/2024/07/09/on-the-value-of-experimentation/ blog post] by WMF staff Johan Jönsson highlights the work of the [[m:Future Audiences#Objectives and Key Results|WMF Future Audience initiative]], where the goal is not to build polished products but test out new ideas, such as a [[m:Future_Audiences/Experiments: conversational/generative AI|ChatGPT plugin]] and [[m:Future_Audiences/Experiment:Add a Fact|Add a Fact]], to help take Wikimedia into the future. 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/30|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]].
&lt;/div&gt;&lt;section end=&quot;technews-2024-W30&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:04, 23 July 2024 (UTC)
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== Tech News: 2024-31 ==

&lt;section begin=&quot;technews-2024-W31&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/31|Translations]] are available.

'''Feature news'''
* Editors using the Visual Editor in languages that use non-Latin characters for numbers, such as Hindi, Manipuri and Eastern Arabic, may notice some changes in the formatting of reference numbers. This is a side effect of preparing a new sub-referencing feature, and will also allow fixing some general numbering issues in Visual Editor. If you notice any related problems on your wiki, please share details at the [[m:Talk:WMDE Technical Wishes/Sub-referencing|project talkpage]].

'''Bugs status'''
* Some logged-in editors were briefly unable to edit or load pages last week. [[phab:T370304|These errors]] were mainly due to the addition of new [[mw:Special:MyLanguage/Help:Extension:Linter|linter]] rules which led to caching problems. Fixes have been applied and investigations are continuing.
* Editors can use the [[mw:Special:MyLanguage/Trust and Safety Product/IP Info|IP Information tool]] to get information about IP addresses. This tool is available as a Beta Feature in your preferences. The tool was not available for a few days last week, but is now working again. Thank you to Shizhao for filing the bug report. You can read about that, and [[m:Tech/News/Recently resolved community tasks#2024-07-25|28 other community-submitted tasks]] that were resolved last week.

'''Project updates'''
* There are new features and improvements to Phabricator from the Release Engineering and Collaboration Services teams, and some volunteers, including: the search systems, the new task creation system, the login systems, the translation setup which has resulted in support for more languages (thanks to Pppery), and fixes for many edge-case errors. You can [[phab:phame/post/view/316/iterative_improvements/|read details about these and other improvements in this summary]].
* There is an [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|update on the Charts project]]. The team has decided which visualization library to use, which chart types to start focusing on, and where to store chart definitions.
* One new wiki has been created: a {{int:project-localized-name-group-wikivoyage}} in [[d:Q9056|Czech]] ([[voy:cs:|&lt;code&gt;voy:cs:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T370905] 

'''Learn more'''
* There is a [[diffblog:2024/07/26/the-journey-to-open-our-first-data-center-in-south-america/|new Wikimedia Foundation data center]] in São Paulo, Brazil which helps to reduce load times.
* There is new [[diffblog:2024/07/22/the-perplexing-process-of-uploading-images-to-wikipedia/|user research]] on problems with the process of uploading images.
* Commons Impact Metrics are [[diffblog:2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/|now available]] via data dumps and API.
* The latest quarterly [[mw:Technical Community Newsletter/2024/July|Technical Community Newsletter]] is now available.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/31|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W31&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:10, 29 July 2024 (UTC)
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== Tech News: 2024-32 ==

&lt;section begin=&quot;technews-2024-W32&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/32|Translations]] are available.

'''Feature news'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Two new parser functions will be available this week: &lt;code&gt;&lt;nowiki&gt;{{&lt;/nowiki&gt;[[mw:Special:MyLanguage/Help:Magic_words#dir|#dir]]&lt;nowiki&gt;}}&lt;/nowiki&gt;&lt;/code&gt; and &lt;code&gt;&lt;nowiki&gt;{{&lt;/nowiki&gt;[[mw:Special:MyLanguage/Help:Magic_words#bcp47|#bcp47]]&lt;nowiki&gt;}}&lt;/nowiki&gt;&lt;/code&gt;. These will reduce the need for &lt;code&gt;Template:Dir&lt;/code&gt; and &lt;code&gt;Template:BCP47&lt;/code&gt; on Commons and allow us to [[phab:T343131|drop 100 million rows]] from the &quot;what links here&quot; database. Editors at any wiki that use these templates, can help by replacing the templates with these new functions. The templates at Commons will be updated during the Hackathon at Wikimania. [https://phabricator.wikimedia.org/T359761][https://phabricator.wikimedia.org/T366623]
* Communities can request the activation of the visual editor on entire namespaces where discussions sometimes happen (for instance ''Wikipedia:'' or ''Wikisource:'' namespaces) if they understand the [[mw:Special:MyLanguage/Help:VisualEditor/FAQ#WPNS|known limitations]]. For discussions, users can already use [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] in these namespaces.
* The tracking category &quot;Pages using Timeline&quot; has been renamed to &quot;Pages using the EasyTimeline extension&quot; [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3ATimeline-tracking-category&amp;namespace=8 in TranslateWiki]. Wikis that have created the category locally should rename their local creation to match.

'''Project updates'''
* Editors who help to organize WikiProjects and similar on-wiki collaborations, are invited to share ideas and examples of successful collaborations with the Campaigns and Programs teams. You can fill out [[m:Special:MyLanguage/Campaigns/WikiProjects|a brief survey]] or share your thoughts [[m:Talk:Campaigns/WikiProjects|on the talkpage]]. The teams are particularly looking for details about successful collaborations on non-English wikis.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The new parser is being rolled out on {{int:project-localized-name-group-wikivoyage}} wikis over the next few months. The {{int:project-localized-name-enwikivoyage}} and {{int:project-localized-name-hewikivoyage}} were [[phab:T365367|switched]] to Parsoid last week. For more information, see [[mw:Parsoid/Parser_Unification|Parsoid/Parser Unification]].

'''Learn more'''
* There will be more than 200 sessions at Wikimania this week. Here is a summary of some of the [[diffblog:2024/08/05/interested-in-product-and-tech-here-are-some-wikimania-sessions-you-dont-want-to-miss/|key sessions related to the product and technology area]].
* The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/07-02|Wikimedia Foundation Bulletin]] is available.
* The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/July|Language and Internationalization newsletter]] is available. It includes: New design previews for Translatable pages; Updates about MinT for Wiki Readers; the release of Translation dumps; and more.
* The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/31|Growth newsletter]] is available.
* The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/July 2024|MediaWiki Product Insights newsletter]] is available.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/32|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W32&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:43, 5 August 2024 (UTC)
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== Tech News: 2024-33 ==

&lt;section begin=&quot;technews-2024-W33&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/33|Translations]] are available.

'''Feature news'''
* [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] editors and maintainers can now [[mw:Special:MyLanguage/Extension:AbuseFilter/Actions#Show a CAPTCHA|make a CAPTCHA show if a filter matches an edit]]. This allows communities to quickly respond to spamming by automated bots. [https://phabricator.wikimedia.org/T20110]
* [[m:Special:MyLanguage/Stewards|Stewards]] can now specify if global blocks should prevent account creation. Before [[phab:T17273|this change]] by the [[mw:Special:MyLanguage/Trust and Safety Product|Trust and Safety Product]] Team, all global blocks would prevent account creation. This will allow stewards to reduce the unintended side-effects of global blocks on IP addresses.

'''Project updates'''
* [[wikitech:Help talk:Toolforge/Toolforge standards committee#August_2024_committee_nominations|Nominations are open on Wikitech]] for new members to refresh the [[wikitech:Help:Toolforge/Toolforge standards committee|Toolforge standards committee]]. The committee oversees the Toolforge [[wikitech:Help:Toolforge/Right to fork policy|Right to fork policy]] and [[wikitech:Help:Toolforge/Abandoned tool policy|Abandoned tool policy]] among other duties. Nominations will remain open until at least 2024-08-26.
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2880037|West Coast Bajau]] ([[w:bdr:|&lt;code&gt;w:bdr:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T371757]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/33|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W33&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:21, 12 August 2024 (UTC)
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== Tech News: 2024-34 ==

&lt;section begin=&quot;technews-2024-W34&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/34|Translations]] are available.

'''Feature news'''
* Editors who want to re-use references but with different details such as page numbers, will be able to do so by the end of 2024, using a new [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Sub-referencing in a nutshell|sub-referencing]] feature. You can read more [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|about the project]] and [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|how to test the prototype]].
* Editors using tracking categories to identify which pages use specific extensions may notice that six of the categories have been renamed to make them more easily understood and consistent. These categories are automatically added to pages that use specialized MediaWiki extensions. The affected names are for: [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aintersection-category&amp;namespace=8 DynamicPageList], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Akartographer-tracking-category&amp;namespace=8 Kartographer], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aphonos-tracking-category&amp;namespace=8 Phonos], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Arss-tracking-category&amp;namespace=8 RSS], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Ascore-use-category&amp;namespace=8 Score], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Awikihiero-usage-tracking-category&amp;namespace=8 WikiHiero]. Wikis that have created the category locally should rename their local creation to match. Thanks to Pppery for these improvements. [https://phabricator.wikimedia.org/T347324]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Technical volunteers who edit modules and want to get a list of the categories used on a page, can now do so using the &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;categories&lt;/bdi&gt;&lt;/code&gt; property of &lt;code&gt;&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;[[mediawikiwiki:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Title objects|mw.title objects]]&lt;/bdi&gt;&lt;/code&gt;. This enables wikis to configure workflows such as category-specific edit notices. Thanks to SD001 for these improvements. [https://phabricator.wikimedia.org/T50175][https://phabricator.wikimedia.org/T85372]

'''Bugs status'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Your help is needed to check if any pages need to be moved or deleted. A maintenance script was run to clean up unreachable pages (due to Unicode issues or introduction of new namespaces/namespace aliases). The script tried to find appropriate names for the pages (e.g. by following the Unicode changes or by moving pages whose titles on Wikipedia start with &lt;code&gt;Talk:WP:&lt;/code&gt; so that their titles start with &lt;code&gt;Wikipedia talk:&lt;/code&gt;), but it may have failed for some pages, and moved them to &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;[[Special:PrefixIndex/T195546/]]&lt;/bdi&gt; instead. Your community should check if any pages are listed there, and move them to the correct titles, or delete them if they are no longer needed. A full log (including pages for which appropriate names could be found) is available in [[phab:P67388]].
* Editors who volunteer as [[mw:Special:MyLanguage/Help:Growth/Mentorship|mentors]] to newcomers on their wiki are once again able to access lists of potential mentees who they can connect with to offer help and guidance. This functionality was restored thanks to [[phab:T372164|a bug fix]]. Thank you to Mbch331 for filing the bug report. You can read about that, and 18 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].

'''Project updates'''
* The application deadline for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product &amp; Technology Advisory Council]] (PTAC) has been extended to September 16. Members will help by providing advice to Foundation Product and Technology leadership on short and long term plans, on complex strategic problems, and help to get feedback from more contributors and technical communities. Selected members should expect to spend roughly 5 hours per month for the Council, during the one year pilot. Please consider applying, and spread the word to volunteers you think would make a positive contribution to the committee.

'''Learn more'''
* The [[m:Special:MyLanguage/Coolest Tool Award#2024 Winners|2024 Coolest Tool Awards]] were awarded at Wikimania, in seven categories. For example, one award went to the ISA Tool, used for adding structured data to files on Commons, which was recently improved during the [[m:Event:Wiki Mentor Africa ISA Hackathon 2024|Wiki Mentor Africa Hackathon]]. You can see video demonstrations of each tool at the awards page. Congratulations to this year's recipients, and thank you to all tool creators and maintainers.
* The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/08-01|Wikimedia Foundation Bulletin]] is available, and includes some highlights from Wikimania, an upcoming Language community meeting, and other news from the movement.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/34|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W34&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:54, 20 August 2024 (UTC)
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== Tech News: 2024-35 ==

&lt;section begin=&quot;technews-2024-W35&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/35|Translations]] are available.

'''Feature news'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Administrators can now test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on test2wiki. This was done to allow cross-wiki testing of temporary accounts, for when temporary accounts switch between projects. The feature was enabled on testwiki a few weeks ago. No further temporary account deployments are scheduled yet. Temporary Accounts is a project to create a new type of user account that replaces IP addresses of unregistered editors which are no longer made public. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]].
* Later this week, editors at wikis that use [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as &quot;Pending Changes&quot;) may notice that the indicators at the top of articles have changed. This change makes the system more consistent with the rest of the MediaWiki interface. [https://phabricator.wikimedia.org/T191156]

'''Bugs status'''
* Editors who use the 2010 wikitext editor, and use the Character Insert buttons, will [[phab:T361465|no longer]] experience problems with the buttons adding content into the edit-summary instead of the edit-window. You can read more about that, and 26 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].

'''Project updates'''
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Please review and vote on [[m:Special:MyLanguage/Community Wishlist/Focus areas|Focus Areas]], which are groups of wishes that share a problem. Focus Areas were created for the newly reopened Community Wishlist, which is now open year-round for submissions. The first batch of focus areas are specific to moderator workflows, around welcoming newcomers, minimizing repetitive tasks, and prioritizing tasks. Once volunteers have reviewed and voted on focus areas, the Foundation will then review and select focus areas for prioritization.
* Do you have a project and are willing to provide a three (3) month mentorship for an intern? [[mw:Special:MyLanguage/Outreachy|Outreachy]] is a twice a year program for people to participate in a paid internship that will start in December 2024 and end in early March 2025, and they need mentors and projects to work on. Projects can be focused on coding or non-coding (design, documentation, translation, research). See the Outreachy page for more details, and a list of past projects since 2013.

'''Learn more'''
* If you're curious about the product and technology improvements made by the Wikimedia Foundation last year, read [[diffblog:2024/08/21/wikimedia-foundation-product-technology-improving-the-user-experience/|this recent highlights summary on Diff]].
* To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out:
** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Community Configuration - Shaping On-Wiki Functionality Together.webm|Community Configuration - Shaping On-Wiki Functionality Together]] (55 mins) - about the [[mw:Special:MyLanguage/Community Configuration|Community Configuration]] project.
** [[c:File:Wikimania 2024 - Belgrade - Day 1 - Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views.webm|Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views]] (30 mins) - an overview for both technical and non technical audiences, covering some of the challenges and open questions, related to the [[mw:MediaWiki Product Insights|platform evolution, stewardship and developer experiences]] research.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/35|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W35&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:33, 26 August 2024 (UTC)
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== Tech News: 2024-36 ==

&lt;section begin=&quot;technews-2024-W36&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/36|Translations]] are available.

'''Weekly highlight'''
* Editors and volunteer developers interested in data visualisation can now test the new software for charts. Its early version is available on beta Commons and beta Wikipedia. This is an important milestone before making charts available on regular wikis. You can [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|read more about this project update]] and help to test the charts.

'''Feature news'''
* Editors who use the [[{{#special:Unusedtemplates}}]] page can now filter out pages which are expected to be there permanently, such as sandboxes, test-cases, and templates that are always substituted. Editors can add the new magic word [[mw:Special:MyLanguage/Help:Magic words#EXPECTUNUSEDTEMPLATE|&lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;__EXPECTUNUSEDTEMPLATE__&lt;/nowiki&gt;&lt;/code&gt;]] to a template page to hide it from the listing. Thanks to Sophivorus and DannyS712 for these improvements. [https://phabricator.wikimedia.org/T184633]
* Editors who use the New Topic tool on discussion pages, will [[phab:T334163|now be reminded]] to add a section header, which should help reduce the quantity of newcomers who add sections without a header. You can read more about that, and {{formatnum:28}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].
* Last week, some Toolforge tools had occasional connection problems. The cause is still being investigated, but the problems have been resolved for now. [https://phabricator.wikimedia.org/T373243]
* Translation administrators at multilingual wikis, when editing multiple translation units, can now easily mark which changes require updates to the translation. This is possible with the [[phab:T298852#10087288|new dropdown menu]].

'''Project updates'''
* A new draft text of a policy discussing the use of Wikimedia's APIs [[m:Special:MyLanguage/API Policy Update 2024|has been published on Meta-Wiki]]. The draft text does not reflect a change in policy around the APIs; instead, it is an attempt to codify existing API rules. Comments, questions, and suggestions are welcome on [[m:Talk:API Policy Update 2024|the proposed update’s talk page]] until September 13 or until those discussions have concluded.

'''Learn more'''
* To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out:
** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Charts, the successor of Graphs - A secure and extensible tool for data visualization.webm|Charts, the successor of Graphs - A secure and extensible tool for data visualization]] (25 mins) – about the above-mentioned Charts project.
** [[c:File:Wikimania 2024 - Ohrid - Day 3 - State of Language Technology and Onboarding at Wikimedia.webm|State of Language Technology and Onboarding at Wikimedia]] (90 mins) – about some of the language tools that support Wikimedia sites, such as [[mw:Special:MyLanguage/Content translation|Content]]/[[mw:Special:MyLanguage/Content translation/Section translation|Section Translation]], [[mw:Special:MyLanguage/MinT|MinT]], and LanguageConverter; also the current state and future of languages onboarding. [https://phabricator.wikimedia.org/T368772]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/36|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W36&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:07, 3 September 2024 (UTC)
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== Tech News: 2024-37 ==

&lt;section begin=&quot;technews-2024-W37&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/37|Translations]] are available.

'''Feature news'''
* Starting this week, the standard [[mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighter]] will receive new colors that make them compatible in dark mode. This is the first of many changes to come as part of a major upgrade to syntax highlighting. You can learn more about what's to come on the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|help page]]. [https://phabricator.wikimedia.org/T365311][https://phabricator.wikimedia.org/T259059]
* Editors of wikis using Wikidata will now be notified of only relevant Wikidata changes in their watchlist. This is because the Lua functions &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;entity:getSitelink()&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw.wikibase.getSitelink(qid)&lt;/code&gt;&lt;/bdi&gt; will have their logic unified for tracking different aspects of sitelinks to reduce junk notifications from [[m:Wikidata For Wikimedia Projects/Projects/Watchlist Wikidata Sitelinks Tracking|inconsistent sitelinks tracking]]. [https://phabricator.wikimedia.org/T295356]

'''Project updates'''
*  Users of all Wikis will have access to Wikimedia sites as read-only for a few minutes on September 25, starting at 15:00 UTC. This is a planned datacenter switchover for maintenance purposes. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T370962]
* Contributors of [[phab:T363538#10123348|11 Wikipedias]], including English will have a new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;MOS&lt;/code&gt;&lt;/bdi&gt; namespace added to their Wikipedias. This improvement ensures that links beginning with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;MOS:&lt;/code&gt;&lt;/bdi&gt; (usually shortcuts to the [[w:en:Wikipedia:Manual of Style|Manual of Style]]) are not broken by [[w:en:Mooré|Mooré]] Wikipedia (language code &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mos&lt;/code&gt;&lt;/bdi&gt;). [https://phabricator.wikimedia.org/T363538]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/37|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W37&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:52, 9 September 2024 (UTC)
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== Tech News: 2024-38 ==

&lt;section begin=&quot;technews-2024-W38&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/38|Translations]] are available.

'''Improvements and Maintenance'''
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Editors interested in templates can help by reading the latest Wishlist focus area, [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|Template recall and discovery]], and share your feedback on the talkpage. This input helps the Community Tech team to decide the right technical approach to build. Everyone is also encouraged to continue adding [[m:Special:MyLanguage/Community Wishlist|new wishes]].
* The new automated [[{{#special:NamespaceInfo}}]] page helps editors understand which [[mw:Special:MyLanguage/Help:Namespaces|namespaces]] exist on each wiki, and some details about how they are configured. Thanks to DannyS712 for these improvements. [https://phabricator.wikimedia.org/T263513]
* [[mw:Special:MyLanguage/Help:Edit check#Reference check|References Check]] is a feature that encourages editors to add a citation when they add a new paragraph to a Wikipedia article. For a short time, the corresponding tag &quot;Edit Check (references) activated&quot; was erroneously being applied to some edits outside of the main namespace. This has been fixed. [https://phabricator.wikimedia.org/T373692]
* It is now possible for a wiki community to change the order in which a page’s categories are displayed on their wiki. By default, categories are displayed in the order they appear in the wikitext. Now, wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Tool authors can now access ToolsDB's [[wikitech:Portal:Data Services#ToolsDB|public databases]] from both [[m:Special:MyLanguage/Research:Quarry|Quarry]] and [[wikitech:Superset|Superset]]. Those databases have always been accessible to every [[wikitech:Portal:Toolforge|Toolforge]] user, but they are now more broadly accessible, as Quarry can be accessed by anyone with a Wikimedia account. In addition, Quarry's internal database can now be [[m:Special:MyLanguage/Research:Quarry#Querying Quarry's own database|queried from Quarry itself]]. This database contains information about all queries that are being run and starred by users in Quarry. This information was already public through the web interface, but you can now query it using SQL. You can read more about that, and {{formatnum:20}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].
* Any pages or tools that still use the very old CSS classes &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mw-message-box&lt;/code&gt;&lt;/bdi&gt; need to be updated. These old classes will be removed next week or soon afterwards. Editors can use a [https://global-search.toolforge.org/?q=mw-message-box&amp;regex=1&amp;namespaces=&amp;title= global-search] to determine what needs to be changed. It is possible to use the newer &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;cdx-message&lt;/code&gt;&lt;/bdi&gt; group of classes as a replacement (see [https://doc.wikimedia.org/codex/latest/components/demos/message.html#css-only-version the relevant Codex documentation], and [https://meta.wikimedia.org/w/index.php?title=Tech/Header&amp;diff=prev&amp;oldid=27449042 an example update]), but using locally defined onwiki classes would be best. [https://phabricator.wikimedia.org/T374499]

'''Technical project updates'''
* Next week, all Wikimedia wikis will be read-only for a few minutes. This will start on September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. This is a planned datacenter switchover for maintenance purposes. [[m:Special:MyLanguage/Tech/Server switch|This maintenance process also targets other services.]] The previous switchover took 3 minutes, and the Site Reliability Engineering teams use many tools to make sure that this essential maintenance work happens as quickly as possible. [https://phabricator.wikimedia.org/T370962]

'''Tech in depth'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/August 2024|MediaWiki Product Insights newsletter]] is available. This edition includes details about: research about [[mw:Special:MyLanguage/Manual:Hooks|hook]] handlers to help simplify development, research about performance improvements, work to improve the REST API for end-users, and more.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: 
** [[c:File:Wikimania 2024 - Auditorium Kyiv - Day 4 - Hackathon Showcase.webm|Hackathon Showcase]] (45 mins) - 19 short presentations by some of the Hackathon participants, describing some of the projects they worked on, such as automated testing of maintenance scripts, a video-cutting command line tool, and interface improvements for various tools. There are [[phab:T369234|more details and links available]] in the Phabricator task.
** [[c:File:Co-Creating a Sustainable Future for the Toolforge Ecosystem.webm|Co-Creating a Sustainable Future for the Toolforge Ecosystem]] (40 mins) - a roundtable discussion for tool-maintainers, users, and supporters of Toolforge about how to make the platform sustainable and how to evaluate the tools available there.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/38|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W38&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:02, 17 September 2024 (UTC)
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== Tech News: 2024-39 ==

&lt;section begin=&quot;technews-2024-W39&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/39|Translations]] are available.

'''Weekly highlight'''
* All wikis will be [[m:Special:MyLanguage/Tech/Server switch|read-only]] for a few minutes on Wednesday September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. Reading the wikis will not be interrupted, but editing will be paused. These twice-yearly processes allow WMF's site reliability engineering teams to remain prepared to keep the wikis functioning even in the event of a major interruption to one of our data centers.

'''Updates for editors'''
[[File:Add alt text from a halfsheet, with the article behind.png|thumb|A screenshot of the interface for the Alt Text suggested-edit feature]]
* Editors who use the iOS Wikipedia app in Spanish, Portuguese, French, or Chinese, may see the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|Alt Text suggested-edit experiment]] after editing an article, or completing a suggested edit using &quot;[[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project#Hypothesis 2 Add an Image Suggested Edit|Add an image]]&quot;. Alt-text helps people with visual impairments to read Wikipedia articles. The team aims to learn if adding alt-text to images is a task that editors can be successful with. Please share any feedback on [[mw:Talk:Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|the discussion page]].
* The Codex color palette has been updated with new and revised colors for the MediaWiki user interfaces. The [[mw:Special:MyLanguage/Design System Team/Color/Design documentation#Updates|most noticeable changes]] for editors include updates for: dark mode colors for Links and for quiet Buttons (progressive and destructive), visited Link colors for both light and dark modes, and background colors for system-messages in both light and dark modes.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] It is now possible to include clickable wikilinks and external links inside code blocks. This includes links that are used within &lt;code&gt;&lt;nowiki&gt;&lt;syntaxhighlight&gt;&lt;/nowiki&gt;&lt;/code&gt; tags and on code pages (JavaScript, CSS, Scribunto and Sanitized CSS). Uses of template syntax &lt;code&gt;&lt;nowiki&gt;{{…}}&lt;/nowiki&gt;&lt;/code&gt; are also linked to the template page. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T368166]
* Two bugs were fixed in the [[m:Special:MyLanguage/Account vanishing|GlobalVanishRequest]] system by improving the logging and by removing an incorrect placeholder message. [https://phabricator.wikimedia.org/T370595][https://phabricator.wikimedia.org/T372223]
* View all {{formatnum:25}} community-submitted {{PLURAL:25|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] From [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]]: 
** The API now enables 5,000 on-demand API requests per month and twice-monthly HTML snapshots freely (gratis and libre). More information on the updates and also improvements to the software development kits (SDK) are explained on [https://enterprise.wikimedia.com/blog/enhanced-free-api/ the project's blog post]. While Wikimedia Enterprise APIs are designed for high-volume commercial reusers, this change enables many more community use-cases to be built on the service too.
** The Snapshot API (html dumps) have added beta Structured Contents endpoints ([https://enterprise.wikimedia.com/blog/structured-contents-snapshot-api/ blog post on that]) as well as released two beta datasets (English and French Wikipedia) from that endpoint to Hugging Face for public use and feedback ([https://enterprise.wikimedia.com/blog/hugging-face-dataset/ blog post on that]). These pre-parsed data sets enable new options for researchers, developers, and data scientists to use and study the content.

'''In depth'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The Wikidata Query Service (WDQS) is used to get answers to questions using the Wikidata data set. As Wikidata grows, we had to make a major architectural change so that WDQS could remain performant. As part of the [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split project]], we have new SPARQL endpoints available for serving the &quot;[https://query-scholarly.wikidata.org scholarly]&quot; and &quot;[https://query-main.wikidata.org main]&quot; subgraphs of Wikidata. The [http://query.wikidata.org query.wikidata.org endpoint] will continue to serve the full Wikidata graph until March 2025. After this date, it will only serve the main graph. For more information, please see [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/September 2024 scaling update|the announcement on Wikidata]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/39|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W39&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:36, 23 September 2024 (UTC)
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== Tech News: 2024-40 ==

&lt;section begin=&quot;technews-2024-W40&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/40|Translations]] are available.

'''Updates for editors'''
* Readers of [[phab:T375401|42 more wikis]] can now use Dark Mode. If the option is not yet available for logged-out users of your wiki, this is likely because many templates do not yet display well in Dark Mode. Please use the [https://night-mode-checker.wmcloud.org/ night-mode-checker tool] if you are interested in helping to reduce the number of issues. The [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations page]] provides guidance on this. Dark Mode is enabled on additional wikis once per month.
* Editors using the 2010 wikitext editor as their default can access features from the 2017 wikitext editor by adding &lt;code dir=ltr&gt;?veaction=editsource&lt;/code&gt; to the URL. If you would like to enable the 2017 wikitext editor as your default, it can be set in [[Special:Preferences#mw-input-wpvisualeditor-newwikitext|your preferences]]. [https://phabricator.wikimedia.org/T239796]
* For logged-out readers using the Vector 2022 skin, the &quot;donate&quot; link has been moved from a collapsible menu next to the content area into a more prominent top menu, next to &quot;Create an account&quot;. This restores the link to the level of prominence it had in the Vector 2010 skin. [[mw:Readers/2024 Reader and Donor Experiences#Donor Experiences (Key Result WE 3.2 and the related hypotheses)|Learn more]] about the changes related to donor experiences. [https://phabricator.wikimedia.org/T373585]
* The CampaignEvents extension provides tools for organizers to more easily manage events, communicate with participants, and promote their events on the wikis. The extension has been [[m:Special:MyLanguage/CampaignEvents/Deployment status|enabled]] on Arabic Wikipedia, Igbo Wikipedia, Swahili Wikipedia, and Meta-Wiki. [[w:zh:Wikipedia:互助客栈/其他#引進CampaignEvents擴充功能|Chinese Wikipedia has decided]] to enable the extension, and discussions on the extension are in progress [[w:es:Wikipedia:Votaciones/2024/Sobre la política de Organizadores de Eventos|on Spanish Wikipedia]] and [[d:Wikidata:Project chat#Enabling the CampaignEvents Extention on Wikidata|on Wikidata]]. To learn how to enable the extension on your wiki, you can visit [[m:Special:MyLanguage/CampaignEvents|the CampaignEvents page on Meta-Wiki]].
* View all {{formatnum:22}} community-submitted {{PLURAL:22|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Developers with an account on Wikitech-wiki should [[wikitech:Wikitech/SUL-migration|check if any action is required]] for their accounts. The wiki is being changed to use the single-user-login (SUL) system, and other configuration changes. This change will help reduce the overall complexity for the weekly software updates across all our wikis.

'''In depth'''
* The [[m:Special:MyLanguage/Tech/Server switch|server switch]] was completed successfully last week with a read-only time of [[wikitech:Switch Datacenter#Past Switches|only 2 minutes 46 seconds]]. This periodic process makes sure that engineers can switch data centers and keep all of the wikis available for readers, even if there are major technical issues. It also gives engineers a chance to do maintenance and upgrades on systems that normally run 24 hours a day, and often helps to reveal weaknesses in the infrastructure. The process involves dozens of software services and hundreds of hardware servers, and requires multiple teams working together. Work over the past few years has reduced the time from 17 minutes down to 2–3 minutes. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/66ZW7B2MG63AESQVTXDIFQBDBS766JGW/]

'''Meetings and events'''
* October 4–6: [[m:Special:MyLanguage/WikiIndaba conference 2024|WikiIndaba Conference's Hackathon]] in Johannesburg, South Africa
* November 4–6: [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] in Vienna, Austria

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/40|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W40&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:20, 30 September 2024 (UTC)
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== Tech News: 2024-41 ==

&lt;section begin=&quot;technews-2024-W41&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/41|Translations]] are available.

'''Weekly highlight'''
* Communities can now request installation of [[mw:Special:MyLanguage/Moderator Tools/Automoderator|Automoderator]] on their wiki. Automoderator is an automated anti-vandalism tool that reverts bad edits based on scores from the new &quot;Revert Risk&quot; machine learning model. You can [[mw:Special:MyLanguage/Extension:AutoModerator/Deploying|read details about the necessary steps]] for installation and configuration. [https://phabricator.wikimedia.org/T336934]

'''Updates for editors'''
* Translators in wikis where [[mw:Special:MyLanguage/Content translation/Section translation#Try the tool|the mobile experience of Content Translation is available]], can now customize their articles suggestion list from 41 filtering options when using the tool. This topic-based article suggestion feature makes it easy for translators to self-discover relevant articles based on their area of interest and translate them. You can [https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;active-list=suggestions try it with your mobile device]. [https://phabricator.wikimedia.org/T368422]
* View all {{formatnum:12}} community-submitted {{PLURAL:12|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* It is now possible for &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;&lt;syntaxhighlight&gt;&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; code blocks to offer readers a &quot;Copy&quot; button if the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;copy=1&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; attribute is [[mw:Special:MyLanguage/Extension:SyntaxHighlight#copy|set on the tag]]. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T40932]
* Customized copyright footer messages on all wikis will be updated. The new versions will use wikitext markup instead of requiring editing raw HTML. [https://phabricator.wikimedia.org/T375789]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Later this month, [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] will be rolled out on several pilot wikis. The final list of the wikis will be published in the second half of the month. If you maintain any tools, bots, or gadgets on [[phab:T376499|these 11 wikis]], and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]].
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Rate limiting has been enabled for the code review tools [[Wikitech:Gerrit|Gerrit]] and [[Wikitech:GitLab|GitLab]] to address ongoing issues caused by malicious traffic and scraping. Clients that open too many concurrent connections will be restricted for a few minutes. This rate limiting is managed through [[Wikitech:nftables|nftables]] firewall rules. For more details, see Wikitech's pages on [[Wikitech:Firewall#Throttling with nftables|Firewall]], [[Wikitech:GitLab/Abuse and rate limiting|GitLab limits]] and [[Wikitech:Gerrit/Operations#Throttling IPs|Gerrit operations]].
* Five new wikis have been created: 
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q49224|Komering]] ([[w:kge:|&lt;code&gt;w:kge:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T374813]
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q36096|Mooré]] ([[m:mos:|&lt;code&gt;m:mos:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T374641]
** a {{int:project-localized-name-group-wiktionary}} in [[d:Q36213|Madurese]] ([[wikt:mad:|&lt;code&gt;wikt:mad:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T374968]
** a {{int:project-localized-name-group-wikiquote}} in [[d:Q2501174|Gorontalo]] ([[q:gor:|&lt;code&gt;q:gor:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T375088]
** a {{int:project-localized-name-group-wikinews}} in [[d:Q56482|Shan]] ([[n:shn:|&lt;code&gt;n:shn:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T375430]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/41|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W41&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:42, 7 October 2024 (UTC)
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== Tech News: 2024-42 ==

&lt;section begin=&quot;technews-2024-W42&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/42|Translations]] are available.

'''Updates for editors'''
* The Structured Discussion extension (also known as Flow) is starting to be removed. This extension is unmaintained and causes issues. It will be replaced by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]], which is used on any regular talk page. [[mw:Special:MyLanguage/Structured Discussions/Deprecation#Deprecation timeline|A first set of wikis]] are being contacted. These wikis are invited to stop using Flow, and to move all Flow boards to sub-pages, as archives. At these wikis, a script will move all Flow pages that aren't a sub-page to a sub-page automatically, starting on 22 October 2024. On 28 October 2024, all Flow boards at these wikis will be set in read-only mode. [https://www.mediawiki.org/wiki/Structured_Discussions/Deprecation][https://phabricator.wikimedia.org/T370722]
* WMF's Search Platform team is working on making it easier for readers to perform text searches in their language. A [[phab:T332342|change last week]] on over 30 languages makes it easier to find words with accents and other diacritics. This applies to both full-text search and to types of advanced search such as the &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;''hastemplate''&lt;/bdi&gt; and &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;''incategory''&lt;/bdi&gt; keywords. More technical details (including a few other minor search upgrades) are available. [https://www.mediawiki.org/wiki/User:TJones_%28WMF%29/Notes/Language_Analyzer_Harmonization_Notes#ASCII-folding/ICU-folding_%28T332342%29]
* View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[mw:Special:MyLanguage/Help:Edit check|EditCheck]] was installed at Russian Wikipedia, and fixes were made for some missing user interface styles.

'''Updates for technical contributors'''
* Editors who use the Toolforge tool [[toolforge:copyvios|Earwig's Copyright Violation Detector]] will now be required to log in with their Wikimedia account before running checks using the &quot;search engine&quot; option. This change is needed to help prevent external bots from misusing the system. Thanks to Chlod for these improvements. [https://en.wikipedia.org/wiki/Wikipedia_talk:New_pages_patrol/Reviewers#Authentication_is_now_required_for_search_engine_checks_on_Earwig's_Copyvio_Tool]
* [[m:Special:MyLanguage/Phabricator|Phabricator]] users can create tickets and add comments on existing tickets via Email again. [[mw:Special:MyLanguage/Phabricator/Help#Using email|Sending email to Phabricator]] has been fixed. [https://phabricator.wikimedia.org/T356077]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Some HTML elements in the interface are now wrapped with a &lt;code&gt;&lt;nowiki&gt;&lt;bdi&gt;&lt;/nowiki&gt;&lt;/code&gt; element, to make our HTML output more aligned with Web standards. More changes like this will be coming in future weeks. This change might break some tools that rely on the previous HTML structure of the interface. Note that relying on the HTML structure of the interface is [[mw:Special:MyLanguage/Stable interface policy/Frontend#What is not stable?|not recommended]] and might break at any time. [https://phabricator.wikimedia.org/T375975]

'''In depth'''
* The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/September 2024|MediaWiki Product Insights newsletter]] is available. This edition includes: updates on Wikimedia's authentication system, research to simplify feature development in the MediaWiki platform, updates on Parser Unification and MathML rollout, and more.
* The latest quarterly [[mw:Technical Community Newsletter/2024/October|Technical Community Newsletter]] is now available. This edition include: research about improving topic suggestions related to countries, improvements to PHPUnit tests, and more.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/42|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W42&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:21, 14 October 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27597254 --&gt;

== Tech News: 2024-43 ==

&lt;section begin=&quot;technews-2024-W43&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/43|Translations]] are available.

'''Weekly highlight'''
* The Mobile Apps team has released an [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh#Phase 1: Creating a user Profile Menu (T373714)|update]] to the iOS app's navigation, and it is now available in the latest App store version. The team added a new Profile menu that allows for easy access to editor features like Notifications and Watchlist from the Article view, and brings the &quot;Donate&quot; button into a more accessible place for users who are reading an article. This is the first phase of a larger planned [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh|navigation refresh]] to help the iOS app transition from a primarily reader-focused app, to an app that fully supports reading and editing. The Wikimedia Foundation has added more editing features and support for on-wiki communication based on volunteer requests in recent years.
[[File:IOS App Navigation refresh first phase 05.png|thumb|iOS Wikipedia App's profile menu and contents]]

'''Updates for editors'''
* Wikipedia readers can now download a browser extension to experiment with some early ideas on potential features that recommend articles for further reading, automatically summarize articles, and improve search functionality. For more details and to stay updated, check out the Web team's [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments|Content Discovery Experiments page]] and [[mw:Special:MyLanguage/Newsletter:Web team's projects|subscribe to their newsletter]].
* Later this month, logged-out editors of [[phab:T376499|these 12 wikis]] will start to have [[mw:Special:Mylanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] created. The list may slightly change - some wikis may be removed but none will be added. Temporary account is a new [[mw:Special:MyLanguage/User account types|type of user account]]. It enhances the logged-out editors' privacy and makes it easier for community members to communicate with them. If you maintain any tools, bots, or gadgets on these 12 wikis, and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]]. Read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|deployment plan across all wikis]].
* View all {{formatnum:33}} community-submitted {{PLURAL:33|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, the [[w:nr:Main Page|South Ndebele]], [[w:rsk:Главни бок|Pannonian Rusyn]], [[w:ann:Uwu|Obolo]], [[w:iba:Lambar Keterubah|Iban]] and [[w:tdd:ᥞᥨᥝᥴ ᥘᥣᥲ ᥖᥥᥰ|Tai Nüa]] Wikipedia languages were created last week. [https://www.wikidata.org/wiki/Q36785][https://www.wikidata.org/wiki/Q35660][https://www.wikidata.org/wiki/Q36614][https://www.wikidata.org/wiki/Q33424][https://www.wikidata.org/wiki/Q36556]
* It is now possible to create functions on Wikifunctions using Wikidata lexemes, through the new [[f:Z6005|Wikidata lexeme type]] launched last week. When you go to one of these functions, the user interface provides a lexeme selector that helps you pick a lexeme from Wikidata that matches the word you type. After hitting run, your selected lexeme is retrieved from Wikidata, transformed into a Wikidata lexeme type, and passed into the selected function. Read more about this in [[f:Special:MyLanguage/Wikifunctions:Status updates/2024-10-17#Function of the Week: select representation from lexeme|the latest Wikifunctions newsletter]].

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Users of the Wikimedia sites can now format dates more easily in different languages with the new &lt;code dir=&quot;ltr&quot;&gt;{{[[mw:Special:MyLanguage/Help:Extension:ParserFunctions##timef|#timef]]:…}}&lt;/code&gt; parser function. For example, &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{#timef:now|date|en}}&lt;/nowiki&gt;&lt;/code&gt; will show as &quot;&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;{{#timef:now|date|en}}&lt;/bdi&gt;&quot;. Previously, &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{#time:…}}&lt;/nowiki&gt;&lt;/code&gt; could be used to format dates, but this required knowledge of the order of the time and date components and their intervening punctuation. &lt;code dir=&quot;ltr&quot;&gt;#timef&lt;/code&gt; (or &lt;code dir=&quot;ltr&quot;&gt;#timefl&lt;/code&gt; for local time) provides access to the standard date formats that MediaWiki uses in its user interface. This may help to simplify some templates on multi-lingual wikis like Commons and Meta. [https://phabricator.wikimedia.org/T223772][https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:ParserFunctions##timef]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Commons and Meta users can now efficiently [[mw:Special:MyLanguage/Help:Magic words#Localization|retrieve the user's language]] using &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{USERLANGUAGE}}&lt;/nowiki&gt;&lt;/code&gt; instead of using &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{int:lang}}&lt;/nowiki&gt;&lt;/code&gt;. [https://phabricator.wikimedia.org/T4085]
* The [[m:Special:MyLanguage/Product and Technology Advisory Council|Product and Tech Advisory Council]] (PTAC) now has its pilot members with representation across Africa, Asia, Europe, North America and South America. They will work to address the [[Special:MyLanguage/Movement Strategy/Initiatives/Technology Council|Movement Strategy's Technology Council]] initiative of having a co-defined and more resilient technological platform. [https://meta.wikimedia.org/wiki/Movement_Strategy/Initiatives/Technology_Council]

'''In depth'''
* The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/32|Growth newsletter]] is available. It includes: an upcoming Newcomer Homepage Community Updates module, new Community Configuration options, and details on new projects.
* The Wikimedia Foundation is [[mw:Special:MyLanguage/Wikimedia Security Team#CNA Partnership|now an official partner of the CVE program]], which is an international effort to catalog publicly disclosed cybersecurity vulnerabilities. This partnership will allow the Security Team to instantly publish [[w:en:Common Vulnerabilities and Exposures|common vulnerabilities and exposures]] (CVE) records that are affecting MediaWiki core, extensions, and skins, along with any other code the Foundation is a steward of.
* The [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]] is now [[m:Community Wishlist/Updates#October 16, 2024: Conversations Made Easier: Machine-Translated Wishes Are Here!|testing machine translations]] for Wishlist content. Volunteers can now read machine-translated versions of wishes and dive into discussions even before translators arrive to translate content.

'''Meetings and events'''
* 24 October - Wiki Education Speaker Series Webinar - [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/N4XTB4G55BUY3M3PNGUAKQWJ7A4UOPAK/ Open Source Tech: Building the Wiki Education Dashboard], featuring Wikimedia interns and a Web developer in the panel.
* 20–22 December 2024 - [[m:Special:MyLanguage/Indic Wikimedia Hackathon Bhubaneswar 2024|Indic Wikimedia Hackathon Bhubaneswar 2024]] in Odisha, India. A hackathon for community members, including developers, designers and content editors, to build technical solutions that improve contributors' experiences.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/43|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W43&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:52, 21 October 2024 (UTC)
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== Tech News: 2024-44 ==

&lt;section begin=&quot;technews-2024-W44&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/44|Translations]] are available.

'''Updates for editors'''
* Later in November, the Charts extension will be deployed to the test wikis in order to help identify and fix any issue. A security review is underway to then enable deployment to pilot wikis for broader testing. You can read [[mw:Special:MyLanguage/Extension:Chart/Project/Updates#October 2024: Working towards production deployment|the October project update]] and see the [https://en.wikipedia.beta.wmflabs.org/wiki/Charts latest documentation and examples on Beta Wikipedia].
* View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[w:en:PediaPress|Pediapress.com]], an external service that creates books from Wikipedia, can now use [[mw:Special:MyLanguage/Wikimedia Maps|Wikimedia Maps]] to include existing pre-rendered infobox map images in their printed books on Wikipedia. [https://phabricator.wikimedia.org/T375761]

'''Updates for technical contributors'''
* Wikis can use [[:mw:Special:MyLanguage/Extension:GuidedTour|the Guided Tour extension]] to help newcomers understand how to edit. The Guided Tours extension now works with [[mw:Special:MyLanguage/Manual:Dark mode|dark mode]]. Guided Tour maintainers can check their tours to see that nothing looks odd. They can also set &lt;code&gt;emitTransitionOnStep&lt;/code&gt; to &lt;code&gt;true&lt;/code&gt; to fix an old bug. They can use the new flag &lt;code&gt;allowAutomaticBack&lt;/code&gt; to avoid back-buttons they don't want. [https://phabricator.wikimedia.org/T73927#10241528]
*  Administrators in the Wikimedia projects who use the [[mw:Special:MyLanguage/Help:Extension:Nuke|Nuke Extension]] will notice that mass deletions done with this tool have the &quot;Nuke&quot; tag. This change will make reviewing and analyzing deletions performed with the tool easier. [https://phabricator.wikimedia.org/T366068]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/44|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W44&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:56, 28 October 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27668811 --&gt;

== Tech News: 2024-45 ==

&lt;section begin=&quot;technews-2024-W45&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/45|Translations]] are available.

'''Updates for editors'''
* Stewards can now make [[m:Special:MyLanguage/Global blocks|global account blocks]] cause global [[mw:Special:MyLanguage/Autoblock|autoblocks]]. This will assist stewards in preventing abuse from users who have been globally blocked. This includes preventing globally blocked temporary accounts from exiting their session or switching browsers to make subsequent edits for 24 hours. Previously, temporary accounts could exit their current session or switch browsers to continue editing. This is an anti-abuse tool improvement for the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project. You can read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|progress on key features for temporary accounts]]. [https://phabricator.wikimedia.org/T368949]
* Wikis that have the [[m:Special:MyLanguage/CampaignEvents/Deployment status|CampaignEvents extension enabled]] can now use the [[m:Special:MyLanguage/Campaigns/Foundation Product Team/Event list#October 29, 2024: Collaboration List launched|Collaboration List]] feature. This list provides a new, easy way for contributors to learn about WikiProjects on their wikis. Thanks to the Campaign team for this work that is part of [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product %26 Technology OKRs#WE KRs|the 2024/25 annual plan]]. If you are interested in bringing the CampaignEvents extension to your wiki, you can [[m:Special:MyLanguage/CampaignEvents/Deployment status#How to Request the CampaignEvents Extension for your wiki|follow these steps]] or you can reach out to User:Udehb-WMF for help.
* The text color for red links will be slightly changed later this week to improve their contrast in light mode. [https://phabricator.wikimedia.org/T370446]
* View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, on multilingual wikis, users [[phab:T216368|can now]] hide translations from the WhatLinksHere special page.

'''Updates for technical contributors'''
* XML [[m:Special:MyLanguage/Data dumps|data dumps]] have been temporarily paused whilst a bug is investigated. [https://lists.wikimedia.org/hyperkitty/list/xmldatadumps-l@lists.wikimedia.org/message/BXWJDPO5QI2QMBCY7HO36ELDCRO6HRM4/]

'''In depth'''
* Temporary Accounts have been deployed to six wikis; thanks to the Trust and Safety Product team for [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|this work]], you can read about [[phab:T340001|the deployment plans]]. Beginning next week, Temporary Accounts will also be enabled on [[phab:T378336|seven other projects]]. If you are active on these wikis and need help migrating your tools, please reach out to [[m:User:Udehb-WMF|User:Udehb-WMF]] for assistance.
*  The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/October|Language and Internationalization newsletter]] is available.  It includes: New languages supported in translatewiki or in MediaWiki; New keyboard input methods for some languages; details about recent and upcoming meetings, and more.

'''Meetings and events'''
* [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] is happening in Vienna, Austria and online from 4 to 6 November 2024. The conference will feature discussions around the usage of MediaWiki software by and within companies in different industries and will inspire and onboard new users.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/45|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W45&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:50, 4 November 2024 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27693917 --&gt;

== Tech News: 2024-46 ==

&lt;section begin=&quot;technews-2024-W46&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/46|Translations]] are available.

'''Updates for editors'''
* On wikis with the [[mw:Special:MyLanguage/Help:Extension:Translate|Translate extension]] enabled, users will notice that the FuzzyBot will now automatically create translated versions of categories used on translated pages. [https://phabricator.wikimedia.org/T285463]
* View all {{formatnum:29}} community-submitted {{PLURAL:29|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the submitted task to use the [[mw:Special:MyLanguage/Extension:SecurePoll|SecurePoll extension]] for English Wikipedia's special [[w:en:Wikipedia:Administrator elections|administrator election]] was resolved on time. [https://phabricator.wikimedia.org/T371454] 

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] In &lt;code dir=&quot;ltr&quot;&gt;[[mw:MediaWiki_1.44/wmf.2|1.44.0-wmf-2]]&lt;/code&gt;, the logic of Wikibase function &lt;code&gt;getAllStatements&lt;/code&gt; changed to behave like &lt;code&gt;getBestStatements&lt;/code&gt;. Invoking the function now returns a copy of values which are immutable. [https://phabricator.wikimedia.org/T270851]
* [https://en.wikipedia.org/api/rest_v1/ Wikimedia REST API] users, such as bot operators and tool maintainers, may be affected by ongoing upgrades. The API will be rerouting some page content endpoints from RESTbase to the newer [[mw:Special:MyLanguage/API:REST API|MediaWiki REST API]] endpoints. The [[phab:T374683|impacted endpoints]] include getting page/revision metadata and rendered HTML content. These changes will be available on testwiki later this week, with other projects to follow. This change should not affect existing functionality, but active users of the impacted endpoints should verify behavior on testwiki, and raise any concerns on the related [[phab:T374683|Phabricator ticket]].

'''In depth'''
* Admins and users of the Wikimedia projects [[mw:Special:MyLanguage/Moderator_Tools/Automoderator#Usage|where Automoderator is enabled]] can now monitor and evaluate important metrics related to Automoderator's actions. [https://superset.wmcloud.org/superset/dashboard/unified-automoderator-activity-dashboard/ This Superset dashboard] calculates and aggregates metrics about Automoderator's behaviour on the projects in which it is deployed. Thanks to the Moderator Tools team for this Dashboard; you can visit [[mw:Special:MyLanguage/Moderator Tools/Automoderator/Unified Activity Dashboard|the documentation page]] for more information about this work. [https://phabricator.wikimedia.org/T369488]

'''Meetings and events'''
* 21 November 2024 ([[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 8:00 UTC|8:00 UTC]] &amp; [[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 16:00 UTC|16:00 UTC]]) - [[c:Commons:WMF support for Commons/Commons community calls|Community call]] with Wikimedia Commons volunteers and stakeholders to help prioritize support efforts for 2025-2026 Fiscal Year. The theme of this call is how content should be organised on Wikimedia Commons.
'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/46|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W46&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:07, 12 November 2024 (UTC)
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== Tech News: 2024-47 ==

&lt;section begin=&quot;technews-2024-W47&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/47|Translations]] are available.

'''Updates for editors'''
* Users of Wikimedia sites will now be warned when they create a [[mw:Special:MyLanguage/Help:Redirects|redirect]] to a page that doesn't exist. This will reduce the number of broken redirects to red links in our projects. [https://phabricator.wikimedia.org/T326057]
* View all {{formatnum:42}} community-submitted {{PLURAL:42|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[mw:Special:MyLanguage/Manual:Pywikibot/Overview|Pywikibot]], which automates work on MediaWiki sites, was upgraded to 9.5.0 on Toolforge. [https://phabricator.wikimedia.org/T378676]

'''Updates for technical contributors'''
* On wikis that use the [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs extension]], pages created or moved by users with the appropriate permissions are marked as flagged automatically. This feature has not been working recently, and changes fixing it should be deployed this week. Thanks to Daniel and Wargo for working on this. [https://phabricator.wikimedia.org/T379218][https://phabricator.wikimedia.org/T368380]

'''In depth'''
* There is a new [https://diff.wikimedia.org/2024/11/05/say-hi-to-temporary-accounts-easier-collaboration-with-logged-out-editors-with-better-privacy-protection Diff post] about Temporary Accounts, available in more than 15 languages. Read it to learn about what Temporary Accounts are, their impact on different groups of users, and the plan to introduce the change on all wikis.

'''Meetings and events'''
* Technical volunteers can now register for the [[mw:Special:MyLanguage/Wikimedia Hackathon 2025|2025 Wikimedia Hackathon]], which will take place in Istanbul, Turkey. [https://pretix.eu/wikimedia/hackathon2025/ Application for travel and accommodation scholarships] is open from '''November 12 to December 10 2024'''. The registration for the event will close in mid-April 2025. The Wikimedia Hackathon is an annual gathering that unites the global technical community to collaborate on existing projects and explore new ideas.
* Join the [[C:Special:MyLanguage/Commons:WMF%20support%20for%20Commons/Commons%20community%20calls|Wikimedia Commons community calls]] this week to help prioritize support for Commons which will be planned for 2025–2026. The theme will be how content should be organised on Wikimedia Commons. This is an opportunity for volunteers who work on different things to come together and talk about what matters for the future of the project. The calls will take place '''November 21, 2024, [[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 8:00 UTC|8:00 UTC]] and [[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 16:00 UTC|16:00 UTC]]'''.
* A [[mw:Special:MyLanguage/Wikimedia_Language_and_Product_Localization/Community meetings#29 November 2024|Language community meeting]] will take place '''November 29, 16:00 UTC''' to discuss updates and technical problem-solving.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/47|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W47&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 02:00, 19 November 2024 (UTC)
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== Tech News: 2024-48 ==

&lt;section begin=&quot;technews-2024-W48&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/48|Translations]] are available.

'''Updates for editors'''
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] A new version of the standard wikitext editor-mode [[mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighter]] will be available as a [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] later this week. This brings many new features and bug fixes, including right-to-left support, [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Template folding|template folding]], [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Autocompletion|autocompletion]], and an improved search panel. You can learn more on the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|help page]].
* The 2010 wikitext editor now supports common keyboard shortcuts such &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Ctrl&lt;/code&gt;+&lt;code&gt;B&lt;/code&gt;&lt;/bdi&gt; for bold and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Ctrl&lt;/code&gt;+&lt;code&gt;I&lt;/code&gt;&lt;/bdi&gt; for italics. A full [[mw:Help:Extension:WikiEditor#Keyboard shortcuts|list of all six shortcuts]] is available. Thanks to SD0001 for this improvement. [https://phabricator.wikimedia.org/T62928]
* Starting November 28, Flow/Structured Discussions pages will be automatically archived and set to read-only at the following wikis: &lt;bdi&gt;bswiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;elwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;euwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;fawiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;fiwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;frwikiquote&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;frwikisource&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;frwikiversity&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;frwikivoyage&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;idwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;lvwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;plwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;ptwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;urwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;viwikisource&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;zhwikisource&lt;/bdi&gt;. This is done as part of [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|StructuredDiscussions deprecation work]]. If you need any assistance to archive your page in advance, please contact [[m:User:Trizek (WMF)|Trizek (WMF)]]. 
* View all {{formatnum:25}} community-submitted {{PLURAL:25|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a user creating a new AbuseFilter can now only set the filter to &quot;protected&quot; [[phab:T377765|if it includes a protected variable]].

'''Updates for technical contributors'''
* The [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]], which can be used in JavaScript, CSS, JSON, and Lua pages, [[phab:T377663|now offers]] live autocompletion. Thanks to SD0001 for this improvement. The feature can be temporarily disabled on a page by pressing &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;Ctrl&lt;/code&gt;+&lt;code&gt;,&lt;/code&gt;&lt;/bdi&gt; and un-selecting &quot;&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;Live Autocompletion&lt;/bdi&gt;&quot;.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Tool-maintainers who use the Graphite system for tracking metrics, need to migrate to the newer Prometheus system. They can check [https://grafana.wikimedia.org/d/K6DEOo5Ik/grafana-graphite-datasource-utilization?orgId=1 this dashboard] and the list in the Description of the [[phab:T350592|task T350592]] to see if their tools are listed, and they should claim metrics and dashboards connected to their tools. They can then disable or migrate all existing metrics by following the instructions in the task. The Graphite service will become read-only in April. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/KLUV4IOLRYXPQFWD6WKKJUHMWE77BMSZ/]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The [[mw:Special:MyLanguage/NewPP parser report|New PreProcessor parser performance report]] has been fixed to give an accurate count for the number of Wikibase entities accessed. It had previously been resetting after 400 entities. [https://phabricator.wikimedia.org/T279069]

'''Meetings and events'''
* A [[mw:Special:MyLanguage/Wikimedia_Language_and_Product_Localization/Community meetings#29 November 2024|Language community meeting]] will take place November 29 at [https://zonestamp.toolforge.org/1732896000 16:00 UTC]. There will be presentations on topics like developing language keyboards, the creation of the Mooré Wikipedia, the language support track at [[m:Wiki Indaba|Wiki Indaba]], and a report from the Wayuunaiki community on their experiences with the Incubator and as a new community over the last 3 years. This meeting will be in English and will also have Spanish interpretation.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/48|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W48&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:42, 25 November 2024 (UTC)
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== Tech News: 2024-49 ==

&lt;section begin=&quot;technews-2024-W49&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/49|Translations]] are available.

'''Updates for editors'''
* Two new parser functions were added this week. The &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{&lt;/nowiki&gt;[[mw:Special:MyLanguage/Help:Magic words#interwikilink|#interwikilink]]&lt;nowiki&gt;}}&lt;/nowiki&gt;&lt;/code&gt; function adds an [[mw:Special:MyLanguage/Help:Links#Interwiki links|interwiki link]] and the &lt;code dir=&quot;ltr&quot;&gt;&lt;nowiki&gt;{{&lt;/nowiki&gt;[[mw:Special:MyLanguage/Help:Magic words#interlanguagelink|#interlanguagelink]]&lt;nowiki&gt;}}&lt;/nowiki&gt;&lt;/code&gt; function adds an [[mw:Special:MyLanguage/Help:Links#Interlanguage links|interlanguage link]]. These parser functions are useful on wikis where namespaces conflict with interwiki prefixes. For example, links beginning with &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;MOS:&lt;/code&gt;&lt;/bdi&gt; on English Wikipedia [[phab:T363538|conflict with the &lt;code&gt;mos&lt;/code&gt; language code prefix of Mooré Wikipedia]].
* Starting this week, Wikimedia wikis no longer support connections using old RSA-based HTTPS certificates, specifically rsa-2048. This change is to improve security for all users. Some older, unsupported browser or smartphone devices will be unable to connect; Instead, they will display a connectivity error. See the [[wikitech:HTTPS/Browser_Recommendations|HTTPS Browser Recommendations page]] for more-detailed information. All modern operating systems and browsers are always able to reach Wikimedia projects. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/CTYEHVNSXUD3NFAAMG3BLZVTVQWJXJAH/]
* Starting December 16, Flow/Structured Discussions pages will be automatically archived and set to read-only at the following wikis: &lt;bdi&gt;arwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;cawiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;frwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;mediawikiwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;orwiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;wawiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;wawiktionary&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;wikidatawiki&lt;/bdi&gt;{{int:comma-separator/en}}&lt;bdi&gt;zhwiki&lt;/bdi&gt;. This is done as part of [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|StructuredDiscussions deprecation work]]. If you need any assistance to archive your page in advance, please contact [[m:User:Trizek (WMF)|Trizek (WMF)]]. [https://phabricator.wikimedia.org/T380910]
* This month the Chart extension was deployed to production and is now available on Commons and Testwiki. With the security review complete, pilot wiki deployment is expected to start in the first week of December. You can see a working version [[testwiki:Charts|on Testwiki]] and read [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|the November project update]] for more details.
* View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug with the &quot;Download as PDF&quot; system was fixed. [https://phabricator.wikimedia.org/T376438]

'''Updates for technical contributors'''
* In late February, temporary accounts will be rolled out on at least 10 large wikis. This deployment will have a significant effect on the community-maintained code. This is about Toolforge tools, bots, gadgets, and user scripts that use IP address data or that are available for logged-out users. The Trust and Safety Product team wants to identify this code, monitor it, and assist in updating it ahead of the deployment to minimize disruption to workflows. The team asks technical editors and volunteer developers to help identify such tools by adding them to [[mw:Trust and Safety Product/Temporary Accounts/For developers/Impacted tools|this list]]. In addition, review the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|updated documentation]] to learn how to adjust the tools. Join the discussions on the [[mw:Talk:Trust and Safety Product/Temporary Accounts|project talk page]] or in the [[discord:channels/221049808784326656/1227616742340034722|dedicated thread]] on the [[w:Wikipedia:Discord|Wikimedia Community Discord server (in English)]] for support and to share feedback. 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/49|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W49&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:22, 2 December 2024 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=27873992 --&gt;

== Tech News: 2024-50 ==

&lt;section begin=&quot;technews-2024-W50&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/50|Translations]] are available.

'''Weekly highlight'''
* Technical documentation contributors can find updated resources, and new ways to connect with each other and the Wikimedia Technical Documentation Team, at the [[mw:Special:MyLanguage/Documentation|Documentation hub]] on MediaWiki.org. This page links to: resources for writing and improving documentation, a new &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;#wikimedia-techdocs&lt;/bdi&gt; IRC channel on libera.chat, a listing of past and upcoming documentation events, and ways to request a documentation consultation or review. If you have any feedback or ideas for improvements to the documentation ecosystem, please [[mw:Wikimedia Technical Documentation Team#Contact us|contact the Technical Documentation Team]].

'''Updates for editors'''
[[File:Edit Check on Desktop.png|thumb|Layout change for the Edit Check feature]]
* Later this week, [[mw:Special:MyLanguage/Edit check|Edit Check]] will be relocated to a sidebar on desktop. Edit check is the feature for new editors to help them follow policies and guidelines. This layout change creates space to present people with [[mw:Edit check#1 November 2024|new Checks]] that appear ''while'' they are typing. The [[mw:Special:MyLanguage/Edit check#Reference Check A/B Test|initial results]] show newcomers encountering Edit Check are 2.2 times more likely to publish a new content edit that includes a reference and is not reverted.
* The Chart extension, which enables editors to create data visualizations, was successfully made available on MediaWiki.org and three pilot wikis (Italian, Swedish, and Hebrew Wikipedias). You can see a working examples [[testwiki:Charts|on Testwiki]] and read [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|the November project update]] for more details.
* Translators in wikis where the [[mw:Special:MyLanguage/Content translation/Section translation#Try the tool|mobile experience of Content Translation is available]], can now discover articles in Wikiproject campaigns of their interest from the &quot;[https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;campaign=specialcx&amp;filter-type=automatic&amp;filter-id=collections&amp;active-list=suggestions&amp;from=es&amp;to=en All collection]&quot; category in the articles suggestion feature. Wikiproject Campaign organizers can use this feature, to help translators to discover articles of interest, by adding the &lt;code dir=ltr&gt;&lt;nowiki&gt;&lt;page-collection&gt; &lt;/page-collection&gt;&lt;/nowiki&gt;&lt;/code&gt; tag to their campaign article list page on Meta-wiki. This will make those articles discoverable in the Content Translation tool. For more detailed information on how to use the tool and tag, please refer to [[mw:Special:MyLanguage/Translation suggestions: Topic-based &amp; Community-defined lists/How to use the features|the step-by-step guide]]. [https://phabricator.wikimedia.org/T378958]
* The [[mw:Special:MyLanguage/Extension:Nuke|Nuke]] feature, which enables administrators to mass delete pages, now has a [[phab:T376379#10310998|multiselect filter for namespace selection]]. This enables users to select multiple specific namespaces, instead of only one or all, when fetching pages for deletion.
* The Nuke feature also now [[phab:T364225#10371365|provides links]] to the userpage of the user whose pages were deleted, and to the pages which were not selected for deletion, after page deletions are queued. This enables easier follow-up admin-actions. Thanks to Chlod and the Moderator Tools team for both of these improvements. [https://phabricator.wikimedia.org/T364225#10371365]
* The Editing Team is working on making it easier to populate citations from archive.org using the [[mw:Special:MyLanguage/Citoid/Enabling Citoid on your wiki|Citoid]] tool, the auto-filled citation generator. They are asking communities to add two parameters preemptively, &lt;code dir=ltr&gt;archiveUrl&lt;/code&gt; and &lt;code dir=ltr&gt;archiveDate&lt;/code&gt;, within the TemplateData for each citation template using Citoid. You can see an [https://en.wikipedia.org/w/index.php?title=Template%3ACite_web%2Fdoc&amp;diff=1261320172&amp;oldid=1260788022 example of a change in a template], and a [https://global-search.toolforge.org/?namespaces=10&amp;q=%5C%22citoid%5C%22%3A%20%5C%7B&amp;regex=1&amp;title= list of all relevant templates]. [https://phabricator.wikimedia.org/T374831]
* One new wiki has been created: a {{int:project-localized-name-group-wikivoyage}} in [[d:Q9240|Indonesian]] ([[voy:id:|&lt;code&gt;voy:id:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T380726]
* Last week, all wikis had problems serving pages to logged-in users and some logged-out users for 30–45 minutes. This was caused by a database problem, and investigation is ongoing. [https://www.wikimediastatus.net/incidents/3g2ckc7bp6l9]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:19}} community-submitted {{PLURAL:19|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug in the [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add Link]] feature has been fixed. Previously, the list of sections which are excluded from Add Link was partially ignored in certain cases. [https://phabricator.wikimedia.org/T380455][https://phabricator.wikimedia.org/T380329]

'''Updates for technical contributors'''
* [[mw:Special:MyLanguage/Codex|Codex]], the design system for Wikimedia, now has an early-stage [[gitiles:design/codex-php|implementation in PHP]]. It is available for general use in MediaWiki extensions and Toolforge apps through [https://packagist.org/packages/wikimedia/codex Composer], with use in MediaWiki core coming soon. More information is available in [[wmdoc:design-codex-php/main/index.html|the documentation]]. Thanks to Doğu for the inspiration and many contributions to the library. [https://phabricator.wikimedia.org/T379662]
* [https://en.wikipedia.org/api/rest_v1/ Wikimedia REST API] users, such as bot operators and tool maintainers, may be affected by ongoing upgrades. On December 4, the MediaWiki Interfaces team began rerouting page/revision metadata and rendered HTML content endpoints on [[testwiki:|testwiki]] from RESTbase to comparable MediaWiki REST API endpoints. The team encourages active users of these endpoints to verify their tool's behavior on testwiki and raise any concerns on the related [[phab:T374683|Phabricator ticket]] before the end of the year, as they intend to roll out the same change across all Wikimedia projects in early January. These changes are part of the work to replace the outdated [[mw:RESTBase/deprecation|RESTBase]] system.
* The [https://wikimediafoundation.limesurvey.net/986172 2024 Developer Satisfaction Survey] is seeking the opinions of the Wikimedia developer community. Please take the survey if you have any role in developing software for the Wikimedia ecosystem. The survey is open until 3 January 2025, and has an associated [[foundation:Legal:Developer Satisfaction Survey 2024 Privacy Statement|privacy statement]].
* There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar]

'''Meetings and events'''
* The next meeting in the series of [[c:Commons:WMF support for Commons/Commons community calls|Wikimedia Foundation discussions with the Wikimedia Commons community]] will take place on [[m:Event:Commons community discussion - 12 December 2024 08:00 UTC|December 12 at 8:00 UTC]] and [[m:Event:Commons community discussion - 12_December 2024 16:00 UTC|at 16:00 UTC]]. The topic of this call is new media and new contributors. Contributors from all wikis are welcome to attend.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/50|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W50&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:16, 9 December 2024 (UTC)
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== Tech News: 2024-51 ==

&lt;section begin=&quot;technews-2024-W51&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/51|Translations]] are available.

'''Weekly highlight'''
* Interested in improving event management on your home wiki? The [[m:Special:MyLanguage/CampaignEvents|CampaignEvents extension]] offers organizers features like event registration management, event/wikiproject promotion, finding potential participants, and more - all directly on-wiki. If you are an organizer or think your community would benefit from this extension, start a discussion to enable it on your wiki today. To learn more about how to enable this extension on your wiki, visit the [[m:CampaignEvents/Deployment status#How to Request the CampaignEvents Extension for your wiki|deployment status page]].

'''Updates for editors'''
* Users of the iOS Wikipedia App in Italy and Mexico on the Italian, Spanish, and English Wikipedias, can see a [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Personalized Wikipedia Year in Review|personalized Year in Review]] with insights based on their reading and editing history.
* Users of the Android Wikipedia App in Sub-Saharan Africa and South Asia can see the new [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Rabbit Holes|Rabbit Holes]] feature. This feature shows a suggested search term in the Search bar based on the current article being viewed, and a suggested reading list generated from the user’s last two visited articles.
* The [[m:Special:MyLanguage/Global reminder bot|global reminder bot]] is now active and running on nearly 800 wikis. This service reminds most users holding temporary rights when they are about to expire, so that they can renew should they want to. See [[m:Global reminder bot/Technical details|the technical details page]] for more information.
* The next issue of Tech News will be sent out on 13 January 2025 because of the end of year holidays. Thank you to all of the translators, and people who submitted content or feedback, this year.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was [[phab:T374988|fixed]] in the Android Wikipedia App which had caused translatable SVG images to show the wrong language when they were tapped.

'''Updates for technical contributors'''
* There is no new MediaWiki version next week. The next deployments will start on 14 January. [https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar/2025] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2024/51|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2024-W51&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:24, 16 December 2024 (UTC)
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== Tech News: 2025-03 ==

&lt;section begin=&quot;technews-2025-W03&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/03|Translations]] are available.

'''Weekly highlight'''
* The Single User Login system is being updated over the next few months. This is the system which allows users to fill out the login form on one Wikimedia site and get logged in on all others at the same time. It needs to be updated because of the ways that browsers are increasingly restricting cross-domain cookies. To accommodate these restrictions, login and account creation pages will move to a central domain, but it will still appear to the user as if they are on the originating wiki. The updated code will be enabled this week for users on test wikis. This change is planned to roll out to all users during February and March. See [[mw:Special:MyLanguage/MediaWiki Platform Team/SUL3#Deployment|the SUL3 project page]] for more details and a timeline.

'''Updates for editors'''
* On wikis with [[mw:Special:MyLanguage/Extension:PageAssessments|PageAssessments]] installed, you can now [[mw:Special:MyLanguage/Extension:PageAssessments#Search|filter search results]] to pages in a given WikiProject by using the &lt;code dir=ltr&gt;inproject:&lt;/code&gt; keyword. (These wikis: {{int:project-localized-name-arwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-enwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-enwikivoyage/en}}{{int:comma-separator/en}}{{int:project-localized-name-frwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-huwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zhwiki/en}}) [https://phabricator.wikimedia.org/T378868] 
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q34129|Tigre]] ([[w:tig:|&lt;code&gt;w:tig:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T381377]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:35}} community-submitted {{PLURAL:35|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, there was a bug with updating a user's edit-count after making a rollback edit, which is now fixed. [https://phabricator.wikimedia.org/T382592]

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Wikimedia REST API users, such as bot operators and tool maintainers, may be affected by ongoing upgrades. Starting the week of January 13, we will begin rerouting [[phab:T374683|some page content endpoints]] from RESTbase to the newer MediaWiki REST API endpoints for all wiki projects. This change was previously available on testwiki and should not affect existing functionality, but active users of the impacted endpoints may raise issues directly to the [[phab:project/view/6931/|MediaWiki Interfaces Team]] in Phabricator if they arise.
* Toolforge tool maintainers can now share their feedback on Toolforge UI, an initiative to provide a web platform that allows creating and managing Toolforge tools through a graphic interface, in addition to existing command-line workflows. This project aims to streamline active maintainers’ tasks, as well as make registration and deployment processes more accessible for new tool creators. The initiative is still at a very early stage, and the Cloud Services team is in the process of collecting feedback from the Toolforge community to help shape the solution to their needs. [[wikitech:Wikimedia Cloud Services team/EnhancementProposals/Toolforge UI|Read more and share your thoughts about Toolforge UI]]. 
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] For tool and library developers who use the OAuth system: The identity endpoint used for [[mw:Special:MyLanguage/OAuth/For Developers#Identifying the user|OAuth 1]] and [[mw:Special:MyLanguage/OAuth/For Developers#Identifying the user 2|OAuth 2]] returned a JSON object with an integer in its &lt;code&gt;sub&lt;/code&gt; field, which was incorrect (the field must always be a string). This has been fixed; the fix will be deployed to Wikimedia wikis on the week of January 13. [https://phabricator.wikimedia.org/T382139]
* Many wikis currently use [[:mw:Parsoid/Parser Unification/Cite CSS|Cite CSS]] to render custom footnote markers in Parsoid output. Starting January 20 these rules will be disabled, but the developers ask you to ''not'' clean up your &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Common.css]]&lt;/bdi&gt; until February 20 to avoid issues during the migration. Your wikis might experience some small changes to footnote markers in Visual Editor and when using experimental Parsoid read mode, but if there are changes these are expected to bring the rendering in line with the legacy parser output. [https://phabricator.wikimedia.org/T370027]

'''Meetings and events'''
* The next meeting in the series of [[c:Special:MyLanguage/Commons:WMF support for Commons/Commons community calls|Wikimedia Foundation Community Conversations with the Wikimedia Commons community]] will take place on [[m:Special:MyLanguage/Event:Commons community discussion - 15 January 2025 08:00 UTC|January 15 at 8:00 UTC]] and [[m:Special:MyLanguage/Event:Commons community discussion - 15 January 2025 16:00 UTC|at 16:00 UTC]]. The topic of this call is defining the priorities in tool investment for Commons. Contributors from all wikis, especially users who are maintaining tools for Commons, are welcome to attend.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/03|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W03&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:42, 14 January 2025 (UTC)
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== Tech News: 2025-04 ==

&lt;section begin=&quot;technews-2025-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/04|Translations]] are available.

'''Updates for editors'''
* Administrators can mass-delete multiple pages created by a user or IP address using [[mw:Special:MyLanguage/Extension:Nuke|Extension:Nuke]]. It previously only allowed deletion of pages created in the last 30 days. It can now delete pages from the last 90 days, provided it is targeting a specific user or IP address. [https://phabricator.wikimedia.org/T380846]
* On [[phab:P72148|wikis that use]] the [[mw:Special:MyLanguage/Help:Patrolled edits|Patrolled edits]] feature, when the rollback feature is used to revert an unpatrolled page revision, that revision will now be marked as &quot;manually patrolled&quot; instead of &quot;autopatrolled&quot;, which is more accurate. Some editors that use [[mw:Special:MyLanguage/Help:New filters for edit review/Filtering|filters]] on Recent Changes may need to update their filter settings. [https://phabricator.wikimedia.org/T302140]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the Visual Editor's &quot;Insert link&quot; feature did not always suggest existing pages properly when an editor started typing, which has now been [[phab:T383497|fixed]].

'''Updates for technical contributors'''
* The Structured Discussion extension (also known as Flow) is being progressively removed from the wikis. This extension is unmaintained and causes issues. It will be replaced by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]], which is used on any regular talk page. [[mw:Special:MyLanguage/Structured Discussions/Deprecation#Deprecation timeline|The last group of wikis]] ({{int:project-localized-name-cawikiquote/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiwikimedia/en}}{{int:comma-separator/en}}{{int:project-localized-name-gomwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kabwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwikibooks/en}}{{int:comma-separator/en}}{{int:project-localized-name-sewikimedia/en}}) will soon be contacted. If you have questions about this process, please ping [[m:User:Trizek (WMF)|Trizek (WMF)]] at your wiki. [https://phabricator.wikimedia.org/T380912]
* The latest quarterly [[mw:Technical_Community_Newsletter/2025/January|Technical Community Newsletter]] is now available. This edition includes: updates about services from the Data Platform Engineering teams, information about Codex from the Design System team, and more.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W04&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:36, 21 January 2025 (UTC)
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== Tech News: 2025-05 ==

&lt;section begin=&quot;technews-2025-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/05|Translations]] are available.

'''Weekly highlight'''
* Patrollers and admins - what information or context about edits or users could help you to make patroller or admin decisions more quickly or easily? The Wikimedia Foundation wants to hear from you to help guide its upcoming annual plan. Please consider sharing your thoughts on this and [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Product &amp; Technology OKRs|13 other questions]] to shape the technical direction for next year.

'''Updates for editors'''
* iOS Wikipedia App users worldwide can now access a [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Personalized Wikipedia Year in Review/How your data is used|personalized Year in Review]] feature, which provides insights based on their reading and editing history on Wikipedia. This project is part of a broader effort to help welcome new readers as they discover and interact with encyclopedic content.
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Edit patrollers now have a new feature available that can highlight potentially problematic new pages. When a page is created with the same title as a page which was previously deleted, a tag ('Recreated') will now be added, which users can filter for in [[{{#special:RecentChanges}}]] and [[{{#special:NewPages}}]]. [https://phabricator.wikimedia.org/T56145]
* Later this week, there will be a new warning for editors if they attempt to create a redirect that links to another redirect (a [[mw:Special:MyLanguage/Help:Redirects#Double redirects|double redirect]]). The feature will recommend that they link directly to the second redirect's target page. Thanks to the user SomeRandomDeveloper for this improvement. [https://phabricator.wikimedia.org/T326056]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Wikimedia wikis allow [[w:en:WebAuthn|WebAuthn]]-based second factor checks (such as hardware tokens) during login, but the feature is [[m:Community Wishlist Survey 2023/Miscellaneous/Fix security key (WebAuthn) support|fragile]] and has very few users. The MediaWiki Platform team is temporarily disabling adding new WebAuthn keys, to avoid interfering with the rollout of [[mw:MediaWiki Platform Team/SUL3|SUL3]] (single user login version 3). Existing keys are unaffected. [https://phabricator.wikimedia.org/T378402]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''

* For developers that use the [[wikitech:Data Platform/Data Lake/Edits/MediaWiki history dumps|MediaWiki History dumps]]: The Data Platform Engineering team has added a couple of new fields to these dumps, to support the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] initiative. If you maintain software that reads those dumps, please review your code and the updated documentation, since the order of the fields in the row will change. There will also be one field rename: in the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;mediawiki_user_history&lt;/code&gt;&lt;/bdi&gt; dump, the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;anonymous&lt;/code&gt;&lt;/bdi&gt; field will be renamed to &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;is_anonymous&lt;/code&gt;&lt;/bdi&gt;. The changes will take effect with the next release of the dumps in February. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/LKMFDS62TXGDN6L56F4ABXYLN7CSCQDI/] 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W05&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:14, 27 January 2025 (UTC)
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== Tech News: 2025-06 ==

&lt;section begin=&quot;technews-2025-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/06|Translations]] are available.

'''Updates for editors'''
* Editors who use the &quot;Special characters&quot; editing-toolbar menu can now see the 32 special characters you have used most recently, across editing sessions on that wiki. This change should help make it easier to find the characters you use most often. The feature is in both the 2010 wikitext editor and VisualEditor. [https://phabricator.wikimedia.org/T110722]
* Editors using the 2010 wikitext editor can now create sublists with correct indentation by selecting the line(s) you want to indent and then clicking the toolbar buttons.[https://phabricator.wikimedia.org/T380438] You can now also insert &lt;code&gt;&lt;nowiki&gt;&lt;code&gt;&lt;/nowiki&gt;&lt;/code&gt; tags using a new toolbar button.[https://phabricator.wikimedia.org/T383010] Thanks to user stjn for these improvements.
* Help is needed to ensure the [[mw:Special:MyLanguage/Citoid/Enabling Citoid on your wiki|citation generator]] works properly on each wiki.
** (1) Administrators should update the local versions of the page &lt;code dir=ltr&gt;MediaWiki:Citoid-template-type-map.json&lt;/code&gt; to include entries for &lt;code dir=ltr&gt;preprint&lt;/code&gt;, &lt;code dir=ltr&gt;standard&lt;/code&gt;, and &lt;code dir=ltr&gt;dataset&lt;/code&gt;; Here are example diffs to replicate [https://en.wikipedia.org/w/index.php?title=MediaWiki%3ACitoid-template-type-map.json&amp;diff=1189164774&amp;oldid=1165783565 for 'preprint'] and [https://en.wikipedia.org/w/index.php?title=MediaWiki%3ACitoid-template-type-map.json&amp;diff=1270832208&amp;oldid=1270828390 for 'standard' and 'dataset'].
** (2.1) If the citoid map in the citation template used for these types of references is missing, [[mediawikiwiki:Citoid/Enabling Citoid on your wiki#Step 2.a: Create a 'citoid' maps value for each citation template|one will need to be added]]. (2.2) If the citoid map does exist, the TemplateData will need to be updated to include new field names. Here are example updates [https://en.wikipedia.org/w/index.php?title=Template%3ACitation%2Fdoc&amp;diff=1270829051&amp;oldid=1262470053 for 'preprint'] and [https://en.wikipedia.org/w/index.php?title=Template%3ACitation%2Fdoc&amp;diff=1270831369&amp;oldid=1270829480 for 'standard' and 'dataset']. The new fields that may need to be supported are &lt;code dir=ltr&gt;archiveID&lt;/code&gt;, &lt;code dir=ltr&gt;identifier&lt;/code&gt;, &lt;code dir=ltr&gt;repository&lt;/code&gt;, &lt;code dir=ltr&gt;organization&lt;/code&gt;, &lt;code dir=ltr&gt;repositoryLocation&lt;/code&gt;, &lt;code dir=ltr&gt;committee&lt;/code&gt;, and &lt;code dir=ltr&gt;versionNumber&lt;/code&gt;. [https://phabricator.wikimedia.org/T383666]
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia/en}} in [[d:Q15637215|Central Kanuri]] ([[w:knc:|&lt;code&gt;w:knc:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T385181]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the [[mediawikiwiki:Special:MyLanguage/Help:Extension:Wikisource/Wikimedia OCR|OCR (optical character recognition) tool]] used for Wikisource now supports a new language, Church Slavonic. [https://phabricator.wikimedia.org/T384782]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W06&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:09, 4 February 2025 (UTC)
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== Tech News: 2025-07 ==

&lt;section begin=&quot;technews-2025-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/07|Translations]] are available.

'''Weekly highlight'''

* The Product and Technology Advisory Council (PTAC) has published [[m:Special:MyLanguage/Product and Technology Advisory Council/February 2025 draft PTAC recommendation for feedback|a draft of their recommendations]] for the Wikimedia Foundation's Product and Technology department. They have recommended focusing on [[m:Special:MyLanguage/Product and Technology Advisory Council/February 2025 draft PTAC recommendation for feedback/Mobile experiences|mobile experiences]], particularly contributions. They request community [[m:Talk:Product and Technology Advisory Council/February 2025 draft PTAC recommendation for feedback|feedback at the talk page]] by 21 February.

'''Updates for editors'''
* The &quot;Special pages&quot; portlet link will be moved from the &quot;Toolbox&quot; into the &quot;Navigation&quot; section of the main menu's sidebar by default. This change is because the Toolbox is intended for tools relating to the current page, not tools relating to the site, so the link will be more logically and consistently located. To modify this behavior and update CSS styling, administrators can follow the instructions at [[phab:T385346|T385346]]. [https://phabricator.wikimedia.org/T333211]
* As part of this year's work around improving the ways readers discover content on the wikis, the Web team will be running an experiment with a small number of readers that displays some suggestions for related or interesting articles within the search bar. Please check out [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments#Experiment 1: Display article recommendations in more prominent locations, search|the project page]] for more information.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Template editors who use TemplateStyles can now customize output for users with specific accessibility needs by using accessibility related media queries (&lt;code dir=ltr&gt;[https://developer.mozilla.org/en-US/docs/Web/CSS/@media/prefers-reduced-motion prefers-reduced-motion]&lt;/code&gt;, &lt;code dir=ltr&gt;[https://developer.mozilla.org/en-US/docs/Web/CSS/@media/prefers-reduced-transparency prefers-reduced-transparency]&lt;/code&gt;, &lt;code dir=ltr&gt;[https://developer.mozilla.org/en-US/docs/Web/CSS/@media/prefers-contrast prefers-contrast]&lt;/code&gt;, and &lt;code dir=ltr&gt;[https://developer.mozilla.org/en-US/docs/Web/CSS/@media/forced-colors forced-colors]&lt;/code&gt;). Thanks to user Bawolff for these improvements. [https://phabricator.wikimedia.org/T384175]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:22}} community-submitted {{PLURAL:22|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the global blocks log will now be shown directly on the {{#special:CentralAuth}} page, similarly to global locks, to simplify the workflows for stewards. [https://phabricator.wikimedia.org/T377024]

'''Updates for technical contributors'''
* Wikidata [[d:Special:MyLanguage/Help:Default values for labels and aliases|now supports a special language as a &quot;default for all languages&quot;]] for labels and aliases. This is to avoid excessive duplication of the same information across many languages. If your Wikidata queries use labels, you may need to update them as some existing labels are getting removed. [https://phabricator.wikimedia.org/T312511]
* The function &lt;code dir=&quot;ltr&quot;&gt;getDescription&lt;/code&gt; was invoked on every Wiki page read and accounts for ~2.5% of a page's total load time. The calculated value will now be cached, reducing load on Wikimedia servers. [https://phabricator.wikimedia.org/T383660]
* As part of the RESTBase deprecation [[mw:RESTBase/deprecation|effort]], the &lt;code dir=&quot;ltr&quot;&gt;/page/related&lt;/code&gt; endpoint has been blocked as of February 6, 2025, and will be removed soon. This timeline was chosen to align with the deprecation schedules for older Android and iOS versions. The stable alternative is the &quot;&lt;code dir=&quot;ltr&quot;&gt;morelike&lt;/code&gt;&quot; action API in MediaWiki, and [[gerrit:c/mediawiki/services/mobileapps/+/982154/13/pagelib/src/transform/FooterReadMore.js|a migration example]] is available. The MediaWiki Interfaces team [[phab:T376297|can be contacted]] for any questions. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/GFC2IJO7L4BWO3YTM7C5HF4MCCBE2RJ2/]

'''In depth'''

* The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/January|Language and Internationalization newsletter]] is available. It includes: Updates about the &quot;Contribute&quot; menu; details on some of the newest language editions of Wikipedia; details on new languages supported by the MediaWiki interface; updates on the Community-defined lists feature; and more. 
* The latest [[mw:Extension:Chart/Project/Updates#January 2025: Better visibility into charts and tabular data usage|Chart Project newsletter]] is available. It includes updates on the progress towards bringing better visibility into global charts usage and support for categorizing pages in the Data namespace on Commons.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W07&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:12, 11 February 2025 (UTC)
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== Tech News: 2025-08 ==

&lt;section begin=&quot;technews-2025-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/08|Translations]] are available.

'''Weekly highlight'''
* Communities using growth tools can now showcase one event on the &lt;code&gt;{{#special:Homepage}}&lt;/code&gt; for newcomers. This feature will help newcomers to be informed about editing activities they can participate in. Administrators can create a new event to showcase at &lt;code&gt;{{#special:CommunityConfiguration}}&lt;/code&gt;. To learn more about this feature, please read [[diffblog:2025/02/12/community-updates-module-connecting-newcomers-to-your-initiatives/|the Diff post]], have a look [[mw:Special:MyLanguage/Help:Growth/Tools/Community updates module|at the documentation]], or contact [[mw:Talk:Growth|the Growth team]].

'''Updates for editors'''
[[File:Page Frame Features on desktop.png|thumb|Highlighted talk pages improvements]]
* Starting next week, talk pages at these wikis – {{int:project-localized-name-eswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-itwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jawiki/en}} – will get [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|a new design]]. This change was extensively tested as a Beta feature and is the last step of [[mw:Special:MyLanguage/Talk pages project/Feature summary|talk pages improvements]]. [https://phabricator.wikimedia.org/T379102]
* You can now navigate to view a redirect page directly from its action pages, such as the history page. Previously, you were forced to first go to the redirect target. This change should help editors who work with redirects a lot. Thanks to user stjn for this improvement. [https://phabricator.wikimedia.org/T5324]
* When a Cite reference is reused many times, wikis currently show either numbers like &quot;1.23&quot; or localized alphabetic markers like &quot;a b c&quot; in the reference list. Previously, if there were so many reuses that the alphabetic markers were all used, [[MediaWiki:Cite error references no backlink label|an error message]] was displayed.  As part of the work to [[phab:T383036|modernize Cite customization]], these errors will no longer be shown and instead the backlinks will fall back to showing numeric markers like &quot;1.23&quot; once the alphabetic markers are all used.
* The log entries for each change to an editor's user-groups are now clearer by specifying exactly what has changed, instead of the plain before and after listings. Translators can [[phab:T369466|help to update the localized versions]]. Thanks to user Msz2001 for these improvements.
* A new filter has been added to the [[{{#special:Nuke}}]] tool, which allows administrators to mass delete pages, to enable users to filter for pages in a range of page sizes (in bytes). This allows, for example, deleting pages only of a certain size or below. [https://phabricator.wikimedia.org/T378488]
* Non-administrators can now check which pages are able to be deleted using the [[{{#special:Nuke}}]] tool. Thanks to user MolecularPilot for this and the previous improvements. [https://phabricator.wikimedia.org/T376378]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:25}} community-submitted {{PLURAL:25|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed in the configuration for the AV1 video file format, which enables these files to play again. [https://phabricator.wikimedia.org/T382193]

'''Updates for technical contributors'''
* Parsoid Read Views is going to be rolling out to most Wiktionaries over the next few weeks, following the successful transition of Wikivoyage to Parsoid Read Views last year. For more information, see the [[mw:Special:MyLanguage/Parsoid/Parser Unification|Parsoid/Parser Unification]] project page. [https://phabricator.wikimedia.org/T385923][https://phabricator.wikimedia.org/T371640]
* Developers of tools that run on-wiki should note that &lt;code dir=ltr&gt;mw.Uri&lt;/code&gt; is deprecated. Tools requiring &lt;code dir=ltr&gt;mw.Uri&lt;/code&gt; must explicitly declare &lt;code dir=ltr&gt;mediawiki.Uri&lt;/code&gt; as a ResourceLoader dependency, and should migrate to the browser native &lt;code dir=ltr&gt;URL&lt;/code&gt; API soon. [https://phabricator.wikimedia.org/T384515]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W08&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:16, 17 February 2025 (UTC)
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== Tech News: 2025-09 ==

&lt;section begin=&quot;technews-2025-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/09|Translations]] are available.

'''Updates for editors'''
* Administrators can now customize how the [[m:Special:MyLanguage/User language|Babel feature]] creates categories using [[{{#special:CommunityConfiguration/Babel}}]]. They can rename language categories, choose whether they should be auto-created, and adjust other settings. [https://phabricator.wikimedia.org/T374348]
* The &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://www.wikimedia.org/ wikimedia.org]&lt;/bdi&gt; portal has been updated – and is receiving some ongoing improvements – to modernize and improve the accessibility of our portal pages. It now has better support for mobile layouts, updated wording and links, and better language support. Additionally, all of the Wikimedia project portals, such as &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[https://wikibooks.org wikibooks.org]&lt;/bdi&gt;, now support dark mode when a reader is using that system setting. [https://phabricator.wikimedia.org/T373204][https://phabricator.wikimedia.org/T368221][https://meta.wikimedia.org/wiki/Project_portals]
* One new wiki has been created: a {{int:project-localized-name-group-wiktionary/en}} in [[d:Q33965|Santali]] ([[wikt:sat:|&lt;code&gt;wikt:sat:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T386619]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed that prevented clicking on search results in the web-interface for some Firefox for Android phone configurations. [https://phabricator.wikimedia.org/T381289]

'''Meetings and events'''
* The next Language Community Meeting is happening soon, February 28th at [https://zonestamp.toolforge.org/1740751200 14:00 UTC]. This week's meeting will cover: highlights and technical updates on keyboard and tools for the Sámi languages, Translatewiki.net contributions from the Bahasa Lampung community in Indonesia, and technical Q&amp;A. If you'd like to join, simply [[mw:Wikimedia Language and Product Localization/Community meetings#28 February 2025|sign up on the wiki page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W09&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:41, 25 February 2025 (UTC)
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== Tech News: 2025-10 ==

&lt;section begin=&quot;technews-2025-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/10|Translations]] are available.

'''Updates for editors'''
* All logged-in editors using the mobile view can now edit a full page. The &quot;{{int:Minerva-page-actions-editfull}}&quot; link is accessible from the &quot;{{int:minerva-page-actions-overflow}}&quot; menu in the toolbar. This was previously only available to editors using the [[mw:Special:MyLanguage/Reading/Web/Advanced mobile contributions|Advanced mobile contributions]] setting. [https://phabricator.wikimedia.org/T387180]
* Interface administrators can now help to remove the deprecated Cite CSS code matching &quot;&lt;code dir=&quot;ltr&quot;&gt;mw-ref&lt;/code&gt;&quot; from their local &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Common.css]]&lt;/bdi&gt;. The list of wikis in need of cleanup, and the code to remove, [https://global-search.toolforge.org/?q=mw-ref%5B%5E-a-z%5D&amp;regex=1&amp;namespaces=8&amp;title=.*css can be found with this global search] and in [https://ace.wikipedia.org/w/index.php?title=MediaWiki:Common.css&amp;oldid=145662#L-139--L-144 this example], and you can learn more about how to help on the [[mw:Parsoid/Parser Unification/Cite CSS|CSS migration project page]]. The Cite footnote markers (&quot;&lt;code dir=&quot;ltr&quot;&gt;[1]&lt;/code&gt;&quot;) are now rendered by [[mw:Special:MyLanguage/Parsoid|Parsoid]], and the deprecated CSS is no longer needed. The CSS for backlinks (&quot;&lt;code dir=&quot;ltr&quot;&gt;mw:referencedBy&lt;/code&gt;&quot;) should remain in place for now. This cleanup is expected to cause no visible changes for readers. Please help to remove this code before March 20, after which the development team will do it for you.
* When editors embed a file (e.g. &lt;code&gt;&lt;nowiki&gt;[[File:MediaWiki.png]]&lt;/nowiki&gt;&lt;/code&gt;) on a page that is protected with cascading protection, the software will no longer restrict edits to the file description page, only to new file uploads.[https://phabricator.wikimedia.org/T24521] In contrast, transcluding a file description page (e.g. &lt;code&gt;&lt;nowiki&gt;{{:File:MediaWiki.png}}&lt;/nowiki&gt;&lt;/code&gt;) will now restrict edits to the page.[https://phabricator.wikimedia.org/T62109]
* When editors revert a file to an earlier version it will now require the same permissions as ordinarily uploading a new version of the file. The software now checks for 'reupload' or 'reupload-own' rights,[https://phabricator.wikimedia.org/T304474] and respects cascading protection.[https://phabricator.wikimedia.org/T140010]
* When administrators are listing pages for deletion with the Nuke tool, they can now also list associated talk pages and redirects for deletion, alongside pages created by the target, rather than needing to manually delete these pages afterwards. [https://phabricator.wikimedia.org/T95797]
* The [[m:Special:MyLanguage/Tech/News/2025/03|previously noted]] update to Single User Login, which will accommodate browser restrictions on cross-domain cookies by moving login and account creation to a central domain, will now roll out to all users during March and April. The team plans to enable it for all new account creation on [[wikitech:Deployments/Train#Tuesday|Group0]] wikis this week. See [[mw:Special:MyLanguage/MediaWiki Platform Team/SUL3#Deployment|the SUL3 project page]] for more details and an updated timeline.
* Since last week there has been a bug that shows some interface icons as black squares until the page has fully loaded. It will be fixed this week. [https://phabricator.wikimedia.org/T387351]
* One new wiki has been created: a {{int:project-localized-name-group-wikipedia/en}} in [[d:Q2044560|Sylheti]] ([[w:syl:|&lt;code&gt;w:syl:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T386441]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed with loading images in very old versions of the Firefox browser on mobile. [https://phabricator.wikimedia.org/T386400]

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.19|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W10&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 02:30, 4 March 2025 (UTC)
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== Tech News: 2025-11 ==

&lt;section begin=&quot;technews-2025-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/11|Translations]] are available.

'''Updates for editors'''
* Editors who use password managers at multiple wikis may notice changes in the future. The way that our wikis provide information to password managers about reusing passwords across domains has recently been updated, so some password managers might now offer you login credentials that you saved for a different Wikimedia site. Some password managers already did this, and are now doing it for more Wikimedia domains. This is part of the [[mw:Special:MyLanguage/MediaWiki Platform Team/SUL3|SUL3 project]] which aims to improve how our unified login works, and to keep it compatible with ongoing changes to the web-browsers we use. [https://phabricator.wikimedia.org/T385520][https://phabricator.wikimedia.org/T384844]
* The Wikipedia Apps Team is inviting interested users to help improve Wikipedia’s offline and limited internet use. After discussions in [[m:Afrika Baraza|Afrika Baraza]] and the last [[m:Special:MyLanguage/ESEAP Hub/Meetings|ESEAP call]], key challenges like search, editing, and offline access are being explored, with upcoming focus groups to dive deeper into these topics. All languages are welcome, and interpretation will be available. Want to share your thoughts? [[mw:Special:MyLanguage/Wikimedia Apps/Improving Wikipedia Mobile Apps for Offline &amp; Limited Internet Use|Join the discussion]] or email &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;aramadan@wikimedia.org&lt;/bdi&gt;!
* All wikis will be read-only for a few minutes on March 19. This is planned at [https://zonestamp.toolforge.org/1742392800 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.20|MediaWiki]]

'''In depth'''
* The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/33|Growth newsletter]] is available. It includes: the launch of the Community Updates module, the most recent changes in Community Configuration, and the upcoming test of in-article suggestions for first-time editors.
* An old API that was previously used in the Android Wikipedia app is being removed at the end of March. There are no current software uses, but users of the app with a version that is older than 6 months by the time of removal (2025-03-31), will no longer have access to the Suggested Edits feature, until they update their app. You can [[diffblog:2025/02/24/sunset-of-wikimedia-recommendation-api/|read more details about this change]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W11&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:09, 10 March 2025 (UTC)
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== Tech News: 2025-12 ==

&lt;section begin=&quot;technews-2025-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/12|Translations]] are available.

'''Weekly highlight'''
* Twice a year, around the equinoxes, the Wikimedia Foundation's Site Reliability Engineering (SRE) team performs [[m:Special:MyLanguage/Tech/Server switch|a datacenter server switchover]], redirecting all traffic from one primary server to its backup. This provides reliability in case of a crisis, as we can always fall back on the other datacenter. [http://listen.hatnote.com/ Thanks to the Listen to Wikipedia] tool, you can hear the switchover take place: Before it begins, you'll hear the steady stream of edits; Then, as the system enters a brief read-only phase, the sound stops for a couple of minutes, before resuming after the switchover. You can [[diffblog:2025/03/12/hear-that-the-wikis-go-silent-twice-a-year/|read more about the background and details of this process on the Diff blog]]. If you want to keep an ear out for the next server switchover, listen to the wikis on [https://zonestamp.toolforge.org/1742392800 March 19 at 14:00 UTC].

'''Updates for editors'''

* The [https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;filter-type=automatic&amp;filter-id=previous-edits&amp;active-list=suggestions&amp;from=en&amp;to=es improved Content Translation tool dashboard] is now available in [[phab:T387820|10 Wikipedias]] and will be available for all Wikipedias [[phab:T387821|soon]]. With [[mw:Special:MyLanguage/Content translation#Improved translation experience|the unified dashboard]], desktop users can now: Translate new sections of an article; Discover and access topic-based [https://ig.m.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;active-list=suggestions&amp;from=en&amp;to=ig&amp;filter-type=automatic&amp;filter-id=previous-edits article suggestion filters] (initially available only for mobile device users); Discover and access the [[mw:Special:MyLanguage/Translation suggestions: Topic-based &amp; Community-defined lists|Community-defined lists]] filter, also known as &quot;Collections&quot;, from wiki-projects and campaigns.
* On Wikimedia Commons, a [[c:Commons:WMF support for Commons/Upload Wizard Improvements#Improve category selection|new system to select the appropriate file categories]] has been introduced: if a category has one or more subcategories, users will be able to click on an arrow that will open the subcategories directly within the form, and choose the correct one. The parent category name will always be shown on top, and it will always be possible to come back to it. This should decrease the amount of work for volunteers in fixing/creating new categories. The change is also available on mobile. These changes are part of planned improvements to the UploadWizard.
* The Community Tech team is seeking wikis to join a pilot for the [[m:Special:MyLanguage/Community Wishlist Survey 2023/Multiblocks|Multiblocks]] feature and a refreshed Special:Block page in late March. Multiblocks enables administrators to impose multiple different types of blocks on the same user at the same time. If you are an admin or steward and would like us to discuss joining the pilot with your community, please leave a message on the [[m:Talk:Community Wishlist Survey 2023/Multiblocks|project talk page]].
* Starting March 25, the Editing team will test a new feature for Edit Check at [[phab:T384372|12 Wikipedias]]: [[mw:Special:MyLanguage/Help:Edit check#Multi-check|Multi-Check]]. Half of the newcomers on these wikis will see all [[mw:Special:MyLanguage/Help:Edit check#ref|Reference Checks]] during their edit session, while the other half will continue seeing only one. The goal of this test is to see if users are confused or discouraged when shown multiple Reference Checks (when relevant) within a single editing session. At these wikis, the tags used on edits that show References Check will be simplified, as multiple tags could be shown within a single edit. Changes to the tags are documented [[phab:T373949|on Phabricator]]. [https://phabricator.wikimedia.org/T379131]
* The [[m:Special:MyLanguage/Global reminder bot|Global reminder bot]], which is a service for notifying users that their temporary user-rights are about to expire, now supports using the localized name of the user-rights group in the message heading. Translators can see the [[m:Global reminder bot/Translation|listing of existing translations and documentation]] to check if their language needs updating or creation.
* The [[Special:GlobalPreferences|GlobalPreferences]] gender setting, which is used for how the software should refer to you in interface messages, now works as expected by overriding the local defaults. [https://phabricator.wikimedia.org/T386584]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:26}} community-submitted {{PLURAL:26|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the Wikipedia App for Android had a bug fixed for when a user is browsing and searching in multiple languages. [https://phabricator.wikimedia.org/T379777]

'''Updates for technical contributors'''
* Later this week, the way that Codex styles are loaded will be changing. There is a small risk that this may result in unstyled interface message boxes on certain pages. User generated content (e.g. templates) is not impacted. Gadgets may be impacted. If you see any issues [[phab:T388847|please report them]]. See the linked task for details, screenshots, and documentation on how to fix any affected gadgets.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.21|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W12&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:48, 17 March 2025 (UTC)
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== Tech News: 2025-13 ==

&lt;section begin=&quot;technews-2025-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/13|Translations]] are available.

'''Weekly highlight'''
* The Wikimedia Foundation is seeking your feedback on the [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Product &amp; Technology OKRs|drafts of the objectives and key results that will shape the Foundation's Product and Technology priorities]] for the next fiscal year (starting in July). The objectives are broad high-level areas, and the key-results are measurable ways to track the success of their objectives. Please share your feedback on the talkpage, in any language, ideally before the end of April.

'''Updates for editors'''
* The [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] will be released to multiple wikis (see [[m:Special:MyLanguage/CampaignEvents/Deployment status#Global Deployment Plan|deployment plan]] for details) in April 2025, and the team has begun the process of engaging communities on the identified wikis. The extension provides tools to organize, manage, and promote collaborative activities (like events, edit-a-thons, and WikiProjects) on the wikis. The extension has three tools: [[m:Special:MyLanguage/Event Center/Registration|Event Registration]], [[m:Special:MyLanguage/CampaignEvents/Collaboration list|Collaboration List]], and [[m:Special:MyLanguage/Campaigns/Foundation Product Team/Invitation list|Invitation Lists]]. It is currently on 13 Wikipedias, including English Wikipedia, French Wikipedia, and Spanish Wikipedia, as well as Wikidata. Questions or requests can be directed to the [[mw:Help talk:Extension:CampaignEvents|extension talk page]] or in Phabricator (with &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; style=&quot;white-space: nowrap;&quot;&gt;#campaigns-product-team&lt;/bdi&gt; tag).
* Starting the week of March 31st, wikis will be able to set which user groups can view private registrants in [[m:Special:MyLanguage/Event Center/Registration|Event Registration]], as part of the [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents]] extension. By default, event organizers and the local wiki admins will be able to see private registrants. This is a change from the current behavior, in which only event organizers can see private registrants. Wikis can change the default setup by [[m:Special:MyLanguage/Requesting wiki configuration changes|requesting a configuration change]] in Phabricator (and adding the &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot; style=&quot;white-space: nowrap;&quot;&gt;#campaigns-product-team&lt;/bdi&gt; tag). Participants of past events can cancel their registration at any time.
* Administrators at wikis that have a customized &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Sidebar]]&lt;/bdi&gt; should check that it contains an entry for the {{int:specialpages}} listing. If it does not, they should add it using &lt;code dir=ltr style=&quot;white-space: nowrap;&quot;&gt;* specialpages-url|specialpages&lt;/code&gt;. Wikis with a default sidebar will see the link moved from the page toolbox into the sidebar menu in April. [https://phabricator.wikimedia.org/T388927]
* The Minerva skin (mobile web) combines both Notice and Alert notifications within the bell icon ([[File:OOjs UI icon bell.svg|16px|link=|class=skin-invert]]). There was a long-standing bug where an indication for new notifications was only shown if you had unseen Alerts. This bug is now fixed. In the future, Minerva users will notice a counter atop the bell icon when you have 1 or more unseen Notices and/or Alerts. [https://phabricator.wikimedia.org/T344029]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* VisualEditor has introduced a [[mw:VisualEditor/Hooks|new client-side hook]] for developers to use when integrating with the VisualEditor target lifecycle. This hook should replace the existing lifecycle-related hooks, and be more consistent between different platforms. In addition, the new hook will apply to uses of VisualEditor outside of just full article editing, allowing gadgets to interact with the editor in DiscussionTools as well. The Editing Team intends to deprecate and eventually remove the old lifecycle hooks, so any use cases that this new hook does not cover would be of interest to them and can be [[phab:T355555|shared in the task]].
* Developers who use the &lt;code dir=ltr&gt;mw.Api&lt;/code&gt; JavaScript library, can now identify the tool using it with the &lt;code dir=ltr&gt;userAgent&lt;/code&gt; parameter: &lt;code dir=ltr&gt;var api = new mw.Api( { userAgent: 'GadgetNameHere/1.0.1' } );&lt;/code&gt;. If you maintain a gadget or user script, please set a user agent, because it helps with library and server maintenance and with differentiating between legitimate and illegitimate traffic. [https://phabricator.wikimedia.org/T373874][https://foundation.wikimedia.org/wiki/Policy:Wikimedia_Foundation_User-Agent_Policy]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.22|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W13&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:42, 24 March 2025 (UTC)
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== Tech News: 2025-14 ==

&lt;section begin=&quot;technews-2025-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/14|Translations]] are available.

'''Updates for editors'''
* The Editing team is working on a new [[mw:Special:MyLanguage/Edit Check|Edit check]]: [[mw:Special:MyLanguage/Edit check#26 March 2025|Peacock check]]. This check's goal is to identify non-neutral terms while a user is editing a wikipage, so that they can be informed that their edit should perhaps be changed before they publish it. This project is at the early stages, and the team is looking for communities' input: [[phab:T389445|in this Phabricator task]], they are gathering on-wiki policies, templates used to tag non-neutral articles, and the terms (jargon and keywords) used in edit summaries for the languages they are currently researching. You can participate by editing the table on Phabricator, commenting on the task, or directly messaging [[m:user:Trizek (WMF)|Trizek (WMF)]].
* [[mw:Special:MyLanguage/MediaWiki Platform Team/SUL3|Single User Login]] has now been updated on all wikis to move login and account creation to a central domain. This makes user login compatible with browser restrictions on cross-domain cookies, which have prevented users of some browsers from staying logged in.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:35}} community-submitted {{PLURAL:35|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Starting on March 31st, the MediaWiki Interfaces team will begin a limited release of generated OpenAPI specs and a SwaggerUI-based sandbox experience for [[mw:Special:MyLanguage/API:REST API|MediaWiki REST APIs]]. They invite developers from a limited group of non-English Wikipedia communities (Arabic, German, French, Hebrew, Interlingua, Dutch, Chinese) to review the documentation and experiment with the sandbox in their preferred language. In addition to these specific Wikipedia projects, the sandbox and OpenAPI spec will be available on the [[testwiki:Special:RestSandbox|on the test wiki REST Sandbox special page]] for developers with English as their preferred language. During the preview period, the MediaWiki Interfaces Team also invites developers to [[mw:MediaWiki Interfaces Team/Feature Feedback/REST Sandbox|share feedback about your experience]]. The preview will last for approximately 2 weeks, after which the sandbox and OpenAPI specs will be made available across all wiki projects.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.23|MediaWiki]]

'''In depth'''
* Sometimes a small, [[gerrit:c/operations/cookbooks/+/1129184|one line code change]] can have great significance: in this case, it means that for the first time in years we're able to run all of the stack serving &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[http://maps.wikimedia.org/ maps.wikimedia.org]&lt;/bdi&gt; - a host dedicated to serving our wikis and their multi-lingual maps needs - from a single core datacenter, something we test every time we perform a [[m:Special:MyLanguage/Tech/Server switch|datacenter switchover]]. This is important because it means that in case one of our datacenters is affected by a catastrophe, we'll still be able to serve the site. This change is the result of [[phab:T216826|extensive work]] by two developers on porting the last component of the maps stack over to [[w:en:Kubernetes|kubernetes]], where we can allocate resources more efficiently than before, thus we're able to withstand more traffic in a single datacenter. This work involved a lot of complicated steps because this software, and the software libraries it uses, required many long overdue upgrades. This type of work makes the Wikimedia infrastructure more sustainable.

'''Meetings and events'''
* [[mw:Special:MyLanguage/MediaWiki Users and Developers Workshop Spring 2025|MediaWiki Users and Developers Workshop Spring 2025]] is happening in Sandusky, USA, and online, from 14–16 May 2025. The workshop will feature discussions around the usage of MediaWiki software by and within companies in different industries and will inspire and onboard new users. Registration and presentation signup is now available at the workshop's website.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W14&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:05, 1 April 2025 (UTC)
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== Tech News: 2025-15 ==

&lt;section begin=&quot;technews-2025-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/15|Translations]] are available.

'''Updates for editors'''
* From now on, [[m:Special:MyLanguage/Interface administrators|interface admins]] and [[m:Special:MyLanguage/Central notice administrators|centralnotice admins]] are technically required to enable [[m:Special:MyLanguage/Help:Two-factor authentication|two-factor authentication]] before they can use their privileges. In the future this might be expanded to more groups with advanced user-rights. [https://phabricator.wikimedia.org/T150898]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* The Design System Team is preparing to release the next major version of Codex (v2.0.0) on April 29. Editors and developers who use CSS from Codex should see the [[mw:Codex/Release Timeline/2.0|2.0 overview documentation]], which includes guidance related to a few of the breaking changes such as &lt;code dir=ltr style=&quot;white-space: nowrap;&quot;&gt;font-size&lt;/code&gt;, &lt;code dir=ltr style=&quot;white-space: nowrap;&quot;&gt;line-height&lt;/code&gt;, and &lt;code dir=ltr style=&quot;white-space: nowrap;&quot;&gt;size-icon&lt;/code&gt;.
* The results of the [[mw:Developer Satisfaction Survey/2025|Developer Satisfaction Survey (2025)]]  are now available. Thank you to all participants. These results help the Foundation decide what to work on next and to review what they recently worked on.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.24|MediaWiki]]

'''Meetings and events'''
* The [[mw:Special:MyLanguage/Wikimedia Hackathon 2025|2025 Wikimedia Hackathon]] will take place in Istanbul, Turkey, between 2–4 May. Registration for attending the in-person event will close on 13 April. Before registering, please note the potential need for a [https://www.mfa.gov.tr/turkish-representations.en.mfa visa] or [https://www.mfa.gov.tr/visa-information-for-foreigners.en.mfa e-visa] to enter the country.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W15&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:52, 7 April 2025 (UTC)
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== Tech News: 2025-16 ==

&lt;section begin=&quot;technews-2025-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/16|Translations]] are available.

'''Weekly highlight'''
* Later this week, the default thumbnail size will be increased from 220px to 250px. This changes how pages are shown in all wikis and has been requested by some communities for many years, but wasn't previously possible due to technical limitations. [https://phabricator.wikimedia.org/T355914]
* File thumbnails are now stored in discrete sizes. If a page specifies a thumbnail size that's not among the standard sizes (20, 40, 60, 120, 250, 330, 500, 960), then MediaWiki will pick the closest larger thumbnail size but will tell the browser to downscale it to the requested size. In these cases, nothing will change visually but users might load slightly larger images. If it doesn't matter which thumbnail size is used in a page, please pick one of the standard sizes to avoid the extra in-browser down-scaling step. [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Images#Thumbnail_sizes][https://phabricator.wikimedia.org/T355914]

'''Updates for editors'''
* The Wikimedia Foundation are working on a system called [[m:Edge Uniques|Edge Uniques]] which will enable [[:w:en:A/B testing|A/B testing]], help protect against [[:w:en:Denial-of-service attack|Distributed denial-of-service attacks]] (DDoS attacks), and make it easier to understand how many visitors the Wikimedia sites have. This is so that they can more efficiently build tools which help readers, and make it easier for readers to find what they are looking for.
* To improve security for users, a small percentage of logins will now require that the account owner input a one-time password [[mw:Special:MyLanguage/Help:Extension:EmailAuth|emailed to their account]]. It is recommended that you [[Special:Preferences#mw-prefsection-personal-email|check]] that the email address on your account is set correctly, and that it has been confirmed, and that you have an email set for this purpose. [https://phabricator.wikimedia.org/T390662]
* &quot;Are you interested in taking a short survey to improve tools used for reviewing or reverting edits on your Wiki?&quot; This question will be [[phab:T389401|asked at 7 wikis starting next week]], on Recent Changes and Watchlist pages. The [[mw:Special:MyLanguage/Moderator Tools|Moderator Tools team]] wants to know more about activities that involve looking at new edits made to your Wikimedia project, and determining whether they adhere to your project's policies.
* On April 15, the full Wikidata graph will no longer be supported on &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;[https://query.wikidata.org/ query.wikidata.org]&lt;/bdi&gt;. After this date, scholarly articles will be available through &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot; style=&quot;white-space:nowrap;&quot;&gt;[https://query-scholarly.wikidata.org/ query-scholarly.wikidata.org]&lt;/bdi&gt;, while the rest of the data hosted on Wikidata will be available through the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;[https://query.wikidata.org/ query.wikidata.org]&lt;/bdi&gt; endpoint. This is part of the scheduled split of the Wikidata Graph, which was [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/September 2024 scaling update|announced in September 2024]]. More information is [[d:Wikidata:SPARQL query service/WDQS graph split|available on Wikidata]].
* The latest quarterly [[m:Special:MyLanguage/Wikimedia Apps/Newsletter/First quarter of 2025|Wikimedia Apps Newsletter]] is now available. It covers updates, experiments, and improvements made to the Wikipedia mobile apps.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* The latest quarterly [[mw:Technical Community Newsletter/2025/April|Technical Community Newsletter]] is now available. This edition includes: an invitation for tool maintainers to attend the Toolforge UI Community Feedback Session on April 15th; recent community metrics; and recent technical blog posts.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.25|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W16&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:24, 15 April 2025 (UTC)
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== Tech News: 2025-17 ==

&lt;section begin=&quot;technews-2025-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/17|Translations]] are available.

'''Updates for editors'''
* [[f:Special:MyLanguage/Wikifunctions:Main Page|Wikifunctions]] is now integrated with [[w:dag:Solɔɣu|Dagbani Wikipedia]] since April 15. It is the first project that will be able to call [[f:Special:MyLanguage/Wikifunctions:Introduction|functions from Wikifunctions]] and integrate them in articles. A function is something that takes one or more inputs and transforms them into a desired output, such as adding up two numbers, converting miles into metres, calculating how much time has passed since an event, or declining a word into a case. Wikifunctions will allow users to do that through a simple call of [[f:Special:MyLanguage/Wikifunctions:Catalogue|a stable and global function]], rather than via a local template. [https://www.wikifunctions.org/wiki/Special:MyLanguage/Wikifunctions:Status_updates/2025-04-16]
* A new type of lint error has been created: [[Special:LintErrors/empty-heading|{{int:linter-category-empty-heading}}]] ([[mw:Special:MyLanguage/Help:Lint errors/empty-heading|documentation]]). The [[mw:Special:MyLanguage/Help:Extension:Linter|Linter extension]]'s purpose is to identify wikitext patterns that must or can be fixed in pages and provide some guidance about what the problems are with those patterns and how to fix them. [https://phabricator.wikimedia.org/T368722]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:37}} community-submitted {{PLURAL:37|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Following its publication on HuggingFace, the &quot;Structured Contents&quot; dataset, developed by Wikimedia Enterprise, is [https://enterprise.wikimedia.com/blog/kaggle-dataset/ now also available on Kaggle]. This Beta initiative is focused on making Wikimedia data more machine-readable for high-volume reusers. They are releasing this beta version in a location that open dataset communities already use, in order to seek feedback, to help improve the product for a future wider release. You can read more about the overall [https://enterprise.wikimedia.com/blog/structured-contents-snapshot-api/#open-datasets Structured Contents project], and about the [https://enterprise.wikimedia.com/blog/structured-contents-wikipedia-infobox/ first release that's freely usable].
* There is no new MediaWiki version this week.

'''Meetings and events'''
* The Editing and Machine Learning Teams invite interested volunteers to a video meeting to discuss [[mw:Special:MyLanguage/Edit check/Peacock check|Peacock check]], which is the latest [[mw:Special:MyLanguage/Edit check|Edit check]] that will detect &quot;peacock&quot; or &quot;overly-promotional&quot; or &quot;non-neutral&quot; language whilst an editor is typing. Editors who work with newcomers, or help to fix this kind of writing, or are interested in how we use artificial intelligence in our projects are encouraged to attend. The [[mw:Special:MyLanguage/Editing team/Community Conversations#Next Conversation|meeting will be on April 28, 2025]] at [https://zonestamp.toolforge.org/1745863200 18:00–19:00 UTC] and hosted on Zoom.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W17&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:00, 21 April 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=28578245 --&gt;

== Tech News: 2025-18 ==

&lt;section begin=&quot;technews-2025-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/18|Translations]] are available.

'''Updates for editors'''
* Event organizers who host collaborative activities on [[m:Special:MyLanguage/CampaignEvents/Deployment status#Global Deployment Plan|multiple wikis]], including Bengali, Japanese, and Korean Wikipedias, will have access to the [[mw:Special:MyLanguage/Extension:CampaignEvents|CampaignEvents extension]] this week. Also, admins in the Wikipedia where the extension is enabled will automatically be granted the event organizer right soon. They won't have to manually grant themselves the right before they can manage events as [[phab:T386861|requested by a community]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:19}} community-submitted {{PLURAL:19|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* The release of the next major version of [[mw:Special:MyLanguage/Codex|Codex]], the design system for Wikimedia, is scheduled for 29 April 2025. Technical editors will have access to the release by the week of 5 May 2025. This update will include a number of [[mw:Special:MyLanguage/Codex/Release_Timeline/2.0#Breaking_changes|breaking changes]] and minor [[mw:Special:MyLanguage/Codex/Release_Timeline/2.0#Visual_changes|visual changes]]. Instructions on handling the breaking and visual changes are documented on [[mw:Special:MyLanguage/Codex/Release Timeline/2.0#|this page]]. Pre-release testing is reported in [[phab:T386298|T386298]], with post-release issues tracked in [[phab:T392379|T392379]] and [[phab:T392390|T392390]].
* Users of [[wikitech:Special:MyLanguage/Help:Wiki_Replicas|Wiki Replicas]] will notice that the database views of &lt;code dir=&quot;ltr&quot;&gt;ipblocks&lt;/code&gt;, &lt;code dir=&quot;ltr&quot;&gt;ipblocks_ipindex&lt;/code&gt;, and &lt;code dir=&quot;ltr&quot;&gt;ipblocks_compat&lt;/code&gt; are [[phab:T390767|now deprecated]]. Users can query the &lt;code dir=&quot;ltr&quot;&gt;[[mw:Special:MyLanguage/Manual:Block_table|block]]&lt;/code&gt; and &lt;code dir=&quot;ltr&quot;&gt;[[mw:Special:MyLanguage/Manual:Block_target_table|block_target]]&lt;/code&gt; new views that mirror the new tables in the production database instead. The deprecated views will be removed entirely from Wiki Replicas in June, 2025.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.27|MediaWiki]]

'''In depth'''
* The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/April|Language and Internationalization Newsletter]] is now available. This edition includes an overview of the improved [https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;campaign=contributionsmenu&amp;to=es&amp;filter-type=automatic&amp;filter-id=previous-edits&amp;active-list=suggestions&amp;from=en#/ Content Translation Dashboard Tool], [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/April#Language Support for New and Existing Languages|support for new languages]], [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/April#Wiki Loves Ramadan Articles Made In Content Translation Mobile Workflow|highlights from the Wiki Loves Ramadan campaign]], [[m:Special:MyLanguage/Research:Languages Onboarding Experiment 2024 - Executive Summary|results from the Language Onboarding Experiment]], an analysis of topic diversity in articles, and information on upcoming community meetings and events.

'''Meetings and events'''
* The [[Special:MyLanguage/Grants:Knowledge_Sharing/Connect/Calendar|Let's Connect Learning Clinic]] will take place on [https://zonestamp.toolforge.org/1745937000 April 29 at 14:30 UTC]. This edition will focus on &quot;Understanding and Navigating Conflict in Wikimedia Projects&quot;. You can [[m:Special:MyLanguage/Event:Learning Clinic %E2%80%93 Understanding and Navigating Conflict in Wikimedia Projects (Part_1)|register now]] to attend.
* The [[mw:Special:MyLanguage/Wikimedia Hackathon 2025|2025 Wikimedia Hackathon]], which brings the global technical community together to connect, brainstorm, and hack existing projects, will take place from May 2 to 4th, 2025, at Istanbul, Turkey.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W18&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:31, 28 April 2025 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=28585685 --&gt;

== Tech News: 2025-19 ==

&lt;section begin=&quot;technews-2025-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/19|Translations]] are available.

'''Weekly highlight'''
* The Wikimedia Foundation has shared the latest draft update to their [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026|annual plan]] for next year (July 2025–June 2026). This includes an [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026|executive summary]] (also on [[diffblog:2025/04/25/sharing-the-wikimedia-foundations-2025-2026-draft-annual-plan/|Diff]]), details about the three main [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Goals|goals]] ([[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Product &amp; Technology OKRs|Infrastructure]], [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Goals/Volunteer Support|Volunteer Support]], and [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Goals/Effectiveness|Effectiveness]]), [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Global Trends|global trends]], and the [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Budget Overview|budget]] and [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026/Financial Model|financial model]]. Feedback and questions are welcome on the [[m:Talk:Wikimedia Foundation Annual Plan/2025-2026|talk page]] until the end of May.

'''Updates for editors'''
* For wikis that have the [[m:Special:MyLanguage/CampaignEvents/Deployment status|CampaignEvents extension enabled]], two new feature improvements have been released:
** Admins can now choose which namespaces are permitted for [[m:Special:MyLanguage/Event Center/Registration|Event Registration]] via [[mw:Special:MyLanguage/Community Configuration|Community Configuration]] ([[mw:Special:MyLanguage/Help:Extension:CampaignEvents/Registration/Permitted namespaces|documentation]]). The default setup is for event registration to be permitted in the Event namespace, but other namespaces (such as the project namespace or WikiProject namespace) can now be added. With this change, communities like WikiProjects can now more easily use Event Registration for their collaborative activities.
** Editors can now [[mw:Special:MyLanguage/Transclusion|transclude]] the Collaboration List on a wiki page ([[mw:Special:MyLanguage/Help:Extension:CampaignEvents/Collaboration list/Transclusion|documentation]]). The Collaboration List is an automated list of events and WikiProjects on the wikis, accessed via {{#special:AllEvents}} ([[w:en:Special:AllEvents|example]]). Now, the Collaboration List can be added to all sorts of wiki pages, such as: a wiki mainpage, a WikiProject page, an affiliate page, an event page, or even a user page.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Developers who use the &lt;code dir=ltr&gt;moment&lt;/code&gt; library in gadgets and user scripts should revise their code to use alternatives like the &lt;code dir=ltr&gt;Intl&lt;/code&gt; library or the new &lt;code dir=ltr&gt;mediawiki.DateFormatter&lt;/code&gt; library. The &lt;code dir=ltr&gt;moment&lt;/code&gt; library has been deprecated and will begin to log messages in the developer console. You can see a global search for current uses, and [[phab:T392532|ask related questions in this Phabricator task]].
* Developers who maintain a tool that queries the Wikidata term store tables (&lt;code dir=ltr style=&quot;white-space: nowrap;&quot;&gt;wbt_*&lt;/code&gt;) need to update their code to connect to a separate database cluster. These tables are being split into a separate database cluster. Tools that query those tables via the wiki replicas must be adapted to connect to the new cluster instead. [[wikitech:News/2025 Wikidata term store database split|Documentation and related links are available]]. [https://phabricator.wikimedia.org/T390954]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.44/wmf.28|MediaWiki]]

'''In depth'''
* The latest [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|Chart Project newsletter]] is available. It includes updates on preparing to expand the deployment to additional wikis as soon as this week (starting May 6) and scaling up over the following weeks, plus exploring filtering and transforming source data.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W19&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:14, 6 May 2025 (UTC)
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== Tech News: 2025-20 ==

&lt;section begin=&quot;technews-2025-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/20|Translations]] are available.

'''Weekly highlight'''
* The [[m:Special:MyLanguage/Wikimedia URL Shortener|&quot;Get shortened URL&quot;]] link on the sidebar now includes a [[phab:T393309|QR code]]. Wikimedia site users can now use it by scanning or downloading it to quickly share and access shared content from Wikimedia sites, conveniently.

'''Updates for editors'''
* The Wikimedia Foundation is working on a system called [[m:Edge Uniques|Edge Uniques]], which will enable [[w:en:A/B testing|A/B testing]], help protect against [[w:en:Denial-of-service attack|distributed denial-of-service attacks]] (DDoS attacks), and make it easier to understand how many visitors the Wikimedia sites have. This is to help more efficiently build tools which help readers, and make it easier for readers to find what they are looking for. Tech News has [[m:Special:MyLanguage/Tech/News/2025/16|previously written about this]]. The deployment will be gradual. Some might see the Edge Uniques cookie the week of 19 May. You can discuss this on the [[m:Talk:Edge Uniques|talk page]].
* Starting May 19, 2025, Event organisers in wikis with the [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] enabled can use [[m:Special:MyLanguage/Event Center/Registration|Event Registration]] in the project namespace (e.g., Wikipedia namespace, Wikidata namespace). With this change, communities don't need admins to use the feature. However, wikis that don't want this change can remove and add the permitted namespaces at [[Special:CommunityConfiguration/CampaignEvents]].
* The Wikipedia project now has a {{int:project-localized-name-group-wikipedia/en}} in [[d:Q36720|Nupe]] ([[w:nup:|&lt;code&gt;w:nup:&lt;/code&gt;]]). This is a language primarily spoken in the North Central region of Nigeria. Speakers of this language are invited to contribute to [[w:nup:Tatacin feregi|new Wikipedia]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Developers can now access pre-parsed Dutch Wikipedia, amongst others (English, German, French, Spanish, Italian, and Portuguese) through the [https://enterprise.wikimedia.com/docs/snapshot/#structured-contents-snapshot-bundle-info-beta Structured Contents snapshots (beta)]. The content includes parsed Wikipedia abstracts, descriptions, main images, infoboxes, article sections, and references.
* The &lt;code dir=&quot;ltr&quot;&gt;/page/data-parsoid&lt;/code&gt; REST API endpoint is no longer in use and will be deprecated. It is [[phab:T393557|scheduled to be turned off]] on June 7, 2025.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.1|MediaWiki]]

'''In depth'''
* The [https://wikitech.wikimedia.org/wiki/News/2025_Cloud_VPS_VXLAN_IPv6_migration IPv6 support] is a newly introduced Cloud virtual network that significantly boosts Wikimedia platforms' scalability, security, and readiness for the future. If you are a technical contributor eager to learn more, check out [https://techblog.wikimedia.org/2025/05/06/wikimedia-cloud-vps-ipv6-support/ this blog post] for an in-depth look at the journey to IPv6.

'''Meetings and events'''
* The 2nd edition of 2025 of [[m:Special:MyLanguage/Afrika Baraza|Afrika Baraza]], a virtual platform for African Wikimedians to connect, will take place on [https://zonestamp.toolforge.org/1747328400 May 15 at 17:00 UTC]. This edition will focus on discussions regarding [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2025-2026|Wikimedia Annual planning and progress]].
* The [[m:Special:MyLanguage/MENA Connect Community Call|MENA Connect Community Call]], a virtual meeting for [[w:en:Middle East and North Africa|MENA]] Wikimedians to connect, will take place on [https://zonestamp.toolforge.org/1747501200 May 17 at 17:00 UTC]. You can [[m:Event:MENA Connect (Wiki_Diwan) APP Call|register now]] to attend.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W20&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:37, 12 May 2025 (UTC)
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== Tech News: 2025-21 ==

&lt;section begin=&quot;technews-2025-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/21|Translations]] are available.

'''Weekly highlight'''
* The Editing Team and the Machine Learning Team are working on a new check for newcomers: [[mw:Edit check/Peacock check|Peacock check]]. Using a prediction model, this check will encourage editors to improve the tone of their edits, using artificial intelligence. We invite volunteers to review the first version of the Peacock language model for the following languages: Arabic, Spanish, Portuguese, English, and Japanese. Users from these wikis interested in reviewing this model are [[mw:Edit check/Peacock check/model test|invited to sign up at MediaWiki.org]]. The deadline to sign up is on May 23, which will be the start date of the test.

'''Updates for editors'''

* From May 20, 2025, [[m:Special:MyLanguage/Oversight policy|oversighters]] and [[m:Special:MyLanguage/Meta:CheckUsers|checkusers]] will need to have their accounts secured with two-factor authentication (2FA) to be able to use their advanced rights. All users who belong to these two groups and do not have 2FA enabled have been informed. In the future, this requirement may be extended to other users with advanced rights. [[m:Special:MyLanguage/Mandatory two-factor authentication for users with some extended rights|Learn more]].
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]]  [[m:Special:MyLanguage/Community Wishlist Survey 2023/Multiblocks|Multiblocks]] will begin mass deployment by the end of the month: all non-Wikipedia projects plus Catalan Wikipedia will adopt Multiblocks in the week of May 26, while all other Wikipedias will adopt it in the week of June 2. Please [[m:Talk:Community Wishlist Survey 2023/Multiblocks|contact the team]] if you have concerns. Administrators can test the new user interface now on your own wiki by browsing to [{{fullurl:Special:Block|usecodex=1}} {{#special:Block}}?usecodex=1], and can test the full multiblocks functionality [[testwiki:Special:Block|on testwiki]]. Multiblocks is the feature that makes it possible for administrators to impose different types of blocks on the same user at the same time. See the [[mw:Special:MyLanguage/Help:Manage blocks|help page]] for more information. [https://phabricator.wikimedia.org/T377121]
* Later this week, the [[{{#special:SpecialPages}}]] listing of almost all special pages will be updated with a new design. This page has been [[phab:T219543|redesigned]] to improve the user experience in a few ways, including: The ability to search for names and aliases of the special pages, sorting, more visible marking of restricted special pages, and a more mobile-friendly look. The new version can be [https://meta.wikimedia.beta.wmflabs.org/wiki/Special:SpecialPages previewed] at Beta Cluster now, and feedback shared in the task. [https://phabricator.wikimedia.org/T219543]
* The [[mw:Special:MyLanguage/Extension:Chart|Chart extension]] is being enabled on more wikis. For a detailed list of when the extension will be enabled on your wiki, please read the [[mw:Special:MyLanguage/Extension:Chart/Project#Deployment Timeline|deployment timeline]].
* [[f:Special:MyLanguage/Wikifunctions:Main Page|Wikifunctions]] will be deployed on May 27 on five Wiktionaries: [[wikt:ha:|Hausa]], [[wikt:ig:|Igbo]], [[wikt:bn:|Bengali]], [[wikt:ml:|Malayalam]], and [[wikt:dv:|Dhivehi/Maldivian]]. This is the second batch of deployment planned for the project. After deployment, the projects will be able to call [[f:Special:MyLanguage/Wikifunctions:Introduction|functions from Wikifunctions]] and integrate them in their pages. A function is something that takes one or more inputs and transforms them into a desired output, such as adding up two numbers, converting miles into metres, calculating how much time has passed since an event, or declining a word into a case. Wikifunctions will allow users to do that through a simple call of [[f:Special:MyLanguage/Wikifunctions:Catalogue|a stable and global function]], rather than via a local template.
* Later this week, the Wikimedia Foundation will publish a hub for [[diffblog:2024/07/09/on-the-value-of-experimentation/|experiments]]. This is to showcase and get user feedback on product experiments. The experiments help the Wikimedia movement [[diffblog:2023/07/13/exploring-paths-for-the-future-of-free-knowledge-new-wikipedia-chatgpt-plugin-leveraging-rich-media-social-apps-and-other-experiments/|understand new users]], how they interact with the internet and how it could affect the Wikimedia movement. Some examples are [[m:Special:MyLanguage/Future Audiences/Generated Video|generated video]], the [[m:Special:MyLanguage/Future Audiences/Roblox game|Wikipedia Roblox speedrun game]] and [[m:Special:MyLanguage/Future Audiences/Discord bot|the Discord bot]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:29}} community-submitted {{PLURAL:29|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, there was a bug with creating an account using the API, which has now been fixed. [https://phabricator.wikimedia.org/T390751]

'''Updates for technical contributors'''
* Gadgets and user scripts that interact with [[{{#special:Block}}]] may need to be updated to work with the new [[mw:Special:MyLanguage/Help:Manage blocks|manage blocks interface]]. Please review the [[mw:Help:Manage blocks/Developers|developer guide]] for more information. If you need help or are unable to adapt your script to the new interface, please let the team know on the [[mw:Help talk:Manage blocks/Developers|talk page]]. [https://phabricator.wikimedia.org/T377121]
* The &lt;code dir=ltr&gt;mw.title&lt;/code&gt; object allows you to get information about a specific wiki page in the [[w:en:Wikipedia:Lua|Lua]] programming language. Starting this week, a new property will be added to the object, named &lt;code dir=ltr&gt;isDisambiguationPage&lt;/code&gt;. This property allows you to check if a page is a disambiguation page, without the need to write a custom function. [https://phabricator.wikimedia.org/T71441]
* [[File:Octicons-tools.svg|15px|link=|class=skin-invert|Advanced item]] User script developers can use a [[toolforge:gitlab-content|new reverse proxy tool]] to load javascript and css from [[gitlab:|gitlab.wikimedia.org]] with &lt;code dir=ltr&gt;mw.loader.load&lt;/code&gt;. The tool's author hopes this will enable collaborative development workflows for user scripts including linting, unit tests, code generation, and code review on &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;gitlab.wikimedia.org&lt;/bdi&gt; without a separate copy-and-paste step to publish scripts to a Wikimedia wiki for integration and acceptance testing. See [[wikitech:Tool:Gitlab-content|Tool:Gitlab-content on Wikitech]] for more information.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.2|MediaWiki]]

'''Meetings and events'''
* The 12th edition of [[m:Special:MyLanguage/Wiki Workshop 2025|Wiki Workshop 2025]], a forum that brings together researchers that explore all aspects of Wikimedia projects, will be held virtually on 21-22 May. Researchers can [https://pretix.eu/wikimedia/wikiworkshop2025/ register now].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W21&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:12, 19 May 2025 (UTC)
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== Tech News: 2025-22 ==

&lt;section begin=&quot;technews-2025-W22&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/22|Translations]] are available.

'''Weekly highlight'''
* A community-wide discussion about a very delicate issue for the development of [[m:Special:MyLanguage/Abstract Wikipedia|Abstract Wikipedia]] is now open on Meta: where to store the abstract content that will be developed through functions from Wikifunctions and data from Wikidata. The discussion is open until June 12 at [[m:Special:MyLanguage/Abstract Wikipedia/Location of Abstract Content|Abstract Wikipedia/Location of Abstract Content]], and every opinion is welcomed. The decision will be made and communicated after the consultation period by the Foundation.

'''Updates for editors'''
* Since last week, on all wikis except [[phab:T388604|the largest 20]], people using the mobile visual editor will have [[phab:T385851|additional tools in the menu bar]], accessed using the new &lt;code&gt;+&lt;/code&gt; toolbar button. To start, the new menu will include options to add: citations, hieroglyphs, and code blocks. Deployment to the remaining wikis is [[phab:T388605|scheduled]] to happen in June.
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The &lt;code dir=ltr&gt;[[mw:Special:MyLanguage/Help:Extension:ParserFunctions##ifexist|#ifexist]]&lt;/code&gt; parser function will no longer register a link to its target page. This will improve the usefulness of [[{{#special:WantedPages}}]], which will eventually only list pages that are the target of an actual red link. This change will happen gradually as the source pages are updated. [https://phabricator.wikimedia.org/T14019]
* This week, the Moderator Tools team will launch [[mw:Special:MyLanguage/2025 RecentChanges Language Agnostic Revert Risk Filtering|a new filter to Recent Changes]], starting at Indonesian Wikipedia. This new filter highlights edits that are likely to be reverted. The goal is to help Recent Changes patrollers identify potentially problematic edits. Other wikis will benefit from this filter in the future.
* Upon clicking an empty search bar, logged-out users will see suggestions of articles for further reading. The feature will be available on both desktop and mobile. Readers of Catalan, Hebrew, and Italian Wikipedias and some sister projects will receive the change between May 21 and mid-June. Readers of other wikis will receive the change later. The goal is to encourage users to read the wikis more. [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments/Search Suggestions|Learn more]].
* Some users of the Wikipedia Android app can use a new feature for readers, [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/TrivaGame|WikiGames]], a daily trivia game based on real historical events. The release has started as an A/B test, available to 50% of users in the following languages: English, French, Portuguese, Russian, Spanish, Arabic, Chinese, and Turkish.
* The [[mw:Special:MyLanguage/Extension:Newsletter|Newsletter extension]] that is available on MediaWiki.org allows the creation of [[mw:Special:Newsletters|various newsletters]] for global users. The extension can now publish new issues as section links on an existing page, instead of requiring a new page for each issue. [https://phabricator.wikimedia.org/T393844]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* The previously deprecated &lt;code dir=ltr&gt;[[mw:Special:MyLanguage/Manual:Ipblocks table|ipblocks]]&lt;/code&gt; views in [[wikitech:Help:Wiki Replicas|Wiki Replicas]] will be removed in the beginning of June. Users are encouraged to query the new &lt;code dir=ltr&gt;[[mw:Special:MyLanguage/Manual:Block table|block]]&lt;/code&gt; and &lt;code dir=ltr&gt;[[mw:Special:MyLanguage/Manual:Block target table|block_target]]&lt;/code&gt; views instead.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.3|MediaWiki]]

'''Meetings and events'''
* [[d:Special:MyLanguage/Event:Wikidata and Sister Projects|Wikidata and Sister Projects]] is a multi-day online event that will focus on how Wikidata is integrated to Wikipedia and the other Wikimedia projects. The event runs from May 29 – June 1. You can [[d:Special:MyLanguage/Event:Wikidata and Sister Projects#Sessions|read the Program schedule]] and [[d:Special:RegisterForEvent/1291|register]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/22|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W22&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:04, 26 May 2025 (UTC)
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== Tech News: 2025-23 ==

&lt;section begin=&quot;technews-2025-W23&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/23|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Extension:Chart|Chart extension]] is now available on all Wikimedia wikis. Editors can use this new extension to create interactive data visualizations like bar, line, area, and pie charts. Charts are designed to replace many of the uses of the legacy [[mw:Special:MyLanguage/Extension:Graph|Graph extension]].

'''Updates for editors'''
* It is now easier to configure automatic citations for your wiki within the visual editor's [[mw:Special:MyLanguage/Citoid/Enabling Citoid on your wiki|citation generator]]. Administrators can now set a default template by using the &lt;code dir=ltr&gt;_default&lt;/code&gt; key in the local &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[MediaWiki:Citoid-template-type-map.json]]&lt;/bdi&gt; page ([[mw:Special:Diff/6969653/7646386|example diff]]). Setting this default will also help to future-proof your existing configurations when [[phab:T347823|new item types]] are added in the future. You can still set templates for individual item types as they will be preferred to the default template. [https://phabricator.wikimedia.org/T384709]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Starting the week of June 2, bots logging in using &lt;code dir=ltr&gt;action=login&lt;/code&gt; or &lt;code dir=ltr&gt;action=clientlogin&lt;/code&gt; will fail more often. This is because of stronger protections against suspicious logins. Bots using [[mw:Special:MyLanguage/Manual:Bot passwords|bot passwords]] or using a loginless authentication method such as [[mw:Special:MyLanguage/OAuth/Owner-only consumers|OAuth]] are not affected. If your bot is not using one of those, you should update it; using &lt;code dir=ltr&gt;action=login&lt;/code&gt; without a bot password was deprecated [[listarchive:list/wikitech-l@lists.wikimedia.org/message/3EEMN7VQX5G7WMQI5K2GP5JC2336DPTD/|in 2016]]. For most bots, this only requires changing what password the bot uses. [https://phabricator.wikimedia.org/T395205]
* From this week, Wikimedia wikis will allow ES2017 features in JavaScript code for official code, gadgets, and user scripts. The most visible feature of ES2017 is &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;async&lt;/code&gt;/&lt;code&gt;await&lt;/code&gt;&lt;/bdi&gt; syntax, allowing for easier-to-read code. Until this week, the platform only allowed up to ES2016, and a few months before that, up to ES2015. [https://phabricator.wikimedia.org/T381537]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.4|MediaWiki]]

'''Meetings and events'''
* Scholarship applications to participate in the [[m:Special:MyLanguage/GLAM Wiki 2025|GLAM Wiki Conference 2025]] are now open. The conference will take place from 30 October to 1 November, in Lisbon, Portugal. GLAM contributors who lack the means to support their participation can [[m:Special:MyLanguage/GLAM Wiki 2025/Scholarships|apply here]]. Scholarship applications close on June 7th.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/23|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W23&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:55, 2 June 2025 (UTC)
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== Tech News: 2025-24 ==

&lt;section begin=&quot;technews-2025-W24&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/24|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Trust and Safety Product|Trust and Safety Product team]] is finalizing work needed to roll out [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] on large Wikipedias later this month. The team has worked with stewards and other users with extended rights to predict and address many use cases that may arise on larger wikis, so that community members can continue to effectively moderate and patrol temporary accounts. This will be the second of three phases of deployment – the last one will take place in September at the earliest. For more information about the recent developments on the project, [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|see this update]]. If you have any comments or questions, write on the [[mw:Talk:Trust and Safety Product/Temporary Accounts|talk page]], and [[m:Event:CEE Catch up Nr. 10 (June 2025)|join a CEE Catch Up]] this Tuesday.

'''Updates for editors'''
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] The [[mw:Special:MyLanguage/Help:Watchlist expiry|watchlist expiry]] feature allows editors to watch pages for a limited period of time. After that period, the page is automatically removed from your watchlist. Starting this week, you can set a preference for the default period of time to watch pages. The [[Special:Preferences#mw-prefsection-watchlist-pageswatchlist|preferences]] also allow you to set different default watch periods for editing existing pages, pages you create, and when using rollback. [https://phabricator.wikimedia.org/T265716]
[[File:Talk pages default look (April 2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]]
* The appearance of talk pages will change at almost all Wikipedias ([[m:Special:MyLanguage/Tech/News/2024/19|some]] have already received this design change, [[phab:T379264|a few]] will get these changes later). You can read details about the changes [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|on ''Diff'']]. It is possible to opt out of these changes [[Special:Preferences#mw-prefsection-editing-discussion|in user preferences]] (&quot;{{int:discussiontools-preference-visualenhancements}}&quot;). [https://phabricator.wikimedia.org/T319146][https://phabricator.wikimedia.org/T392121]
* Users with specific extended rights (including administrators, bureaucrats, checkusers, oversighters, and stewards) can now have IP addresses of all temporary accounts [[phab:T358853|revealed automatically]] during time-limited periods where they need to combat high-speed account-hopping vandalism. This feature was requested by stewards. [https://phabricator.wikimedia.org/T386492]
* This week, the Moderator Tools and Machine Learning teams will continue the rollout of [[mw:Special:MyLanguage/2025 RecentChanges Language Agnostic Revert Risk Filtering|a new filter to Recent Changes]], releasing it to several more Wikipedias. This filter utilizes the Revert Risk model, which was created by the Research team, to highlight edits that are likely to be reverted and help Recent Changes patrollers identify potentially problematic contributions. The feature will be rolled out to the following Wikipedias: {{int:project-localized-name-afwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-simplewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}. The rollout will continue in the coming weeks to include [[mw:Special:MyLanguage/2025 RecentChanges Language Agnostic Revert Risk Filtering|the rest of the Wikipedias in this project]]. [https://phabricator.wikimedia.org/T391964]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* AbuseFilter editors active on Meta-Wiki and large Wikipedias are kindly asked to update AbuseFilter to make it compatible with temporary accounts. A link to the instructions and the private lists of filters needing verification are [[phab:T369611|available on Phabricator]].
* Lua modules now have access to the name of a page's associated thumbnail image, and on [https://gerrit.wikimedia.org/g/operations/mediawiki-config/+/2e4ab14aa15bb95568f9c07dd777065901eb2126/wmf-config/InitialiseSettings.php#10849 some wikis] to the WikiProject assessment information. This is possible using two new properties on [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#added-by-extensions|mw.title objects]], named &lt;code dir=ltr&gt;pageImage&lt;/code&gt; and &lt;code dir=ltr&gt;pageAssessments&lt;/code&gt;. [https://phabricator.wikimedia.org/T131911][https://phabricator.wikimedia.org/T380122]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.5|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/24|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W24&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:16, 10 June 2025 (UTC)
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== Tech News: 2025-25 ==

&lt;section begin=&quot;technews-2025-W25&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/25|Translations]] are available.

'''Updates for editors'''
* You can [https://wikimediafoundation.limesurvey.net/359761?lang=en nominate your favorite tools] for the sixth edition of the [[m:Special:MyLanguage/Coolest Tool Award|Coolest Tool Award]]. Nominations are anonymous and will be open until June 25. You can re-use the survey to nominate multiple tools.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:33}} community-submitted {{PLURAL:33|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.6|MediaWiki]]

'''In depth'''
* Foundation staff and technical volunteers use Wikimedia APIs to build the tools, applications, features, and integrations that enhance user experiences. Over the coming years, the MediaWiki Interfaces team will be investing in Wikimedia web (HTTP) APIs to better serve technical volunteer needs and protect Wikimedia infrastructure from potential abuse. You can [https://techblog.wikimedia.org/2025/06/12/apis-as-a-product-investing-in-the-current-and-next-generation-of-technical-contributors/ read more about their plans to evolve the APIs in this Techblog post].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/25|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W25&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:38, 16 June 2025 (UTC)
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== Tech News: 2025-26 ==

&lt;section begin=&quot;technews-2025-W26&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/26|Translations]] are available.

'''Weekly highlight'''
* This week, the Moderator Tools and Machine Learning teams will continue the rollout of [[mw:Special:MyLanguage/2025 RecentChanges Language Agnostic Revert Risk Filtering|a new filter to Recent Changes]], releasing it to the third and last batch of Wikipedias. This filter utilizes the Revert Risk model, which was created by the Research team, to highlight edits that are likely to be reverted and help Recent Changes patrollers identify potentially problematic contributions. The feature will be rolled out to the following Wikipedias: {{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-swwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tlwiki/en}}. The rollout will continue in the coming weeks to include [[mw:Special:MyLanguage/2025 RecentChanges Language Agnostic Revert Risk Filtering|the rest of the Wikipedias in this project]]. [https://phabricator.wikimedia.org/T391964]

'''Updates for editors'''
* Last week, [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] were rolled out on Czech, Korean, and Turkish Wikipedias. This and next week, deployments on larger Wikipedias will follow. [[mw:Talk:Trust and Safety Product/Temporary Accounts|Share your thoughts]] about the project. [https://phabricator.wikimedia.org/T340001]
* Later this week, the Editing team will release [[mw:Special:MyLanguage/Help:Edit check#Multi check|Multi Check]] to all Wikipedias (except English Wikipedia). This feature shows multiple [[mw:Special:MyLanguage/Help:Edit check#Reference check|Reference checks]] within the editing experience. This encourages users to add citations when they add multiple new paragraphs to a Wikipedia article. This feature was previously available as an A/B test. [https://analytics.wikimedia.org/published/reports/editing/multi_check_ab_test_report_final.html#summary-of-results The test shows] that users who are shown multiple checks are 1.3 times more likely to add a reference to their edit, and their edit is less likely to be reverted (-34.7%). [https://phabricator.wikimedia.org/T395519]
* A few pages need to be renamed due to software updates and to match more recent Unicode standards. All of these changes are related to title-casing changes. Approximately 71 pages and 3 files will be renamed, across 15 wikis; the complete list is in [[phab:T396903|the task]]. The developers will rename these pages next week, and they will fix redirects and embedded file links a few minutes later via a system settings update.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:24}} community-submitted {{PLURAL:24|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed that had caused pages to scroll upwards when text near the top was selected. [https://phabricator.wikimedia.org/T364023]

'''Updates for technical contributors'''
* Editors can now use Lua modules to filter and transform tabular data for use with [[mw:Special:MyLanguage/Extension:Chart|Extension:Chart]]. This can be used for things like selecting a subset of rows or columns from the source data, converting between units, statistical processing, and many other useful transformations. [[mw:Special:MyLanguage/Extension:Chart/Transforms|Information on how to use transforms is available]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Extension:Chart/Project/Updates]
* The &lt;code dir=ltr&gt;all_links&lt;/code&gt; variable in [[Special:AbuseFilter|AbuseFilter]] is now renamed to &lt;code dir=ltr&gt;new_links&lt;/code&gt; for consistency with other variables. Old usages will still continue to work. [https://phabricator.wikimedia.org/T391811]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.7|MediaWiki]]

'''In depth'''
* The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/34|Growth newsletter]] is available. It includes: the recent updates for the &quot;Add a Link&quot; Task, two new Newcomer Engagement Features, and updates to Community Configuration.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/26|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W26&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:21, 23 June 2025 (UTC)
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== Tech News: 2025-27 ==

&lt;section begin=&quot;technews-2025-W27&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/27|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] has been enabled on all Wikipedias. The extension makes it easier to organize and participate in collaborative activities, like edit-a-thons and WikiProjects, on the wikis. The extension has three features: [[m:Special:MyLanguage/Event Center/Registration|Event Registration]], [[m:Special:MyLanguage/CampaignEvents/Collaboration list|Collaboration List]], and [[m:Campaigns/Foundation Product Team/Invitation list|Invitation List]]. To request the extension for your wiki, visit the [[m:Special:MyLanguage/CampaignEvents/Deployment status#How to Request the CampaignEvents Extension for your wiki|Deployment information page]].

'''Updates for editors'''
* AbuseFilter maintainers can now [[mw:Special:MyLanguage/Extension:IPReputation/AbuseFilter variables|match against IP reputation data]] in [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilters]]. IP reputation data is information about the proxies and VPNs associated with the user's IP address. This data is not shown publicly and is not generated for actions performed by registered accounts. [https://phabricator.wikimedia.org/T354599]
* Hidden content that is within [[mw:Special:MyLanguage/Manual:Collapsible elements|collapsible parts of wikipages]] will now be revealed when someone searches the page using the web browser's &quot;Find in page&quot; function (Ctrl+F or ⌘F) in supporting browsers. [https://phabricator.wikimedia.org/T327893][https://developer.mozilla.org/en-US/docs/Web/HTML/Reference/Global_attributes/hidden#browser_compatibility]
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] A new feature, called [[mw:Special:MyLanguage/Help:TemplateData/Template discovery|Favourite Templates]], will be deployed later this week on all projects (except English Wikipedia, which will receive the feature next week), following a piloting phase on Polish and Arabic Wikipedia, and Italian and English Wikisource. The feature will provide a better way for new and experienced contributors to recall and discover templates via the template dialog, by allowing users to put templates on a special &quot;favourite list&quot;. The feature works with both the visual editor and the wikitext editor. The feature is a [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|community wishlist focus area]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed that had caused some Notifications to be sent multiple times. [https://phabricator.wikimedia.org/T397103]

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.8|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/27|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W27&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:40, 30 June 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=28917415 --&gt;

== Tech News: 2025-28 ==

&lt;section begin=&quot;technews-2025-W28&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/28|Translations]] are available.

'''Weekly highlight'''
* [[mw:Special:MyLanguage/Help:Temporary accounts|Temporary accounts]] have been rolled out on 18 large and medium-sized Wikipedias, including German, Japanese, French, and Chinese. Now, about 1/3 of all logged-out activity across wikis is coming from temporary accounts. Users involved in patrolling may be interested in two new documentation pages: [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Access to IP|Access to IP]], explaining everything related to access to temporary account IP addresses, and [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Repository|Repository]] with a list of new gadgets and user scripts.

'''Updates for editors'''
* Anyone can play an experimental new game, [[mw:Special:MyLanguage/New Engagement Experiments/WikiRun|WikiRun]], that lets you race through Wikipedia by clicking from one article to another, aiming to reach a target page in as few steps and in as little time as possible. The project's goal is to explore new ways of engaging readers. [https://wikirun-game.toolforge.org/ Try playing the game] and let the team know what you think [[mw:Talk:New Engagement Experiments/WikiRun|on the talk page]].
* Users of the Wikipedia Android app in some languages can now play the new [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/TrivaGame|trivia game]]. ''Which came first?'' is a simple history game where you guess which of two events happened earlier on today's date. It was previously available as an A/B test. It is now available to all users in English, German, French, Spanish, Portuguese, Russian, Arabic, Turkish, and Chinese. The goal of the feature is to help engage with new generations of readers. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/News/2025/22]
* Users of the iOS Wikipedia App in some languages may see a new tabbed browsing feature that enables you to open multiple tabs while reading. This feature makes it easier to explore related topics and switch between articles. The A/B test is currently running in Arabic, English, and Japanese in selected regions. More details are available on the [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Tabbed Browsing (Tabs)|Tabbed Browsing project page]].
* Bureaucrats on Wikimedia wikis can now use [[{{#special:VerifyOATHForUser}}]] to check if users have enabled [[mw:Special:MyLanguage/Help:Two-factor authentication|two-factor authentication]]. [https://phabricator.wikimedia.org/T265726]
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] A new feature related to [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|Template Recall and Discovery]] will be deployed later this week to all Wikimedia projects: a [[mw:Special:MyLanguage/Help:TemplateData/Template discovery#Template categories|template category browser]] will be introduced to assist users in finding templates to put in their “favourite” list. The browser will allow users to browse a list of templates which have been organised into a given category tree. The feature has been requested by the community [[m:Special:MyLanguage/Community Wishlist/Wishes/Select templates by categories|through the Community Wishlist]].
* It is now possible to access watchlist preferences from the watchlist page. Also the redundant button to edit the watchlist has been removed. [https://www.mediawiki.org/wiki/Moderator_Tools/Watchlist]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* As part of [[mw:MediaWiki_1.44|MediaWiki 1.44]] there is now a unified built-in Notifications system that makes it easier for developers to send, manage, and customize notifications. Check out the updated documentation at [[mw:Manual:Notifications|Manual:Notifications]], information about migration in [[phab:T388663|T388663]] and details on deprecated hooks in [[phab:T389624|T389624]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.9|MediaWiki]]

'''Meetings and events'''
* [[d:Special:MyLanguage/Event:WikidataCon 2025|WikidataCon 2025]], the conference dedicated to Wikidata is now open for [https://pretalx.com/wikidatacon-2025/cfp session proposals] and for [[d:Special:RegisterForEvent/1340|registration]]. This year's event will be held online from October 31 – November 02 and will explore on the theme of &quot;Connecting People through Linked Open Data&quot;.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/28|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W28&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:05, 8 July 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=28930584 --&gt;

== Tech News: 2025-29 ==

&lt;section begin=&quot;technews-2025-W29&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/29|Translations]] are available.

'''Updates for editors'''
* [[mw:Special:MyLanguage/Help:TemplateData/Template discovery#Featured templates|Featured templates]], a new feature related to [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|Template Recall and Discovery]] will be deployed this week to all Wikimedia projects: With this feature, editors will be able to quickly access a list of templates that are likely to be useful. These templates will be displayed in a list, under the &quot;featured&quot; tab of the template discovery interface. Administrators can define the list via the Community Configuration interface. The feature fulfills a request by the community [[m:Special:MyLanguage/Community Wishlist/Wishes/Easy access Templates|through the Community Wishlist]]. [https://phabricator.wikimedia.org/T367428][https://phabricator.wikimedia.org/T392896]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the request to add Malayalam fonts in the [[oldWikisource:Special:MyLanguage/Wikisource:WS Export|Wikisource Book Export Tool]] was resolved and now, the rendering of Malayalam letters in exported Wikisource books are accurate. [https://phabricator.wikimedia.org/T374457]

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.10|MediaWiki]]

'''In depth'''
* Developers, designers, and all Wikimedians are invited to [https://phabricator.wikimedia.org/project/board/7953/ submit a project idea] for the Wikimania Hackathon 2025. Read [https://diff.wikimedia.org/2025/06/30/call-for-projects-wikimania-hackathon-2025-is-coming-to-nairobi/ this Diff blog post] for more details.

'''Meetings and events'''
* [[m:WikiIndaba conference 2025|WikiIndaba 2025]] scholarship application and program submission is open until 23:59 GMT on July 20. WikiIndaba is a regional conference for African Wikimedians both on the continent and in the diaspora to unite and grow together. Submit [https://docs.google.com/forms/d/e/1FAIpQLSdJTv68R1OPASXXDfpIl8EWiMLTM-TDwh6_5gNVvFuWccFZ2Q/viewform your scholarship application] and [https://ee.kobotoolbox.org/x/BI3omIfH program proposal] now!
* [https://br.wikimedia.org/wiki/WikiCon_Brasil_2025 WikiCon Brasil 2025] will take place on July 19-20 in Salvador, Bahia, Brazil. The Brazilian community members are encouraged to register and attend!

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/29|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W29&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:09, 14 July 2025 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=28980963 --&gt;

== Tech News: 2025-30 ==

&lt;section begin=&quot;technews-2025-W30&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/30|Translations]] are available.

'''Updates for editors'''
* The Translation Suggestions feature in the [[mw:Special:MyLanguage/Content translation|Content Translation tool]] now has another level of article filters added to the &quot;[https://en.wikipedia.org/w/index.php?title=Special:ContentTranslation&amp;filter-type=automatic&amp;filter-id=previous-edits&amp;active-list=suggestions&amp;from=en&amp;to=fi#/ ... More]&quot; category. Translators who use the Suggestions feature can now select and receive article suggestions that are customized to geographical locations of their interest using the new &quot;{{int:Cx-sx-suggestions-filters-tab-regions}}&quot; filter. [https://phabricator.wikimedia.org/T113257]
* Administrators can now limit &quot;Add a Link&quot; to newcomers. The [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|&quot;Add a Link&quot;]] Structured Task [[mw:Special:MyLanguage/Growth/Constructive activation experimentation#Enwiki A/B test &amp; &quot;Add a Link&quot; Improvements (Wiki Experiences 1.2.11 &amp; 1.2.16)|helps new account holders start editing]], but some communities have requested the ability to restrict it to its intended audience: newcomers. Administrators can configure this setting within the [[Special:CommunityConfiguration/GrowthSuggestedEdits|Community Configuration]] feature.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:29}} community-submitted {{PLURAL:29|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* For AbuseFilter editors on [[phab:T392144|some wikis]], it is now possible to filter edits based on the RevertRisk score of the edit being attempted. It is only populated if the action being evaluated is an edit. For more information, please see the [[mw:Special:MyLanguage/Extension:ORES/AbuseFilter variables#What variables are available for use|ORES/AbuseFilter variables]] documentation.
* The [[mw:Special:MyLanguage/Beta Cluster|Beta Cluster]] wikis have [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/YDABPV75LADRQCXMJAFWUP256N4EQ25B/|been moved]] from &lt;code dir=ltr&gt;beta.wmflabs.org&lt;/code&gt; to &lt;code dir=ltr&gt;beta.wmcloud.org&lt;/code&gt;. Users may need to update URLs in any tools, or in their password managers. Any related issues can be [[phab:T289318|reported in the task]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.11|MediaWiki]]

'''Meetings and events'''
* [[m:Special:MyLanguage/WikiCite 2025|WikiCite 2025]] will take place from 29–31 August, both online and in-person in Bern, Switzerland. The event's goals are to reconnect communities, institutions, and individuals working with open citations, bibliographic data, and the Wikidata/Wikibase ecosystem. Registration is open and the call for proposals will be announced soon. [https://lists.wikimedia.org/hyperkitty/list/wikidata@lists.wikimedia.org/message/KQZUG3ETKLBWPBYSB2YAWZIRPWHS24TG/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/30|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W30&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:42, 21 July 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29005283 --&gt;

== Tech News: 2025-31 ==

&lt;section begin=&quot;technews-2025-W31&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/31|Translations]] are available.

'''Weekly highlight'''
* The Community Tech team will be focusing on wishes related to Watchlists and Recent Changes pages, over the next few months. They are looking for feedback. Please [[m:Special:MyLanguage/Community Wishlist/Updates#July 24, 2025: Watchlists and Recent Changes pages|read the latest update]], and if you have ideas, please [[m:Special:MyLanguage/Community Wishlist|submit a wish]] on the topic.

'''Updates for editors'''
* The Wikimedia Commons community has decided to block [[:mw:Special:MyLanguage/Upload dialog|cross-wiki uploads]] to Wikimedia Commons, for all users without autoconfirmed rights on that wiki, starting on August 16. This is because of [[:c:Commons:Cross-wiki media upload tool/History|widespread problems]] related to files that are uploaded by newcomers. Users who are affected by this will get an error message with a link to the less restrictive UploadWizard on Commons. Please help translating the [[:c:Special:MyLanguage/MediaWiki:Abusefilter-disallowed-cross-wiki-upload|message]] or give feedback on the message text. Please also update your local help pages to explain this restriction. [https://phabricator.wikimedia.org/T370598]
* On wikis with temporary accounts enabled and Meta-Wiki, administrators may now set up a footer for the Special:Contributions pages of temporary accounts, similar to those which can be shown on IP and user-account pages. They may do it by creating the page named &lt;code dir=ltr&gt;MediaWiki:Sp-contributions-footer-temp&lt;/code&gt;. [https://phabricator.wikimedia.org/T398347]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.12|MediaWiki]]

'''Meetings and events'''
* [[wmania:Special:MyLanguage/2025:Wikimania|Wikimania 2025]] will run from August 6–9. The [https://wikimedia.eventyay.com/talk/wikimania2025/schedule/ program is available] for you to plan which sessions you want to attend. Most sessions will be live-streamed, with exceptions for those that show the &quot;no camera&quot; icon. If you are joining online to watch live-streams and use the interactive features, please [[wmania:Special:MyLanguage/2025:Registration|register]] for a free virtual ticket. For example, you may be interested in technical sessions such as:
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/KFEFVG/ Temporary Accounts: Enhancing privacy for our unregistered editors]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/TVCVAB/ Building a Sustainable Future for Wikimedia Contributors]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/WTRQCJ/ A dozen visions for wikitext!]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/8YKKP9/ Coordinate Across Stakeholders with the Product and Technology Advisory Council]
* The [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2025|MediaWiki Users and Developers Conference, Fall 2025]] will be held 28–30 October 2025 in Hanover, Germany. This event is organized by and for the third-party MediaWiki community. You can propose sessions and register to attend.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/31|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W31&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:26, 29 July 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29051727 --&gt;

== Tech News: 2025-32 ==

&lt;section begin=&quot;technews-2025-W32&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/32|Translations]] are available.

'''Updates for editors'''
* Editors can now enable the [[mw:Special:MyLanguage/Product Safety and Integrity/Anti-abuse signals/User Info|User Info card]]. This feature adds an icon next to usernames on history pages and similar user-contribution log pages. When you tap or click on the icon, it displays data related to that user account such as the number of edits, reverted edits, blocks, and more. It's part of a broader project to make it easier for moderators to evaluate account trustworthiness. The feature can be enabled in [[testwiki:Special:GlobalPreferences#mw-prefsection-rendering|your global preferences]], and later this week it will be available in local preferences. [https://phabricator.wikimedia.org/T386439]
* Everybody is invited to share comments on [[m:Special:MyLanguage/CampaignEvents/Collaborative contributions|Collaborative Contributions]], a project recently launched by the [[m:Special:MyLanguage/Connection Team|Connection team]]. The project aims to create a new way to display the impact of collaborative editing activities (such as edit-a-thons, backlog drives, and WikiProjects) on the wikis. Post your comments on the [[m:Talk:CampaignEvents/Collaborative contributions|project talk page]]. [https://phabricator.wikimedia.org/T378035]
* Administrators can now define the default block duration for temporary accounts. To do that, they need to create a page named &lt;code dir=ltr&gt;MediaWiki:Ipb-default-expiry-temporary-account&lt;/code&gt; and use a value defined in &lt;code dir=ltr&gt;MediaWiki:Ipboptions&lt;/code&gt;. This allows administrators to easily block temporary accounts for 90 days, which is functionally equivalent to an indefinite block. The advantage of this solution is that it does not clutter Special:BlockList. [[mw:Special:MyLanguage/Manual:Block and unblock#Default block duration options|More documentation]] is available. [https://phabricator.wikimedia.org/T398626]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Gadgets can now include &lt;code dir=ltr&gt;.vue&lt;/code&gt; files. This makes it easier to develop modern user interfaces using [[mw:Vue.js|Vue.js]], in particular using [[mw:Special:MyLanguage/Codex|Codex]], the official design system of Wikimedia. [[wmdoc:codex/latest/icons/overview.html|Codex icons]] can be loaded through the gadget definition. [[mw:Special:MyLanguage/Extension:Gadgets#Pages|The documentation]] has examples. For user scripts that use Vue.js, an [[mw:API:CodexIcons|API module]] now exists to load Codex icons. [https://phabricator.wikimedia.org/T340460][https://phabricator.wikimedia.org/T311099]
* Module developers can now use a [[mw:Help:Extension:Translate/Message Bundles/Lua reference|Lua interface]] to simplify the preparation of Lua modules for translation on Meta-Wiki. This improvement makes it easier for translators to find and edit module strings without dealing with raw Lua code. It helps prevent mistakes that could break the module during translation. Module developers and translators are invited to [[commons:File:Translatable modules video demo July 2025.webm|watch the demo video]], read more about [[mw:Special:MyLanguage/Translatable modules|translatable modules]] to understand how it works, refer to Meta-Wiki's [[m:Module:User Wikimedia project|Module:User Wikimedia project]] for example usage, and [[mw:Talk:Translatable modules|share their feedback]] on how well it addresses the challenges in their workflow. The interface still has some performance issues, so it should not be used in widely used modules yet. [https://phabricator.wikimedia.org/T359918]
* Developers of external tools that connect to Wikimedia pages must set a user-agent that complies with [[foundation:Special:MyLanguage/Policy:Wikimedia Foundation User-Agent Policy|the user-agent policy]]. This policy will start to be more strongly enforced in August because of external crawlers that are [[diffblog:2025/04/01/how-crawlers-impact-the-operations-of-the-wikimedia-projects/|overusing]] Wikimedia's resources. Tools that are hosted on Wikimedia's Toolforge or Cloud VPS will not be affected by this for now, but should still set a user-agent. [[phab:T400119|More technical details are available]], and related questions are welcome in that task.
* Parsoid Read Views is going to be rolling out to some smaller Wikipedias over the next few weeks, following the successful transition of Wikivoyages and Wiktionaries to Parsoid Read Views. For more information, see the [[mw:Special:MyLanguage/Parsoid/Parser Unification|Parsoid/Parser Unification]] project page. [https://phabricator.wikimedia.org/project/profile/7694/]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.13|MediaWiki]]

'''Meetings and events'''
* [[wmania:Special:MyLanguage/2025:Wikimania|Wikimania 2025]] will run from August 6–9. The [https://wikimedia.eventyay.com/talk/wikimania2025/schedule/ program is available] for you to plan which sessions you want to attend. Most sessions will be live-streamed, with exceptions for those that show the &quot;no camera&quot; icon. If you are joining online to watch live-streams and use the interactive features, please [[wmania:Special:MyLanguage/2025:Registration|register]] for a free virtual ticket. For example, you may be interested in technical sessions such as:
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/GEH9DH/ Wikimedia’s knowledge infrastructure in a changing internet: Establishing sustainable pathways for content reuse]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/7ELN9Q/ Wikifunctions is coming soon to a wiki near you!]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/ZMGVJV/ Shaping the Future of Wikipedia’s Reader Experience]
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/KCKTFZ/ Making Wikipedia More Readable: What Comes Next]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/32|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W32&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 03:40, 5 August 2025 (UTC)
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== Tech News: 2025-33 ==

&lt;section begin=&quot;technews-2025-W33&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/33|Translations]] are available.

'''Updates for editors'''
* The WikiEditor toolbar now includes [[mw:Special:MyLanguage/Help:Extension:WikiEditor#Keyboard shortcuts|its keyboard shortcuts]] in the tooltips for its buttons. This will help to improve the discoverability of this feature. [https://phabricator.wikimedia.org/T400583]
* The [[m:Special:MyLanguage/Product and Technology Advisory Council|Product and Technology Advisory Council]] published a set of [[m:Special:MyLanguage/Product and Technology Advisory Council/August 2025 draft PTAC proposals for feedback|proposed experiments]] the Wikimedia Foundation can try to improve communication with community. Feedback on the proposals are welcomed until August 22 on [[m:Talk:Product and Technology Advisory Council/August 2025 draft PTAC proposals for feedback|this talk page]].
* The search bar on the Minerva skin (mobile) has been updated to use the same type-ahead search component that is used on the Vector 2022 skin. There are no changes in search functionality but there are minor visual changes. Specifically, the close-search button has been changed from an &quot;X&quot; to a back arrow. This helps to distinguish it from the other &quot;X&quot; button that is used to clear any text. [https://phabricator.wikimedia.org/T393944]
* Editors on some wikis will see a new toggle for &quot;Group results by page&quot; on watchlist, related changes, and recent changes pages. This is [[mw:Special:MyLanguage/Moderator Tools/Watchlist/Experiment|an A/B experiment]] that is planned to start on August 11, and will run for 3–6 weeks on the Bengali, Chinese, Czech, French, Greek, Portuguese, and Urdu Wikipedias. The experiment will examine how making this feature more discoverable might affect editors' ability to find the edits they are looking for. [https://phabricator.wikimedia.org/T396789]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* The multiwiki datasets of [[:wikt:en:Module:Unicode data|Unicode data]] have been moved to [[c:Category:Unicode Module Datasets|Category:Unicode Module Datasets]] on Wikimedia Commons, to follow the idea of &quot;One common data source, multiple local wikis&quot;. Most wikis have been updated to use the Commons version. You can ask questions at [[c:Category talk:Unicode Module Datasets|the talkpage]]. [https://en.wiktionary.org/wiki/Module_talk:Unicode_data#Data_from_commons]
* Lua code can add warnings when something is wrong, by using the &lt;code dir=ltr&gt;mw.addWarning()&lt;/code&gt; function. It is now possible to add more than one warning, instead of new warnings replacing old ones. If you maintain a Lua module that used warnings, you should check it still works as expected. [https://phabricator.wikimedia.org/T398390]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.14|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/33|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W33&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:29, 11 August 2025 (UTC)
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== Tech News: 2025-34 ==

&lt;section begin=&quot;technews-2025-W34&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/34|Translations]] are available.

'''Updates for editors'''
* Later this week, people who are logged-in and have the &quot;[[mw:Special:MyLanguage/Talk pages project/Feature summary|Discussion tools]]&quot; [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] enabled will gain the ability to &quot;Thank&quot; individual comments directly from talk pages, rather than needing to navigate to page history. [[mw:Special:MyLanguage/Talk pages project/Feature summary#Comment actions|Learn more about this feature]]. [https://phabricator.wikimedia.org/T400849]
* An A/B test comparing two versions of the desktop donate link launched on testwiki on 12 August and on English Wikipedia 14 August for 0.1% of logged out users on the desktop site. The experiment will run for three weeks, ending on 12 September. [https://phabricator.wikimedia.org/T395716]
* An A/A test to measure the baseline for reader retention was launched 12 August using [[wikitech:Experimentation Lab|Experimentation Lab]]. This measures the percentage of users who revisit a wiki after their initial visit over a 14-day period. No visual changes are expected. The experiment will run through 31 August. [https://phabricator.wikimedia.org/T399227]
* Five new wikis have been created:
** a {{int:project-localized-name-group-wikisource/en}} in [[d:Q34057|Tagalog]] ([[s:tl:|&lt;code&gt;s:tl:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T388639]
** a {{int:project-localized-name-group-wikisource/en}} in [[d:Q36213|Madurese]] ([[s:mad:|&lt;code&gt;s:mad:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T391747]
** a {{int:project-localized-name-group-wikipedia/en}} in [[d:Q3450749|Rakhine]] ([[w:rki:|&lt;code&gt;w:rki:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T392490]
** a {{int:project-localized-name-group-wikibooks/en}} in [[d:Q13324|Minangkabau]] ([[b:min:|&lt;code&gt;b:min:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T395452]
** a {{int:project-localized-name-group-wiktionary/en}} in [[d:Q7598268|Standard Moroccan Amazigh]] ([[wikt:zgh:|&lt;code&gt;wikt:zgh:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T399684]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:46}} community-submitted {{PLURAL:46|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.15|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/34|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W34&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:38, 19 August 2025 (UTC)
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== Tech News: 2025-35 ==

&lt;section begin=&quot;technews-2025-W35&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/35|Translations]] are available.

'''Updates for editors'''
* [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Template authors can now use additional CSS properties, since the CSS sanitizer used by [[mw:Special:MyLanguage/Help:TemplateStyles|TemplateStyles]] was updated. For example: &lt;code&gt;width: fit-content&lt;/code&gt;; &lt;code&gt;ruby-align&lt;/code&gt;; relative units such as &lt;code&gt;lh&lt;/code&gt;; and custom strings in &lt;code&gt;list-style-type&lt;/code&gt;. These improvements are a [[m:Special:MyLanguage/Community Wishlist/Wishes/Allow use of modern CSS in templates by updating the TemplateStyles CSS sanitizer|Community Wishlist wish]]. [https://phabricator.wikimedia.org/T271958][https://phabricator.wikimedia.org/T277755][https://phabricator.wikimedia.org/T293633][https://phabricator.wikimedia.org/T295088][https://phabricator.wikimedia.org/T326906][https://phabricator.wikimedia.org/T340057][https://phabricator.wikimedia.org/T360725][https://phabricator.wikimedia.org/T371809][https://phabricator.wikimedia.org/T375344][https://phabricator.wikimedia.org/T394619]
* On large wikis, the default time period to display edits from, within the Special:RecentChanges page, has been changed from 7 days to 1 day. This is part of a performance improvement project. This should have no user-facing impact due to the quantity of edits on these wikis. [https://phabricator.wikimedia.org/T399455]
* Administrators can now access the [[{{#special:BlockedExternalDomains}}]] page from the [[{{#special:CommunityConfiguration}}]] list page. This makes it easier to find. [https://phabricator.wikimedia.org/T393240]
* Wikimedia Commons videos were not shown in the Videos tab in Google Search. The problem was investigated and reported to Google who have now fixed the issue. [https://phabricator.wikimedia.org/T396168][https://meta.wikimedia.org/wiki/Community_Wishlist/Wishes/Do_something_about_Google_%26_DuckDuckGo_search_not_indexing_media_files_and_categories_on_Commons] 
* One new wiki has been created: a {{int:project-localized-name-group-wiktionary/en}} in [[d:Q33014|Betawi]] ([[wikt:bew:|&lt;code&gt;wikt:bew:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T402130]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:39}} community-submitted {{PLURAL:39|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* Two fields of the [[mw:Special:MyLanguage/Manual:Recentchanges table|recentchanges database table]] are being removed. &lt;code&gt;rc_new&lt;/code&gt; and &lt;code&gt;rc_type&lt;/code&gt; are being removed in favor of &lt;code&gt;rc_source&lt;/code&gt;. Queries to these older fields will start to fail starting this week and developers should use &lt;code&gt;rc_source&lt;/code&gt; instead. These older fields were deprecated over 10 years ago and should not be in use. This is part of work to improve the performance and stability of queries to the recentchanges table. [https://phabricator.wikimedia.org/T400696] 
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.16|MediaWiki]]

'''In depth'''
* The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2025/July|Language and Internationalization Newsletter]] is now available. This edition includes: support for new languages in MediaWiki and translatewiki; the start of the Language Onboarding and Development project to help support the growth of new and small wikis; updates on research projects; and more.

'''Meetings and events'''
* The next [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Community meetings#29 August 2025|Language Community Meeting]] is happening soon, August 29th at [https://zonestamp.toolforge.org/1756479600 15:00 UTC]. This week's meeting will cover: the Avro keyboard developers from Wikimedia Bangladesh, who were recently awarded a national award for their contributions to this keyboard; and other topics. 

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/35|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W35&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 00:12, 26 August 2025 (UTC)
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== Tech News: 2025-36 ==

&lt;section begin=&quot;technews-2025-W36&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/36|Translations]] are available.

'''Weekly highlight'''
* The Editing team wants to compile a list of templates, jargon terms, and policies used in edit summaries when a copyright violation is removed. This will help them identify the number of edits reverted due to copyright issues. We invite community members from the following Wikis to list these terms in [[Phab:T402601|T402601]], or to share their list with [[User:Trizek (WMF)|Trizek_(WMF)]]: {{int:project-localized-name-arwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-enwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-itwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-plwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-viwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zhwiki/en}}. This project is open until September 9th 2025.

'''Updates for editors'''
* The [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] has been enabled for all Wikisources. The extension makes it easier to organize and participate in collaborative activities, like edit-a-thons and WikiProjects, on the wikis. The extension has three features: [[m:Special:MyLanguage/Event Center/Registration|Event Registration]], [[m:Special:MyLanguage/CampaignEvents/Collaboration list|Collaboration List]], and [[m:Special:MyLanguage/Connection Team/Invitation list|Invitation List]]. To request the extension for your wiki, visit the Deployment information page. [https://meta.wikimedia.org/wiki/CampaignEvents/Deployment_status#How_to_Request_the_CampaignEvents_Extension_for_your_wiki]
* The lists in the footer of the editing interface, such as &quot;Templates used on this page,&quot; will now be organized into columns when there is enough space. This enhancement minimizes scrolling when editing lengthy articles on Wikipedia. [https://phabricator.wikimedia.org/T401066]
* On September 3rd, 2025 we will increase the sampling percentages of our [[mw:Special:MyLanguage/Moderator Tools/Watchlist/Experiment#Scope of the experiment|group by toggle experiment]] of the &lt;code&gt;Special:RecentChanges&lt;/code&gt;, &lt;code&gt;Special:Watchlist&lt;/code&gt;, and &lt;code&gt;Special:RelatedChanges&lt;/code&gt; pages on the Chinese, French, and Portuguese Wikipedias to 100 percent, allowing more editors to be part of this experiment. This adjustment is intended to ensure we have sufficient data to make informed decisions when evaluating the experiment results. [https://phabricator.wikimedia.org/T402958][https://phabricator.wikimedia.org/T396789]
* Upon clicking an empty search bar, logged-out users will see suggestions of articles for further reading on English Wikipedia beginning the week of September 22. The feature will be available on both desktop and mobile. All non-English wikis received this change in June and July. The goal is to make it easier for users to find articles. [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments/Search Suggestions|Learn more]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:37}} community-submitted {{PLURAL:37|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.17|MediaWiki]]

'''In depth'''
* Wikifunctions now has a new capability called &quot;lightweight enumeration types&quot;, an enumeration type is simply a fixed set of values that's in the type's definition. This capability makes it quick and easy to define such a type, and allows for the reuse of values that are already present in Wikidata. Here is [[f:Special:MyLanguage/Wikifunctions:Status updates/2025-07-19|a newsletter]] to learn more.
* The latest [[mw:Special:MyLanguage/Readers/Newsletter updates#August 2025: Newsletter #1|Readers Newsletter]] is now available. This edition includes: the formation of two new teams — Reader Growth and Reader Experience; insights into declining pageviews and account creations; highlights from the Wikimania Nairobi panel on improving the reading experience; upcoming experiments to engage new and existing readers; and more.

'''Meetings and events'''
* Spotlight on some Wikimania 2025 Sessions:
** Identifying AI-generated text by searching for ISBNs whose checksums fail: Mathias Schindler of WMDE [https://www.youtube.com/watch?v=Dw9o8Lsl974&amp;t=15910s shared tools to help communities search for these].
** [https://wikimedia.eventyay.com/talk/wikimania2025/talk/TCHZKH/ La durabilité du mouvement Wikimedia face aux défis actuels et futurs]: This session explored how Wikimedia can stay a trusted source of knowledge in the age of generative AI, information overload, and disinformation.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/36|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W36&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:50, 1 September 2025 (UTC)
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== Tech News: 2025-37 ==

&lt;section begin=&quot;technews-2025-W37&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/37|Translations]] are available.

'''Weekly highlight'''
* The Editing team is working on a new check: [[mw:Special:MyLanguage/Paste check|Paste check]]. This check informs newcomers who paste text into Wikipedia that the content might not be accepted. This check is an effort to increase the likelihood that the new content people are adding to Wikipedia is aligned with the Movement's commitment to offering information under a free content license. This check will soon be tested at a few wikis. If your community is interested in this test, please [[phab:T403680|tell us in this task]], or [[mw:Talk:Edit check|contact the team]].

'''Updates for editors'''
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Later this week, users of the &quot;{{int:codemirror-beta-feature-title}}&quot; [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] will be able to use a [[w:en:Lint (software)|linting tool]] to see errors or other potential problems in wikitext in real time. See the [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Linting|help page for more information]]. [https://phabricator.wikimedia.org/T381577]
* [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] When browsing a wiki (like &lt;code dir=ltr&gt;en.wikipedia.org&lt;/code&gt;), the software responds in one of two ways: a desktop page, or a redirect to a mobile version on an &quot;m&quot; domain (like &lt;code dir=ltr&gt;en.m.wikipedia.org&lt;/code&gt;). Over the next three weeks, MediaWiki will start displaying the mobile version to mobile devices directly on the standard domain, without this redirect. This change does not affect existing m-dot URLs, or the &quot;Desktop view&quot; opt-out. [[mw:Requests for comment/Mobile domain sunsetting/2025 Announcement|Learn more]]. [https://phabricator.wikimedia.org/T214998]
* When an edit changes the categories of a page, the changes to the category membership counts are now happening asynchronously. This improves the speed of saving edits, especially when moving many pages to or from the same category, and reduces the risk of site outages, but it means that the counts can show outdated information for a few minutes. [https://phabricator.wikimedia.org/T365303] 
* Edits on Wikidata to qualifiers (properties and values) and references (properties and values) in a Wikidata item statement will now not add entries to the RecentChanges or Watchlist pages on all other Wikis. This is a temporary change to improve performance while other solutions are created. Wikidata's own pages remain unchanged. [[m:Wikidata For Wikimedia Projects/Reduce change propagation noise#Phase 1: Turn off (temporarily) Qualifiers and References Wikidata edits to the Recent Changes tables|Learn more]]. [https://phabricator.wikimedia.org/T401286][https://phabricator.wikimedia.org/T400698]
* Japanese-language wikis have had a major upgrade to the way that search works. The new search should generally give more accurate and more relevant search results. [https://phabricator.wikimedia.org/T318269]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.18|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/37|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W37&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 01:14, 9 September 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29238161 --&gt;

== Tech News: 2025-38 ==

&lt;section begin=&quot;technews-2025-W38&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/38|Translations]] are available.

'''Updates for editors'''
* References lists that are made using the &lt;code dir=ltr&gt;&lt;nowiki&gt;&lt;references/&gt;&lt;/nowiki&gt;&lt;/code&gt; [[mw:Special:MyLanguage/Help:Cite#references-tag|tag]] will now automatically display with columns in Vector 2022 when readers are using its 'standard' settings for text-size and page-width. [https://phabricator.wikimedia.org/T334941]
* Starting in the week of October 6, on [[gitiles:operations/mediawiki-config/+/a2d2aaab9ace84280dd2f4c70a33bb69cd73850f/dblists/small.dblist|small wikis]] and [[gitiles:operations/mediawiki-config/+/a2d2aaab9ace84280dd2f4c70a33bb69cd73850f/dblists/medium.dblist|medium wikis]] that have the [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] enabled, all autoconfirmed users will be able to use [[m:Special:MyLanguage/Event Center/Registration|Event Registration]] as an organizer. No changes will be made for [[gitiles:operations/mediawiki-config/+/a2d2aaab9ace84280dd2f4c70a33bb69cd73850f/dblists/large.dblist|large wikis]] unless requested in Phabricator. This change is being made to make it easier for more people to use Event Registration, especially on wikis that are less likely to have policies related to the Event Organizer right. [[m:Special:MyLanguage/CampaignEvents/Proposal to grant autoconfirmed users on small and medium wikis the organizer access to the event registration tool|Learn more]].
* Users that search using regular expressions (regex) can now use additional features including:
** for the &lt;code dir=ltr&gt;intitle:&lt;/code&gt; keyword: [[mw:Special:MyLanguage/Help:CirrusSearch#Metacharacters|metacharacters]] for start-of-line (&lt;code dir=ltr&gt;^&lt;/code&gt;) and end-of-line (&lt;code dir=ltr&gt;$&lt;/code&gt;) anchors [https://phabricator.wikimedia.org/T317599]
** for both &lt;code dir=ltr&gt;intitle:&lt;/code&gt; and &lt;code dir=ltr&gt;insource:&lt;/code&gt; keywords: shorthand [[mw:Special:MyLanguage/Help:CirrusSearch#Character_Classes|character classes]] for digits (&lt;code dir=ltr&gt;\d&lt;/code&gt;), whitespace (&lt;code dir=ltr&gt;\s&lt;/code&gt;), and word characters (&lt;code dir=ltr&gt;\w&lt;/code&gt;); and [[mw:Special:MyLanguage/Help:CirrusSearch#Escape codes|escape codes]] for line feed (&lt;code dir=ltr&gt;\r&lt;/code&gt;), newline (&lt;code dir=ltr&gt;\n&lt;/code&gt;), tab (&lt;code dir=ltr&gt;\t&lt;/code&gt;), and unicode (e.g. &lt;code dir=ltr&gt;\uHHHH&lt;/code&gt;). [https://phabricator.wikimedia.org/T403212]
* When you search for text that looks like an IP, the system will now show search results. It used to take you to the contributions for that IP instead of showing search results. [https://phabricator.wikimedia.org/T306325]
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on September 24. This is planned at [https://zonestamp.toolforge.org/1758726000 15:00 UTC]. This is for the datacenter server switchover backup tests which happen twice a year. You can [[diffblog:2025/03/12/hear-that-the-wikis-go-silent-twice-a-year/|read more about the background and details of this process on the Diff blog]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:24}} community-submitted {{PLURAL:24|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug was fixed that affected users who used the page-tabs to switch from wikitext editing of a section into the visualeditor. [https://phabricator.wikimedia.org/T401043]

'''Updates for technical contributors'''
* The MediaWiki Interfaces team is redesigning the Wikimedia REST API Sandbox with Codex. If you have feedback on improvements for the API documentation or what makes developer experiences smooth (or frustrating), you’re invited to [https://calendar.google.com/calendar/u/0/appointments/schedules/AcZssZ2aZzbXeQvjOF7gB1fJXiwAYemQjKf4sXNaRODPA7_obFyNBwkzNkoVCoTF-aeov89kIjXHbCQm join an upcoming discovery interview], or [[mw:MediaWiki Interfaces Team/Developer Feedback/Wikimedia Web APIs|leave feedback onwiki]]. [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/C4FBAOA57PH6G5ORVMAUF5TGYBLZDU5Q/|Learn more]].
* Edits to Wikidata aliases (an alternative name for an item or a property) will now be shown in RecentChanges and Watchlist entries on other wikis less often, reducing unnecessary notifications. This will reduce the overall quantity of 'noisy' entries. Wikidata's own pages remain unchanged. [[m:Wikidata For Wikimedia Projects/Reduce change propagation noise#Phase 1: More granular Alias tracking|Learn more]]. [https://phabricator.wikimedia.org/T401288]
* The new [https://www.unicode.org/versions/Unicode17.0.0/ Unicode 17.0] version has been released. The [[:c:Category:Unicode Module Datasets|datasets on Commons]] for the [[:d:Q39301585|Module:Unicode data]] have been updated. Wikipedias that do not use the Commons datasets should either update their own data or switch to the Commons datasets.
* Users of the [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] Structured Contents endpoints can now access [https://enterprise.wikimedia.com/blog/parsed-wikipedia-tables/ Parsed Tables]. The new Parsed Tables feature extracts and represents Wikipedia tables in structured JSON. This improves machine accessibility as part of the [https://enterprise.wikimedia.com/api/structured-contents/ Structured Contents initiative]. Structured Contents output is freely available through the [https://enterprise.wikimedia.com/docs/on-demand/#article-structured-contents-beta On-demand API], or through Wikimedia Cloud Services. 
* A [https://www.kaggle.com/datasets/wikimedia-foundation/english-wikipedia-people-dataset dataset of English Wikipedia biographical information] from [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] has been published on Kaggle, for evaluation and research. This provides structured data from more than 1.5 million biographies, including birth and death dates, education, affiliations, careers, awards, and more (from a June 2024 snapshot).
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.19|MediaWiki]]

'''Meetings and events'''
* [[wmania:Special:MyLanguage/2026:Scholarships|Scholarship applications]] for Wikimania 2026 in Paris, France, are open until October 31.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/38|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W38&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:07, 15 September 2025 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29263921 --&gt;

== Tech News: 2025-39 ==

&lt;section begin=&quot;technews-2025-W39&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/39|Translations]] are available.

'''Weekly highlight'''
* [https://zonestamp.toolforge.org/1758726000 On September 24th at 15:00 UTC], all Wikimedia sites users will experience a brief read-only period due to a scheduled [[m:Special:MyLanguage/Tech/Server switch|datacenter server switchover]]. The Wikimedia Foundation's Site Reliability Engineering (SRE) team will redirect all traffic from one primary server to its backup. You can listen to the switchover using the [http://listen.hatnote.com/ &quot;Listen to Wikipedia&quot;] tool, where you will hear edits stop for a few minutes during the read-only phase, then resume. This twice-yearly datacenter server switchover ensures reliability by testing the backup datacenter, so that our sites can stay online even if the primary datacenter fails. You can [[diffblog:2025/03/12/hear-that-the-wikis-go-silent-twice-a-year/|read more about the process on the Diff blog]].

'''Updates for editors'''
* Editors of [[f:Special:Mylanguage/Wikifunctions:Status updates/2025-09-12#Next round of Wiktionaries to receive embedded Wikifunctions calls|60 more Wiktionaries]] will soon be able to call [[f:Special:MyLanguage/Wikifunctions:Introduction|functions from Wikifunctions]] and integrate them into their pages. A function takes one or more inputs and transforms them into a desired output, like adding numbers, converting miles to meters, calculating elapsed time, or declining a word into a case. They will join the other [[f:Special:MyLanguage/Wikifunctions:Status updates/2025-08-29#Wikifunctions available on 65 Wiktionaries|65 Wiktionary language editions]], which already have access to embedded Wikifunctions calls. Later this year, plans are in place to expand to more Wiktionaries and the Incubator.
* A new [[mw:Special:MyLanguage/Help:Magic words#Technical metadata of another page|parser function]] has been added: &lt;code&gt;&lt;nowiki&gt;{{#contentmodel}}&lt;/nowiki&gt;&lt;/code&gt;. Template editors and admins can use it to get the localized or canonical name of the [[mw:Special:MyLanguage/Help:ChangeContentModel|content model]] of a specific page. The function makes it easier to create and edit system messages, such as ''MediaWiki:editinginterface'', even when you switch types of pages, like wiki, JavaScript, CSS or JSON page. [https://phabricator.wikimedia.org/T328254]
* Adding or editing a &lt;code&gt;DISPLAYTITLE&lt;/code&gt; for an article using VisualEditor will no longer be broken. Editors who use VisualEditor mode to modify the &lt;code&gt;&lt;nowiki&gt;{{DISPLAYTITLE}}&lt;/nowiki&gt;&lt;/code&gt; would no longer have the literal text &quot;DISPLAYTITLE&quot; or its localized variant added to their articles. A list of pages that may have been affected and might need cleanup is documented in [[phab:P83438|this ticket]]. 
* Beta users of the Wikipedia Android app can now try the redesigned [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Activity Tab Experiment|Activity tab]], which replaces the Edits tab. The new tab offers personalized insights into reading, editing, and donation activity, while simplifying navigation and making app use more engaging.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:12}} community-submitted {{PLURAL:12|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.20|MediaWiki]]

'''In depth'''
* Wikifunctions users can now import many essential facts involving [[f:Special:MyLanguage/Z6011|geo-coordinates]], [[f:Special:MyLanguage/Z6010|quantities]] and [[f:Special:MyLanguage/Z6064|time]] values from Wikidata. This is made possible by the creation of Wikifunctions types for these values, which makes them available for use by functions in Wikifunctions. Learn more about how this works in [[c:File:ImportingWikidataDatatypesIntoWikifunctions.webm|this video]] and Wikifunctions' [[f:Special:MyLanguage/Wikifunctions:Status updates/2025-08-01#News in Types I: Wikidata quantity|August 1 newsletter]] (for quantities) and [[f:Special:MyLanguage/Wikifunctions:Status updates/2025-08-22#News in Types: Wikidata geo-coordinate|August 22 newsletter]] (for geo-coordinates).

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/39|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W39&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 22:55, 22 September 2025 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29305556 --&gt;

== Tech News: 2025-40 ==

&lt;section begin=&quot;technews-2025-W40&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/40|Translations]] are available.

'''Weekly highlight'''
* A major software upgrade has been made to [[phab:|Phabricator]]. The update introduces performance improvements, a refreshed search interface, enhancements to Maniphest task search, updates to user profile pages and project workboards, new Herald automation features, as well as general text input, mobile experience improvements and more. [https://phabricator.wikimedia.org/phame/post/view/321/iterative_improvements_september_2025/]

'''Updates for editors'''
* The Community Tech team will release the new Community Wishlist extension on October 1, that will improve the way wishes will be submitted. The new extension will allow users to add tags to their wishes to better categorise them, and (in a future iteration) to filter them by status, tags and focus areas. It will also be possible to support individual wishes again, as requested by the community in many instances. The old system will be retired. There will be a brief period of downtime while the extension is deployed and wishes are migrated to the new system. You can read more about this [[:m:Special:MyLanguage/Community Wishlist/Updates|in the latest update]] or you can consult the [[:mw:Special:MyLanguage/Help:Extension:CommunityRequests|current documentation on MediaWiki]].
* As announced [[diffblog:2025/09/02/better-detecting-bots-and-replacing-our-captcha/|on Diff blog]], the production trial of the [[mw:Special:MyLanguage/Product Safety and Integrity/Anti-abuse signals/hCaptcha|hCaptcha]] service for bot detection has begun. The trial is currently using hCaptcha to protect account creation on Chinese, Persian, Portuguese, Indonesian, Japanese, and Turkish Wikipedias, where it will replace our existing [[mw:Special:MyLanguage/Extension:ConfirmEdit#FancyCaptcha|CAPTCHA]] (FancyCaptcha). The goal with the trial is to better block bots while also improving usability and accessibility for users who encounter CAPTCHA challenges.
* The [[mw:Special:MyLanguage/Extension:CampaignEvents|CampaignEvents]] extension has been [[m:Special:MyLanguage/CampaignEvents/Deployment status|deployed]] to Wikimedia Commons. The extension makes it easier to organize and participate in collaborative activities, like edit-a-thons and WikiProjects, on the wikis. On Commons, anyone who is a registered user can use it as an event participant. To use it as an organizer, someone needs to have the [[c:Special:MyLanguage/Commons:Event organizers|event organizer right]].
* [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|Sub-referencing]], a new feature to re-use references with different details has been released to German Wikipedia. You can [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#test|test the feature]] on testwiki or [https://en.wikipedia.beta.wmcloud.org/wiki/Sub-referencing on betawiki] as well. Please share your thoughts on [[:m:Talk:WMDE Technical Wishes/Sub-referencing#Templates used in sub-references|using templates in sub-references]] or [[:m:Talk:WMDE Technical Wishes/Sub-referencing#Pilot wikis|volunteer to become a pilot wiki]].
* On wikis using the [[mw:Special:MyLanguage/Help:Growth/Mentorship|Mentorship]] system, communities can now opt experienced editors out of Mentorship through [[{{#special:CommunityConfiguration/Mentorship}}]]. Within this setting, communities may define thresholds, based on edit count and account age, to decide when an editor is considered experienced enough to no longer receive Mentorship. [https://phabricator.wikimedia.org/T403563]
* The Editing Team and the Machine Learning Team are working on a new check for newcomers: [[mw:Special:MyLanguage/Edit check/Tone Check|Tone check]]. Using a prediction model, this check will encourage editors to improve the tone of their edits, using artificial intelligence. We invite volunteers to review the first version of the Tone language model for the following languages: Arabic, Czech, German, Hebrew, Indonesian, Dutch, Polish, Russian, Turkish, Chinese, Farsi, Italian, Norwegian, Romanian and Latvian. Users from these wikis interested in reviewing this model are [[mw:Special:MyLanguage/Edit_check/Tone_Check/Model_evaluation|invited to sign up at MediaWiki.org]]. The deadline to sign up is on October 3, which will be the start date of the test.
* The rollout of [[:mw:Special:MyLanguage/Help:Manage blocks|multiblocks]] had the side effect that non-active block logs may have been shown on {{#special:Contributions}} and on blocked users' user and user_talk pages. This issue will be fully resolved in a few days. As part of the fix, [{{fullurl:Special:Allmessages|prefix=sp-contributions-blocked-notice}} messages prefixed with &lt;code&gt;sp-contributions-blocked-notice&lt;/code&gt;] will be removed and replaced with [{{fullurl:Special:Allmessages|prefix=blocked-notice-logextract}} those prefixed with &lt;code&gt;blocked-notice-logextract&lt;/code&gt;] in a few weeks. Please help translate the new messages and update any local overrides if needed.
* There was a bug with links added using visual editor if they included characters such as &lt;code dir=ltr&gt;&lt;nowiki&gt;[ ] |&lt;/nowiki&gt;&lt;/code&gt; after the fragment identifier (&lt;code&gt;&lt;nowiki&gt;#&lt;/nowiki&gt;&lt;/code&gt;). They were not encoded properly creating an incorrect link. This has been fixed. [https://phabricator.wikimedia.org/T404823]
* One new wiki has been created: a {{int:project-localized-name-group-wikiquote/en}} in [[d:Q9237|Malay]] ([[q:ms:|&lt;code&gt;q:ms:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T404698]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the [[mw:Special:MyLanguage/Product Safety and Integrity/Anti-abuse signals/User Info|User Info Card]] now displays currently active global lock/blocks. [https://phabricator.wikimedia.org/T401128]

'''Updates for technical contributors'''
* Later this week, editors using Lua modules will be able to use the &lt;code&gt;[[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#mw.title.newBatch|mw.title.newBatch]]&lt;/code&gt; function to look up the existence of up to 25 pages at once, in a way that only increases the [[mw:Special:MyLanguage/Manual:Parser functions#Expensive parser functions|expensive function]] count once.
* A new [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group|Unsupported Tools Working Group]] has been formed as part of ongoing efforts to collectively determine technical work priorities, similar to the [[m:Special:MyLanguage/Product and Technology Advisory Council|Product &amp; Technology Advisory Council]] (PTAC). The working group will help prioritize and review requests for support of unmaintained extensions, gadgets, bots, and tools. For the first cycle, the group will be prioritizing an unsupported Wikimedia Commons tool.
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.21|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/40|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W40&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:52, 29 September 2025 (UTC)
&lt;!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=29355230 --&gt;

== Tech News: 2025-41 ==

&lt;section begin=&quot;technews-2025-W41&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/41|Translations]] are available.

'''Weekly highlight'''
* [[mw:Special:MyLanguage/Help:Edit check#paste|Paste Check]] is a new Edit Check feature to help avoid and fight copyright violations. When editors paste text into an article, Paste Check prompts them to confirm the origin and licensing of the content. Starting Wednesday, 8 October, [[phab:T403680|22 wikis will test Paste Check]]. Paste Check will help new volunteers understand and follow the policies and guidelines necessary to make constructive contributions to Wikipedia projects.
'''Updates for editors'''
* Mobile devices will receive mobile articles directly on the standard domain (like &lt;code&gt;en.wikipedia.org&lt;/code&gt;), instead of via a redirect to an &quot;m&quot; domain (like &lt;code&gt;en.m.wikipedia.org&lt;/code&gt;). This change improves performance. This week it will be enabled on Wikipedias. The existing mobile URLs and the &quot;Desktop view&quot; opt-out remain available. [[mw:Requests for comment/Mobile domain sunsetting/2025 Announcement|Learn more]]. [https://phabricator.wikimedia.org/T214998]
* New [[mw:Special:MyLanguage/Help:CirrusSearch#creationdate and lasteditdate|date filters]], &lt;code dir=ltr&gt;creationdate:&lt;/code&gt; and &lt;code dir=ltr&gt;lasteditdate:&lt;/code&gt;, are now available in the wiki search engine. This allows users to filter search results by a page's first or last revision date. The filters support comparison operators (e.g. &lt;code dir=ltr&gt;&gt;2024&lt;/code&gt;) and relative dates (e.g. &lt;code dir=ltr&gt;today-1d&lt;/code&gt;), making it easier to find recently updated content or pages within specific age ranges. [https://phabricator.wikimedia.org/T403593]
* [[f:|Wikifunctions]] now supports rich text in embedded calls across the 150 wikis where it's enabled. To showcase this, the team created a [[f:Z26333|Latin declination table]] that Wiktionary editors can use to automatically generate noun forms, producing clear, formatted results — see an [[f:Wikifunctions:Embedded function calls/Wiktionary tables demonstration|example output]]. If you need any help or have any feedback, please [[f:Wikifunctions:Project chat|contact the Wikifunctions Team]]. [https://phabricator.wikimedia.org/T397402]
* An edit link will now appear inside the categories box on article pages for logged in users, which will directly launch the VisualEditor category dialog. [https://phabricator.wikimedia.org/T291691]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:34}} community-submitted {{PLURAL:34|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, there was a problem downloading pdf files last week and that has been resolved. [https://phabricator.wikimedia.org/T405957]
'''Updates for technical contributors'''
* The field &lt;code dir=ltr&gt;rev_sha1&lt;/code&gt; in the revision database table is being removed in favor of &lt;code dir=ltr&gt;content_sha1&lt;/code&gt; in the content database table. See [https://lists.wikimedia.org/hyperkitty/list/cloud@lists.wikimedia.org/thread/2D2M3SP4WHR6BXXKTZ2PBLZQYR3EGQVR/ the announcement] for more information.
* The [[mw:Special:MyLanguage/Reading/Web|Reader Experience team]] will roll out [[w:en:Light-on-dark color scheme|Dark Mode]] user interface on all Wikimedia sites on October 29, 2025. All anonymous users of Wikimedia sites will have the option to activate a color scheme that features light-colored text on a dark background. This is designed to provide a more comfortable reading experience, especially in low-light situations. Template authors and technical contributors are encouraged to [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-04|learn how to make pages ready for Dark mode]] and address any compatibility issues found in templates in their wiki before the enablement. Please contact the Web team for questions or any support on [[mw:Talk:Reading/Web/Accessibility for reading#|this talk page]] before the enablement. [https://phabricator.wikimedia.org/T395628]
* Starting on Monday, October 6, API endpoints under the &lt;code&gt;rest.php&lt;/code&gt; path will be rerouted through a new internal API Gateway. Individual wikis will be updated based on the standard release groups, with total traffic increased over time. This change is expected to be non-breaking and non-disruptive. If any issues are observed, please file a Phabricator ticket to the [[phab:tag/serviceops/|Service Ops team board]]. [https://phabricator.wikimedia.org/T400130]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.22|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/41|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W41&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:23, 6 October 2025 (UTC)
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== Tech News: 2025-42 ==

&lt;section begin=&quot;technews-2025-W42&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/42|Translations]] are available.

'''Weekly highlight'''
* Last week, improvements to account security and two-factor authentication (2FA) features were enabled across all wikis. These changes include user interface improvements for [https://auth.wikimedia.org/metawiki/wiki/Special:AccountSecurity Special:AccountSecurity], the support of multiple 2FA methods via authenticator apps and portable security keys (previously users could only enable one method), and a new Recovery Codes module which facilitates fewer account lockouts due to lost two-factor apps and devices. As part of the [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security|Account Security]] project, work is continuing through the rest of 2025 on further user experience improvements, and support for passkeys as an alternate second factor. 

'''Updates for editors'''

* Another part of the Account security project is making 2FA generally available to all users. Along with editors with advanced privileges, such as administrators and bureaucrats, 40% of editors now have access to 2FA. You can check if you have access at [https://auth.wikimedia.org/metawiki/wiki/Special:AccountSecurity Special:AccountSecurity]. Instructions for activation are on the linked page. The plan is to continue increasing availability if it is determined that the user support capabilities are able to support global usage. [https://phabricator.wikimedia.org/T400579]
* This week, users at wikis where talk page [[mw:Special:MyLanguage/Talk pages project/Usability|Usability Improvements]] are already available by default (everywhere ''except'' the 12 wikis listed in [[phab:T379264|T379264]]) will gain the ability to Thank a comment directly from the talk page it appears on. Before this change, Thanking could only be done by visiting the revision history of the talk page. You can [[diffblog:2025/10/13/revolutionizing-gratitude-a-new-era-of-thanking-comments/|learn more about this change]]. [https://phabricator.wikimedia.org/T366095]
* Users who have not [[Special:Preferences#mw-prefsection-personal-email|verified their email address]] will soon be receiving monthly Notification reminders to do so. This is because users who have verified their email can more easily recover their account. These reminders will not be sent if the user is inactive or removes the unverified email from their account. [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Email_confirmation][https://phabricator.wikimedia.org/T58074]
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a fix was made for an occasional error with saving translated paragraphs in the Content Translation tool, and the related error messages are now easier to see. [https://phabricator.wikimedia.org/T376531]

'''Updates for technical contributors'''

* The Unsupported Tools Working Group has chosen [[c:Special:MyLanguage/Commons:Video2commons|Video2Commons]] as the first tool for its pilot cycle. The group will explore ways to improve and sustain the tool over the coming months. [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group|Learn more on Meta]].
* [[File:Octicons-sync.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.23|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/42|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W42&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:59, 13 October 2025 (UTC)
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== Tech News: 2025-43 ==

&lt;section begin=&quot;technews-2025-W43&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/43|Translations]] are available.

'''Updates for editors'''
* To optimize how user data is stored in our databases, the saved preferences of users who haven't logged in for over five years and have fewer than 100 edits will be cleared. When those users return, default settings will apply. [https://phabricator.wikimedia.org/T406724]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, there was a broken link from the GlobalContributions interface message to the XTools GlobalContributions page which has now been fixed. [https://phabricator.wikimedia.org/T406415]

'''Updates for technical contributors'''
* The work to reroute all traffic to API endpoints under the &lt;code dir=ltr&gt;&lt;nowiki&gt;rest.php&lt;/nowiki&gt;&lt;/code&gt; route through a common API gateway is now complete. If any issues are observed, please file a phabricator ticket to the [[phab:tag/serviceops/|Service Ops team board]].
* Edits to Wikidata references or qualifiers will now be shown in RecentChanges and Watchlist entries on other wikis less often, reducing unnecessary notifications. This will reduce the overall quantity of 'noisy' entries. Wikidata's own pages remain unchanged. [https://phabricator.wikimedia.org/T401290]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.24|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/43|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W43&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:36, 20 October 2025 (UTC)
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== Tech News: 2025-44 ==

&lt;section begin=&quot;technews-2025-W44&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/44|Translations]] are available.

'''Updates for editors'''
* The Wikipedia iOS app has launched an A/B/C test of improvements made to the tabbed browsing feature for select regions and languages. The test, named “More dynamic tabs”, explores new tab experiences and includes “Did you know” and “Because you read” article recommendations. You can [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Tabbed Browsing (Tabs)/New Tab Experience and Recommendations Experiment|read more on the project page]].
* Autoconfirmed users on [[gitiles:operations/mediawiki-config/+/a2d2aaab9ace84280dd2f4c70a33bb69cd73850f/dblists/small.dblist|small]] and [[gitiles:operations/mediawiki-config/+/a2d2aaab9ace84280dd2f4c70a33bb69cd73850f/dblists/medium.dblist|medium wikis]] with the CampaignEvents extension can now use [[m:Special:MyLanguage/Event Center/Registration|Event Registration]] without the Event Organizer right. This feature lets organizers enable registration, manage participants, and lets users register with one click instead of signing event pages.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue of flashing colors when holding or pressing the arrow keys under the dark mode settings in Vector 2022 has been fixed. [https://phabricator.wikimedia.org/T402285]

'''Updates for technical contributors'''

* The CampaignEvents extension will be deployed to all remaining wikis during the week of 17 November 2025. The extension currently includes three features: Event Registration, Collaboration List, and Invitation List. For this rollout, Invitation List will not be enabled on Wikifunctions and MediaWiki unless requested by those communities. [[m:Special:MyLanguage/CampaignEvents/Deployment status|Visit the deployment page to learn more]].
* The SwaggerUI-based REST sandbox experience is now live on all wiki projects. The sandbox can be accessed through the [[{{#special:RestSandbox}}]] page. Please report any issues to the MediaWiki Interfaces team board, or join the discussion on the [[mw:Special:MyLanguage/MediaWiki Interfaces Team/Feature Feedback/REST Sandbox|project launch]] page. [https://phabricator.wikimedia.org/project/board/6931/]
* Transform endpoints with a trailing slash path in the MediaWiki REST API are now marked as deprecated. They will remain functional during this time, but removal is expected by the end of January 2026. All API users currently calling them are encouraged to transition to the non-trailing slash versions. Both endpoint variations can be found and tested using the [https://test.wikipedia.org/w/index.php?api=mw-extra&amp;title=Special%3ARestSandbox REST Sandbox]. See the [[mw:API/Deprecation|MediaWiki REST API Deprecation]] page for more detailed information about the API deprecation policies and procedures.
* A dedicated [[mw:API:REST API/Changelog|changelog now exists for the MediaWiki REST API]]. The changelog provides an overview of these changes, making it easier for developers to keep track of improvements and iterations. Announcements will also continue to flow through the standard communication channels, including Tech News and email distribution lists, but can now be more easily referenced from a central location. If you have feedback about the style, structure, or content of this changelog, please [[mw:API talk:REST API/Changelog|join the discussion]].
* Administrators can delete the tracking category which was previously added by the JsonConfig extension, as it is no longer used. See the categories linked from [[d:Q130635582#sitelinks-wikipedia|Q130635582]]. It is OK if there are still pages listed in the category as that is just a caching issue, and they will be automatically cleared out the next time each page is edited. [https://phabricator.wikimedia.org/T378352]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.25|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/44|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W44&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:31, 27 October 2025 (UTC)
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== Tech News: 2025-45 ==

&lt;section begin=&quot;technews-2025-W45&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/45|Translations]] are available.

'''Updates for editors'''
* Administrators will now find that [[{{#special:MergeHistory}}]] is now significantly more flexible about what it can merge. It can now merge sections taken from the middle of the history of the source (rather than only the start) and insert revisions anywhere in the history of the destination page (rather than only the start). [https://phabricator.wikimedia.org/T382958]
* For users with &quot;{{int:discussiontools-preference-autotopicsub}}&quot; [[Special:Preferences#mw-prefsection-editing|enabled in their preferences]], starting a new topic or adding a reply to an existing topic will now subscribe them to replies to that topic. Previously, this would only happen if the DiscussionTools &quot;{{int:Skin-action-addsection}}&quot; or &quot;{{int:Discussiontools-replybutton}}&quot; widgets were used. When DiscussionTools was originally launched existing accounts were not opted in to automatic topic subscriptions, so this change should primarily affect newer accounts and users who have deliberately changed their preferences since that time. [https://phabricator.wikimedia.org/T290778]
* Scribunto modules can now be used to [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#SVG library|generate SVG images]]. This can be used to build charts, graphics and other visualizations dynamically through Lua, reducing the need to compose them externally and upload them as files. [https://phabricator.wikimedia.org/T405861]
* Wikimedia sites now provide all anonymous users with the option to enable a dark mode color scheme, featuring light-colored text on a dark background. This enhancement aims to deliver a more enjoyable reading experience, especially in dimly lit environments.  [https://phabricator.wikimedia.org/T395628]
* Users with large watchlists have long faced timeouts when editing [[Special:EditWatchlist|Special:EditWatchlist]]. The page now loads entries in smaller sections instead of all at once due to a paging update, allowing everyone to edit their watchlists smoothly. As part of the database update, sorting by expiry has been removed because it was over 100× slower than sorting by title. A [https://meta.wikimedia.org/wiki/Community_Wishlist/W454 community wish] has been created to explore alternative ways to restore sort-by-expiry. If this feature is important to you, please support the wish! [https://phabricator.wikimedia.org/T41510]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:31}} community-submitted {{PLURAL:31|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the fixing of the persisting highlighting when using VisualEditor find and replace during a query. [https://phabricator.wikimedia.org/T407318]
'''Updates for technical contributors'''
* Since 2019 the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]] at https://w.wiki is available for all Wikimedia wikis to create short links to articles, permalinks, diffs, etc. It is available in the sidebar as &quot;Get shortened URL&quot;. There are 30 wikis that also install an older &quot;ShortUrl&quot; extension. The old extension will soon be removed. This means &lt;code&gt;/s/&lt;/code&gt; URLs will not be advertised under article titles via HTML &lt;code dir=ltr&gt;class=&quot;title-shortlink&quot;&lt;/code&gt;. The &lt;code&gt;/s/&lt;/code&gt; URLs will keep working. [https://phabricator.wikimedia.org/T107188]
* On Thursday, October 30, the [[:mw:Special:MyLanguage/MediaWiki Interfaces Team|MediaWiki Interfaces]] and [[:mw:Special:MyLanguage/Wikimedia Site Reliability Engineering|SRE Service Operations]] teams began rerouting Action API traffic through a common API gateway. Individual wikis will be updated based on the standard release groups, with total traffic increased over time. This change is expected to be non-breaking and non-disruptive. If any issues are observed, please file a Phabricator ticket to the [https://phabricator.wikimedia.org/tag/serviceops/ Service Ops team] board.
* MediaWiki Train deployments will pause for the final two weeks of 2025: 22 December and 29 December. Backport windows will also pause between Monday, 22 December 2025 and Thursday, 2 January 2026. A backport window is a scheduled time to add things like bug fixes and configuration changes. There are seven deployment trains remaining for 2025. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/SMWTEAES4SDLDUSK4HMWNBSKNCXZAWYN/]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.45/wmf.26|MediaWiki]]

'''In depth'''
* In 2025, the Wikimedia Foundation reported that AI systems and search engines increasingly use Wikipedia content without driving users to the site, contributing to an 8% drop in human pageviews compared to 2024. After detecting bots disguised as humans, Wikimedia updated its traffic data to reflect this shift. Read more about current user trends on Wikipedia in [[diffblog:2025/10/17/new-user-trends-on-wikipedia/|a Diff blog post]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/45|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W45&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:34, 3 November 2025 (UTC)
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== Tech News: 2025-46 ==

&lt;section begin=&quot;technews-2025-W46&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/46|Translations]] are available.

'''Updates for editors'''
[[File:Talk pages default look (April 2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]]
* Starting November 12, users will see a change in the [[m:Special:MyLanguage/Talk pages project/Feature summary#Usability improvements|appearance of talk pages]] on [[Phab:T379264|some Wikipedias]]. Almost [[phab:T392121|all wikis]] have received this design change; [[phab:T409297|English Wikipedia]] will get these changes later. You can read more [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|on ''Diff'']]. Users can opt out of these changes [[Special:Preferences#mw-prefsection-editing|in their user preferences]] in &quot;{{int:discussiontools-preference-visualenhancements}}&quot;. [https://phabricator.wikimedia.org/T379264]
* MediaWiki can now display a [[mw:Special:MyLanguage/Help:Protection indicators|page indicator]] automatically while a page is protected. This feature is disabled by default. It can be enabled by [[m:Special:MyLanguage/Requesting wiki configuration changes|community request]]. [https://phabricator.wikimedia.org/T12347]
* Using the &quot;{{int:showpreview}}&quot; or &quot;{{int:showdiff}}&quot; buttons in the wikitext editor will now carry over certain URL parameters like '[[mw:Special:MyLanguage/Manual:Parameters to index.php#useskin|useskin]]', '[[mw:Special:MyLanguage/Manual:Parameters to index.php#uselang|uselang]]' and '[[mw:Special:MyLanguage/Help:Section#Editing sections|section]]'. This update also fixes an issue where, if the browser crashed while previewing an edit to a single section, saving this edit could overwrite the entire page with just that section’s content. [https://phabricator.wikimedia.org/T62744][https://phabricator.wikimedia.org/T24029][https://phabricator.wikimedia.org/T155097]
* Wikivoyage wikis can use [[mw:Special:MyLanguage/Help:Extension:Kartographer#Markers and counters|colored map markers in the article text]]. The text of these markers will now be shown in contrasting black or white color, instead of always being white. Local workarounds for the problem can be removed. [https://phabricator.wikimedia.org/T369454]
* The Activity tab in the Wikipedia Android app is now available for all users. The new tab offers personalized insights into reading, editing, and donation activity, while simplifying navigation and making app use more engaging. [https://www.mediawiki.org/wiki/Wikimedia_Apps/Team/Android/Activity_Tab_Experiment]
* The Reader Growth team is launching an experiment called &quot;Image browsing&quot; to test how to make it easier for readers to browse and discover images on Wikipedia articles. This experiment, a mobile-only A/B test, will go live on English Wikipedia in the week of November 17 and will run for four weeks, affecting 0.05% of users on English wiki. The test launched on November 3 on Arabic, Chinese, French, Indonesian, and Vietnamese wikis, affecting up to 10% of users on those wikis. [https://www.mediawiki.org/wiki/Readers/Reader_Growth/WE3.1.3_Image_Browsing]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example the inability to lock accounts on mobile sites has been fixed. [https://phabricator.wikimedia.org/T256185]

'''Updates for technical contributors'''
* [[wikitech:Help talk:Toolforge/Toolforge standards committee#November 2025 committee nominations|Nominations are open on Wikitech]] for new [[wikitech:Help:Toolforge/Toolforge standards committee|Toolforge standards committee]] members. The committee oversees the Toolforge [[wikitech:Help:Toolforge/Right to fork policy|Right to fork policy]] and [[wikitech:Help:Toolforge/Abandoned tool policy|Abandoned tool policy]] among other duties. Nominations will remain open through 2025-11-28.
* The [[w:JSON Web Token#Standard fields|JWT issuer field]] in [[mw:Special:MyLanguage/OAuth/For Developers#OAuth 2|OAuth 2 access tokens]] for [[m:Special:MyLanguage/Help:Unified login|SUL wikis]] has been changed to &lt;code&gt;&lt;nowiki&gt;https://meta.wikimedia.org&lt;/nowiki&gt;&lt;/code&gt;. Old access tokens will still work. [https://phabricator.wikimedia.org/T399199]
* The [[w:JSON Web Token#Standard fields|JWT subject field]] in [[mw:Special:MyLanguage/OAuth/For Developers#OAuth 2|OAuth 2 access tokens]] will soon change from &lt;code&gt;&lt;user id&gt;&lt;/code&gt; to &lt;code dir=ltr style=&quot;white-space:nowrap&quot;&gt;mw:&lt;identity type&gt;:&lt;user id&gt;&lt;/code&gt;, where &lt;code&gt;&lt;identity type&gt;&lt;/code&gt; is typically &lt;code dir=ltr&gt;CentralAuth:&lt;/code&gt;&lt;!-- not a typo --&gt; (for [[m:Special:MyLanguage/Help:Unified login|SUL wikis]]) or &lt;code dir=ltr style=&quot;white-space:nowrap&quot;&gt;local:&lt;wiki id&gt;&lt;/code&gt; (for other wikis). This is to avoid conflicts between different user ID types, and to make OAuth 2 access tokens and the &lt;code&gt;sessionJwt&lt;/code&gt; cookie more similar. Old access tokens will still work. [https://phabricator.wikimedia.org/T399199]
* MediaWiki's block messages ([[MediaWiki:Blockedtext|blockedtext]], [[MediaWiki:Blockedtext-partial|blockedtext-partial]], [[MediaWiki:Autoblockedtext|autoblockedtext]], [[MediaWiki:Systemblockedtext|systemblockedtext]], [[MediaWiki:Blockedtext-tempuser|blockedtext-tempuser]], [[MediaWiki:Autoblockedtext-tempuser|autoblockedtext-tempuser]]) now support additional parameters indicating whether the user is blocked from editing their own user talk page &lt;code&gt;&lt;nowiki&gt;$9&lt;/nowiki&gt;&lt;/code&gt; or emailing other users &lt;code&gt;&lt;nowiki&gt;$&lt;/nowiki&gt;&lt;nowiki&gt;10&lt;/nowiki&gt;&lt;/code&gt;. [https://phabricator.wikimedia.org/T285612]
* A &lt;code&gt;REL1_45&lt;/code&gt; branch for MediaWiki core and each of the extensions and skins in Wikimedia git has been created. This is the first step in the release process for MediaWiki 1.45.0, scheduled for late November 2025. If you are working on a critical bug fix or working on a new feature, you may need to take note of this change. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/ZUY7TY3Z6XPZWZVAZV63OPO5OW52Q6GE/]
* The process for generating CirrusSearch dumps has been updated due to slowing performance. If you encounter any issues migrating to the replacement dumps, please contact the Search Platform Team for support. [https://phabricator.wikimedia.org/T366248][https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/3KQPOR6ACVN6OVLMLZPIBXQSWQKW4E3K/]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.2|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/46|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W46&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:38, 10 November 2025 (UTC)
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== Tech News: 2025-47 ==

&lt;section begin=&quot;technews-2025-W47&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/47|Translations]] are available.

'''Updates for editors'''
* The [[mw:Special:MyLanguage/Readers/Reader Experience|Reader Experience team]] is experimenting with [[mw:Special:MyLanguage/Readers/Reader Experience/WE3.3.4_Reading lists|reading lists on mobile web]], allowing logged-in readers with no edits to save private lists of articles for later. The experiment is running on Arabic, Chinese, French, Indonesian, and Vietnamese Wikipedias since the week of 10 November, and will begin on English Wikipedia the week of 17 November.
* Users who can’t receive their email verification code during login can now get help by submitting a form on a new special page. This update is part of the [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security|Account Security]] initiative. If your account has an email address, please make sure you still have access to it. When logging in from a new device or location without 2FA, you may be asked to enter a 6-digit code sent by email to finish logging in. [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security#Why are you requiring me to enter a code from my email to log in? Can I opt out of this?|Learn more]].
* One new wiki has been created: a {{int:project-localized-name-group-wikisource}} in [[d:Q13324|Minangkabau]] ([[s:min:|&lt;code&gt;s:min:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T408317]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]].

'''Updates for technical contributors'''
* As part of the [[mw:Special:MyLanguage/Parsoid/Parser Unification|Parser Unification]] project, the Content Transform Team rolled out Parsoid as the default parser to many low-traffic Wikipedias and is preparing the next step to high traffic ones. This message is an invitation for you to opt-in to Parsoid, as described in the [[mw:Special:MyLanguage/Help:Extension:ParserMigration|Extension:ParserMigration]] documentation, and identify any issues you might encounter with your own workflow using bots, gadgets, or user scripts. Please, let us know through the ''&quot;Report Visual Bug&quot;'' link in the Tools sidebar or create a phab ticket and tag the [[phab:project/view/5846|Content Transform Team in Phabricator]].
* Unsupported Tools: Several issues with [[:c:Special:MyLanguage/Commons:Video2commons|Video2Commons]] have been fixed, including filename-related upload failures, black-video imports, and retry handling. AV1 support has also been added. Ongoing work focuses on backend stability, ffmpeg errors, subtitle imports, metadata handling, and playlist uploads. To track specific tasks, check the [[phab:tag/video2commons/|Phabricator board]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.3|MediaWiki]]

'''Meetings and events'''
* Save the date for the next Wikimedia Hackathon happening in Milan, Italy from May 1–3, 2026. Registration will open in January 2026. [https://pretix.eu/wikimedia/Hackathon-2026/ Scholarship applications are currently open], and will close on November 28, 2025. If you have any questions, please email &lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;hackathon@wikimedia.org&lt;/bdi&gt;.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/47|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W47&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:26, 17 November 2025 (UTC)
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== Tech News: 2025-48 ==

&lt;section begin=&quot;technews-2025-W48&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/48|Translations]] are available.

'''Updates for editors'''
* Last week, the [[mw:Special:MyLanguage/Wikimedia Search Platform|Wikimedia Search Team]] recreated the &quot;DWIM&quot; (Do What I Mean) gadget functionality server-side, for Russian and Hebrew Wikipedias. This feature adds cross-keyboard suggestions to the standard search-box suggestions. For example, searching for ''&lt;span lang=&quot;und&quot; dir=&quot;ltr&quot;&gt;cxfcnmt&lt;/span&gt;'' on Russian Wikipedia will now add suggestions for ''&lt;span lang=&quot;ru&quot; dir=&quot;ltr&quot;&gt;счастье&lt;/span&gt;'' (&quot;happiness&quot;) that the user probably intended. They plan to enable this feature for other Russian and Hebrew wikis this week. [https://phabricator.wikimedia.org/T408734]
* Later this week, users of the &quot;{{int:codemirror-beta-feature-title}}&quot; [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] will have syntax highlighting available in [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]]. This requires that the &quot;{{int:discussiontools-preference-sourcemodetoolbar}}&quot; preference be set. [https://phabricator.wikimedia.org/T407918]
* [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|Campaign events extension]] – the set of tools for coordinating events and other on-wiki collaborations has now been deployed to all Wikimedia wikis. A new feature known as [[m:Special:MyLanguage/CampaignEvents/Collaborative contributions|Collaborative contribution]] to help organizers and participants see the impact of activities has also been added. Join the upcoming [[m:Special:MyLanguage/Event:Connection learning session 3|learning session]] to see the new feature in action and share your feedback.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:24}} community-submitted {{PLURAL:24|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the bug which stopped CodeReviewBot from working, has now been fixed. [https://phabricator.wikimedia.org/T410417]

'''Updates for technical contributors'''
*  Users of Wikimedia API can join a usability study to help validate the new design of Wikimedia REST API sandboxes. Interested participants should fill the [https://wikimediafoundation.limesurvey.net/487662 recruitment survey]. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IREJRRWTZTGCYWQHDMSNJFTQAEPOOAE3/]
* The MediaWiki Interfaces team is deprecating XSLT stylesheets within the Action API. Support for &lt;code dir=ltr&gt;format=xml'''&amp;xlst={stylesheet}'''&lt;/code&gt; will be removed from Wikimedia projects by the end of November, 2025. In addition, it will soon be disabled by default in MediaWiki release versions: v1.43 (LTS), v1.44, and v1.45. Support for XSLT stylesheets will be fully removed from MediaWiki v1.46 (expected to release between April and May 2026). [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/5AX7UWAVVUNUSBOIRHMNOKWOZ5EZI3JX/]
* The WDQS legacy endpoint ([https://query-legacy-full.wikidata.org/ query-legacy-full.wikidata.org]) will be decommissioned at the end of December 2025, and finally closed down on 7th January 2026. After this date, users should expect requests to query.wikidata.org that require the full graph to fail or return invalid results if they are not rewritten to use SPARQL federation. The team encourages users to ensure that tools and workflows use the supported WDQS endpoints (&lt;span dir=ltr&gt;&lt;nowiki&gt;https://query.wikidata.org/&lt;/nowiki&gt;&lt;/span&gt; - Main graph or &lt;span dir=ltr&gt;&lt;nowiki&gt;https://query-scholarly.wikidata.org/&lt;/nowiki&gt;&lt;/span&gt; - Scholarly graph). For support with migrating use cases, please review the [[d:Special:MyLanguage/Wikidata:Data_access|Data Access]] and [[d:Wikidata:Request_a_query|Request a Query]] pages for details and assistance on alternative access methods.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.4|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/48|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W48&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:56, 24 November 2025 (UTC)
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== Tech News: 2025-49 ==

&lt;section begin=&quot;technews-2025-W49&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/49|Translations]] are available.

'''Updates for editors'''
* The Wikipedia Year in Review 2025 will be available on December 2 for users of iOS and Android Wikipedia apps, featuring new personalized insights, updated reading highlights, and refreshed designs. Learn more on the review's [[mw:Special:MyLanguage/Wikimedia Apps/Team/Wikipedia Year in Review/Updates|project page]].
* The Growth team is working on improving the text and presentation of the Verification Email sent to new users to make them more welcoming, useful and informative. Some new text have been drafted for A/B testing and you can help by translating them. See [[phab:T396155|Phabricator]].
* [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]] will now be deployed at Japanese, Urdu and Chinese Wikipedias on December 2. Add a link is based on a prediction model that suggests links to be added to articles. While this feature has already been available on most Wikipedias, the prediction model could not support certain languages. A new model has now been developed to handle these languages, and it will be gradually rolled out to other Wikipedias over time. If you would like to know more, please contact [[mw:user:Trizek (WMF)|Trizek (WMF)]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:34}} community-submitted {{PLURAL:34|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where search boxes on some Commons pages showed no results due to switch from SpecialSearch to MediaSearch, has now been fixed. [https://phabricator.wikimedia.org/T399476]
* Two new wikis have been created:
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q36846|Toki Pona]] ([[w:tok:|&lt;code&gt;w:tok:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T404457]
** a {{int:project-localized-name-group-wikiquote}} in [[d:Q33655|Nigerian Pidgin]] ([[q:pcm:|&lt;code&gt;q:pcm:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T408318]
'''Updates for technical contributors'''
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.5|MediaWiki]]

'''In depth'''
* The Wikimedia Foundation is in the early stages of exploring approaches to '''Article guidance'''. The initiative aims to identify interventions that could help new editors easily understand and apply existing Wikipedia practices and policies when creating an article. The project is in the exploration and early experimental design phase. All community members are encouraged to [[mw:Special:MyLanguage/Article guidance|learn more]] about the project, and share their thoughts on [[mw:Special:MyLanguage/Talk:Article guidance|the talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/49|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W49&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:57, 1 December 2025 (UTC)
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== Tech News: 2025-50 ==

&lt;section begin=&quot;technews-2025-W50&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/50|Translations]] are available.

'''Weekly highlight'''
* Anybody who wishes to secure their user account can now use [[m:Special:MyLanguage/Help:Two-factor authentication|two-factor authentication]] (2FA). This is available to all registered users of all Wikimedia projects. This is part of the [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security|Account Security]] initiative. Later, 2FA will be required for all users who can take security- or privacy-sensitive actions.

'''Updates for editors'''
* Following last week's deployments, the [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]] feature, which allows editors to add suggested links during editing, will be available to an additional [[Phab:T410469|33 Wikipedias]] starting on 9 December. This expansion is possible thanks to the new prediction model that now supports all languages, including those that were previously not covered. While the feature has been available on most Wikipedias for some time, this rollout brings us closer to using the improved model everywhere. If you have any questions or would like more details please contact [[mw:user:Trizek (WMF)|Trizek (WMF)]].
* Last week, the [[mw:Special:MyLanguage/Wikimedia Search Platform|Search Platform team]] added [[w:en:Transliteration|transliterated]] as-you-type search suggestions to Georgian wikis. If there are only a few regular search suggestions, then queries in Latin or Cyrillic script [[phab:T127003|are now rewritten into Georgian script]] to look for more matches. For example, searching for either &lt;bdi lang=&quot;ka-Latn&quot; dir=&quot;ltr&quot;&gt;''bedniereba''&lt;/bdi&gt; or &lt;bdi lang=&quot;ka-Cyrl&quot; dir=&quot;ltr&quot;&gt;''бедниереба''&lt;/bdi&gt; will now suggest the existing article about &lt;bdi lang=&quot;ka&quot; dir=&quot;ltr&quot;&gt;ბედნიერება&lt;/bdi&gt; (&quot;happiness&quot;). You can recommend other languages where transliterated suggestions would be useful [[phab:T375215|on Phabricator]] for future development.
* Later this week, a controlled experiment will begin for editors on the 100 largest Wikipedias who are editing a section in the mobile web visual editor. 50% of these editors will notice a new &quot;Edit full page&quot; button that will enable them to expand their editing session to the whole page. This feature is intended to make it easier for people on mobile web to edit any article section, regardless of which section-edit icon they tapped to begin. The experiment will last ~4 weeks. You can find [[phab:T409112|more details]] about the project.
* Later this week, the [[mw:Special:MyLanguage/Readers/Reader Growth|Reader Growth team]] will launch a [[mw:Special:MyLanguage/Readers/Reader Growth/WE3.1.14 Expanded Mobile Sections|mobile web experiment]] to expand all article sections by default (currently they are collapsed by default) and pin the section header the user is currently reading to the top of the page. The experiment will affect 10% of users on Arabic, Chinese, French, Indonesian, and Vietnamese Wikipedias. [https://phabricator.wikimedia.org/T409485]
* The [[mw:Special:MyLanguage/Wikimedia Apps/Team/Wikipedia Year in Review/2025 Year in Review|Wikipedia Year in Review 2025]], a feature in the Wikipedia mobile apps (iOS and Android) that provides users with a personalised summary of their engagement with Wikipedia over the year, is now available on the iOS and Android apps. This edition includes expanded personalised insights, improved reading highlights, new donor messaging, and updated designs. Open the app to view your Year in Review and explore your reading journey from 2025.
* A recent software bug caused edits made with VisualEditor to make unintended changes to wikitext, including removing whitespace and replacing spaces with underscores in wikilinks inside citations. This was partially fixed last week, and further fixes are in progress. Editors who used VisualEditor between November 28 and December 2 should review their edits for unexpected modifications. [https://phabricator.wikimedia.org/T411238]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the incorrect handling of URLs copied from the address bar of Microsoft Edge users, has been resolved. [https://phabricator.wikimedia.org/T341281]

'''Updates for technical contributors'''
* Starting this week, users of the &quot;{{int:codemirror-beta-feature-title}}&quot; [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] will have [[mw:Special:MyLanguage/Help:Extension:CodeMirror|CodeMirror]] as the editor for Lua, JavaScript, CSS, JSON and Vue content models, instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]]. With this, the [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Linting|linters]] will be upgraded. This is part of a larger effort to eventually replace CodeEditor and provide a consistent code editing experience. [https://phabricator.wikimedia.org/T373711]
* Developers are encouraged to take the [https://wikimediafoundation.limesurvey.net/552643 2025 Developer Satisfaction Survey], which remains open until 5 January 2026. If you build software for the Wikimedia ecosystem and would like to share your experiences or feedback, your participation is greatly appreciated. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/W4WBKO6Q55UWWCCSFWQATKEXBEHP3QNR/]
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/50|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W50&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:45, 8 December 2025 (UTC)
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== Tech News: 2025-51 ==

&lt;section begin=&quot;technews-2025-W51&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/51|Translations]] are available.

'''Updates for editors'''
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:18}} community-submitted {{PLURAL:18|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, one of the fixes addressed an issue for temporary accounts adding an external URL, which triggered an hCaptcha request in more cases than intended, and did not display the required popup on the first attempt to publish the edit. [https://phabricator.wikimedia.org/T411927]

'''Updates for technical contributors'''
* To improve database and site performance, external links to Wikimedia projects will no longer be stored in the database. This means they will not be searchable in [[{{#special:LinkSearch}}]], will not be checked by the Spam Blacklist or AbuseFilter as new links, and will not be in the &lt;code dir=ltr&gt;externallinks&lt;/code&gt; table on database replicas. In the future this may be extended to other highly-linked trusted websites on a per-wiki basis, such as Creative Commons links on Wikimedia Commons. [https://phabricator.wikimedia.org/T405005]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.7|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/51|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W51&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:03, 15 December 2025 (UTC)
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== Tech News: 2025-52 ==

&lt;section begin=&quot;technews-2025-W52&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2025/52|Translations]] are available.

'''Updates for editors'''
* From January, edit filters [[mw:Special:MyLanguage/Extension:AbuseFilter/Access flags|can be set]] to automatically suppress their details such as rules and list of attempted edits and actions. This will help oversighters use edit filters to prevent doxxing or other suppressible material. [https://phabricator.wikimedia.org/T290324]
* The next issue of Tech News will be sent out on 12 January 2026 because of the end of year holidays. Thank you to all of the translators, and people who submitted content or feedback, this year.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:16}} community-submitted {{PLURAL:16|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the crash that occurred when tapping &quot;First Steps&quot; in the Wikipedia Android Year in Review has now been fixed, and the feature opens as expected. [https://phabricator.wikimedia.org/T411546]

'''Updates for technical contributors'''
* Interface elements such as diffs and categories generated by MediaWiki used to have the attribute &lt;code dir=ltr&gt;data-mw=&quot;interface&quot;&lt;/code&gt; to distinguish from wiki content. The attribute has been replaced with &lt;code dir=ltr&gt;data-mw-interface=&quot;&quot;&lt;/code&gt;, to avoid potential conflicts with other &lt;code dir=ltr&gt;data-mw&lt;/code&gt; attributes, which are generated by Parsoid. [https://phabricator.wikimedia.org/T409187]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] There is no new MediaWiki version this week or next week.
'''Meetings and events'''
* The [[mw:Wikimedia Hackathon Northwestern Europe 2026|Wikimedia Hackathon Northwestern Europe 2026]] will take place on 13-14 March 2026 in Arnhem, the Netherlands. Applications just opened mid-December and will close in mid-January or earlier if capacity is reached. With space for approximately 100 participants, early application is encouraged.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2025/52|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2025-W52&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:45, 22 December 2025 (UTC)
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== Tech News: 2026-03 ==

&lt;section begin=&quot;technews-2026-W03&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/03|Translations]] are available.

'''Weekly highlight'''
* The Wikimedia Foundation has shared some guiding questions for the July 2026–June 2027 Annual Plan on [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2026-2027/Product &amp; Technology OKRs|Meta]] and ''[[diffblog:2025/12/10/shaping-wikimedia-foundations-2026-2027-annual-goals-key-questions-for-the-wikimedia-movement/|Diff]]''. These focus on global trends, faster and healthier experimentation, better support for newcomers, strengthening editors and advanced users, improving collaboration across projects, and growing and retaining readership. Feedback and ideas are welcome on the [[m:Talk:Wikimedia Foundation Annual Plan/2026-2027|talk page]].

'''Updates for editors'''
* As part of the current work of Community Tech team on the [[m:Special:MyLanguage/Community Wishlist/W372|Multiple watchlists]] project, the display of [[Special:EditWatchlist|EditWatchlist]] will be updated as a first step towards multiple watchlists. Additionally, the pagination on [[Special:Search|Search]] will be updated too, as a part of the work on the [[m:Special:MyLanguage/Community Wishlist/W186|Revamp pagination / page navigation]] wish. [https://phabricator.wikimedia.org/T411596]
* [[m:Special:GlobalWatchlist|The Global Watchlist]] is a MediaWiki [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] that lets you see your watchlists from different wikis on the same page. It was recently updated to look more like the regular [[Special:Watchlist|Watchlist]], such as preparing it for temporary accounts in IP masking (including rerouting user links to contributions pages), making page titles bold, and opening links in edit summaries and tags in new browser tabs. [https://phabricator.wikimedia.org/T398361][https://phabricator.wikimedia.org/T298919][https://phabricator.wikimedia.org/T273526][https://phabricator.wikimedia.org/T286309]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:28}} community-submitted {{PLURAL:28|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where global blocks did not have the option to disable sending emails, has now been fixed, and will be available for use in the week of January 13. [https://phabricator.wikimedia.org/T401293]

'''Updates for technical contributors'''
* The [[mw:Special:MyLanguage/VisualEditor/Citation tool|VisualEditor citation tool]] and [[mw:Special:MyLanguage/Help:Reference Previews|Reference Previews]] now support &quot;map&quot; as a reference type. [https://phabricator.wikimedia.org/T411083]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.10|MediaWiki]]/[[mw:MediaWiki 1.46/wmf.11|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/03|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W03&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:33, 12 January 2026 (UTC)
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== Tech News: 2026-04 ==

&lt;section begin=&quot;technews-2026-W04&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/04|Translations]] are available.

'''Updates for editors'''
* The tray shown on [[Special:Diff|Special:Diff]] in mobile view has been redesigned. It is now collapsed by default, and incorporates a link to undo the edit being viewed, making it easier for mobile editors and reviewers to take action while keeping the interface uncluttered. [https://phabricator.wikimedia.org/T402297] 
* [[m:Special:GlobalWatchlist|The Global Watchlist]] lets you view your watchlists from multiple wikis on one page. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] continues to improve — it now automatically determines the text direction (ensuring correct display of sites with unusual domain names) and shows detailed descriptions for log actions. Later this week, a new permanent link for page creations and CSS classes for each entry element will be added. [https://phabricator.wikimedia.org/T412505][https://phabricator.wikimedia.org/T287929][https://phabricator.wikimedia.org/T262768][https://phabricator.wikimedia.org/T414135]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the previously observed issue in Vector 2022, where anchor link targets were obscured by the sticky header, has now been addressed. [https://phabricator.wikimedia.org/T406114]

'''Updates for technical contributors'''
* As mentioned in the [[m:Special:MyLanguage/Tech/News/2025/44|October 2025 deprecation announcement]], MediaWiki Interfaces team will begin sunsetting all transform endpoints containing a trailing slash from the MediaWiki REST API the week of January 26. Changes are expected to roll out to all wikis on or before January 30th. All API users currently calling them are encouraged to transition to the non-trailing slash versions. Both endpoint variations can be found, compared, and tested using the [https://test.wikipedia.org/wiki/Special:RestSandbox REST Sandbox]. If you have questions or encounter any problems, please file a ticket in Phabricator to the [https://phabricator.wikimedia.org/project/view/6931/ #MW-Interfaces-Team board].
* Interactive reference documentation for the [[mw:Special:MyLanguage/Wikimedia REST API|Wikimedia REST API]] has moved. Requests to API docs previously hosted through [[mw:Special:MyLanguage/RESTBase|RESTBase]] (e.g.: &lt;code dir=ltr&gt;https://en.wikipedia.org/api/rest_v1/&lt;/code&gt;) are now redirected to the [[w:en:Special:RestSandbox|REST Sandbox]].
* The [[mw:Special:MyLanguage/Wikidata Platform|WMF Wikidata Platform team]] (WDP) has published its [[d:Special:MyLanguage/Wikidata:Wikidata Platform team/Newsletter|January 2026 newsletter]]. It includes updates on the legacy full-graph endpoint decommissioning, the User-Agent policy change, the monthly Blazegraph migration office hours, and efforts to reduce regressions caused by the legacy endpoint shutdown. As a reminder, you can [[m:Special:MyLanguage/Global message delivery/Targets/WDP team updates|subscribe to the WDP newsletter]]!
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.12|MediaWiki]]

'''Meetings and events'''
* The [[mw:Wikimedia Hackathon Northwestern Europe 2026|Wikimedia Hackathon Northwestern Europe 2026]] will take place on 13-14 March 2026 in Arnhem, the Netherlands. Applications opened mid-December and will close soon or when capacity is reached. It's a two-day, technically oriented hackathon bringing together Wikimedians from the region. Hope to see you there!

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/04|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W04&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:29, 19 January 2026 (UTC)
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== Tech News: 2026-05 ==

&lt;section begin=&quot;technews-2026-W05&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/05|Translations]] are available.

'''Updates for editors'''
* Wikimedia Foundation invites comments on [[m:Special:MyLanguage/Product and Technology Advisory Council/Year1 Reflections and Proposed Way Forward 2026 Update|proposed future]] of the [[:m:Special:MyLanguage/Product and Technology Advisory Council|Product and Technology Advisory Council]] until 28 February.
* All users with registered accounts can now use passkeys for [[m:Special:MyLanguage/Help:Two-factor authentication|two-factor authentication]] (2FA). Passkeys are a simple way to log in without using a second device. They verify the user's identity using a fingerprint, face scan, or a PIN code. To set up a passkey, first set up a regular 2FA method. Currently, to log in with a passkey, users must also use a password. Later this quarter, passwordless login will allow users to log in with a single click and a passkey. Users with advanced rights will also be required to have 2FA enabled. This is part of the [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security|Account Security]] project.
* Unregistered contributors on blocked IPs or blocked IP ranges can now interact on-wiki to appeal a block by creating a temporary account to appeal a block on the user talk page, unless the &quot;prevent this user from editing their own talk page&quot; is enabled. This solves the problem of logged-out users unable to use the default unblock process via user talk page. [https://phabricator.wikimedia.org/T398673]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the Two-Factor Authentication (2FA) methods description on the management page has been updated. It is now clearer and easier for users to understand and make use of. [https://phabricator.wikimedia.org/T332385]

'''Updates for technical contributors'''
* A new AbuseFilter variable, &lt;code&gt;account_type&lt;/code&gt;, has been added to provide a reliable way to determine the account type being created in the &lt;code&gt;createaccount&lt;/code&gt; and &lt;code&gt;autocreateaccount&lt;/code&gt; actions. As part of this change, the variable &lt;code&gt;accountname&lt;/code&gt; has been renamed to &lt;code&gt;account_name&lt;/code&gt;, and &lt;code&gt;accountname&lt;/code&gt; is now deprecated. Edit filter managers should update any filters that use hardcoded account type checks or the deprecated variable. [https://phabricator.wikimedia.org/T414049]
* Image thumbnails that are requested in non-standard sizes, and using non-standard methods such as direct requests to &lt;code dir=ltr&gt;&lt;nowiki&gt;upload.wikimedia.org/…&lt;/nowiki&gt;&lt;/code&gt; will stop working in the near future. This change is to prevent ongoing external abuse by web-scrapers and bots. Some users with custom CSS/JS, Interface Admins who can fix gadgets and local skins, and Tool-authors, will need to update their code to use standard thumbnail sizes. [[phab:T414805|Details, search-links, and examples of how to fix them, are available in the task]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.13|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/05|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W05&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 21:17, 26 January 2026 (UTC)
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== Tech News: 2026-06 ==

&lt;section begin=&quot;technews-2026-W06&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/06|Translations]] are available.

'''Updates for editors'''
* The &quot;{{int:pageinfo-toolboxlink}}&quot; feature, which gives validating information about a page ([{{fullurl:{{FULLPAGENAME}}|action=info}} example]), now automatically includes a table of contents. If there is a local [[{{ns:8}}:Pageinfo-header]] page created by individual users, it can now be removed. [https://phabricator.wikimedia.org/T363726]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, VisualEditor previously added bold or italic formatting inside link descriptions, making the wikicode complex. This has now been fixed. [https://phabricator.wikimedia.org/T409669]

'''Updates for technical contributors'''
* There was no XML dump on 20 January. Additionally, from now on, dumps will be generated once per month only. [https://phabricator.wikimedia.org/T414389]
* The MediaWiki Interfaces team removed support for all transform endpoints containing a trailing slash from the [https://www.mediawiki.org/wiki/Special:MyLanguage/API:REST%20API MediaWiki REST API]. All API users currently calling those endpoints are encouraged to transition to the non-trailing slash versions. If you have questions or encounter any problems, please file a ticket in phabricator to the [https://phabricator.wikimedia.org/project/view/6931/ #MW-Interfaces-Team board].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.14|MediaWiki]]

'''Weekly highlight'''
* Users are reminded that the Wikimedia Foundation has shared some guiding questions for the July 2026–June 2027 Annual Plan on [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2026-2027/Product &amp; Technology OKRs|Meta]] and ''[[diffblog:2025/12/10/shaping-wikimedia-foundations-2026-2027-annual-goals-key-questions-for-the-wikimedia-movement/|Diff]]''. These focus on global trends, faster and healthier experimentation, better support for newcomers, strengthening editors and advanced users, improving collaboration across projects, and growing and retaining readership. Feedback and ideas are welcome on the [[m:Talk:Wikimedia Foundation Annual Plan/2026-2027|talk page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/06|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W06&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:43, 2 February 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30000986 --&gt;

== Tech News: 2026-07 ==

&lt;section begin=&quot;technews-2026-W07&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/07|Translations]] are available.

'''Updates for editors'''
* [[File:Maki-gift-15.svg|12px|link=|class=skin-invert|Wishlist item]] Logged-in contributors who manage large or complex watchlists can now organise and filter watched pages in ways that improve their workflows with the new [[mw:Special:MyLanguage/Help:Watchlist labels|Watchlist labels]] feature. By adding custom labels (for example: pages you created, pages being monitored for vandalism, or discussion pages) users can more quickly identify what needs attention, reduce cognitive load, and respond more efficiently. This improves watchlist usability, especially for highly active editors.
* A new feature available on [[Special:Contributions|Special:Contributions]] shows [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] that are likely operated by the same person, and so makes patrolling less time-consuming. Upon checking contributions of a temporary account, users with access to temporary account IP addresses can now see a view of contributions from the related temporary accounts. The feature looks up all the IPs associated with a given temporary account within the data retention period and shows all the contributions of all temporary accounts that have used these IPs. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts#February 2026: Improvements to the patroller tooling|Learn more]]. [https://phabricator.wikimedia.org/T415674] 
* When editors preview a wikitext edit, the reminder box that they are only seeing a preview (which is shown at the top), now has a grey/neutral background instead of a yellow/warning background. This makes it easier to distinguish preview notes from actual warnings (for example, edit conflicts or problematic redirect targets), which will now be shown in separate warning or error boxes. [https://phabricator.wikimedia.org/T414742]
* The [[m:Special:GlobalWatchlist|Global Watchlist]] lets you view your watchlists from multiple wikis on one page. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] continues to improve — it now properly supports more than one Wikibase site, for example both [[d:|Wikidata]] and [[testwikidata:|testwikidata]]. In addition, issues regarding text direction have been fixed for users who prefer Wikidata or other Wikibase sites in right-to-left (RTL) languages. [https://phabricator.wikimedia.org/T415440][https://phabricator.wikimedia.org/T415458]
* The automatic &quot;magic links&quot; for ISBN, RFC, and PMID numbers have been [[mw:Special:MyLanguage/Help:Magic links|deprecated in wikitext since 2021]] due to inflexibility and difficulties with localization. Several wikis have successfully replaced RFC and PMID magic links with equivalent external links, but a template was often required to replace the functionality of the ISBN magic link. There is now a new [[mw:Special:MyLanguage/Help:Magic words#isbn|built-in parser function]] &lt;code dir=ltr&gt;&lt;nowiki&gt;{{#isbn}}&lt;/nowiki&gt;&lt;/code&gt; available to replace the basic functionality of the ISBN magic link. This makes it easier for wikis who wish to migrate off of the deprecated magic link functionality to do so. [https://phabricator.wikimedia.org/T145604]
* Two new wikis have been created: 
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35401|Jju]] ([[w:kaj:|&lt;code&gt;w:kaj:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T413283]
** a {{int:project-localized-name-group-wikipedia}} in [[d:Q1186896|Nawat]] ([[w:ppl:|&lt;code&gt;w:ppl:&lt;/code&gt;]]) [https://phabricator.wikimedia.org/T413273]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. 

'''Updates for technical contributors'''
* A new global user group has been created: [[{{int:grouppage-local-bot}}|{{int:group-local-bot}}]]. It will be used internally by the software to allow community bots to bypass rate limits that are applied to abusive [[w:en:Web scraping|web scrapers]]. Accounts that are approved as bots on at least one Wikimedia wiki will be automatically added to this group. It will not change what user permissions the bot has. [https://phabricator.wikimedia.org/T415588]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.15|MediaWiki]]

'''Meetings and events'''
* The [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Spring 2026|MediaWiki Users and Developers Conference, Spring 2026]] will be held March 25–27 in Salt Lake City, USA. This event is organized by and for the third-party MediaWiki community. You can propose sessions and register to attend. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/AZBWVI46SDEB65PGR5J6E4TYOQQEZXM7/]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/07|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W07&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 23:30, 9 February 2026 (UTC)
&lt;!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30026671 --&gt;

== Tech News: 2026-08 ==

&lt;section begin=&quot;technews-2026-W08&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/08|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Wikimedia Site Reliability Engineering|SRE Team]] will be performing a cleanup of Wikimedia's [[m:Special:MyLanguage/Etherpad|Etherpad]] instance, the web-based editor for real-time collaborative document editing. All pads will be permanently deleted after 30 April, 2026 – if there are still migration projects in progress at that point the team can revisit the date on a case by case basis. Please create local backups of any content you wish to keep, as deleted data cannot be recovered. This cleanup helps reduce database size and minimize infrastructure footprint. Etherpad will continue to support real-time collaboration, but long-term storage should not be expected. Additional cleanups may occur in the future without prior notice. [https://phabricator.wikimedia.org/T415237]

'''Updates for editors'''
* The Information Retrieval team will be launching an [[mw:Special:MyLanguage/Readers/Information Retrieval/Phase 1|Android mobile app experiment]] that tests hybrid search capabilities which can handle both semantic and keyword queries. The improvement of on-platform search will enable readers to find what they’re looking for directly on Wikipedia more easily. The experiment will first be launched on Greek Wikipedia in late February, followed by English, French, and Portuguese in March. [https://diff.wikimedia.org/2026/01/08/semantic-search-making-it-easier-to-find-the-information-readers-want/ Read more] on Diff blog. [https://www.mediawiki.org/wiki/Readers/Information_Retrieval]
* The Reader Growth team will run [[mw:Special:MyLanguage/Readers/Reader Growth/WE3.10.2 Mobile Table of Contents|an experiment]] for mobile web users, that adds a table of contents and automatically expands all article sections, to learn more about navigation issues they face. The test will be available on Arabic, Chinese, English, French, Indonesian, and Vietnamese Wikipedias.
* Previously, site notices ([[{{ns:8}}:Sitenotice]] and [[{{ns:8}}:Anonnotice]]) would only render on the desktop site. Now, they will render on all platforms. Users on mobile web will now see these notices and be informed. Site administrators should be prepared to test and fix notices on mobile devices to avoid interference with articles. To opt out, interface admins can add &lt;code dir=&quot;ltr&quot;&gt;#siteNotice { display: none; }&lt;/code&gt; to [[{{ns:8}}:Minerva.css]]. [https://phabricator.wikimedia.org/T138572][https://phabricator.wikimedia.org/T416644]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:19}} community-submitted {{PLURAL:19|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue on [[Special:RecentChanges|Special:RecentChanges]] has been fixed. Previously, clicking hide in the active filters caused the &quot;view new changes since…&quot; button to disappear, though it should have remained visible. The button now behaves as expected. [https://phabricator.wikimedia.org/T406339]

'''Updates for technical contributors'''
* New documentation is now available to help editors debug on-site search features. It supports troubleshooting when pages do not appear in results, when ranking seems unexpected, and when you need to inspect what content is being indexed, helping make search behavior easier to understand and analyze. [[mw:Help:CirrusSearch/Debug|Learn more]]. [https://phabricator.wikimedia.org/T411169]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.16|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/08|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W08&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:17, 16 February 2026 (UTC)
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== Tech News: 2026-09 ==

&lt;section begin=&quot;technews-2026-W09&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/09|Translations]] are available.

'''Weekly highlight'''
* [[mw:Special:MyLanguage/Edit check/Reference Check|Reference Check]] has been deployed to English Wikipedia, completing its rollout across all Wikipedias. The feature prompts newcomers to add a citation before publishing new content, helping reduce common citation-related reverts and improve verifiability. In A/B testing, the impact was substantial: newcomers shown Reference Check were approximately 2.2 times more likely to include a reference on desktop and about 17.5 times more likely on mobile web. [https://analytics.wikimedia.org/published/reports/editing/reference_check_ab_test_report_final_2025.html]
'''Updates for editors'''
* The [[mw:Special:MyLanguage/Extension:InterwikiSorting|InterwikiSorting extension]], which allowed for the [[m:Special:MyLanguage/Interwiki sorting order|sorting of interwiki links]], has been undeployed from Wikipedia. As a result, editors who had enabled interwiki link sorting in non-compact mode (full list format) will now see links reordered. The links moving forward will be listed in the alphabetical order of language code. [https://phabricator.wikimedia.org/T253764]
* Later this week, people who are editing a page-section using the mobile visual editor, will notice a new &quot;Edit full page&quot; button. When tapped, you will be able to edit the entire article. This helps when the change you want to make is outside the section you initially opened. [https://phabricator.wikimedia.org/T387175][https://phabricator.wikimedia.org/T409112]
* [[mw:Special:MyLanguage/Readers/Reader Experience|The Reader Experience team]] is inviting editors to assess whether dark mode should still be considered &quot;beta&quot; on their wiki, based on their experience of how well it functions on desktop and mobile. If the feature is deemed mature, editors can update the interface messages in &lt;code dir=ltr&gt;MediaWiki:skin-theme-description&lt;/code&gt; and &lt;code dir=ltr&gt;MediaWiki:Vector-night-mode-beta-tag&lt;/code&gt; to indicate that dark mode is ready and no longer considered beta.
* The improved [[mw:Wikimedia_Apps/Team/iOS/Activity_Tab|Activity tab]] which displays user-insights is now available to all users of the Wikipedia iOS app (version 7.9.0 and later). Following earlier A/B testing that showed higher account creation among users with access to the feature, it has been rolled out to 100% of users along with some updates. The Activity tab now shows your edited articles in the timeline, offers editing impact insights like contribution counts and article view trends, and customization options to improve in-app experience for users.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:21}} community-submitted {{PLURAL:21|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, a bug that prevented [[mw:Special:MyLanguage/Extension:DiscussionTools|DiscussionTools]] from working on mobile has now been fixed, restoring full functionality. [https://phabricator.wikimedia.org/T415303]

'''Updates for technical contributors'''
* The [[m:Special:GlobalWatchlist|Global Watchlist]] lets you view your watchlists from multiple wikis on one page. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] that makes this possible continues to improve. The latest upgrade is the inclusion of a [[mw:Extension:GlobalWatchlist#hook|new hook]], &lt;code dir=ltr&gt;ext.globalwatchlist.rebuild&lt;/code&gt;, which fires after each watchlist rebuild. This allows you to run gadgets and user scripts for the Special page. [https://phabricator.wikimedia.org/T275159]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.17|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/09|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W09&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:03, 23 February 2026 (UTC)
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== Tech News: 2026-10 ==

&lt;section begin=&quot;technews-2026-W10&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/10|Translations]] are available.

'''Weekly highlight'''
* Wikipedia 25 [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments|Birthday mode]] is now live on Betawi, Breton, Chinese, Czech, Dutch, English, French, Gorontalo, Indonesian, Italian, Luxembourgish, Madurese, Sicilian, Spanish, Thai, and Vietnamese Wikipedias! This limited-time campaign feature celebrates 25 years of Wikipedia with a birthday mascot, Baby Globe. When turned on, Baby Globe is shown on [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments/article configuration|~2,500 articles]], waiting to be discovered by readers. Communities can choose to turn Birthday mode on by getting consensus from their community and asking an admin to enable the feature and customize it via [[m:Special:MyLanguage/Wikipedia 25/Easter egg experiments#Community Configuration Demo|community configuration]] on the local wiki.

'''Updates for editors'''
* [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|Sub-referencing]], a new feature to re-use references with different details has been released to Swedish Wikipedia, Polish Wikipedia and [[:phab:T418209|a couple of other wikis]]. You can [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#test|try the feature]] on these projects or on testwiki and [https://en.wikipedia.beta.wmcloud.org/wiki/Sub-referencing betawiki]. Learnings from the first pilot wiki German Wikipedia have been [[:m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing/Learnings|published in a report]]. Reach out to the Wikimedia Deutschland team if you are [[:m:Talk:WMDE Technical Wishes/Sub-referencing#Pilot wikis|interested in becoming a pilot wiki]].
* [[mw:Special:MyLanguage/Help:Edit check#Paste check|Paste Check]] will become available at all Wikipedias this week. The feature prompts newcomers who are pasting text they are not likely to have written into VisualEditor to consider whether doing so risks a copyright violation. Paste Check [[mw:Special:MyLanguage/Edit check/Tags|tags]] all edits where it is shown for potential review. Local administrators can configure various aspects of the feature via [[{{#special:EditChecks}}]]. [[mw:Special:MyLanguage/Edit check/Paste Check#A/B Experiment|Research]] across 22 wikis found that Paste Check resulted in an 18% decrease in relative reverted-edits compared to the control group. Translators can [https://translatewiki.net/w/i.php?title=Special%3ATranslate&amp;group=ext-visualeditor-ve-mw-editcheck&amp;filter=&amp;optional=1&amp;action=translate help to localize] this and related features.
* The [[mw:Special:MyLanguage/Readers/Reader Experience|Reader Experience team]] will be standardizing the user menu in the top right for all mobile users so that it is closer to the desktop experience. Currently this user menu is only visible to users with Advanced Mobile Controls (AMC) turned on. The only change is that a couple buttons previously in the left-side menu will move to the top right for users who do not have AMC turned on. This change is expected to go out March 9 and seeks to improve the user interface. [https://phabricator.wikimedia.org/T413912]
* Starting in the week of March 2, the emails sent out when an email address was added, removed, or changed for an account will switch to a substantially nicer and clearer HTML email from the prior plaintext one. [https://phabricator.wikimedia.org/T410807]
* Notifications are currently limited to 2,000 historic entries per user, and extend back to 2013 when the feature was released. This is going to be changed to only store Notifications from the last 5 years, but up to 10,000 of them. This will help with long-term infrastructure health and help to prevent more recent notifications from disappearing too soon. [https://phabricator.wikimedia.org/T383948]
* The [[m:Special:GlobalWatchlist|Global Watchlist]] which lets you view your watchlists from multiple wikis on a single page continues to see improvements. The latest update improves label usage experience. The [[mw:Special:MyLanguage/Extension:GlobalWatchlist|extension]] now allows activating the [[mw:Special:MyLanguage/Manual:Language#Fallback languages|language fallback system]] for Wikidata items without labels in the viewed language, and showing those labels in the user’s preferred Wikidata language if no &lt;code dir=ltr&gt;uselang=&lt;/code&gt; URL parameter is provided. [https://phabricator.wikimedia.org/T373686][https://phabricator.wikimedia.org/T416111]
* The Wikipedia Android team has started a beta test of [[mw:Special:MyLanguage/Readers/Information Retrieval/Phase 1|hybrid search]] on Greek Wikipedia. Hybrid search capabilities can handle both semantic and keyword queries enabling readers to find what they’re looking for directly on Wikipedia more easily.
* For security reasons, members of certain user groups are [[m:Special:MyLanguage/Mandatory two-factor authentication for users with some extended rights|required to have two-factor authentication]] (2FA) enabled. Currently, 2FA is required to use the group, but not to be a member of it. Given that this model still has some vulnerabilities, the situation will [[phab:T418580|gradually change in March]]. Members of these groups will be unable to disable last 2FA method on their account, and it will be impossible to add users without 2FA to these groups. Users will still be able to add new authentication methods or remove them, as long as at least one method is continuously enabled. In the second half of March, users without 2FA will be removed from these groups. This applies to: CentralNotice administrators, checkusers, interface administrators, suppressors, Wikidata staff, Wikifunctions staff, WMF Office IT and WMF Trust &amp; Safety. Nothing will change for other users. See the linked task for deployment schedule. [https://phabricator.wikimedia.org/T418580]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue preventing users from creating an instance in [https://www.wikibase.cloud/ Wikibase.cloud] has now been fixed. [https://phabricator.wikimedia.org/T416807]

'''Updates for technical contributors'''
* To help ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]], over the next month the Wikimedia Foundation will implement global API rate limits across our APIs. In early March, stricter limits will be applied to unidentified requests from outside Toolforge/WMCS and API requests that are made from web browsers. In April, higher limits will be applied to identified traffic. These limits are intentionally set as high as possible to minimise impact on the community. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]].
* The Wikidata Query Service Linked Data Fragment (LDF) endpoint will be decommissioned in February. This endpoint served limited traffic, which was successfully migrated to other data access methods that were better suited to support existing use cases. The hardware used to support the LDF endpoint will be reallocated to support the ongoing backend migration efforts. [https://phabricator.wikimedia.org/T415696]
* The new Parsoid parser [[mw:Special:MyLanguage/Parsoid/Parser Unification/Updates|continues to be deployed to additional wikis]], improving platform sustainability and making it easier to introduce new reading and editing features. Parsoid is now the default parser on 488 WMF wikis (268 Wikipedias), now covering more than 10% of all Wikipedia page views.
* The process and criteria for [[Special:MyLanguage/Wikimedia Enterprise#Access|requesting exceptional access]] to the high volume feed of the ''Wikimedia Enterprise'' APIs (at no cost for mission-aligned usecases), [[m:Talk:Wikimedia Enterprise#Exceptional access criteria|have now been published]]. This is to provide more thorough and clearer documentation for users.
* [https://techblog.wikimedia.org/ Tech Blog], the blog dedicated to the Wikimedia technical community [https://techblog.wikimedia.org/2026/02/24/a-tech-blog-diff/ will be migrating] to [[diffblog:|Diff]], the community news and event blog. The migration should be complete in April 2026, after which new posts will be accepted for publishing. Readers will be able to access posts – old and new – on the landing page at https://diff.wikimedia.org/techblog.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.18|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/10|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W10&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 17:51, 2 March 2026 (UTC)
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== Tech News: 2026-11 ==

&lt;section begin=&quot;technews-2026-W11&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/11|Translations]] are available.

'''Weekly highlight'''
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on Wednesday, 25 March 2026 at [https://zonestamp.toolforge.org/1774450800 15:00 UTC]. This is for the datacenter server switchover backup tests, [[wikitech:Deployments/Yearly calendar|which happen twice a year]]. During the switchover, all Wikimedia website traffic is shifted from one primary data center to the backup data center to test availability and prevent service disruption even in emergencies.
* Last week, all wikis had 2 hours of read-only time, and extended unavailability for user-scripts and gadgets. This was due to a security incident which has since been resolved. Work is ongoing to prevent re-occurrences. For current information please see the [[m:Steward's noticeboard#Statement on Meta about today's user script security incident|post on the Stewards' noticeboard]] ([[m:Special:MyLanguage/Wikimedia Foundation/Product and Technology/Product Safety and Integrity/March 2026 User Script Incident|translations]]).

'''Updates for editors'''
* Users facing multiple blocks on mobile will now see the reasons for each block separately, instead of a generic message. This helps them understand why they are blocked and what steps they can take to resolve the issue. For example, users affected for using common VPNs (such as [[Special:MyLanguage/Apple iCloud Private Relay|iCloud Private Relay]]) will receive clearer guidance on what they need to do to start editing again. [https://phabricator.wikimedia.org/T357118]
* Later this week, [[mw:Special:MyLanguage/VisualEditor/Suggestion Mode|Suggestion Mode]] will become available as a beta feature within the visual editor at all Wikipedias. This feature proactively suggests various types of actions that people can consider taking to improve Wikipedia articles, and learn about related guidelines. The feature is locally configurable, and can also be locally expanded with custom Suggestions. Current settings can be seen at [[Special:EditChecks]] and there are [[mw:Special:MyLanguage/Help:Suggestion mode#For administrators %E2%80%93 local customization|instructions for how administrators can customize]] the links to point to local guidelines. The feature is connected to [[mw:Special:MyLanguage/Help:Edit check|Edit check]] which suggests improvements while someone is writing new content. In the future, the Editing team plans to evaluate the feature's impact with newcomers through a controlled experiment. [https://phabricator.wikimedia.org/T404600]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where the cursor became misaligned during the use of CodeMirror’s syntax highlighting, which makes wikitext and code easier to read, has now been fixed. This problem specifically affected users who defined a font rule in a custom stylesheet while creating a new topic with DiscussionTools. [https://phabricator.wikimedia.org/T418793]

'''Updates for technical contributors'''
* API rate limiting update: To help ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]], global API rate limits will be applied this week to requests without a compliant User-Agent that originate from outside Toolforge/WMCS and to unauthenticated requests made from web browsers. Higher limits will be applied to identified traffic in April. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]].
* The new GraphQL API has been released. The API was developed as a flexible alternative to select features of the Wikidata Query Service (WDQS), to improve developer experience and foster adaptability, and efficient data access. Try it out and [[d:Wikidata:Wikibase GraphQL#Feedback and development|give feedback]]. You can also [https://greatquestion.co/wikimediadeutschland/GraphQLAPI/apply sign up for usability tests].
* The [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group|PTAC Unsupported Tools Working Group]] continued improvements to [[commons:Special:MyLanguage/Commons:Video2commons#|Video2Commons]] in February, with fixes addressing authentication errors, large-file handling, task queue visibility, and clearer upload behavior. Work is still ongoing in some areas, including changes related to deprecated server-side uploads. Read [[m:Special:MyLanguage/Product and Technology Advisory Council/Unsupported Tools Working Group#February 2026|this update]] to learn more.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.19|MediaWiki]]

'''In depth'''
* The Article Guidance team invites experienced Wikipedia editors from selected [[mw:Special:MyLanguage/Article guidance/Pilot wikis and collaborators#Collaborators|pilot wikis]] and interested contributors from other Wikipedias to fill out this questionnaire which is available in [https://docs.google.com/forms/d/e/1FAIpQLSfmLeVWnxmsCbPoI_UF2jyRcn73WRGWCVPHzerXb4Cz97X_Ag/viewform English], [https://docs.google.com/forms/d/e/1FAIpQLSd6rzr4XXQw8r4024fE3geTPFe13M_6w7Mitj-YJi0sOlWTAw/viewform?usp=header Arabic], [https://docs.google.com/forms/d/e/1FAIpQLSdok3-RfB18lcugYTUMGkpwmqG_8p760Wv4dCXitOXOszjUDw/viewform?usp=header Bengali], [https://docs.google.com/forms/d/e/1FAIpQLSfjTfYp4jEo0akA4B1e-Nfg3QZPCudUjhJzHzzDi6AHyAaMGA/viewform?usp=header Japanese], [https://docs.google.com/forms/d/e/1FAIpQLScteVoI29Aue4xc72dekk-6RYtvmMgQxzMI900UOawrFrSTWg/viewform?usp=header Portuguese], [https://docs.google.com/forms/d/e/1FAIpQLSetdxnYwL3ub2vqA7awCg5hJZPMIYcDPaiTe12rY9h0GYnVlw/viewform?usp=header Persian], and [https://docs.google.com/forms/d/e/1FAIpQLScNvfJF-Ot-4pzA4qAN771_0QDJ4Li19YcUsaTgSKW8Nc7U_Q/viewform?usp=header Turkish]. Your answers will help the team customize guidance for less experienced editors and help them learn community policies and practices while creating an article. Learn more [[mw:Special:MyLanguage/Article guidance|on the project page]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/11|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W11&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:53, 9 March 2026 (UTC)
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== Tech News: 2026-12 ==

&lt;section begin=&quot;technews-2026-W12&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/12|Translations]] are available.

'''Updates for editors'''
* The [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature, also known as [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror 6]], has been used for wikitext syntax highlighting since November 2024. It will be promoted out of beta by May 2026 in order to bring improvements and new [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Features|features]] to all editors who use the standard syntax highlighter. If you have any questions or concerns about promoting the feature out of beta, [[mw:Special:MyLanguage/Help talk:Extension:CodeMirror|please share]]. [https://phabricator.wikimedia.org/T259059]
* Some changes to local user groups are performed by stewards on Meta-Wiki and logged there only. Now, interwiki rights changes will be logged both on Meta-Wiki and the wiki of the target user to make it easier to access a full record of user's rights changes on a local wiki. Past log entries for such changes will be backfilled in the coming weeks. [https://phabricator.wikimedia.org/T6055]
* On wikis using [[m:Special:MyLanguage/Flagged Revisions|Flagged Revisions]], the number of pending changes shown on [[{{#Special:PendingChanges}}]] previously counted pages which were no longer pending review, because they have been removed from the system without being reviewed, e.g. due to being deleted, moved to a different namespace, or due to wiki configuration changes. The count will be correct now. On some wikis the number shown will be much smaller than before. There should be no change to the list of pages itself. [https://phabricator.wikimedia.org/T413016]
* Wikifunctions composition language has been rewritten, resulting in a new version of the language. This change aims to increase service stability by reducing the orchestrator's memory consumption. This rewrite also enables substantial latency reduction, code simplification, and better abstractions, which will open the door to later feature additions. Read more about [[f:Special:MyLanguage/Wikifunctions:Status updates/2026-03-11|the changes]].
* Users can now sort search results alphabetically by page title. The update gives an additional option to finding pages more easily and quickly. Previously, results could be sorted by Edit date, Creation date, or Relevance. To use the new option, open 'Advanced Search' on the search results page and select 'Alphabetically' under 'Sorting Order'. [https://phabricator.wikimedia.org/T403775]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:28}} community-submitted {{PLURAL:28|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the bug that prevented UploadWizard on Wikimedia Commons from importing files from Flickr has now been fixed. [https://phabricator.wikimedia.org/T419263]
'''Updates for technical contributors'''
* A new special page, [[{{#special:LintTemplateErrors}}]], has been created to list transcluded pages that are flagged as containing lint errors to help users discover them easily. The list is sorted by the number of transclusions with errors. For example: [[{{#special:LintTemplateErrors}}/night-mode-unaware-background-color]]. [https://phabricator.wikimedia.org/T170874]
* Users of the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature have been using [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] for syntax highlighting when editing JavaScript, CSS, JSON, Vue and Lua content pages, for some time now. Along with promoting CodeMirror 6 out of beta, the plan is to replace CodeEditor as the standard editor for these content models by May 2026. [[mw:Special:MyLanguage/Help talk:Extension:CodeMirror|Feedback or concerns are welcome]]. [https://phabricator.wikimedia.org/T419332]
* The [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] JavaScript modules will soon be upgraded to CodeMirror 6. Leading up to the upgrade, loading the &lt;code dir=ltr&gt;ext.CodeMirror&lt;/code&gt; or &lt;code dir=ltr&gt;ext.CodeMirror.lib&lt;/code&gt; modules from gadgets and user scripts was deprecated in July 2025. The use of the &lt;code dir=ltr&gt;ext.CodeMirror.switch&lt;/code&gt; hook was also deprecated in March 2025. Contributors can now make their scripts or gadgets compatible with CodeMirror 6. See the [[mw:Special:MyLanguage/Extension:CodeMirror#Gadgets and user scripts|migration guide]] for more information. [https://phabricator.wikimedia.org/T373720]
* The MediaWiki Interfaces team is expanding coverage of REST API module definitions to include [[mw:Special:MyLanguage/API:REST API/Extensions|extension APIs]]. REST API modules are groups of related endpoints that can be independently managed and versioned. Modules now exist for [https://phabricator.wikimedia.org/T414470 GrowthExperiments] and [https://phabricator.wikimedia.org/T419053 Wikifunctions] APIs. As we migrate extension APIs to this structure, documentation will move out of the main MediaWiki OpenAPI spec and REST Sandbox view, and will instead be accessible via module-specific options in the dropdown on the [https://test.wikipedia.org/wiki/Special:RestSandbox REST Sandbox] (i.e., [[{{#Special:RestSandbox}}]], available on all wiki projects).
* The [[mw:Special:MyLanguage/Extension:Scribunto|Scribunto]] extension provides different pieces of information about the wiki where the module is being used via the [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual|mw.site]] library. Starting last week, the library also provides a [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#mw.site.wikiId|way]] of accessing the [[mw:Special:MyLanguage/Manual:Wiki ID|wiki ID]] that can be used to facilitate cross-wiki module maintenance. [https://phabricator.wikimedia.org/T146616]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.20|MediaWiki]]

'''In depth'''
* The [[m:Special:MyLanguage/Coolest Tool Award|2026 Coolest Tool Award]] celebrating outstanding community tools, is now open for nominations! Nominate your favorite tool using the [https://wikimediafoundation.limesurvey.net/435684?lang=en nomination survey] form by 23 March 2026. For more information on privacy and data handling, please see the [[foundation:Special:MyLanguage/Legal:Coolest_Tool_Award_2026_Survey_Privacy_Statement|survey privacy statement]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/12|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W12&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:35, 16 March 2026 (UTC)
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== Tech News: 2026-13 ==

&lt;section begin=&quot;technews-2026-W13&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/13|Translations]] are available.

'''Weekly highlight'''
* Wikimedia site users can now log in without a password using passkeys. This is a secure method supported by fingerprint, facial recognition, or PIN. With this change, all users who opt for passwordless login will find it easier, faster, and more secure to log in to their accounts using any device. The new passkey login option currently appears as an autofill suggestion in the username field. An additional [[phab:T417120|&quot;Log in with passkey&quot; button]] will soon be available for users who have already registered a passkey. This update will improve security and user experience. The [[c:File:Passwordless_login_screencast.webm|screen recording]] demonstrates the passwordless login process step by step.
* [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on Wednesday, 25 March 2026 at [https://zonestamp.toolforge.org/1774450800 15:00 UTC]. This is for the datacenter server switchover backup tests, [[wikitech:Deployments/Yearly calendar|which happen twice a year]]. During the switchover, all Wikimedia website traffic is shifted from one primary data center to the backup data center to test availability and prevent service disruption even in emergencies.

'''Updates for editors'''
* Wikimedia site users can now export their notifications older than 5 years using a [[toolforge:echo-chamber|new Toolforge tool]]. This will ensure that users retain their important notifications and avoid them being lost based on the planned change to delete notifications older than 5 years, as previously announced. [https://phabricator.wikimedia.org/T383948]
* Wikipedia editors in Indonesian, Thai, Turkish, and Simple English now have access to Special:PersonalDashboard. This is an [[mw:Special:MyLanguage/Moderator Tools/Dashboard|early version of an experience]] that introduces newer editors to patrolling workflows, making it easier for them to move from making edits to participating in more advanced moderation work on their project. [https://phabricator.wikimedia.org/T402647]
* The [[Special:Block]] now has two minor interface changes. Administrators can now easily perform indefinite blocks through a dedicated radio button in the expiry section. Also, choosing an indefinite expiry provides a different set of common reasons to select from, which can be changed at: [[MediaWiki:Ipbreason-indef-dropdown]]. [https://phabricator.wikimedia.org/T401823]
* Mobile editors [[mw:Special:MyLanguage/Contributors/Account Creation Experiments#Logged-out|at several wikis]] can now see an improved logged-out edit warning, thanks to the recent updates from the Growth team. These changes released last week are part of ongoing efforts and tests to enhance [[mw:Special:MyLanguage/Contributors/Account Creation Experiments|account creation experience on mobile]] and then increase participation. [https://phabricator.wikimedia.org/T408484]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:36}} community-submitted {{PLURAL:36|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the bug that prevented mobile web users from seeing the block information when affected by multiple blocks has been fixed. They can now see messages of all the blocks currently affecting them when they access Wikipedia.

'''Updates for technical contributors'''
* Images built using Toolforge will soon get the upgraded buildpacks version, bringing support for newer language versions and other upstream improvements and fixes. If you use Toolforge Build Service, review the recent [https://lists.wikimedia.org/hyperkitty/list/cloud-announce@lists.wikimedia.org/thread/EMYTA32EV2V5SQ2JIEOD2CL66YFIZEKV/ cloud-announce email] and update your build configuration as necessary to ensure your tools are compatible. [https://wikitech.wikimedia.org/w/index.php?title=Help:Toolforge/Building_container_images&amp;oldid=2392097#Buildpack_environment_upgrade_process][https://phabricator.wikimedia.org/T380127]

* The [https://api.wikimedia.org/wiki/Main_Page API Portal] documentation wiki will shut down in June 2026. API keys created on the API Portal will continue to work normally. api.wikimedia.org endpoints will be deprecated gradually starting in July 2026. Documentation on the API Portal is moving to [[mw:Wikimedia APIs|mediawiki.org]]. Learn more on the [[wikitech:API Portal/Deprecation|project page]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.21|MediaWiki]]

'''In depth'''
* [[m:Special:MyLanguage/WMDE Technical Wishes|WMDE Technical Wishes]] is considering improvements to [[m:WMDE Technical Wishes/References/VisualEditor automatic reference names|automatically generated reference names in VisualEditor]]. Please check out the [[m:WMDE Technical Wishes/References/VisualEditor automatic reference names#Proposed solutions|proposed solutions]] and participate in the [[m:Talk:WMDE Technical Wishes/References/VisualEditor automatic reference names#Request for comment|request for comment]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/13|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W13&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:51, 23 March 2026 (UTC)
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== Tech News: 2026-14 ==

&lt;section begin=&quot;technews-2026-W14&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/14|Translations]] are available.

'''Weekly highlight'''
* The Beta version of [[abstract:|Abstract Wikipedia]] a new Wikimedia project which is language-independent, was launched last week. The project allows communities to build Wikipedia articles in their native language, which can be readily accessed by other users in their own languages. The wiki is powered by instructions from Wikifunctions and also based on structured content from Wikidata. [[:f:Special:MyLanguage/Wikifunctions:Status updates/2026-03-26|Read more]].

'''Updates for editors'''
* The Growth team is running an A/B test to evaluate a clearer, more user-friendly message that promotes account creation on wikis. Currently when logged-out mobile users begin editing, they see a jarring warning message that can feel abrupt and discouraging. This also presents temporary account editing as the default rather than encouraging account creation. The test is running on ten Wikipedias, including Arabic, French, Spanish and German. [[mw:Special:MyLanguage/Contributors/Account Creation Experiments#2. Improve logged-out warning message (T415160)|Read more]].
* The Wikimedia Apps team is inviting feedback on [[mw:Special:MyLanguage/Wikimedia Apps/Team/Future of Editing on the Mobile Apps|how editing should work on the Wikipedia mobile apps]]. The discussion focuses on improving how users access editing tools when they tap &quot;Edit&quot;. This is part of a broader effort to convert readers who develop an interest in editing, to access a more user-friendly pathway to start contributing.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:45}} community-submitted {{PLURAL:45|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where citation fetching from the large newspaper archive [https://www.newspapers.com Newspapers.com] was no longer working, due to a block in [[mw:Special:MyLanguage/Citoid|Citoid]] requests, has now been fixed. [https://phabricator.wikimedia.org/T419903]

'''Updates for technical contributors'''
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.22|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/14|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W14&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:25, 30 March 2026 (UTC)
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== Tech News: 2026-15 ==

&lt;section begin=&quot;technews-2026-W15&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/15|Translations]] are available.

'''Updates for editors'''

* The [[mw:Special:MyLanguage/Help:Extension:CampaignEvents|CampaignEvents extension]] now includes a new group goal-setting feature, enabling organizers to set and track event goals such as the number of articles created and participating contributors in real time. Similarly, participants can work toward shared targets and see their collective impact as the event unfolds. The feature is now available on all Wikimedia wikis. Learn more in [[mw:Special:MyLanguage/Help:Extension:CampaignEvents/Registration/Collaborative contributions#Goal setting|the documentation]].
* [[File:Maki-gift-15.svg|12px|link=|class=skin-invert|Wishlist item]] The new [[mw:Special:MyLanguage/Help:Watchlist labels|watchlist labels]] feature (announced in [[m:Special:MyLanguage/Tech/News/2026/07|Tech News 2026-07]]) is now available via VisualEditor, the source editor, and the 'watchstar' (or watch link, for skins that don't have a star icon). Previously it was only possible to assign labels via [[Special:EditWatchlist|EditWatchlist]]. In all three places it is a new field following the expiry field.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:23}} community-submitted {{PLURAL:23|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where talk pages on mobile with Parsoid are unusable after empty section headers, has now been fixed. [https://phabricator.wikimedia.org/T419171]

'''Updates for technical contributors'''
* The [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|sub-referencing feature]], which lets editors add details to an existing reference without duplicating it, will be gradually rolled out to [[phab:T414094|more wikis]] later this year. Wikis using the [[mw:Special:MyLanguage/Reference Tooltips|Reference Tooltips]] gadget are encouraged to update their version (typically at [[m:MediaWiki:Gadget-ReferenceTooltips.js|MediaWiki:Gadget-ReferenceTooltips.js]] as shown [https://en.wikipedia.org/w/index.php?diff=1344408362 here]) to ensure compatibility. Other reference-related gadgets may also be affected. [https://phabricator.wikimedia.org/T416304]
* All Wikinews editions will be closed and switched to read-only mode on 4 May 2026. Content will remain accessible, but no new edits or articles can be added. This closure was approved by the Board of Trustees of the Wikimedia Foundation following extended discussions. [[m:Wikimedia Foundation Board noticeboard#Board of Trustees Approves Closure of Wikinews|Read more]].
* The [[:mw:Special:MyLanguage/API:Action API|Action API]] has had several formats for requested output. One of them, &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;format=php&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, is being removed soon. Please ensure your scripts or bots use the [[mw:Special:MyLanguage/API:Data formats#Output|JSON format]]. This removal should affect very few scripts and bots. [https://phabricator.wikimedia.org/T118538]
* The [[Special:NamespaceInfo|Special:NamespaceInfo]] page now includes namespace aliases. For example &quot;WP&quot; for the &quot;Project&quot; (&quot;Wikipedia&quot;) namespace on the German Wikipedia. [https://phabricator.wikimedia.org/T381455]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.23|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/15|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W15&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 16:19, 6 April 2026 (UTC)
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== Tech News: 2026-16 ==

&lt;section begin=&quot;technews-2026-W16&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/16|Translations]] are available.

'''Weekly highlight'''
* Experienced editors are invited to [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Main_Page test] the [[mw:Special:MyLanguage/Article guidance|Article guidance]] feature, designed to help less-experienced editors create well-structured, policy-compliant Wikipedia articles. Testing instructions are [[mw:Special:MyLanguage/Article guidance/Test feature guide|available]]. Also, after reviewing [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Category:Pages_using_article_guidance the outlines], please provide feedback on the [[mw:Talk:Article guidance|project talk page]]. Based on your input, the feature will be refined and transferred to the pilot Wikipedias to translate and adapt. Check out [[c:File:Article Guidance workflow demo - April 2026.webm|the video]] explaining the feature.
'''Updates for editors'''
* On most wikis, all autoconfirmed users can now use [[Special:ChangeContentModel|Special:ChangeContentModel]] page to [[mw:Special:MyLanguage/Help:ChangeContentModel|create new pages with custom content models]], such as mass message lists, making custom page formats more accessible. Check [[Special:ListGroupRights|Special:ListGroupRights]] for the status of your wiki. [https://phabricator.wikimedia.org/T248294]
* The Growth team has launched an [[mw:Special:MyLanguage/Contributors/Account_Creation_Experiments|account creation experiment]] to evaluate whether adding an account creation button to the mobile web header increases new account registrations and encourages more mobile users to contribute to the wikis. The experiment is currently live on Hindi, Indonesian, Bengali, Thai, and Hebrew Wikipedia, and targets 10% of logged-out mobile web users.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where VisualEditor could get stuck loading on Windows devices with animations turned off, has now been fixed. [https://phabricator.wikimedia.org/T382856]

'''Updates for technical contributors'''
* Starting later this week, {{int:group-abusefilter}} who have the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]] beta feature enabled will have [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] as the editor at [[Special:AbuseFilter|Special:AbuseFilter]]. This is part of the broader effort to make the user experience more consistent across all editors. [https://phabricator.wikimedia.org/T399673][https://phabricator.wikimedia.org/T419332]
* Tools and bots that access the [[mw:Special:MyLanguage/Notifications/API|Notifications API]] (&lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;action=query&amp;meta=notifications&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;) will need to update their OAuth or BotPassword grants to also include access to private notifications. [https://phabricator.wikimedia.org/T421991]
* Due to a library upgrade, listings on category pages may be displayed out of order starting on Monday, 20th April. A migration script will be run to correct this, and will take hours to days depending on the size of the wiki (up to a week for English Wikipedia). [https://phabricator.wikimedia.org/T422544]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.24|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/16|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W16&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:19, 13 April 2026 (UTC)
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== Tech News: 2026-17 ==

&lt;section begin=&quot;technews-2026-W17&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/17|Translations]] are available.

'''Weekly highlight'''
* After two years of development, [[mw:Special:MyLanguage/Help:Extension:CodeMirror|{{int:codemirror-beta-feature-title}}]], also known as [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror 6]], is to be promoted out of beta on Tuesday, April 21. It brings better code and wikitext readability, reduction in typing errors, and other [[mw:Special:MyLanguage/Help:Extension:CodeMirror|benefits]] to all users of the standard syntax highlighter. A huge thank you to volunteer [https://phabricator.wikimedia.org/p/Bhsd/ Bhsd] who developed many of the new features, including [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Code folding|code folding]], [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Autocompletion|autocompletion]], and [[mw:Special:MyLanguage/Help:Extension:CodeMirror#Linting|linting]]. [https://phabricator.wikimedia.org/T259059]
* A major update to the Wikipedia app for iOS is now rolling out, redesigning the interface to align with Apple's latest &quot;Liquid Glass&quot; visual design. [https://apps.apple.com/us/app/wikipedia/id324715238 Download the latest version] and explore the update.

'''Updates for editors'''
* [[mw:Special:MyLanguage/Readers/Reader Experience/WE3.3.4 Reading lists|Reading lists]] is a feature which allows readers to save articles to a list for reading later. This feature is now in beta on Arabic, French, Indonesian, Vietnamese, and Chinese Wikipedias and by default for all new accounts on all Wikipedias.
* An experiment which explores extending [[mw:Special:MyLanguage/Readers/Reader Growth/Mobile page previews|Page Previews to mobile web]] will be launched in the week of April 20 on Arabic, English, French, Italian, Polish, and Vietnamese Wikipedias. Page Previews are pop-ups that display a thumbnail, lead paragraph, and a link to open the full article of a blue link, thereby improving content discovery. The feature is already available on desktop and in the apps. [[m:Special:MyLanguage/List of experiments in Product and Technology#Template|Read more about this experiment and others]].
* On several wikis, logged-in editors who haven't [[mw:Special:MyLanguage/Help:Email confirmation|confirmed their email addresses]] can now see a banner encouraging them to do so. Having the email address confirmed allows a user to restore access to the account if they lose it. [[mw:Special:MyLanguage/Product Safety and Integrity/Account Security#Encouraging users to confirm their email addresses|Learn more]]. [https://phabricator.wikimedia.org/T421366]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:15}} community-submitted {{PLURAL:15|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where editing very large wiki pages in the 2017 wikitext editor caused slow loading, preview and scrolling lag, and performance issues when selecting, cutting, or pasting content, has now been fixed. [https://phabricator.wikimedia.org/T184857]

'''Updates for technical contributors'''
* As part of the promotion of [[mw:Special:MyLanguage/Help:Extension:CodeMirror|CodeMirror]] from a beta feature, all users will use [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] instead of [[mw:Special:MyLanguage/Extension:CodeEditor|CodeEditor]] for syntax highlighting when editing JavaScript, CSS, JSON, Vue and Lua content pages. [https://phabricator.wikimedia.org/T419332]
* The &lt;code&gt;mirrors.wikimedia.org&lt;/code&gt; service for Debian and Ubuntu users will sunset and stop working on May 15. The resources for the service will be replaced with new and better options. Some users may need to switch to a different server which should take about a minute. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/LJYRIS4WB66HIRCAO4GIDTXCMDVZRBMA/ You can read more]. [https://phabricator.wikimedia.org/T416707]
* The &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;image&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;oldimage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; table will be removed from [[wikitech:Help:Wiki Replicas|wikireplicas]]. If your tools or queries access &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;image&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; or &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;oldimage&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; directly, please update them to use the &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;file&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; and &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;filerevision&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt; table before 28 May. [https://phabricator.wikimedia.org/T28741]
* Following the recent implementation of global API rate limits on unidentified traffic, the Wikimedia Foundation will continue efforts to ensure [[mw:Special:MyLanguage/MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]] by applying global limits to identified API traffic beginning the last week of April. These limits are intentionally set as high as possible to minimise impact on the community. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, see [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]] and [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits/FAQ|Frequently Asked Questions]].
* The [[mw:Special:MyLanguage/Attribution API|Attribution API]] is now available as a [[mw:Special:MyLanguage/Wikimedia APIs/Stability policy|beta]]. The API fetches information for crediting Wikimedia articles and media files wherever they are used. Reference documentation is available through the REST Sandbox special page available on all Wikimedia wikis (such as the [https://en.wikipedia.org/w/index.php?api=attribution.v0-beta&amp;title=Special%3ARestSandbox REST sandbox on English Wikipedia]). Share your feedback on the [[mw:Talk:Attribution API|project talk page]].
* There is no new MediaWiki version this week.

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/17|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W17&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 15:00, 20 April 2026 (UTC)
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== Tech News: 2026-18 ==

&lt;section begin=&quot;technews-2026-W18&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/18|Translations]] are available.

'''Updates for editors'''
* There is a change in how new users are autoconfirmed that will improve anti-vandalism protection. Currently, users who have had an account for a few days and made a few edits are automatically added to the [[{{int:grouppage-autoconfirmed/{{CONTENTLANGUAGE}}}}|{{int:group-autoconfirmed}}]] group. This configuration tends to be exploited by some vandals, who create accounts and start to use them only after some time. To mitigate this, the configuration will be updated next week so that – for the purpose of becoming autoconfirmed – the account age will be counted from their first edit, instead of registration date. The numeric value of the age threshold will remain the same. This change will be deployed only to wikis which require at least one edit as part of the autoconfirmation conditions. [https://phabricator.wikimedia.org/T418484]
* All Wikipedia users with new accounts and those who activated the &quot;automatically enable most beta features&quot; option in their preference can now use the [[mw:Special:MyLanguage/Readers/Reader Experience/WE3.3.4 Reading lists|reading lists]] beta feature to save articles for later reading. This helps organize reading interests in one place for convenient access. 
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:30}} community-submitted {{PLURAL:30|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the issue where infobox images have huge padding in Firefox, has been fixed. [https://phabricator.wikimedia.org/T423676]

'''Updates for technical contributors'''
* As a reminder, the global API rate limits will be applied this week to identified API traffic. This is to help ensure [[mw:MediaWiki Product Insights/Responsible Reuse|fair use of infrastructure]]. Bots running in Toolforge/WMCS or with the bot user right on any wiki should not be affected for now. However, all developers are advised to follow updated best practices. For more information, including the actual rate limits, see [[mw:Wikimedia APIs/Rate limits|Wikimedia APIs/Rate limits]] and [[mw:Wikimedia APIs/Rate limits/FAQ|Frequently Asked Questions]].
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.26|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/18|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W18&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 18:06, 27 April 2026 (UTC)
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== Tech News: 2026-19 ==

&lt;section begin=&quot;technews-2026-W19&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/19|Translations]] are available.

'''Weekly highlight'''
* The [[mw:Special:MyLanguage/Article guidance|Article guidance]] team invites experienced editors of [[mw:Special:MyLanguage/Article guidance/Pilot wikis and collaborators|pilot Wikipedias]]—Arabic, Bangla, Japanese, Portuguese, Persian, Turkish, Simple English, Spanish, and French—to help translate and adapt [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Category:Pages_using_article_guidance sample outlines]. These outlines will guide editors in creating clear, well-structured, and policy-compliant articles when using [https://b24e11a4f1.catalyst.wmcloud.org/wiki/Special:NewArticle the feature] once it is launched in May 2026. [[mw:Special:MyLanguage/Article guidance#Adapting a sample outline in a Wikipedia|Simple instructions]] on how to translate and adapt the outlines are available.
'''Updates for editors'''
* The [[:m:Special:MyLanguage/Product and Technology Advisory Council|Product and Technology Advisory Council]] has published [[:m:Special:MyLanguage/Product and Technology Advisory Council/May 2026 draft PTAC recommendation for feedback|draft recommendations]] on a model that affiliates can follow when contributing to the technical space. Community members are invited to provide feedback on the recommendation until May 8th [[:m:Talk:Product and Technology Advisory Council/May 2026 draft PTAC recommendation for feedback|on the talk page]].
* The number of available thumbnail size preferences in MediaWiki is being reduced to three standardized options—Small (180px), Regular (250px), and Large (400px), as part of ongoing efforts to improve performance and reduce strain on thumbnail services. As a result, existing preferences will be mapped to the nearest new size (for example, smaller selections like 120px or 150px will render at 180px, while larger ones like 300px or 360px will render at 400px). The preferences interface will soon be updated to reflect these changes, and users who wish to opt out or provide feedback can do so. [https://phabricator.wikimedia.org/T424909]
* From now on, even when a permission expires automatically, users will receive an Echo notification similar to the standard notification for permission changes. There is a difference between this and [[m:Special:MyLanguage/Global reminder bot|Global reminder bot]] in that the latter reminds users a week ''before'' the rights are due to expire, so that they can renew the rights.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the problem where the ULS language selector in [[m:Special:Translate|Special:Translate]] would scroll vertically when it shouldn't, has been resolved. Previously, when users opened the &quot;Translate to English&quot; dropdown and typed certain inputs, the dialog would scroll vertically by a few pixels even when there was enough space to display all results. The dropdown no longer shifts unnecessarily when filtering languages. [https://phabricator.wikimedia.org/T358864] 
* The [[m:Special:GlobalWatchlist|Global Watchlist]], which lets you view your watchlists from multiple wikis on a single page, continues to improve. For example, watchlists for Wikibase sites such as [[:d:|Wikidata]] now support [[mw:Special:MyLanguage/Extension:EntitySchema|EntitySchema]] elements for better tracking. The Live Updates mode now refreshes the special page every 60 seconds to comply with the updated [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|global API rate limits]] for improved real-time responsiveness. Additionally, a directionality bug that displayed links as &quot;changes 3&quot; instead of &quot;3 changes&quot; in mixed-direction lists has been fixed. [https://phabricator.wikimedia.org/T415450][https://phabricator.wikimedia.org/T424422][https://phabricator.wikimedia.org/T418091]
'''Updates for technical contributors'''
* The second phase of [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits|global API rate limits]] has been rolled out to reduce the [[diffblog:2026/03/26/quo-vadis-crawlers-progress-and-whats-next-on-safeguarding-our-infrastructure/|impact of AI crawlers]] and ensure fair, sustainable access to Wikimedia resources, prioritising human and mission-aligned traffic. [[mw:Special:MyLanguage/Wikimedia APIs/Rate limits#Limits|Limits]] have been shifted from per-hour to per-minute, producing smoother traffic patterns and more predictable API load. Community users are not expected to be affected, and no action is required. Early indications show some User-Agent-based requestors are adjusting behaviour, and around 64% of automated API traffic has been identified. Monitoring continues, and Wikimedia Enterprise remains available for commercial support.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.46/wmf.27|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/19|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W19&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:43, 4 May 2026 (UTC)
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== Tech News: 2026-20 ==

&lt;section begin=&quot;technews-2026-W20&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/20|Translations]] are available.

'''Weekly highlight'''
* Community Tech has published [[m:Special:MyLanguage/Community Wishlist/How to write a good wish|new guidance]] explaining how wishes on Community Wishlist are triaged and prioritized. The documentation is intended to help contributors write stronger proposals by clarifying the factors that influence prioritization decisions. Beyond vote counts, the guidance highlights considerations such as potential impact on the community when determining which wishes move forward.

'''Updates for editors'''
* The Reader Growth team is launching an experiment to test a new [[mw:Special:MyLanguage/Readers/Reader_Growth/Share_Card|Share Card feature]] that allows readers to create visually engaging cards from Wikipedia articles or selected article sections and share them online, with each card linking back to the original article to help expand readership and article discovery. The mobile-only A/B test will be available to a portion of readers on Arabic, Chinese, French, Vietnamese, and English Wikipedia to better understand reading and sharing habits, and is scheduled to begin the week of May 18 and run for four weeks.
* The Android and iOS Wikipedia apps recently released the [[mw:Special:MyLanguage/Wikimedia_Apps/Team/25th_Birthday_Reading_Challenge|25-day reading challenge]] into Beta, as part of efforts to drive reader engagement by encouraging users to complete reading milestones. To track their reading streak during the challenge, App users can add a widget featuring Baby Globe to their home screen. The challenge officially begins May 11.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:17}} community-submitted {{PLURAL:17|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue where the global preference for enabling syntax highlighting in wikitext could unexpectedly disable itself after being turned on, has now been fixed. [https://phabricator.wikimedia.org/T425286]

'''Updates for technical contributors'''
* [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The ResourceLoader module &lt;bdi lang=&quot;zxx&quot; dir=&quot;ltr&quot;&gt;&lt;code&gt;&lt;nowiki&gt;mediawiki.ui.input&lt;/nowiki&gt;&lt;/code&gt;&lt;/bdi&gt;, deprecated since [[m:Special:MyLanguage/Tech/News/2023/39|September 2023]], will be removed this week. There is a [[mw:Special:MyLanguage/Codex/Migrating_from_MediaWiki_UI|guide for migrating from MediaWiki UI to Codex]] for any tools that use it. [https://phabricator.wikimedia.org/T420125]
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.47/wmf.2|MediaWiki]]

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/20|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W20&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 19:20, 11 May 2026 (UTC)
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== Tech News: 2026-21 ==

&lt;section begin=&quot;technews-2026-W21&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;
Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2026/21|Translations]] are available.

'''Weekly highlight'''
* The Abstract Wikipedia team has identified five potential pilot wikis to assess their interest in adopting abstract articles on their wikis. The pilots are Malayalam, Bengali, Dagbani, Arabic, and Indonesian Wikipedia. The feedback period will be open until May 22. If your community is interested in becoming a pilot, [[m:Talk:Abstract Wikipedia|let us know on Meta]].

'''Updates for editors'''
* An experiment to show [[mw:Special:MyLanguage/Readers/Reader Experience/Reading lists|Reading Lists]] to logged-out readers on mobile web will launch on May 18 across German, Spanish, Italian, Portuguese, Polish, Dutch, Turkish, and Urdu Wikipedias, and will run for one month. The effort supports broader goals of helping readers save and organize articles for later reading, while encouraging habits that could lead to future Wikipedia contributions.
* To support a bookmark button in the Reading List beta feature, the &quot;Tools &gt; Action&quot; menu has been updated to display icons, including the watch star indicator that helps editors identify temporarily watched articles. The icons now also match those used on mobile, improving consistency across platforms. The change is currently limited to the actions menu and mainly affects editors with privileged user rights. [https://phabricator.wikimedia.org/T426008]
* [[mw:Special:MyLanguage/VisualEditor/Suggestion Mode|Suggestion Mode]] was released as an [[w:en:A/B test|A/B test]] for newcomer editors on the mobile website at [[phab:T421189|~15 Wikipedias]]. The experiment will measure the impact that Suggestion Mode has on the proportion of newcomer mobile web edit sessions that result in constructive (un-reverted) article edits. The experiment will also evaluate the feature's impact on editor retention, and monitor changes in revert and block rates.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] View all {{formatnum:27}} community-submitted {{PLURAL:27|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, an issue in the Wikipedia Android app where images could sometimes fail to load after opening a recommended reading list notification, has now been fixed. [https://phabricator.wikimedia.org/T418231]

'''Updates for technical contributors'''
* The [[mw:Special:MyLanguage/Wikidata Platform|Wikidata Platform team]] has published its [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/Backend Replacement|backend replacement recommendation]] and accompanying [[wikitech:Wikidata Query Service/WDQS Architecture re-design|technical architecture]] for the migration of the Wikidata Query Service (WDQS) away from Blazegraph. Feedback is invited until May 25th 2026, especially on potential gaps and impacts on advanced use cases. Wikidata community members and WDQS users are also encouraged to help identify high-impact tools and workflows that may need attention on [[d:Wikidata:SPARQL query service/WDQS backend update/High-Impact Use Cases|this page]]. Feedback can be shared on the [[d:Wikidata talk:SPARQL query service/WDQS backend update|Migration talk page]] or during the [[d:Special:MyLanguage/Wikidata:Blazegraph Migration Office Hours|next office hour]]. See the [[d:Special:MyLanguage/Wikidata:Wikidata Platform team/Newsletter|WDP team newsletter]] for more details.
* [[File:Reload icon with two arrows.svg|12px|link=|class=skin-invert|Recurrent item]] Detailed code updates later this week: [[mw:MediaWiki 1.47/wmf.3|MediaWiki]]

'''In depth'''

* On English, French, Japanese, and a few other Wikipedias, there was a [[diffblog:2025/09/02/better-detecting-bots-and-replacing-our-captcha/|trial of hCaptcha]], a third-party bot detection service. The trial showed that hCaptcha effectively detects and deters some bad-faith automated activity, on its own and by giving [[w:en:Wikipedia:Village pump (technical)/Archive 225#Introducing SuggestedInvestigations|checkusers and stewards]] signals to look into. Because the results were positive, hCaptcha will be rolled out across all wikis over the next few weeks. [[mw:Special:MyLanguage/Product Safety and Integrity/Anti-abuse signals/hCaptcha|See the hCaptcha project page]] for technical information about the implementation and privacy protections. [[diffblog:2026/05/04/better-detecting-bots-and-replacing-our-captcha-part-2/|Learn more]].
* The latest Community Tech update is now available, with progress across several Community Wishlist initiatives, including Reading Lists expansion from the mobile app to the website, new language support for &quot;Who Wrote That&quot; and the Personal Dashboard, improvements to 3D rendering and Charts, and upcoming work on talk page sorting, audio playback, and editing workflows. The update also shares current priorities, wishlist status trends, and opportunities for community feedback on future focus areas and the Wikimedia Foundation’s 2026–2027 Annual Plan. [[m:Special:MyLanguage/Community Wishlist/Updates#May 13, 2026: Latest updates from the Community Tech team|Read the full newsletter for details]].

'''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&amp;nbsp;• [[m:Special:MyLanguage/Tech/News/2026/21|Translate]]&amp;nbsp;• [[m:Tech|Get help]]&amp;nbsp;• [[m:Talk:Tech/News|Give feedback]]&amp;nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].''
&lt;/div&gt;&lt;section end=&quot;technews-2026-W21&quot;/&gt;

&lt;bdi lang=&quot;en&quot; dir=&quot;ltr&quot;&gt;[[User:MediaWiki message delivery|MediaWiki message delivery]]&lt;/bdi&gt; 20:21, 18 May 2026 (UTC)
&lt;!-- Message sent by User:STei (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&amp;oldid=30539262 --&gt;</text>
      <sha1>0eo70o2o9h2y2f1vbl2vvqhx11ymhab</sha1>
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  </page>
  <page>
    <title>Precision Global Health</title>
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      <text bytes="9138" sha1="85d9jwlzv0re3l6yyltvp8z7pg1yse9" xml:space="preserve">[[File:World Health Organisation building from south.jpg|thumb|Headquarters of the [[w:en:World Health Organization|World Health Organization]] in [[w:en:Geneva|Geneva]], [[w:en:Switzerland|Switzerland]].]]
[[File:Sustainable Development Goal 03GoodHealth.svg|thumb|[[SDG3]]: Good Health and Well-being - Learning Resouce supports the [[SDG-Tagging]] - &lt;ref&gt;UN-Guidelines for Use of SDG logo and the 17 SDG icons (2016/10) - http://www.un.org/sustainabledevelopment/wp-content/uploads/2016/10/UN-Guidelines-for-Use-of-SDG-logo-and-17-icons.October-2016.pdf&lt;/ref&gt;]]
[[File:Sustainable Development Goal 11SustainableCities.svg|thumb|[[SDG11]]: Sustainable Cities and Communities - Learning Resource supports the SDGs - [http://www.un.org/sustainabledevelopment/wp-content/uploads/2016/10/UN-Guidelines-for-Use-of-SDG-logo-and-17-icons.October-2016.pdf UN-Guidelines]&lt;ref&gt;UN-Guidelines for Use of SDG logo and the 17 SDG icons (2016/10) - http://www.un.org/sustainabledevelopment/wp-content/uploads/2016/10/UN-Guidelines-for-Use-of-SDG-logo-and-17-icons.October-2016.pdf&lt;/ref&gt;]]
[[File:Basic Risk Response Cycle.png|thumb|Resource Management for the Response in the Risk Management Cycle]]

'''Precision Global health''' is tailored approach for the [[w:en:health|health]] of populations in the global context of [[w:en:Public_health|Public Health]];&lt;ref&gt;{{cite journal |vauthors=Brown TM, Cueto M, Fee E|title=The World Health Organization and the transition from &quot;international&quot; to &quot;global&quot; public health |journal=Am J Public Health |volume=96 |issue=1 |pages=62–72 |date=January 2006 |pmid=16322464 |pmc=1470434 |doi=10.2105/AJPH.2004.050831 }}&lt;/ref&gt;. Different regions differ in their requirements and constraints for global health measures and therefore global health interventions that work very well in one region might be not as effective in other regions. Potential drivers for the difference in prevalence of diseases and/or mortality are represented by a spatial analysis, that provides granular information which measures have more impact in specific reqions areas in a global comparision. A &quot;precision&quot; approach to global health contributes to the progress towards regional and localized health intervention with regard of the area of study, research and practice. Furthermore e.g. the geographically tailored global health interventions and measures places a priority on improving health and achieving equity in [[w:en:health for all|health for all]] people worldwide.&lt;ref name=Koplan&gt;{{cite journal |vauthors=Koplan JP, Bond TC, Merson MH |title=Towards a common definition of global health |journal=Lancet |volume=373 |issue=9679 |pages=1993–5 |date=June 2009 |pmid=19493564 |doi=10.1016/S0140-6736(09)60332-9 |displayauthors=etal  |citeseerx=10.1.1.610.7968 }}&lt;/ref&gt; Problems that transcend national borders or have a global political and economic impact are often emphasized.&lt;ref&gt;{{cite book | last = Global Health Initiative | title = Why Global Health Matters | publisher = FamiliesUSA | year = 2008 | location = Washington, DC | url = http://www.familiesusa.org/issues/global-health/matters/ | access-date = 2008-06-10 | archive-url = https://web.archive.org/web/20110308223639/http://www.familiesusa.org/issues/global-health/matters/ | archive-date = 2011-03-08 | url-status = dead }}&lt;/ref&gt; Precision global health is about the identification of local and regional requirements and constraints on the global scale and represent these scientific results in a [[Spatial Decision Support System]]. The precision aims to address worldwide health improvement (including mental health) with regional and local measures and a feedback loop into the [[Spatial Decision Support System]], how successful these tailored intervention were. The tailored regional interventions are successful if they repects the national or regional requirements and constraints, reduce regional and global disparities, and create a globally coherent approach for protection against global threats that disregard national borders.&lt;ref&gt;{{cite journal |vauthors=Macfarlane SB, Jacobs M, Kaaya EE|title=In the name of global health: trends in academic institutions |journal=J Public Health Policy |volume=29 |issue=4 |pages=383–401 |date=December 2008 |pmid=19079297 |doi=10.1057/jphp.2008.25 }}&lt;/ref&gt;

== Learning Tasks ==
* '''([[Spatial Decision Support System]])''' Explore the concept of an [[Spatial Decision Support System]] (SDSS) and explain the role of the Geographic Information Systems (GIS) for a Precision Global Health Approach!
* '''([[Precision_agriculture|Precision Agriculture]] and [[One Health]])''' Analyze the concept of precision agriculture and the use of agrochemicals. Analyse the similarities and differences of [[Precision_agriculture|Precision Agriculture]] and precision [[w:en:Global_health|global health]]. If you considere the linkage between 
** Human Health,
** Environmental Health and
**.Animal Health 
: (see [[One Health]]) the both approaches are link by loss of biodiversity, exposure to nephrotoxic chemicals in the environment and to humans. Explore the scientific evidence for these links and suggest some tailored interventions for the regions you live in. How can data be collected to identify regional and local global health requirements and constraints and how can this data be used for tailored regional global health interventions. Consider [[Grand challenges|global challenges]] in the health domain and discuss the local and regional contributions to these global challenges.
* '''([[Resource Management]])''' Analyse the concept of Resource Management and define the need to integrate that concept in Precision Global Health (see also [[Space and Global Health/Software/AccessMod|AccessMod]])
* '''([[Space and Global Health/Space4Health|Benefits of Space for Global Health]])''' Analyse the [https://www.unoosa.org/oosa/en/benefits-of-space/global-health.html benefits of Space for Global Health on the UNOOSA Web site] and analyse the contribution of space technology for precision global health. Discuss the PROs and CONs of Space Technology in the context of global health.

== Global Health and United Nations ==
The predominant agency associated with global health (and international health) is the [[w:en:World Health Organization|World Health Organization]] (WHO). Other important agencies impacting global health include [[w:en:UNICEF|UNICEF]] and [[w:en:World Food Programme|World Food Programme]]. The United Nations system has also played a part with cross-sectoral actions to address global health and its underlying socioeconomic determinants with the declaration of the [[w:en:Millennium Development Goals|Millennium Development Goals]]&lt;ref&gt;{{cite web|url=https://www.un.org/millenniumgoals/ |title=Millennium Development Goals |publisher=United Nations |accessdate=2013-03-15}}&lt;/ref&gt; and the more recent [[w:en:Sustainable Development Goals|Sustainable Development Goals]]. Furthermore United Nations has established a working group for Space and Global Health&lt;ref&gt;UNOOSA - Scientific and Technical Subcommittee (2019) Working Group for Space and Global Health URL: https://www.unoosa.org/oosa/en/ourwork/copuos/stsc/gh/index.html (accessed 2020/02/07)&lt;/ref&gt;.

==External links==
* [https://web.archive.org/web/20131112223610/http://alison.com/mod/resource/view.php?id=7089 Global Health Initiative] – free courses on the world's top diseases
* [http://www.globalhealth.gov/ GlobalHealth.gov] (hosted by U.S. Department of Health &amp; Human Services)
* [https://at6fui.weebly.com Action Team 6 Follow-Up Initiative] - Member State Activity for improvement of Public Health by application of Space Technology.

== See also ==
{{Col list|2|
* [[w:en:Public health|Public Health]]
* [[Spatial Decision Support System]]
* [[Precision Agriculture]]
* [[One Health]]
* [[Grand challenges|Global Challenges]]
* [[w:en:Global mental health|Global mental health]]
* [[w:en:Global Strategy for Women's and Children's Health|Global Strategy for Women's and Children's Health]]
* [[w:en:Health system|Health system]]
* [[w:en:Public health|Public health]]
* [[w:en:Social determinants of health|Social determinants of health]]
* [[w:en:Universal health care|Universal health care]]
* [[w:en:Migrant health|Migrant health]]
* [[w:en:Child health and nutrition in Africa|Child health and nutrition in Africa]]
* [[w:en:CAB Direct (database)#Global Health database|CAB Direct – Global Health database]]
}}

==References==
{{Reflist|30em}}


== Page Information ==
This page was based on the following [https://en.wikipedia.org/wiki/Global%20health Wikipedia source page]:
* [https://en.wikipedia.org/wiki/Global%20health Global health] https://en.wikipedia.org/wiki/Global%20health
* Date: 2/9/2020 - [https://en.wikipedia.org/w/index.php?action=history&amp;title=Global%20health Source History Wikipedia]
* [https://niebert.github.com/Wikipedia2Wikiversity?lang=en&amp;domain=wikipedia&amp;title=Global%20health Wikipedia2Wikiversity-Converter]: https://niebert.github.com/Wikipedia2Wikiversity

[[Category:Global health]]
[[Category:Space Technology]]
[[Category:SDG 3 - Good Health and Well-being]]</text>
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Introduces water’s role as the basis of life and the functions of macromolecules like lipids and proteins.&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-biology College Board: AP Biology]&lt;/ref&gt;

== Objectives and Skills ==
Topics may include:&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-biology College Board: AP Biology]

[https://learro.com/doc/chemistry-periodic-table-for-ap-students/ Chemistry Periodic Table for AP Students]&lt;/ref&gt;
* The structure and chemical properties of water
* The makeup and properties of macromolecules
* The structure of DNA and RNA

==Study Notes==
[[File:3D model hydrogen bonds in water.svg|thumb|right|Shape of H&lt;sub&gt;2&lt;/sub&gt;O]]
;Properties of Water
*Water is '''polar''' because of its shape (104.5 degrees). Oxygen is more negatively charged than the hydrogen, causing oxygen to house all the electrons. This causes a huge imbalance in the charge, causes the '''oxygen to have a partial negative charge''' while the '''hydrogen has a partial positive charge'''. Water is polar also because of the '''polar covalent bond''' and its '''bent shape'''. Water molecules are attracted to ''polar'' molecules but not nonpolar molecules.
*'''Hydrogen bonding''' are the types of bonds where the water links up with other molecules. The molecules within the H&lt;sub&gt;2&lt;/sub&gt;O molecule are covalently bond. The hydrogen atoms in the hydrogen bonds must be linked up with an '''oxygen, nitrogen or flourine''' (FON) atom. 
*'''Capillary Action''' is the reason why we see a small curve (meniscus) in a glass beaker filled with water. In this specific incident, the water molecules are attracted to the polar molecules of the glass. This incident displays the concept of '''adhesion''', where water molecules stick to other [polar] substances (this incident being the glass beaker). 
*'''Surface Tension''' is the tendency for water to go against disturbances to its natural state. The ability for water to keep its shape is demonstrating the principle of '''cohesion'''. In cohesion, the water molecules to stick to other water molecules via hydrogen bonds. Water molecules will be the strongest at the top of the water, this is because of the lack of water molecules upon the surface. Surface tension is what allows water droplets to have its shape and for small items, such as paper clips and water striders, to stay on the surface of the water.
*'''Universal Solvent''' describes the water's ability for anything hydrophilic (or water-loving molecules) to dissolve in the water. Hydrophobic, or water-hating molecules, do not dissolve and they just shrink and unable to react with the water.  
*'''High Specific Heat''' is the water's ability to resist temperature changes and prevent itself from heating or cooling down fast (which explains why the land is colder/hotter than water and vice versa).

==Macromolecules==
*'''Polymer''' - Long molecule of blocks connected by ''covalent'' bonds. They make up the macromolecules (the nucleic acids, carbohydrates, proteins, etc.) except for lipids. 
*'''Monomers''' - Repeating unts of polymers. 
[[File:213 Dehydration Synthesis and Hydrolysis-01.jpg|thumb|left|Overview of dehydration synthesis and hydrolysis ]]
A '''condensation reaction''' is when a monomer covalently bonds with another monomer/polymer. This process may be sped up by an [[Biochemistry/Enzymes|enzyme]]. If a water molecule is lost, it is known as '''dehydration synthesis'''. One monomer provides a hydroxyl group, OH, and the other monomer provides hydrogen, an H. 
[[File:Generic hydrolysis of an ester.png|thumb|right|500px|Hydrolysis being performed in equations form]]
Polymers are broken down by the process of '''hydrolysis''', where the covalent bond between monomers is broken by the addition of a water molecule. The hydrogen from water attaches to one monomer while the OH from water links up with the other monomer. Various arrangements of the 40-50 common monomers + rare ones give to the polymer diversity.
===Carbohydrates===
*'''Basic unit''': Monosaccharide (monomers combined by sugar blocks).
*'''Formula''': Containing CH&lt;sub&gt;2&lt;/sub&gt;O.
*'''Names''': End with &quot;-ose&quot; [mostly]. 
*'''Purpose''': Energy and structures (chitin in arthropods).

'''Carbohydrates''' include sugars and polymers of sugars, including starch, cellulose and glucose. '''Disaccharides''' are sugars made from two monosaccharides, linked together by a ''glycosidic linkage''. '''Polysaccharides''' are polymers built of sugar building blocks combined together through dehydration synthesis. 

All monosaccharides contain at least 3 carbon atoms, a carboxyl group linked to one carbon and hydroxyl group, while simultaneously combined with other carbons. They are organized by the length of their carbon skeleton, carboxyl group's location and the spacial arrangement of hydrogen atoms and hydroxyl groups around the carbon skeleton. 

Monosaccharides with a terminal carboxyl group are '''aldoses''', while ones with a non-terminal carboxyl group are '''ketoses'''. 

Carbohydrates contain ''carbon, hydrogen and oxygen''. 
;Important Carbohydrates
*'''Starch [p] and Glycogen [a]''' Both storage molecules for glucose. Starch is used in plants while Glycogen is used in animals. 
*'''Cellulose''' Found in all plant cells' cell walls.
*'''Chitin''' Serves as a exoskeleton for arthropods and is found in the cell walls of fungi. 
*'''Glucose''' C&lt;sub&gt;6&lt;/sub&gt;H&lt;sub&gt;12&lt;/sub&gt;O&lt;sub&gt;6&lt;/sub&gt; = Major source of energy in plants and animals.

===Lipids===
[[File:Common lipid types.svg|thumb|right|Lipids]]
*'''Basic Unit''': Fats [not polymers]

Lipids are made from fats, which are big molecules combined with small molecules by dehydration synthesis. A typical lipid is a '''glycerol molecule linked to 3 fatty acids'''. '''Fatty acids''' are long carbon skeletons. Fats are the number of double bonds in the hydrocarbon tails. 

In making a fat, every fatty acid molecule is me with a glycerol through dehydration synthesis. An '''ester linkage''' is a bond between a hydroxyl group (-OH) and a carboxyl group. Fats vary in size and locations of their double bonds. 

'''Saturated fasts''' do not have any double bonds and the carbons are saturated by hydrogen atoms. Solid at room temp.

'''Unsaturated fats''' have at least 1 double bond between carbon atoms and are liquid at room temp. 

Fats provide '''energy and make up biological membranes'''.

Lipids contain ''carbon, hydrogen and oxygen''. 
;Important
*'''Phospholipids''' - Major part of cell membrane. Composed of 2 fatty acids and a glycerol molecule. Made up of a hydrophilic head and hydrophobic tail. 
*'''Saturated/unsaturated fats''' - Used for protection.
*'''Steroids and hormones''' - Cholesterol (component of animal cell membrane), Estradiol (female sex hormone), Testosterone (male sex horomone) and Vitamin D (aids in calcium and metabolism).
*'''Cuticle layer in plants''' - Protects plants from drying out.
*'''Wax in ears''' - Protect bacteria from invading the ears
*'''Fats protecting our organs'''

===Proteins===
https://www.google.com/search?q=protein+monomer&amp;tbm=isch&amp;ved=2ahUKEwjdxfzBnfjoAhWqnnIEHTGDBYQQ2-cCegQIABAA&amp;oq=protein+monomer&amp;gs_lcp=CgNpbWcQAzICCAAyAggAMgIIADICCAAyAggAMgIIADICCAAyBggAEAcQHjIECAAQHjIGCAAQBRAeUIueAViSpQFg36YBaABwAHgAgAGBBIgBuguSAQszLjAuMS4wLjEuMZgBAKABAaoBC2d3cy13aXotaW1n&amp;sclient=img&amp;ei=-zmeXp3cI6q9ytMPsYaWoAg&amp;bih=625&amp;biw=1366&amp;safe=strict#imgrc=aoPBynbBCz_XtM

Arguably the most important macromolecule to exist, '''proteins''' create 20 amino acids. Each of the 20 amino acid is made up of a different side chain (R group). They contain ''carbon, oxygen, nitrogen, sulfur and hydrogen''. A protein is made up of an amino group, central carbon atom, a different R group and carboxyl group. 

A protein's basic units are '''amino acids'''. The bond between amino acids are '''peptide bonds''', and thus, a polymer of amino acids are known as a '''polypeptide'''. Amino acids are bound together by '''dehydration reactions'''. 

;Important Proteins
*'''Structural Proteins (support)''' - Webs and cocoons in spiders and insects, such as Kertain in skin appendages like hair and feathers.
*'''Storage proteins (storage of amino acids)''' - Ovalbumin (protein of white egg), amino acid source for embryo, Casein (protein of milk), plants have storage proteins in their seeds. 
*'''Transport proteins (transport of substances)''' - They either circulate throughout the body or they're neclosed in a membrane to regulate movement in or out of the cell. 
*'''Hormonal proteins (signals between cells)''' - Insulin, a hormone, regulates the sugar concentration in blood of vertebrates. Glucagon is produced to maintain glucose levels.
*'''Receptor proteins (recieve a signal and pass it on to the cell)''' - Bound in the cell membrane.
*'''Contractile proteins (responsible for movement)''' - Actin and myosin are responsible for movement in the muscles.
*'''Defensive proteins (protection against diseases)''' - Antibodies. 
*'''Enzyme proteins (accelerate all chemical reactions)''' - Digestive enzymes accelerate hydrolysis for the polymers in food
;Structure
A protein's structure determines its function (shape = function).

All proteins have the same three structures:
*'''Primary structure''' - Determined by amino acid sequence. Changes in this can be caused by mutations (determined by instructions written in a cell's DNA).
*'''Secondary structure''' - Determined by hydrogen bonding between the R-group of the amino acids. There are two kinds of secondary structure: B-plated sheet and alpha helix.
*'''Tertiary structure''' - Additional interactions: Ionic/Hydrogen bonding, covalent bonding between sulfurs (disulfide bridges) and movement of hydrophilic/phobic regions of the protein to be towards/away from water (3-dimensional).
*'''Quaternary structure''' - Protein subunits held by hydrogen bonds. Only in some proteins (two or more polypeptide chains). 

Environmental conditions can lead to a change in protein structure. '''Denatured proteins''' are where the bonds break apart, no longer able to function.

===Nucleic Acids===
https://www.google.com/search?q=nucleic+acid+monomer&amp;safe=strict&amp;hl=en&amp;sxsrf=ALeKk00YEs0chdJNjLRHUjDV56ab8XeX4g:1587427913205&amp;source=lnms&amp;tbm=isch&amp;sa=X&amp;ved=2ahUKEwie4f3mnfjoAhXimHIEHfFIAUgQ_AUoAXoECBUQAw&amp;biw=1366&amp;bih=625#imgrc=EDKaxTbjbirTPM

*DNA
*RNA

'''Nucleic acids''' consist of ''carbon, hydrogen, oxygen, nitrogen and phosphorus''. They store, transmit and help express hereditary information. They contain a phosphate group, 5-carbon sugar, and nitrogenous bases. Nucleotides are connected together by phosphodiester bonds. 
==RNA vs. DNA==
;Differences
*'''[[DNA]]''': Double-stranded, thymine, deoxyribose 
*'''[[RNA]]''': Single-stranded, uracil, ribose.

DNA and RNA work hand in hand to produce proteins in all of the cells. DNA has the original pattern of how to create a protein and transfers that info over to mRNA. mRNA takes that info (code) to a ribosome, which checks to see if the ''right'' amino acids have been brought to produce the protein that it has been ordered to code for. 

DNA is self-replicating (copy of itself), which is necessary for the cell to divide (DNA = molecule of inheritance).

== References ==
{{Reflist}}

{{subpage navbar}}
{{CourseCat}}</text>
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      <comment>Reverted edit by [[Special:Contributions/~2026-29924-07|~2026-29924-07]] ([[User_talk:~2026-29924-07|talk]]) to last version by [[User:Usernames.are.hard.ngl|Usernames.are.hard.ngl]] using [[Wikiversity:Rollback|rollback]]</comment>
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Introduces water’s role as the basis of life and the functions of macromolecules like lipids and proteins.&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-biology College Board: AP Biology]&lt;/ref&gt;

== Objectives and Skills ==
Topics may include:&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-biology College Board: AP Biology]&lt;/ref&gt;
* The structure and chemical properties of water
* The makeup and properties of macromolecules
* The structure of DNA and RNA

==Study Notes==
[[File:3D model hydrogen bonds in water.svg|thumb|right|Shape of H&lt;sub&gt;2&lt;/sub&gt;O]]
;Properties of Water
*Water is '''polar''' because of its shape (104.5 degrees). Oxygen is more negatively charged than the hydrogen, causing oxygen to house all the electrons. This causes a huge imbalance in the charge, causes the '''oxygen to have a partial negative charge''' while the '''hydrogen has a partial positive charge'''. Water is polar also because of the '''polar covalent bond''' and its '''bent shape'''. Water molecules are attracted to ''polar'' molecules but not nonpolar molecules.
*'''Hydrogen bonding''' are the types of bonds where the water links up with other molecules. The molecules within the H&lt;sub&gt;2&lt;/sub&gt;O molecule are covalently bond. The hydrogen atoms in the hydrogen bonds must be linked up with an '''oxygen, nitrogen or flourine''' (FON) atom. 
*'''Capillary Action''' is the reason why we see a small curve (meniscus) in a glass beaker filled with water. In this specific incident, the water molecules are attracted to the polar molecules of the glass. This incident displays the concept of '''adhesion''', where water molecules stick to other [polar] substances (this incident being the glass beaker). 
*'''Surface Tension''' is the tendency for water to go against disturbances to its natural state. The ability for water to keep its shape is demonstrating the principle of '''cohesion'''. In cohesion, the water molecules to stick to other water molecules via hydrogen bonds. Water molecules will be the strongest at the top of the water, this is because of the lack of water molecules upon the surface. Surface tension is what allows water droplets to have its shape and for small items, such as paper clips and water striders, to stay on the surface of the water.
*'''Universal Solvent''' describes the water's ability for anything hydrophilic (or water-loving molecules) to dissolve in the water. Hydrophobic, or water-hating molecules, do not dissolve and they just shrink and unable to react with the water.  
*'''High Specific Heat''' is the water's ability to resist temperature changes and prevent itself from heating or cooling down fast (which explains why the land is colder/hotter than water and vice versa).

==Macromolecules==
*'''Polymer''' - Long molecule of blocks connected by ''covalent'' bonds. They make up the macromolecules (the nucleic acids, carbohydrates, proteins, etc.) except for lipids. 
*'''Monomers''' - Repeating unts of polymers. 
[[File:213 Dehydration Synthesis and Hydrolysis-01.jpg|thumb|left|Overview of dehydration synthesis and hydrolysis ]]
A '''condensation reaction''' is when a monomer covalently bonds with another monomer/polymer. This process may be sped up by an [[Biochemistry/Enzymes|enzyme]]. If a water molecule is lost, it is known as '''dehydration synthesis'''. One monomer provides a hydroxyl group, OH, and the other monomer provides hydrogen, an H. 
[[File:Generic hydrolysis of an ester.png|thumb|right|500px|Hydrolysis being performed in equations form]]
Polymers are broken down by the process of '''hydrolysis''', where the covalent bond between monomers is broken by the addition of a water molecule. The hydrogen from water attaches to one monomer while the OH from water links up with the other monomer. Various arrangements of the 40-50 common monomers + rare ones give to the polymer diversity.
===Carbohydrates===
*'''Basic unit''': Monosaccharide (monomers combined by sugar blocks).
*'''Formula''': Containing CH&lt;sub&gt;2&lt;/sub&gt;O.
*'''Names''': End with &quot;-ose&quot; [mostly]. 
*'''Purpose''': Energy and structures (chitin in arthropods).

'''Carbohydrates''' include sugars and polymers of sugars, including starch, cellulose and glucose. '''Disaccharides''' are sugars made from two monosaccharides, linked together by a ''glycosidic linkage''. '''Polysaccharides''' are polymers built of sugar building blocks combined together through dehydration synthesis. 

All monosaccharides contain at least 3 carbon atoms, a carboxyl group linked to one carbon and hydroxyl group, while simultaneously combined with other carbons. They are organized by the length of their carbon skeleton, carboxyl group's location and the spacial arrangement of hydrogen atoms and hydroxyl groups around the carbon skeleton. 

Monosaccharides with a terminal carboxyl group are '''aldoses''', while ones with a non-terminal carboxyl group are '''ketoses'''. 

Carbohydrates contain ''carbon, hydrogen and oxygen''. 
;Important Carbohydrates
*'''Starch [p] and Glycogen [a]''' Both storage molecules for glucose. Starch is used in plants while Glycogen is used in animals. 
*'''Cellulose''' Found in all plant cells' cell walls.
*'''Chitin''' Serves as a exoskeleton for arthropods and is found in the cell walls of fungi. 
*'''Glucose''' C&lt;sub&gt;6&lt;/sub&gt;H&lt;sub&gt;12&lt;/sub&gt;O&lt;sub&gt;6&lt;/sub&gt; = Major source of energy in plants and animals.

===Lipids===
[[File:Common lipid types.svg|thumb|right|Lipids]]
*'''Basic Unit''': Fats [not polymers]

Lipids are made from fats, which are big molecules combined with small molecules by dehydration synthesis. A typical lipid is a '''glycerol molecule linked to 3 fatty acids'''. '''Fatty acids''' are long carbon skeletons. Fats are the number of double bonds in the hydrocarbon tails. 

In making a fat, every fatty acid molecule is me with a glycerol through dehydration synthesis. An '''ester linkage''' is a bond between a hydroxyl group (-OH) and a carboxyl group. Fats vary in size and locations of their double bonds. 

'''Saturated fasts''' do not have any double bonds and the carbons are saturated by hydrogen atoms. Solid at room temp.

'''Unsaturated fats''' have at least 1 double bond between carbon atoms and are liquid at room temp. 

Fats provide '''energy and make up biological membranes'''.

Lipids contain ''carbon, hydrogen and oxygen''. 
;Important
*'''Phospholipids''' - Major part of cell membrane. Composed of 2 fatty acids and a glycerol molecule. Made up of a hydrophilic head and hydrophobic tail. 
*'''Saturated/unsaturated fats''' - Used for protection.
*'''Steroids and hormones''' - Cholesterol (component of animal cell membrane), Estradiol (female sex hormone), Testosterone (male sex horomone) and Vitamin D (aids in calcium and metabolism).
*'''Cuticle layer in plants''' - Protects plants from drying out.
*'''Wax in ears''' - Protect bacteria from invading the ears
*'''Fats protecting our organs'''

===Proteins===
https://www.google.com/search?q=protein+monomer&amp;tbm=isch&amp;ved=2ahUKEwjdxfzBnfjoAhWqnnIEHTGDBYQQ2-cCegQIABAA&amp;oq=protein+monomer&amp;gs_lcp=CgNpbWcQAzICCAAyAggAMgIIADICCAAyAggAMgIIADICCAAyBggAEAcQHjIECAAQHjIGCAAQBRAeUIueAViSpQFg36YBaABwAHgAgAGBBIgBuguSAQszLjAuMS4wLjEuMZgBAKABAaoBC2d3cy13aXotaW1n&amp;sclient=img&amp;ei=-zmeXp3cI6q9ytMPsYaWoAg&amp;bih=625&amp;biw=1366&amp;safe=strict#imgrc=aoPBynbBCz_XtM

Arguably the most important macromolecule to exist, '''proteins''' create 20 amino acids. Each of the 20 amino acid is made up of a different side chain (R group). They contain ''carbon, oxygen, nitrogen, sulfur and hydrogen''. A protein is made up of an amino group, central carbon atom, a different R group and carboxyl group. 

A protein's basic units are '''amino acids'''. The bond between amino acids are '''peptide bonds''', and thus, a polymer of amino acids are known as a '''polypeptide'''. Amino acids are bound together by '''dehydration reactions'''. 

;Important Proteins
*'''Structural Proteins (support)''' - Webs and cocoons in spiders and insects, such as Kertain in skin appendages like hair and feathers.
*'''Storage proteins (storage of amino acids)''' - Ovalbumin (protein of white egg), amino acid source for embryo, Casein (protein of milk), plants have storage proteins in their seeds. 
*'''Transport proteins (transport of substances)''' - They either circulate throughout the body or they're neclosed in a membrane to regulate movement in or out of the cell. 
*'''Hormonal proteins (signals between cells)''' - Insulin, a hormone, regulates the sugar concentration in blood of vertebrates. Glucagon is produced to maintain glucose levels.
*'''Receptor proteins (recieve a signal and pass it on to the cell)''' - Bound in the cell membrane.
*'''Contractile proteins (responsible for movement)''' - Actin and myosin are responsible for movement in the muscles.
*'''Defensive proteins (protection against diseases)''' - Antibodies. 
*'''Enzyme proteins (accelerate all chemical reactions)''' - Digestive enzymes accelerate hydrolysis for the polymers in food
;Structure
A protein's structure determines its function (shape = function).

All proteins have the same three structures:
*'''Primary structure''' - Determined by amino acid sequence. Changes in this can be caused by mutations (determined by instructions written in a cell's DNA).
*'''Secondary structure''' - Determined by hydrogen bonding between the R-group of the amino acids. There are two kinds of secondary structure: B-plated sheet and alpha helix.
*'''Tertiary structure''' - Additional interactions: Ionic/Hydrogen bonding, covalent bonding between sulfurs (disulfide bridges) and movement of hydrophilic/phobic regions of the protein to be towards/away from water (3-dimensional).
*'''Quaternary structure''' - Protein subunits held by hydrogen bonds. Only in some proteins (two or more polypeptide chains). 

Environmental conditions can lead to a change in protein structure. '''Denatured proteins''' are where the bonds break apart, no longer able to function.

===Nucleic Acids===
https://www.google.com/search?q=nucleic+acid+monomer&amp;safe=strict&amp;hl=en&amp;sxsrf=ALeKk00YEs0chdJNjLRHUjDV56ab8XeX4g:1587427913205&amp;source=lnms&amp;tbm=isch&amp;sa=X&amp;ved=2ahUKEwie4f3mnfjoAhXimHIEHfFIAUgQ_AUoAXoECBUQAw&amp;biw=1366&amp;bih=625#imgrc=EDKaxTbjbirTPM

*DNA
*RNA

'''Nucleic acids''' consist of ''carbon, hydrogen, oxygen, nitrogen and phosphorus''. They store, transmit and help express hereditary information. They contain a phosphate group, 5-carbon sugar, and nitrogenous bases. Nucleotides are connected together by phosphodiester bonds. 
==RNA vs. DNA==
;Differences
*'''[[DNA]]''': Double-stranded, thymine, deoxyribose 
*'''[[RNA]]''': Single-stranded, uracil, ribose.

DNA and RNA work hand in hand to produce proteins in all of the cells. DNA has the original pattern of how to create a protein and transfers that info over to mRNA. mRNA takes that info (code) to a ribosome, which checks to see if the ''right'' amino acids have been brought to produce the protein that it has been ordered to code for. 

DNA is self-replicating (copy of itself), which is necessary for the cell to divide (DNA = molecule of inheritance).

== References ==
{{Reflist}}

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  <page>
    <title>Collaborative enterprising</title>
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      <text bytes="5524" sha1="qos3vo8hq4oiqws87m310jc7olk1yc6" xml:space="preserve">[[File:Sustainable Development Goal 11SustainableCities.svg|thumb|[[SDG11]]: Sustainable Cities and Communities - Learning Resource supports the SDGs - [https://www.un.org/sustainabledevelopment/wp-content/uploads/2019/01/SDG_Guidelines_AUG_2019_Final.pdf UN-Guidelines]&lt;ref&gt;UN-Guidelines for Use of SDG logo and the 17 SDG icons (2019) - https://www.un.org/sustainabledevelopment/wp-content/uploads/2019/01/SDG_Guidelines_AUG_2019_Final.pdf&lt;/ref&gt;]]
Collaborative Enterprising is an approach for independent operating economical units in conjunction with research and development units. The units can be 
* self-employed professionals,
* small and medium business enterprises (SME) or 
* even units in a large company that can operate independently. 

== Learning Tasks ==
* '''(Agile Developement)''' Identify the role of agile and flexible business structure that enables the self-organisation for those units into competitive and sustainable business network. The networks of enterprises must assure that the collaborative works generates a benefit for all enterprises in a mutual accepted way. 
* '''([[COVID-19/Economy|COVID-19 Innovation and Risk Mitigation]])''' Explain how small and medium business enterprise can use collaborative enterprising approach to create innvoation that creates a [[COVID-19/Workflow Transformation|sustainable transformation of workflows]] with a sustainable business model.
* '''(The winner-takes-it-all)''' The winner-takes-it-all strategy must be avoided in the sense that finding solutions in a collaborative way (e.g. collaborative research and development) produces a few successful tries. E.g. 100 different test scenarios are shared among the different SMEs and development units. How successful these scenarios are in a pre-assessment might vary. The outcome is that 1 test scenario with a high risk of failure and 1 test scenario with [[Risk Management|low risk of failure]]. These agile development leads to 98 failures of test scenarios and 2 successes. In a collaborative scenario most of SMEs or self-employed professional or in general collaborativ operating units failed. Nevertheless they supported the problem solving and finding successful test scenarios. Explain why a winner-takes-it-all strategy has negative impact on a sustainable collaboration of collaborative enterprising.
* '''(Benefits of Collaborative Enterprising)''' Explain how a collaborative network of enterprises can be established without the requirement for capital, infrastructure or additional fixed employment? What are your strategies to establish the collaborative effort and how can you assure that others participate from the collaborative effort in fair approach. Assume we can establish this approach with almost zero fixed costs, how would you share the benefit according to the investment of person hours into the collaborative approach. 
* '''([[Open Community Approach]] - OCA)''' If you address this collaborative effort from the angle of the [[Open Community Approach]] and the investment of the development of product that can be used for providing a payed service, then Open Source and Open Content are developed for a mutual use for all involved units working in the collaborative way. This approach is suitable for collaborative enterprising if they are going to provide services to customers, such as consultants, freelancers, coaches,  home based businesses, assistants providing support with [[video conferencing]] infrastructure. For applicaation in an economical context there must be a 
* Pre-OCA phase and 
* an OCA phase of collaborative enterprising.
During the Pre-OCA phase all developements are used just as they would used in a collaborative enterprising approach in the private sector by a network of collaborative operating SMEs or self-employed professional. This covers all the costs of participating units and provides the maximum revenue that must be generated by collaborative enterprising approach. The Pre-OCA phase can take longer due to slower economic success or could have a rapid development due to very good market success. Nevertheless it is recommended that there is maximum time span for the Pre-OCA phase, because the after the Pre-OCA phase the enterpreneural units will work in new networks and they use the product in new collaborative settings. This is important because the SMEs and  must assure, that self-employed professionals like consultants, freelancers, coaches, ... can the use the jointly developed product afterwards without the dependency on the previous collaborative partners. Collaboration might not end in harmony all the time and a well-defined exit strategy has to incorporate also the post &quot;collaborative enterprising&quot; use. 
* '''(Collaborative)''' Compare the approach of [[Collaborative Mapping]] with Collaborative Enterprising. What are similarities and what are the differences between those approaches.
* '''(Swarm Intelligence)''' How is collaborative enterprising linked to [[Swarm Intelligence]] and what are the additional aspects that must be considered in an economical environment.
* '''([[Commercial Data Harvesting]])''' How is [[Commercial Data Harvesting]] related to this concept? Discuss benefits and drawbacks?

== See also ==
* [[Risk Management]]
* [[Risk Literacy]]
* [[Close-to-Homeoffice]]
* [[COVID-19/Economy]]
* [[COVID-19/Workflow Transformation]]
* [[Swarm Intelligence]]
* [[Systems Thinking]]

== References ==

[[Category:Economics]]
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    <title>Social Victorians/People/Sarah Spencer-Churchill Wilson</title>
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      <text bytes="23198" sha1="gkzx5nt4fwq12tvix07m39e0vy18tsb" xml:space="preserve">== Overview ==
== Acquaintances, Friends and Enemies ==
== Organizations ==

=== Lady Sarah Wilson ===
*&quot;[[Social Victorians/People/Working in Publishing#Journalists|aristocratic lady journalist]]&quot;
*Lady Sarah Wilson, journalist for the ''Daily Mail''&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|date=2020-07-06|title=Sarah Wilson (war correspondent)|url=https://en.wikipedia.org/w/index.php?title=Sarah_Wilson_(war_correspondent)&amp;oldid=966295858|journal=Wikipedia|language=en}}&lt;/ref&gt;

=== Gordon Wilson ===
*Gordon Wilson, Royal Horse Guards
*Gordon Wilson, Robert Baden-Powell's aide de camp at Mafeking

=== Wilfred Wilson ===

* 5th Battalion Imperial Yeomanry

== Timeline ==
'''1861''', Sir Samuel Wilson and Jeanne Campbell married.&lt;ref name=&quot;:2&quot;&gt;&quot;Sir Samuel Wilson.&quot; {{Cite book|url=https://books.google.com/books?id=KDw6AQAAMAAJ|title=Armorial Families: A Complete Peerage, Baronetage, and Knightage, and a Directory of Some Gentlemen of Coat-armour, and Being the First Attempt to Show which Arms in Use at the Moment are Borne by Legal Authority|last=Fox-Davies|first=Arthur Charles|date=1895|publisher=Jack|language=en}} 1047, Col. 1a.&lt;/ref&gt;

'''1891 November 21''', Sarah Isabella Augusta Spencer-Churchill and Gordon Chesney Wilson married.&lt;ref&gt;&quot;Lady Sarah Isabella Augusta Spencer-Churchill.&quot; {{Cite web|url=https://www.thepeerage.com/p10633.htm#i106326|title=Person Page|website=www.thepeerage.com|access-date=2020-10-20}}&lt;/ref&gt;

'''1892 June 11''', Adeline Constance Wilson and Right Hon. the Earl of Huntingdon married.&lt;ref name=&quot;:2&quot; /&gt;

'''1897 July 2, Friday''', Lady Sarah Wilson and Captain Gordon Wilson attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House, as did Mr. Wilfred Wilson, Mr. Clarence Wilson, and Mr. Herbert Wilson.
[[File:Madame de Pompadour.jpg|alt=Old painting of a woman in a very ornate dress with an open book|thumb|Madame de Pompadour, 1756, ]]

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
=== Lady Sarah Wilson ===
[[File:Lady-Sarah-Isabella-Augusta-Wilson-ne-Spencer-Churchill-as-Madame-de-Pompadour.jpg|thumb|left|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a dog|Lady Sarah Wilson as Madame de Pompadour. ©National Portrait Gallery, London.]]
At the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]], Lady Sarah Wilson went as Madame de Pompadour.&lt;ref&gt;&quot;Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses.&quot; London ''Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and https://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.&lt;/ref&gt;{{rp|p. 5, Col. 7c}} 

John Thomson's portrait (left) of &quot;Lady Sarah Isabella Augusta Wilson (née Spencer-Churchill) as Madame de Pompadour&quot; in costume is photogravure #157 in the [[Social Victorians/1897 Fancy Dress Ball/Photographs#The Album of Photographs|album]] presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:1&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;Lady Sarah Wilson as Madame de Pompadour.&quot;&lt;ref&gt;&quot;Lady Sarah Wilson as Madame de Pompadour.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158520/Lady-Sarah-Isabella-Augusta-Wilson-ne-Spencer-Churchill-as-Madame-de-Pompadour.&lt;/ref&gt; 

If Lady Sarah Wilson's dress is indeed blue, as the descriptions say, then Thomson's portrait is an excellent example of how difficult it can be to guess the colors of things in black-and-white photographs. Although the album (and the National Portrait Gallery, London) credit Thomson for the photograph, the portrait of Lady Sarah from the album looks more like a painting than a photograph. Perhaps it was retouched to make it look less photographic and more painterly. 

Surprisingly, two portraits of Lady Sarah appear in the Lafayette Archive, suggesting that she also had her photograph taken by the Lafayette firm, perhaps at the ball itself. The Lafayette Archive lists 2 photographs but provides only one: 

* http://lafayette.org.uk/wil1366.html

This image is a higher resolution and more clear, and it is not retouched to appear more like a painted portrait. Not all particulars of her costume are identical in the Lafayette and Thomson portraits. 

Another image of Lady Sarah Wilson in costume appeared in the ''Queen'' (bottom middle of the page, the numeral 17 below the line drawing, seated, facing slightly to her right, the drawing shows a dress similar to her costume in her photograph, bows and ruffles emphasized; the drawing apparently signed by “Rook”).&lt;ref name=&quot;:8&quot;&gt;“Dresses Worn at the Duchess of Devonshire’s Fancy Ball on July 2.” The ''Queen'', The Lady’s Newspaper 10 July 1897, Saturday: 52 [of 98 BNA; p. 78 on printed page], full page [3 of 3 cols.]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18970710/174/0052.&lt;/ref&gt;{{rp|Col. 2b–c}} 

François Boucher's 1756 portrait of Madame de Pompadour (above right) shows Jeanne Antoinette Poisson, Madame de Pompadour at about 35 years old.&lt;ref name=&quot;:7&quot;&gt;{{Cite journal|date=2023-12-13|title=Madame de Pompadour|url=https://en.wikipedia.org/w/index.php?title=Madame_de_Pompadour&amp;oldid=1189755757|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Madame_de_Pompadour.&lt;/ref&gt; Lady Sarah Wilson was nearly 32 years old at the time of the ball. (The color of the dress in this image may not be true to the painting; a different copy shows it looking bluer.&lt;ref&gt;{{Cite journal|date=2023-12-13|title=Madame de Pompadour|url=https://en.wikipedia.org/w/index.php?title=Madame_de_Pompadour&amp;oldid=1189755757|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Madame_de_Pompadour#/media/File:Madame_de_Pompadour.jpg&lt;/ref&gt;) 
[[File:François Boucher - Portrait of Marquise de Pompadour - WGA02909.jpg|thumb|Madame de Pompadour, Boucher, 1759, with Friendship's consolation of Love behind her]]
Another Boucher portrait of Madame de Pompadour (right), painted in 1759 when she was 38,&lt;ref name=&quot;:7&quot; /&gt; shows her in a very similar dress, though pink and yellow rather than blue or blue-green. We can see how the skirt falls when she is standing. 

==== Madame de Pompadour ====
Politically active, Madame de Pompadour was Louis XV's official chief mistress until 1751 and lady in waiting to the Queen, Polish Marie Leszczyńska.&lt;ref name=&quot;:7&quot; /&gt; She was leader of fashionable society until Louis XV's death and Marie Antoinette's rise displaced her.

==== Newspaper Accounts ====
Most of the descriptions of Lady Sarah Wilson's costume were published in fashion rather than news perioodicals, unlike the descriptions of politically important people.
* &quot;(Mme. de Pompadour), blue and magenta, silk, lace, and pink roses; bunch of wild hyacinths, yellow daisies, and pink roses on left shoulder.&quot;&lt;ref name=&quot;:6&quot; /&gt;{{rp|p. 40, Col. 2b}}
* The ''Queen'' has 2 descriptions, this one which is included in the descriptions of the &quot;general company&quot; and the one below, highlighting the dressmaker, Mrs Mason:&lt;blockquote&gt;Lady Sarah Wilson wore a Pompadour costume of rich china-blue satin, the quaint bodice with deep point in front, fastened with old-fashioned bows of vieux-rose silk, graduating in size to the waist; the tight satin sleeves had deep frills of silk, pinked at the edged at the elbow with an inner frill of lace; the dress was trimmed with white blonde lace and pink Banksia roses; the skirt was of blue satin, with very full paniers, and flounced with two frills, edged with blonde lace and pink button roses.&lt;ref&gt;“Dresses Worn at the Duchess of Devonshire’s Fancy Ball on July 2.” The ''Queen'', The Lady’s Newspaper 10 July 1897, Saturday: 50 [of 98 BNA; p. 76 on printed page], full page [3 of 3 cols.]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/BL/0002627/18970710/171/0050.&lt;/ref&gt;{{rp|Col. 2b}}&lt;/blockquote&gt;
* The description accompanying the line drawing in the ''Queen'' says the original was owned by Baron Ferdinand de Rothschild, which means that Boucher's blue-dress portrait (above right) is the original:&lt;blockquote&gt;Made by Mrs Mason, 4, New Burlington Street, W. …   No. 17. L&lt;small&gt;ADY&lt;/small&gt; S&lt;small&gt;ARAH&lt;/small&gt; W&lt;small&gt;ILSON&lt;/small&gt;, Madame de Pompadour (copied from the picture of “La Pompadour” of Baron Ferdinand de Rothschild). — Rich / blue satin, with ruchings of satin and white blonde lace, with wreath of roses; Alençon lace ruffles; headdress, small wreath of roses, with high aigrette.&lt;ref name=&quot;:8&quot; /&gt;{{rp|Col. 2–3c}}&lt;/blockquote&gt;
==== Commentary on Lady Sarah's Costume ====
These descriptions are based on the Thomson portrait published in the commemorative album (above left).
* Lady Sarah is holding her skirt in her left hand oddly, making the layers of the skirt confusing but suggesting that the overskirt has no trim other than what is at the opening.
* The dresses in the Boucher portraits are very similar to each other, but the blue 1856 one is the original for Lady Sarah's dress.&lt;ref&gt;{{Cite web|url=http://lafayette.org.uk/wil1366.html|title=Lady Sarah Wilson at the Devonshire House Ball 1897, by Lafayette|website=lafayette.org.uk|access-date=2026-05-13}}&lt;/ref&gt;
* The skirts in the Boucher portraits are voluminous, unlike the skirt Lady Sarah is wearing, which may be influenced by 1890s style, whose close-fitted skirts had a smooth, bell-shaped flare.&lt;ref&gt;Matthews, Mimi. A Victorian Lady's Guide to Fashion and Beauty. Pen &amp; Sword History, 2018.&lt;/ref&gt;{{rp|73}} She may be wearing paniers (or a bum-roll), but like the skirt they are more modest than what Madame de Pompadour is wearing in the Boucher portraits. Or perhaps the modesty in Lady Sarah's costume means that it was less expensive? Or that she, appropriately, did not want to compete with the opulence of the costume of Daisy, Countess Warwick as Marie Antoinette?
* According to the description, the bows on the bodice — or eschelles — are &quot;graduating in size to the waist,&quot; but in fact they diminish in size.
* In some respects, this costume is an 18th-century design: the graduated bows in the bodice, the multiple layers of ruffled lace in the sleeves, the overskirt and petticoat construction, the v-point below the waist of the bodice, the double-ruffle and flower trim on the skirt and bodice and the piled-up powdered hair with ringlets. The symmetry of the dress is consistent with 18th-century design. The design has 18th-century elements, but the line of the skirt is not 18th or 19th century.
* According to the ''Queen'', the roses on Lady Sarah's dress were Banksia roses, ''Rosa banksiae'', which have more, frillier petals than the long-stemmed roses we're accustomed to seeing, and they grow in clusters on short stems on longer trailing stems.
* As in the Pompadour portraits, Lady Sarah is accompanied by a small dog.
* The large cluster of flowers on her left shoulder breaks the symmetry of the design of her costume.
[[File:Gordon-Chesney-Wilson-as-a-Captain-in-the-Blues-1680.jpg|thumb|alt=Black-and-white photograph of a standing man richly dressed in an historical costume|Gordon Chesney Wilson as a Captain in the Blues, 1680. ©National Portrait Gallery, London.]]

=== Captain Gordon Wilson ===
Most newspapers say Captain Gordon Wilson was in costume as a member of the Royal Horse Guard of John Churchill, 1st Duke of Marlborough (1650–1722&lt;ref&gt;{{Cite journal|date=2023-12-03|title=John Churchill, 1st Duke of Marlborough|url=https://en.wikipedia.org/w/index.php?title=John_Churchill,_1st_Duke_of_Marlborough&amp;oldid=1188192102|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/John_Churchill,_1st_Duke_of_Marlborough.&lt;/ref&gt;). According to the typographical visualization of the quadrilles and processions in the ''Morning Post'', however, Captain Gordon Wilson was one of the Mousquetaires et Militaires de l'Epoque in the Louis XV and Louis XVI Quadrille, along with Sir Samuel Scott.&lt;ref name=&quot;:3&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;{{rp|7, Col. 6b}} But only one newspaper says he was a Mousquetaire.

Lafayette's portrait of &quot;Gordon Chesney Wilson as a Captain in the Blues, 1680&quot; in costume is photogravure #158 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:1&quot; /&gt; The printing on the portrait says, &quot;Captain Gordon Wilson as a Captain in the Blues temp 1680.&quot;&lt;ref&gt;&quot;Captain Gordon Wilson as a Captain in the Blues.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158521/Gordon-Chesney-Wilson-as-a-Captain-in-the-Blues-1680.&lt;/ref&gt;

The Blues were the Royal Regiment of Horse Guards, part of the [[Social Victorians/Terminology#Household Cavalry|Household Cavalry]]: the coat was blue, with red facings, collar and plumes.&lt;ref&gt;{{Cite journal|date=2021-11-11|title=Royal Horse Guards|url=https://en.wikipedia.org/w/index.php?title=Royal_Horse_Guards&amp;oldid=1054735721|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Royal_Horse_Guards.&lt;/ref&gt;

==== Newspaper Descriptions of His Costume ====
*He wore a &quot;Costume of his own regiment at the time of the Duke of Marlborough, blue with red facings, embroidered gold crimson sash, and embroidered baldric, large velvet hat and plumes.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{rp|p. 8, Col. 1c}}
*&quot;Sir Samuel Scott and Captain Gordon Wilson [wore] uniforms of the R.H.G. [Royal Horse Guards] in the great Duke of Marlborough's time.&quot;&lt;ref&gt;“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.&lt;/ref&gt;{{rp|42, Col. 2b}}
*&quot;Captain Gordon Wilson and Sir Samuel Scott (costume of their own regiments at the time of the Duke of Marlborough), blue with red facings; velvet hat and plumes.&quot;&lt;ref name=&quot;:6&quot; /&gt;{{rp|p. 36, Col. 3b}}

==== Commentary on His Costume ====

* Gordon Chesney Wilson seems to have been a member of the [[Social Victorians/Terminology#Royal Horse Guards|Royal Horse Guards]] and wore a 17th-century uniform to the ball.
* This is not the uniform of a captain dressed for battle. Wilson is in court dress. The shoes, for example, are court shoes with a high tongue, a large buckle and bow in the buckle, and possibly red heels. His jabot (neck treatment) is appropriate for court dress of c. 1680, as are his curly wig and the bows on the knee bands of his breeches and at the shoulders. Wilson's shirt has full sleeves that are gathered into lacy ruffles at the wrist and are pulled out over the hands from the cuffs of the jacket.
* Wilson's costume has some Cavalier elements, appropriately, but it is less ornate than non-military outfits would have been.
* The embroidered or appliquéd trim is the same on the cuffs, the front of the jacket and the baldric — a distinctive curled feather shape. The wide decorated cuffs on the jacket were fashionable at the end of the 17th century.

=== Wilfred Wilson ===
Wilfred Wilson was among the Suite of Men in the &quot;Oriental&quot; procession.&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:4&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt; The ''Gentlewoman'' says, &quot;Messrs [[Social Victorians/People/Halifax|Gordon Wood]] and Wilfred Wilson were attendants on [&lt;nowiki/&gt;[[Social Victorians/People/Keppel|George Keppel]]'s] King Solomon,&quot; wearing &quot;green silk tunics elaborately embroidered in gold and studs, with cloaks embroidered and lined with white; jewelled headdresses, swords.&quot;&lt;ref name=&quot;:6&quot; /&gt;{{rp|p. 34, Col. 3a}} No photograph of him in costume can be found at this time.

=== Clarence Wilson ===
Mr. Clarence Wilson, likely Chesney Clarence Wilson?, was dressed as Buffone in the Venetians procession.&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:4&quot; /&gt;

* &quot;Mr. Clarence Wilson (jester), in satin, with gold thread embroidery.&quot;&lt;ref name=&quot;:6&quot;&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032. Print p. 50, Col. 3a.&lt;/ref&gt;{{rp|p. 34, Col. 1b}}

=== Herbert Wilson ===
Mr. Herbert Wilson was dressed as Antonio Priali&lt;ref name=&quot;:3&quot; /&gt; (misspelled as Briali&lt;ref name=&quot;:4&quot; /&gt;&lt;ref&gt;“Ball at Devonshire House.” Evening ''Mail'' 05 July 1897 Monday: 8 [of 8], Col. 1a–4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003187/18970705/070/0008.&lt;/ref&gt;{{rp|p. 8, Col. 1c}}) in the Venetians procession.

* &quot;Mr. Herbert Wilson (Venetian noble), vieux rose brocaded velvet.&quot;&lt;ref name=&quot;:6&quot; /&gt;{{rp|p. 34, Col. 1b}}

=== Wilsons Who Attended by Family ===

==== Lady Sarah and Captain Gordon Wilson Family ====

* Lady Sarah Wilson and Captain Gordon Wilson
* Mr. Wilfred Wilson
* Mr. Clarence Wilson
* Mr. Herbert Wilson

==== [[Social Victorians/People/Arthur Stanley Wilson|Arthur Stanley and Mary Wilson Family]] ====

* Arthur and Mary Wilson
* Clive Wilson
* Tottie (Susannah West) Wilson Menzies and Jack Graham Menzies
* [[Social Victorians/People/Muriel Wilson|Muriel Wilson]]
* Mr. and Mrs. Charles Henry Wilson
* Enid Wilson

==== Unknown Family ====

* Mr. T.W. Wilson

== Demographics ==
*Nationality: she, English&lt;ref name=&quot;:0&quot; /&gt;; he, Australian
*Samuel Wilson, born in Ireland, his wife and many of children born in Australia&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2020-03-15|title=Samuel Wilson (Portsmouth MP)|url=https://en.wikipedia.org/w/index.php?title=Samuel_Wilson_(Portsmouth_MP)&amp;oldid=945720739|journal=Wikipedia|language=en}}&lt;/ref&gt;

=== Residences ===

==== Sir Samuel Wilson ====

* After returning from Australia
* 9 Grosvenor Square, London (March 1895 – 11 June 1895)&lt;ref name=&quot;:2&quot; /&gt;
* Hughenden Manor, High Wycombe, Bucks (1881– September 1893?)&lt;ref name=&quot;:2&quot; /&gt;

== Family ==
=== Gordon Chesney Wilson's Family ===

* Sir Samuel Wilson (7&lt;ref name=&quot;:2&quot; /&gt; or 17&lt;ref name=&quot;:9&quot;&gt;Ancestry.com. ''UK and Ireland, Find a Grave® Index, 1300s-Current'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2012.&lt;/ref&gt; February 1832 – 11 June 1895)&lt;ref name=&quot;:5&quot; /&gt;
* Jeanne Campbell, Lady Wilson (8 May 1841 – 8 February 1925)&lt;ref name=&quot;:9&quot; /&gt;
*# '''Gordon Chesney Wilson''' (1 August 1865 – 6 November 1914)
*# Mary Wilson (c. 1870 –&lt;ref name=&quot;:10&quot;&gt;''Census Returns of England and Wales, 1901''. Kew, Surrey, England: The National Archives, 1901. Class: ''RG13''; Piece: ''82''; Folio: ''199''; Page: ''49''.&lt;/ref&gt; )
*# '''Wilfred Wilson''' (3 March 1872 – February 1901&lt;ref&gt;&quot;Man and Matters.&quot; ''Globe'' 26 February 1901 Tuesday: 3 [of 10], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/19010226/030/0003.&lt;/ref&gt;)
*# '''Clarence Chesney Wilson''' (2 March 1873 – )
*# Bertie (Herbert Hayden) Wilson (4 February 1875 – )
*# Adeline Constance Wilson Lloyd (c. 1867&lt;ref&gt;''Census Returns of England and Wales, 1901''. Kew, Surrey, England: The National Archives, 1901. Class: ''RG13''; Piece: ''82''; Folio: ''198''; Page: ''48''.&lt;/ref&gt;– 24 October 1933&lt;ref&gt;Principal Probate Registry; London, England; ''Calendar of the Grants of Probate and Letters of Administration made in the Probate Registries of the High Court of Justice in England''. Ancestry.com. ''England &amp; Wales, National Probate Calendar (Index of Wills and Administrations), 1858-1995'' [database on-line]. Lehi, UT, USA: Ancestry.com Operations, Inc., 2010.&lt;/ref&gt;)
*# Maud Margaret Wilson (1870&lt;ref name=&quot;:11&quot;&gt;The National Archives of the UK (TNA); Kew, Surrey, England; ''Census Returns of England and Wales, 1891''; Class: ''RG12''; Piece: ''68''; Folio: ''21''; Page: ''38''; GSU roll: ''6095178''.&lt;/ref&gt;– ) [Maud, Countess Huntington?&lt;ref name=&quot;:10&quot; /&gt;]
*# Florence Mabel Wilson ()
*# Herbert H. Wilson (1878&lt;ref name=&quot;:11&quot; /&gt;–) [see Bertie, above]


*Sarah Isabella Augusta [[Social Victorians/People/Marlborough | Spencer-Churchill]] Wilson (4 July 1865 – 22 October 1929)
*Gordon Chesney Wilson (1 August 1865 – 6 November 1914)&lt;ref&gt;&quot;Lt.-Col. Gordon Chesney Wilson.&quot; {{Cite web|url=https://www.thepeerage.com/p10633.htm#i106327|title=Person Page|website=www.thepeerage.com|access-date=2020-10-20}}&lt;/ref&gt;
#Randolph Gordon Wilson (1893–1956)&lt;ref name=&quot;:0&quot; /&gt;

=== Relations ===

* Sarah Isabella Augusta Spencer-Churchill's brothers were [[Social Victorians/People/Churchill|Lord Randolph Churchill]] and Sunny (Charles Richard John) Spencer-Churchill, [[Social Victorians/People/Marlborough|9th Duke of Marlborough]] (9 November 1892 – 30 June 1934).

== Also Known As ==
*Family name: Wilson
*Sarah Isabella Augusta [[Social Victorians/People/Marlborough | Spencer-Churchill]]
*Captain Gordon Wilson, M.V.O.
*Lady Sarah Wilson
*The family of [[Social Victorians/People/Arthur Stanley Wilson|Arthur Stanley Wilson]]

== Questions and Notes ==
#Lady Sarah Wilson is the 11th child and 6th daughter of John Winston Spencer-Churchill, 7th [[Social Victorians/People/Marlborough | Duke of Marlborough]] and Frances Anne Emily Vane Spencer-Churchill, [[Social Victorians/People/Marlborough | Duchess of Marlborough]].
#Lady Sarah Wilson is one of the &quot;aristocratic lady journalists&quot; and was at Mafeking with her husband, Capt. Gordon Wilson.
#Gordon Chesney Wilson died in at the first battle of Ypres, 6ths November 1914.
#For the Samuel Wilson family, any Miss Wilson after 1892 has to have been Florence Mabel Wilson.
#Three somewhat difficult-to-identify men were among the Suite of Men in the &quot;Oriental&quot; procession: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]], Wilfred Wilson, and [[Social Victorians/People/Bourke|Hon. Algernon Bourke]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts; the Hon. Algernon Bourke is not difficult to identify at all; Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#There is a problem with Herbert Hayden Wilson and Herbert H. Wilson's birth dates.
#Captain Gordon Wilson is #96 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who attended]] the[[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House; Lady Sarah Wilson is #392; Wilfred Wilson is #232; Mr. Clarence Wilson is #300; Mr. Herbert Wilson is #307.

== Footnotes ==
{{reflist}}</text>
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  <page>
    <title>AP United States History/1491-1607</title>
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Introduces Native American societies as well as how and why Europeans first explored, and then began to colonize, the Americas.&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-united-states-history College Board: AP United States History]&lt;/ref&gt;

== Objectives and Skills ==
Topics may include:&lt;ref&gt;[https://apstudents.collegeboard.org/courses/ap-united-states-history College Board: AP United States History]&lt;/ref&gt;
* Native American societies before European contact
* European exploration in the New World
* The Columbian Exchange
* Labor, slavery, and caste in the Spanish colonial system
* Cultural interactions between Europeans, Native Americans, and Africans

==Study Notes==
#Bering Strait - people from Siberia crossed this ice bridge to reach warmer climate while it was frozen. as the glaciers melted the people who crossed it could never get back
#Christopher Columbus - skilled Italian seafarer persuaded the Spanish monarchs to outfit him with three tiny but seaworthy ships, manned by a motley crew. Six weeks at sea he discovered land (the Bahamas) on October 6th, 1492. Global economic trade market developed to his finding of the two Americas. Went back in 1493 and found Hispanola, with 17 ships which unloaded 1200 men and horses, cattle, and swine.
#Montezuma - chief of the Aztecs, allowed Hernan Cortes to approach his city of Tenochtitlan, because he believed he was Quetzacoatl, god who returned from the eastern sea. He lived in harmony with Cortes until they needed gold. On June30th, 1520, the Aztecs attack driving the Spanish down the causeways from Tenochtitlan in a frantic, bloody, retreat. Cortes then laid siege to the city and it capitulated on August 13th, 1521. Smallpox also afftected his people and it helped them lose the war. Tenochtitlan was destroyed.
#William Berkeley - governor of Virginia appointed by Charles I, favored no expansion of Virginia; fled his state when Bacon’s Rebellion started but came back when Bacon died. He crushed the servants’ uprising and hung 20 of them.
#Nathaniel Bacon - cousin of William Berkeley, an indentured servant who was moved to the backcountry, led '''Bacon's Rebellion''' - teamed up with poor people, slaves, Natives, to destruction of Jamestown for 3 months in retaliation of disintegrating economy
#Powhatan - native American tribe, dominated Virginia vs. '''Chief Powhatan''' - leader of Indians in James River formed Powhatan Confederacy. Tried keeping peace but was unsuccessful. Fought in first Anglo-Powhatan war and lost but gained a peace treaty; launched a raid on colonists that killed 347; started the second war and lost again; fell victim to three D’s: disease, disorganization and disposability
#population of Americas in 1492 -  54 million people inhabited the 2 continents split into countless tribes over 200 languages and religions, cultures, and ways of life eliminated  90% of its original population by white peoples diseases and guns
#maize - important crop introduced by the natives, the colonists nearly lived off of it
#three-sister agriculture - skillful planting of squash, maize, and beans; produces a favorable relationship - maize provides structures for beans to climb, beans provide nitrogen to soil for other plants, squash spreads around thus preventing weeds
#Iroquois confederacy -  5 Indian tribes : the Mohawks, the Oneidas, the Onondagas, the Cayugas, and the Senecas. Founded by Deganawidah and Hiawatha. Remained independent of one another and banded together to be a force against the Dutch, English and the French. Were nearly wiped out by white mans diseases and muskets. \
#the Crusades - many Spanish ships raided
#Jamestown - first permanent settlement, built by Virginia Company
#Massachusetts Bay - John Winthrop founded it, revived after King Philip's war
#Hernando de Soto - six hundred armored men, undertook a fantastic gold seeking quest during 1539-1542. Going through marshes and pine barrens from Florida westward, he discovered the Mississippi River just north of its junction with Arkansas River. Mistreating the Indians he died of fever and wounds. Troops buried him in Mississippi, lest the Indians exhume and abuse his body
#defeat of Spanish Armada - Philip II of Spain created an invincible armada (ships) for an invasion of England. It happened in 1588 when the ships went into the English Channel. English sea dogs fought back. Using craft that were swifter, more maneuverable, and more ably manned, they inflicted heavy damage on the cumbersome, overladen Spanish ships. Storm arose scattering the Crippled Spanish fleet.

== References ==
{{Reflist}}

{{subpage navbar}}
{{CourseCat}}</text>
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  <page>
    <title>Easy Readers</title>
    <ns>0</ns>
    <id>277562</id>
    <revision>
      <id>2810274</id>
      <parentid>2317909</parentid>
      <timestamp>2026-05-18T22:35:31Z</timestamp>
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      <text bytes="1516" sha1="0eb2wtr2qtrogptprspbcqhfaul92wf" xml:space="preserve">{{Translations|Easy Readers}}

The idea of ''Easy Readers'' is to give you simple stories that you can read in many different languages. Each ''Easy Reader'' will be listed from this page, the level for the reader, the kind of content and which languages it can be read in.

You can add your own in whatever language. Please do write some yourself! Much of the content is being translated by tatoeba volunteers. Please consider contributing translations there!

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Title !! Languages Available !! In progress !! Translate these!  !! Content !! Translate this at Tatoeba
|-
| [[Easy Readers/A1-Cinema|At the cinema]] || [[Easy Readers/A1-Cinema/es|Espanol]], [[Easy Readers/A1-Cinema/eo|Esperanto]] || [[Easy Readers/A1-Cinema/de|Deutsch]], [[Easy Readers/A1-Cinema/ru|русский язык]]|| [[Easy Readers/A1-Cinema/la|Latina]] || Anna meets Ben at the cinema. || [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-A day at school|A day at school]] || NA || || || Camilla talks to David when they arrive at school || [https://tatoeba.org/en/sentences_lists/show/169662?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-At the baker|At the baker]] || NA ||  || || At the baker || [https://tatoeba.org/en/sentences_lists/show/169665?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-Getting the bus|Getting the bus]] || NA ||  || || || 
|}

[[Category:Easy Readers]]</text>
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      <text bytes="1546" sha1="agvyk7g5epbfuaqdxgpmq96g45pxxmx" xml:space="preserve">{{literature}}
{{elementary}}
{{Translations|Easy Readers}}

The idea of ''Easy Readers'' is to give you simple stories that you can read in many different languages. Each ''Easy Reader'' will be listed from this page, the level for the reader, the kind of content and which languages it can be read in.

You can add your own in whatever language. Please do write some yourself! Much of the content is being translated by tatoeba volunteers. Please consider contributing translations there!

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Title !! Languages Available !! In progress !! Translate these!  !! Content !! Translate this at Tatoeba
|-
| [[Easy Readers/A1-Cinema|At the cinema]] || [[Easy Readers/A1-Cinema/es|Espanol]], [[Easy Readers/A1-Cinema/eo|Esperanto]] || [[Easy Readers/A1-Cinema/de|Deutsch]], [[Easy Readers/A1-Cinema/ru|русский язык]]|| [[Easy Readers/A1-Cinema/la|Latina]] || Anna meets Ben at the cinema. || [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-A day at school|A day at school]] || NA || || || Camilla talks to David when they arrive at school || [https://tatoeba.org/en/sentences_lists/show/169662?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-At the baker|At the baker]] || NA ||  || || At the baker || [https://tatoeba.org/en/sentences_lists/show/169665?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-Getting the bus|Getting the bus]] || NA ||  || || || 
|}

[[Category:Easy Readers]]</text>
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        <username>Atcovi</username>
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{{primary}}
{{Translations|Easy Readers}}

The idea of ''Easy Readers'' is to give you simple stories that you can read in many different languages. Each ''Easy Reader'' will be listed from this page, the level for the reader, the kind of content and which languages it can be read in.

You can add your own in whatever language. Please do write some yourself! Much of the content is being translated by tatoeba volunteers. Please consider contributing translations there!

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Title !! Languages Available !! In progress !! Translate these!  !! Content !! Translate this at Tatoeba
|-
| [[Easy Readers/A1-Cinema|At the cinema]] || [[Easy Readers/A1-Cinema/es|Espanol]], [[Easy Readers/A1-Cinema/eo|Esperanto]] || [[Easy Readers/A1-Cinema/de|Deutsch]], [[Easy Readers/A1-Cinema/ru|русский язык]]|| [[Easy Readers/A1-Cinema/la|Latina]] || Anna meets Ben at the cinema. || [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-A day at school|A day at school]] || NA || || || Camilla talks to David when they arrive at school || [https://tatoeba.org/en/sentences_lists/show/169662?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-At the baker|At the baker]] || NA ||  || || At the baker || [https://tatoeba.org/en/sentences_lists/show/169665?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-Getting the bus|Getting the bus]] || NA ||  || || || 
|}

[[Category:Easy Readers]]</text>
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    <revision>
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      <text bytes="1543" sha1="osepz2psa6duzgo94n1octuxkzzjoj3" xml:space="preserve">{{Translations|Easy Readers}}
{{literature}}
{{primary}}

The idea of ''Easy Readers'' is to give you simple stories that you can read in many different languages. Each ''Easy Reader'' will be listed from this page, the level for the reader, the kind of content and which languages it can be read in.

You can add your own in whatever language. Please do write some yourself! Much of the content is being translated by tatoeba volunteers. Please consider contributing translations there!

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Title !! Languages Available !! In progress !! Translate these!  !! Content !! Translate this at Tatoeba
|-
| [[Easy Readers/A1-Cinema|At the cinema]] || [[Easy Readers/A1-Cinema/es|Espanol]], [[Easy Readers/A1-Cinema/eo|Esperanto]] || [[Easy Readers/A1-Cinema/de|Deutsch]], [[Easy Readers/A1-Cinema/ru|русский язык]]|| [[Easy Readers/A1-Cinema/la|Latina]] || Anna meets Ben at the cinema. || [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-A day at school|A day at school]] || NA || || || Camilla talks to David when they arrive at school || [https://tatoeba.org/en/sentences_lists/show/169662?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-At the baker|At the baker]] || NA ||  || || At the baker || [https://tatoeba.org/en/sentences_lists/show/169665?sort=sentence_id&amp;direction=asc Tatoeba list]
|-
| [[Easy Readers/A1-Getting the bus|Getting the bus]] || NA ||  || || || 
|}

[[Category:Easy Readers]]</text>
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  <page>
    <title>Easy Readers/de</title>
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      <text bytes="569" sha1="1if2pyfap8h3smor069f9otc7q6j5nh" xml:space="preserve">{{Translations|Easy Readers}}

Die Idee von ''Easy Readers'' besteht darin, mehrere einfache Geschichten zu schreiben, die Sie in vielen verschiedenen Sprachen lesen können. Jeder ''Easy Reader'' wird von dieser Seite aus aufgelistet, das Niveau für den Leser, die Art des Inhalts und in welchen Sprachen er gelesen werden kann.

{| class=&quot;wikitable&quot;
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|-
! Titel !! Sprachen !! Inhalt
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| [[Easy Readers/Test|Test Reader]] || Example || Example
|-
| Example || Example || Example
|-
| Example || Example || Example
|}

[[Category:Easy Readers]]</text>
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    <title>Easy Readers/A1-Cinema</title>
    <ns>0</ns>
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    <revision>
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      <timestamp>2026-05-18T22:37:40Z</timestamp>
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      <text bytes="818" sha1="h597aeavqvnq75qzmfhyi3bpilx77j8" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

'''''At the Cinema: Anna meets Ben'''''

A: Hello, you look a bit lost. I'm Anna. What's your name?

B: Hi there, I'm Ben.

A: Nice to meet you Ben. So, what is the matter? Why do you look sad and annoyed?

B: I am not doing so well. My friends are not here.

A: Why aren't they here?

B: I don't know. We are going to see a film, but it starts very soon.

A: Maybe they are buying drinks to hide and drink at the back?

B: That is very likely. They always sneak beer into the cinema.

A: I think it is best if you go into the cinema and watch the film. Your friends are probably there already, getting drunk.

'''''View these sentences and translations on [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba].'''''

[[Category:Easy Readers]]</text>
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    <title>Easy Readers/A1-Cinema/de</title>
    <ns>0</ns>
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    <revision>
      <id>2810281</id>
      <parentid>2317419</parentid>
      <timestamp>2026-05-18T22:38:10Z</timestamp>
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      <text bytes="341" sha1="figco4069oc9f5miv8l8iw4w474f9y5" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

'''''Anna trifft im Kino auf Ben'''''

A: Hallo! Du siehst so aus, als hättest du dich verlaufen. Ich bin die Anna. Wie heißt du?

B: Hallo! Ich bin Ben.

A: Schön, dich kennenzulernen, Ben! Was ist denn nun los mit dir? Warum schaust du so traurig und verdrossen drein?

[[Category:Easy Readers]]</text>
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    <title>Easy Readers/A1-Cinema/la</title>
    <ns>0</ns>
    <id>277570</id>
    <revision>
      <id>2810283</id>
      <parentid>2317113</parentid>
      <timestamp>2026-05-18T22:38:27Z</timestamp>
      <contributor>
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      <text bytes="84" sha1="fkcqagvli27793s5ekd1v822nqtyk5c" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

Haec est fabula.

[[Category:Easy Readers]]</text>
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    <ns>0</ns>
    <id>277572</id>
    <revision>
      <id>2810277</id>
      <parentid>2317389</parentid>
      <timestamp>2026-05-18T22:36:51Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810277</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="562" sha1="i9teyb6ztmxot0eg9uax1lmcr3xrx9j" xml:space="preserve">{{Translations|Easy Readers}}

Idea ''Easy Readers'' est multiplex fabulas simplices scribere quae in multis variisque linguis legere potes. Singulae ''Easy Reader'' ex hac pagina recensentur, campus ad lectorem, genus argumenti et quae lingua legi potest.

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Titulus !! Linguae !! Contenta
|-
| [[Easy Readers/Test|Test Reader]] || [[Easy Readers/Test/de|Deutsch]]; [[Easy Readers/Test/la|Latina]]|| Not very much.
|-
| Example || Example || Example
|-
| Example || Example || Example
|}

[[Category:Easy Readers]]</text>
      <sha1>i9teyb6ztmxot0eg9uax1lmcr3xrx9j</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-A day at school</title>
    <ns>0</ns>
    <id>277580</id>
    <revision>
      <id>2810284</id>
      <parentid>2317391</parentid>
      <timestamp>2026-05-18T22:38:47Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810284</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="770" sha1="fc2d1gaivhkywzsvrbwsxyl9p89s7bz" xml:space="preserve">{{Translations|Easy Readers/A1-A day at school}}

'''''At the start of a day at school: Camilla talks to David'''''

C: Hi David, how are you today?

D: Not good, my pen is at home and so is my homework and my textbook.

C: Do you forget everything? How about your head? Did you remember that or is it at home too?

D: Ha ha, very funny. Oh! My mobile phone: I don't know where it is.

C: I can call your phone. Give me a second.

''[ The phone does not ring.''

Your phone is going to voicemail.

D: Oh God, today is going so badly. Why do I lose everything?

C: Because you are forgetful, careless and your Mum doesn't tell you off. I blame your parents.

D: It is all their fault, definitely.

''[ The school bell rings and the day begins''

[[Category:Easy Readers]]</text>
      <sha1>fc2d1gaivhkywzsvrbwsxyl9p89s7bz</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-At the baker</title>
    <ns>0</ns>
    <id>277581</id>
    <revision>
      <id>2810285</id>
      <parentid>2317536</parentid>
      <timestamp>2026-05-18T22:38:58Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810285</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1084" sha1="aotc7z9x12cbq4bvz9m5oaabybxfgzl" xml:space="preserve">{{Translations|Easy Readers/A1-A day at school}}

'''''Edward is at Francisca's Bakery'''''

E: Good morning, it's cold out, isn't it?

F: Yes, very cold for the time of year. What can I get you?

E: Oh, a large brown loaf, please. 

F: I've only got small brow, I'm afraid, or large white. The Russian ryebread is nice.

E: No, my wife says it gets in her teeth, and the kids just leave the crusts everywhere. 

F: Oh well, I don't know then. 

E: Me neither.

F: Maybe they would like some cakes?

E: I'm on a diet, I don't want them eat nice food while I have to watch. The small brown loaf is fine. Give me that.

F: Yes of course. Come earlier tomorrow. That will be two pounds please.

E: Here you go, here is my card. Is contactless ok? I think my card is working.

F: But my machine isn't. 

E: Oh no what a mess.

F: Don't worry, pay me tomorrow. And say hello to your wife when you see her. 

E: Yes of course. And thank you, that is really very helpful of you indeed. 

F: Bye now and take care.

E: Bye, see you in the morning, bright and early.

[[Category:Easy Readers]]</text>
      <sha1>aotc7z9x12cbq4bvz9m5oaabybxfgzl</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-Getting the bus</title>
    <ns>0</ns>
    <id>277584</id>
    <revision>
      <id>2810286</id>
      <parentid>2319194</parentid>
      <timestamp>2026-05-18T22:39:07Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810286</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="553" sha1="87iicq1x8mjwvadj5ncse2fp727qzfg" xml:space="preserve">{{Translations|Easy Readers/A1-Getting the bus}}

'''''Getting the bus: Gerald takes Helen's Bus to the town centre'''''

[''The bus stops at the bus stop. The door opens and Gerald gets onto the bus.''

[''Helen is driving the bus.''

G: Do you go into town?

H: Yes of course. Tap there with your card or phone.

G: Do you take cash?

H: No, we don't. Cards only.

G: OK. How much is it?

H: One pound fifty. Cheaper than Uber. And better conversation.

[''Graham sits down at the back. Two school children are sat nearby.''

[[Category:Easy Readers]]</text>
      <sha1>87iicq1x8mjwvadj5ncse2fp727qzfg</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-Cinema/es</title>
    <ns>0</ns>
    <id>277594</id>
    <revision>
      <id>2810279</id>
      <parentid>2317439</parentid>
      <timestamp>2026-05-18T22:37:50Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810279</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="867" sha1="bgdvqkzoqhkpu57la7zw9ox36l7l4dw" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

'''''En el cine, Anna conoce a Ben'''''

A: Hola, pareces un poco perdido. Yo soy Anna. ¿Cómo te llamas?

B: Qué tal, yo soy Ben

A: Encantada, Ben. Bueno, ¿qué pasa? ¿Por qué pareces triste y molesto?

B: No me va bien. Mis amigos no están aquí. 

A: ¿Por qué no están aquí?

B: No lo sé. Vamos a ver una película pero empieza dentro de un momento.

A: ¿Quizá estén comprando bebidas para bebérselas a escondidas en la parte de atrás?

B: Es muy probable. Siempre cuelan cerveza en el cine.

A: Creo que es mejor que entres en el cine a ver la película. Probablemente tus amigos ya estén dentro emborrachándose.

'''''Traducción: [https://tatoeba.org/en/user/profile/Seael Seael], [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba].'''''

[[Category:Easy Readers]]</text>
      <sha1>bgdvqkzoqhkpu57la7zw9ox36l7l4dw</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/es</title>
    <ns>0</ns>
    <id>277596</id>
    <revision>
      <id>2810276</id>
      <parentid>2317390</parentid>
      <timestamp>2026-05-18T22:36:41Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810276</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="820" sha1="oxknofotrpw02pik3c98v1vvq174r4u" xml:space="preserve">{{Translations|Easy Readers}}

La idea de ''Easy Readers'' es brindarle historias simples que pueda leer en muchos idiomas diferentes. Cada ''Easy Reader'' se enumerará en esta página, el nivel para el lector, el tipo de contenido y en qué idiomas se puede leer.

{| class=&quot;wikitable&quot;
|+ Easy Readers for A1
|-
! Título !! Idiomas !! Contenido
|-
| [[Easy Readers/A1-Cinema/es|En el cine]] || [[Easy Readers/A1-Cinema/de|Deutsch]];  [[Easy Readers/A1-Cinema/es|Espanol]] [[Easy Readers/A1-Cinema/la|Latina]]|| En el cine, Anna conoce a Ben.
|-
| [[Easy Readers/A1-A day at school|A day at school]] || NA || Camilla habla con David cuando llegan a la escuela.
|-
| [[Easy Readers/A1-At the baker|At the baker]] || NA || 
|-
| [[Easy Readers/A1-Getting the bus|Getting the bus]] || NA || 
|}

[[Category:Easy Readers]]</text>
      <sha1>oxknofotrpw02pik3c98v1vvq174r4u</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-Cinema/eo</title>
    <ns>0</ns>
    <id>277599</id>
    <revision>
      <id>2810280</id>
      <parentid>2317440</parentid>
      <timestamp>2026-05-18T22:38:00Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810280</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="918" sha1="akmj326pg14gollfzbfiwjxmaqtf7ai" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

'''''Ĉe la kinejo: Anjo renkontas Beĉjon'''''

A: Saluton, vi ŝajnas iom vojerarinta. Mi estas Anjo. Kio estas via nomo? 

B: Saluton, mi estas Beĉjo. 

A: Mi ĝojas renkonti vin, Beĉjo. Do, kio estas la problemo? Kial vi aspektas malfeliĉa kaj ĝenita? 

B: Mi ne fartas tre bone. Miaj amikoj ne estas ĉi tie. 

A: Kial ili ne ĉeestas? 

B: Mi ne scias. Ni vidos filmon sed ĝi komenciĝos tre baldaŭ. 

A: Eble ili aĉetas drinkaĵojn por kaŝi kaj trinki malantaŭe? 

B: Tio estas tre verŝajna. Ili ĉiam ŝtelprenas bieron en la kinejon. 

A: Laŭ mi estas plej bone ke vi iru en la kinejon kaj spektu la filmon. Viaj amikoj verŝajne jam estas tie, ebriiĝante. 

'''''Traducción: [https://tatoeba.org/en/user/profile/Shekitten Shekitten], [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba].'''''

[[Category:Easy Readers]]</text>
      <sha1>akmj326pg14gollfzbfiwjxmaqtf7ai</sha1>
    </revision>
  </page>
  <page>
    <title>Easy Readers/A1-Cinema/ru</title>
    <ns>0</ns>
    <id>277649</id>
    <revision>
      <id>2810282</id>
      <parentid>2317908</parentid>
      <timestamp>2026-05-18T22:38:17Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810282</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1182" sha1="jt2qkonrkje7xo9bgv7dncap8by3dix" xml:space="preserve">{{Translations|Easy Readers/A1-Cinema}}

'''''В кинотеатре Анна встречает Бена.'''''

A: Привет, ты выглядишь немного потерянным. Я Анна. Как тебя зовут?

Б: Привет, я Бен.

A: Приятно познакомиться, Бен. А в чём же дело? Почему ты такой грустный и сердитый?

Б: У меня дела идут неважно. Здесь нет моих друзей.

A: Почему их нет?

Б: Не знаю. Мы собирались фильм посмотреть, а он уже вот-вот начнётся.

A: Maybe they are buying drinks to hide and drink at the back?

Б: That is very likely. They always sneak beer into the cinema.

A: Думаю, будет лучше, если ты зайдёшь в кинотеатр и будешь фильм смотреть. Твои друзья, наверно, уже там сидят и напиваются.

'''''View these sentences and translations on [https://tatoeba.org/en/sentences_lists/show/169660?sort=created&amp;direction=asc Tatoeba].'''''

[[Category:Easy Readers]]</text>
      <sha1>jt2qkonrkje7xo9bgv7dncap8by3dix</sha1>
    </revision>
  </page>
  <page>
    <title>Liquidity Trap</title>
    <ns>0</ns>
    <id>283903</id>
    <revision>
      <id>2810142</id>
      <parentid>2478484</parentid>
      <timestamp>2026-05-18T19:00:16Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>cat(s)</comment>
      <origin>2810142</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6646" sha1="iv3cedww2zwnemu7ajvm9if5266nkqt" xml:space="preserve">Liquidity Trap is an economic state where interest rates are low and savings rates are high, which renders monetary policies to be ineffective. A gloomy economic outlook causes consumers to be hesitant in purchasing bonds or assets that have a higher yield than cash. Beyond investments, the period includes an overall decrease in economic activity; the decrease in consumption leads to less business hirings and unemployment. 

=== Public Notion ===
The negative outlook for the economy is shared between individuals and firms. Even when interests are low and investing would mean greater profits, individual investors are hesitant to purchase bonds because of the belief of a potential drop in bond prices ([https://www.investopedia.com/ask/answers/061715/how-bond-yield-affected-monetary-policy.asp#:~:text=A%20bond's%20yield%20is%20based,and%20bond%20yields%20to%20rise. from an anticipated rise in interest rates in the future, which lowers bond prices]), and firms are hesitant because they expect a further decrease in consumer demand. Both parties are not compelled to invest by the gloomy economic outlook; the preference to hold cash and fear to invest further diminishes economic activity and perpetuates deflation.  

=== Monetary Policy ===
In a period of low inflation, the common approach for the government or the central bank would be to increase the money supply, which would decrease interest rates. Following that, the general expectation is a rise in investments. However, during a liquidity trap, interest rates are already low (close to 0) so shifting the money supply will no longer have an impact on interest rates or induce economic activity; during periods of low interest rates, the decision of holding cash or investing money become perfectly elastic.  

=== Fiscal Approach ===
There have been various approaches, both in theory and in practice, that aim to tackle the liquidity trap throughout history. Classic Keynesian Economics believe in the adoption of fiscal policies to jumpstart economic activity while Japan adopted methods such as quantitative easing and inflation targeting.  

==== Expansionary Fiscal Policy ====
Keynesian economics, proposed by [[wikipedia:John_Maynard_Keynes|John Maynard Keynes]], suggests that expansionary fiscal policies have the effect of activating private spending. Increased government spending is a  expansionary fiscal policy that aims to increase aggregate demand. This typically includes increasing government borrowing and selling bonds to the private sector. Keynes believes this approach to be effective to stimulate economic activity. Additionally, as the demand for employment rises (from the multiplier effect from increased aggregate demand), unemployment will drop down. It is important to underline the importance of proper execution of this measure. When its country encountered the liquidity trap, the Japanese government allocated money to inefficient public works and business going under, resulting in wasted money.  

Decrease in income tax is another fiscal approach. This might contain a higher risk than increasing government spending. The aim of decreasing income tax is to increase disposable income in the private sector, thereby potentially stimulating more spending and investments. However, during a liquidity trap, if agents continue to possess a negative economic outlook, an increase in disposable income may not directly lead to an increase in their willingness to spend. 

=== Escaping Liquidity Trap ===
Looking at Japan in the last two decades of the 20th century (commonly referred to as the &quot;[[wikipedia:Lost_Decades|Lost Decades]]&quot;), we can see the impact within the Japanese economic bubble. Following the appreciation of the Japanese Yen, the Japanese government decided to compensate that through implementing a sharp expansionary monetary policy and advocated its banks to loan more to the private sector. The policy aimed to increase consumption and included a 50% decrease in interest rates. With the lowered interest rates and greater disposable income, the population was able to be involved in real-estate investment. Higher asset demand increased prices as well as collateral value, which caused greater price stimulation. On the other hand, a foul corporate accounting system, Zaitech, that allowed capital gains to be counted as profits accounted for the inflation of the stock market. Higher stock prices meant companies had higher valuations, which increased their power to borrow more money to fuel the bubble. It was too late when the government sensed the negative impacts of this inflation and decided to increase interest rates. The bubble bursted, leaving the majority of corporate Japan in debt. Banks lost monetary power because of the high volume lending, becoming &quot;zombie&quot; banks. 

To escape this low-growth period, Japanese academics proposed inflation targeting to manage expectations and increase economic activity, which will in turn decrease real interest rates. The idea was proposed to the BOJ on multiple accounts but was never put in motion. Some skepticism included: interest rates were already at zero-bound, so there were no traditional instruments in place to further lower interest rates; adopting inflation targeting during deflation to stimulate economic growth was unprecedented; economists at the BOJ believed that deflation caused by supply-side shocks may be desired since it showed technological innovation and lower prices; it was difficult to identify an acceptable range of price stability because of the economy's deflationary state, thus expected inflation was unidentifiable; inflation targeting will not achieve its goal in managing expectation because of the low credibility of banks during the time, low expectation of growth was said to remain.  

Instead, the BOJ settled on the Zero Interest Rate Policy (ZIRP). ZIRP was in play during two periods of time from 1999 to 2003. The aim of the first period was to eliminate Japan's further deflationary concerns, and the second was to ensure inflation returns to or rises above zero level. 

Quantitative easing was also adopted by the BOJ as a more aggressive policy during the early 2000s. The BOJ increased its purchase in asset-backed securities, long-term government bonds and equities to supply commercial banks with large excess reserves, which will allow larger amounts of private lending. Quantitative easing has been deemed an effective measure when short-term interests are near zero level as countries like the US, UK and ones in the EU implemented the measure after the 2008 financial crisis.

[[Category:Macroeconomics]]</text>
      <sha1>iv3cedww2zwnemu7ajvm9if5266nkqt</sha1>
    </revision>
  </page>
  <page>
    <title>Module:Userbox</title>
    <ns>828</ns>
    <id>283979</id>
    <revision>
      <id>2810263</id>
      <parentid>2615085</parentid>
      <timestamp>2026-05-18T22:02:44Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <comment>Importing from English Wikipedia.</comment>
      <origin>2810263</origin>
      <model>Scribunto</model>
      <format>text/plain</format>
      <text bytes="16370" sha1="310mo9tctsu9310xhk46tk6d7jx8wl9" xml:space="preserve">-- This module implements {{userbox}}.

local categoryHandler = require('Module:Category handler').main

local p = {}

--------------------------------------------------------------------------------
-- Helper functions
--------------------------------------------------------------------------------

local function checkNum(val, default)
	-- Checks whether a value is a number greater than or equal to zero. If so,
	-- returns it as a number. If not, returns a default value.
	val = tonumber(val)
	if val and val &gt;= 0 then
		return val
	else
		return default
	end
end

local function addSuffix(num, suffix)
	-- Turns a number into a string and adds a suffix.
	if num then
		return tostring(num) .. suffix
	else
		return nil
	end
end

local function checkNumAndAddSuffix(num, default, suffix)
	-- Checks a value with checkNum and adds a suffix.
	num = checkNum(num, default)
	return addSuffix(num, suffix)
end

local function makeCat(cat, sort)
	-- Makes a category link.
	if sort then
		return mw.ustring.format('[[Category:%s|%s]]', cat, sort)
	else
		return mw.ustring.format('[[Category:%s]]', cat)
	end
end

--------------------------------------------------------------------------------
-- Argument processing
--------------------------------------------------------------------------------

local function makeInvokeFunc(funcName)
	return function (frame)
		local origArgs = require('Module:Arguments').getArgs(frame)
		local args = {}
		for k, v in pairs(origArgs) do
			args[k] = v
		end
		return p.main(funcName, args)
	end
end

p.userbox = makeInvokeFunc('_userbox')
p['userbox-2'] = makeInvokeFunc('_userbox-2')
p['userbox-r'] = makeInvokeFunc('_userbox-r')

--------------------------------------------------------------------------------
-- Main functions
--------------------------------------------------------------------------------

function p.main(funcName, args)
	local userboxData = p[funcName](args)
	local userbox = p.render(userboxData)
	local cats = p.categories(args)
	return userbox .. (cats or '')
end

function p._userbox(args)
	-- Does argument processing for {{userbox}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-width'] or args['border-s'], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-color'] or args['border-c'] or args[1] or args['id-c']
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-background'] or args[2] or args['info-c']

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-size'] or args['info-s'], nil, 'pt')
	data.infoHeight = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.infoPadding = args['info-padding'] or args['info-p']
	data.infoLineHeight = args['info-line-height'] or args['info-lh']
	data.infoColor = args['info-color'] or args['info-fc']
	data.infoOtherParams = args['info-other-param'] or args['info-op']
	data.infoClass = args['info-class']

	-- Get id values.
	local id = args.logo or args[3] or args.id
	data.id = id
	data.showId = id and true or false
	data.idWidth = checkNumAndAddSuffix(args['logo-width'] or args['id-w'], nil, 'px')
	data.idHeight = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.idBackgroundColor = args['logo-background'] or args[1] or args['id-c']
	data.idTextAlign = args['id-a']
	data.idFontSize = checkNum(args['logo-size'] or args[5] or args['id-s'], nil)
	data.idColor = args['logo-color'] or args['id-fc'] or data.infoColor
	data.idPadding = args['logo-padding'] or args['id-p']
	data.idLineHeight = args['logo-line-height'] or args['id-lh']
	data.idOtherParams = args['logo-other-param'] or args['id-op']
	data.idClass = args['id-class']

	return data
end

p['_userbox-2'] = function (args)
	-- Does argument processing for {{userbox-2}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-s'] or args[9], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-c'] or args[6] or args['id1-c'] or args[1]
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-c'] or args[2]

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-s'], nil, 'pt')
	data.infoColor = args['info-fc'] or args[8]
	data.infoPadding = args['info-p']
	data.infoLineHeight = args['info-lh']
	data.infoOtherParams = args['info-op']

	-- Get id values.
	data.showId = true
	data.id = args.logo or args[3] or args.id1 or 'id1'
	data.idWidth = checkNumAndAddSuffix(args['id1-w'], nil, 'px')
	data.idHeight = checkNumAndAddSuffix(args['id-h'], nil, 'px')
	data.idBackgroundColor = args['id1-c'] or args[1]
	data.idTextAlign = args['id-a']
	data.idFontSize = checkNum(args['id1-s'], nil)
	data.idLineHeight = args['id1-lh']
	data.idColor = args['id1-fc'] or data.infoColor
	data.idPadding = args['id1-p']
	data.idOtherParams = args['id1-op']

	-- Get id2 values.
	data.showId2 = true
	data.id2 = args.logo or args[5] or args.id2 or 'id2'
	data.id2Width = checkNumAndAddSuffix(args['id2-w'], nil, 'px')
	data.id2Height = data.idHeight
	data.id2BackgroundColor = args['id2-c'] or args[7] or args[1]
	data.id2TextAlign = nil -- Always center, but don't set if no content
	data.id2FontSize = checkNum(args['id2-s'], nil)
	data.id2LineHeight = args['id2-lh']
	data.id2Color = args['id2-fc'] or data.infoColor
	data.id2Padding = args['id2-p']
	data.id2OtherParams = args['id2-op']

	return data
end

p['_userbox-r'] = function (args)
	-- Does argument processing for {{userbox-r}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-width'] or args['border-s'], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-color'] or args['border-c'] or args[1] or args['id-c']
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-background'] or args[2] or args['info-c']

	-- Get id values.
	data.showId = false -- We only show id2 in userbox-r.

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-align'] or args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-size'] or args['info-s'], nil, 'pt')
	data.infoPadding = args['info-padding'] or args['info-p']
	data.infoLineHeight = args['info-line-height'] or args['info-lh']
	data.infoColor = args['info-color'] or args['info-fc']
	data.infoOtherParams = args['info-other-param'] or args['info-op']

	-- Get id2 values.
	data.showId2 = true  -- userbox-r always shows the ID cell (as id2)
	data.id2 = args.logo or args[3] or args.id or 'id'
	data.id2Width = checkNumAndAddSuffix(args['logo-width'] or args['id-w'], nil, 'px')
	data.id2Height = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.id2BackgroundColor = args['logo-background'] or args[1] or args['id-c']
	data.id2TextAlign = args['id-a']
	data.id2FontSize = checkNum(args['logo-size'] or args[5] or args['id-s'], nil)
	data.id2Color = args['logo-color'] or args['id-fc'] or data.infoColor
	data.id2Padding = args['logo-padding'] or args['id-p']
	data.id2LineHeight = args['logo-line-height'] or args['id-lh']
	data.id2OtherParams = args['logo-other-param'] or args['id-op']

	return data
end

function p.render(data)
	-- Renders the userbox html using the content of the data table.
	-- Add TemplateStyles
	local templateStyles = mw.getCurrentFrame():extensionTag{
		name = 'templatestyles', args = { src = 'Template:Userbox/styles.css' }
	}

	-- Render the div tag html.
	local root = mw.html.create('div')
	root:addClass('wikipediauserbox')

	-- Only add CSS properties if they have values
	if data.float then root:css('float', data.float) end
	if data.borderWidth then 
		root:css('border-width', data.borderWidth)
	end
	if data.borderColor then 
		root:css('border-color', data.borderColor)
		-- Set border style if we have a color but potentially no width set
		if not data.borderWidth then
			root:css('border-width', '1px')  -- default border width
		end
		root:css('border-style', 'solid')
	end
	if data.width then root:css('width', data.width) end
	if data.bodyClass then root:addClass(data.bodyClass) end

	-- Render the table tag html.
	local tableroot = root:tag('table')
	tableroot:attr('role', 'presentation')

	-- Only add CSS if values exist
	if data.width then tableroot:css('width', data.width) end
	if data.backgroundColor then tableroot:css('background', data.backgroundColor):css('color', 'inherit') end

	local tablerow = tableroot:tag('tr')

	-- Create cells based on what should actually be shown
	if data.showId == false then
		-- userbox-r: info cell first, then id2 cell (if showId2 is true)
		local infoCell = tablerow:tag('td')
		infoCell:addClass('userbox-info')
		if data.infoTextAlign then infoCell:css('text-align', data.infoTextAlign) end
		if data.infoFontSize then infoCell:css('font-size', data.infoFontSize) end
		if data.infoPadding then infoCell:css('padding', data.infoPadding) end
		if data.infoHeight then infoCell:css('height', data.infoHeight) end
		if data.infoLineHeight then infoCell:css('line-height', data.infoLineHeight) end
		if data.infoColor then infoCell:css('color', data.infoColor) end
		if data.infoOtherParams then infoCell:cssText(data.infoOtherParams) end
		if data.infoClass then infoCell:addClass(data.infoClass) end
		if data.info then infoCell:wikitext(data.info) end
		
		-- Create id2 cell only if showId2 is true
		if data.showId2 then
			local id2Cell = tablerow:tag('td')
			id2Cell:addClass('userbox-id2')
			if data.id2Width then id2Cell:css('width', data.id2Width) end
			if data.id2Height then id2Cell:css('height', data.id2Height) end
			if data.id2BackgroundColor then id2Cell:css('background', data.id2BackgroundColor) end
			if data.id2TextAlign then id2Cell:css('text-align', data.id2TextAlign) end
			if data.id2FontSize then id2Cell:css('font-size', data.id2FontSize .. 'pt') end
			if data.id2Color then id2Cell:css('color', data.id2Color) else id2Cell:css('color', 'inherit') end
			if data.id2Padding then id2Cell:css('padding', data.id2Padding) end
			if data.id2LineHeight then id2Cell:css('line-height', data.id2LineHeight) end
			if data.id2OtherParams then id2Cell:cssText(data.id2OtherParams) end
			if data.id2 then id2Cell:wikitext(data.id2) end
		end
	else
		-- userbox and userbox-2: create id cell only if showId is true
		if data.showId then
			local idCell = tablerow:tag('td')
			idCell:addClass('userbox-id')
			if data.idWidth then idCell:css('width', data.idWidth) end
			if data.idHeight then idCell:css('height', data.idHeight) end
			if data.idBackgroundColor then idCell:css('background', data.idBackgroundColor) end
			if data.idTextAlign then idCell:css('text-align', data.idTextAlign) end
			if data.idFontSize then idCell:css('font-size', data.idFontSize .. 'pt') end
			if data.idColor then idCell:css('color', data.idColor) else idCell:css('color', 'inherit') end
			if data.idPadding then idCell:css('padding', data.idPadding) end
			if data.idLineHeight then idCell:css('line-height', data.idLineHeight) end
			if data.idOtherParams then idCell:cssText(data.idOtherParams) end
			if data.idClass then idCell:addClass(data.idClass) end
			if data.id then idCell:wikitext(data.id) end
		end
		
		-- Always create info cell for userbox and userbox-2
		local infoCell = tablerow:tag('td')
		infoCell:addClass('userbox-info')
		if data.infoTextAlign then infoCell:css('text-align', data.infoTextAlign) end
		if data.infoFontSize then infoCell:css('font-size', data.infoFontSize) end
		if data.infoPadding then infoCell:css('padding', data.infoPadding) end
		if data.infoHeight then infoCell:css('height', data.infoHeight) end
		if data.infoLineHeight then infoCell:css('line-height', data.infoLineHeight) end
		if data.infoColor then infoCell:css('color', data.infoColor) end
		if data.infoOtherParams then infoCell:cssText(data.infoOtherParams) end
		if data.infoClass then infoCell:addClass(data.infoClass) end
		if data.info then infoCell:wikitext(data.info) end
		
		-- Create id2 cell only for userbox-2 and only if showId2 is true
		if data.showId2 then
			local id2Cell = tablerow:tag('td')
			id2Cell:addClass('userbox-id2')
			if data.id2Width then id2Cell:css('width', data.id2Width) end
			if data.id2Height then id2Cell:css('height', data.id2Height) end
			if data.id2BackgroundColor then id2Cell:css('background', data.id2BackgroundColor) end
			if data.id2TextAlign then id2Cell:css('text-align', data.id2TextAlign) end
			if data.id2FontSize then id2Cell:css('font-size', data.id2FontSize .. 'pt') end
			if data.id2Color then id2Cell:css('color', data.id2Color) else id2Cell:css('color', 'inherit') end
			if data.id2Padding then id2Cell:css('padding', data.id2Padding) end
			if data.id2LineHeight then id2Cell:css('line-height', data.id2LineHeight) end
			if data.id2OtherParams then id2Cell:cssText(data.id2OtherParams) end
			if data.id2 then id2Cell:wikitext(data.id2) end
		end
	end

	local title = mw.title.getCurrentTitle()
	if (title.namespace == 2) and not title.text:match(&quot;/&quot;) then
		return templateStyles .. tostring(root) -- regular user page
	elseif title.namespace == 14 then
		return templateStyles .. tostring(root) -- category
	elseif title.isTalkPage then
		return templateStyles .. tostring(root) -- talk page
	end

	-- Color contrast checking (simplified for TemplateStyles)
	local legible = true
	local contrast = require('Module:Color contrast')._ratio
	local function has_text(wikitext)
		if not wikitext then return false end
		wikitext = wikitext:gsub(&quot;]]&quot;, &quot;|]]&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Mm][Ee][Dd][Ii][Aa]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Ii][Mm][Aa][Gg][Ee]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Ff][Ii][Ll][Ee]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		return mw.text.trim(wikitext) ~= &quot;&quot;
	end

	if data.infoColor and data.backgroundColor and contrast { data.infoColor, data.backgroundColor, error = 0 } &lt; 4.5 then
		legible = false
	end

	-- For bold text &gt;= 14pt, requirement is only 3.
	local idContrastThreshold = 4.5
	local id2ContrastThreshold = 4.5
	if (data.idFontSize or 0) &gt;= 14 then idContrastThreshold = 3 end
	if (data.id2FontSize or 0) &gt;= 14 then id2ContrastThreshold = 3 end

	if data.showId and data.idColor and data.idBackgroundColor and contrast { data.idColor, data.idBackgroundColor, error = 0 } &lt; idContrastThreshold then
		if has_text(data.id or &quot;&quot;) then legible = false end
	end

	if data.showId2 and data.id2Color and data.id2BackgroundColor and contrast { data.id2Color, data.id2BackgroundColor, error = 0 } &lt; id2ContrastThreshold then
		if has_text(data.id2 or &quot;&quot;) then legible = false end
	end

	if not legible then
		root:wikitext('[[Category:Userboxes with insufficient color contrast]]')
	end

	return templateStyles .. tostring(root)
end

function p.categories(args, page)
	-- Gets categories from [[Module:Category handler]].
	-- The page parameter makes the function act as though the module was being called from that page.
	-- It is included for testing purposes.
	local cats = {}
	cats[#cats + 1] = args.usercategory
	cats[#cats + 1] = args.usercategory2
	cats[#cats + 1] = args.usercategory3
	cats[#cats + 1] = args.usercategory4
	cats[#cats + 1] = args.usercategory5

	-- Get the title object
	local title
	if page then
		title = mw.title.new(page)
	else
		title = mw.title.getCurrentTitle()
	end

	-- Build category handler arguments.
	local chargs = {}
	chargs.page = page
	chargs.nocat = args.nocat
	chargs.main = '[[Category:Pages with templates in the wrong namespace]]'
	if args.notcatsubpages then
		chargs.subpage = 'no'
	end

	-- User namespace.
	local user = ''
	for i, cat in ipairs(cats) do
		user = user .. makeCat(cat)
	end
	chargs.user = user

	return categoryHandler(chargs)
end

return p</text>
      <sha1>310mo9tctsu9310xhk46tk6d7jx8wl9</sha1>
    </revision>
    <revision>
      <id>2810266</id>
      <parentid>2810263</parentid>
      <timestamp>2026-05-18T22:08:29Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <minor />
      <comment>Changed protection settings for &quot;[[Module:Userbox]]&quot;: To match the same protections as its parent page. ([Edit=Allow only curators and custodians] (indefinite) [Move=Allow only curators and custodians] (indefinite))</comment>
      <origin>2810263</origin>
      <model>Scribunto</model>
      <format>text/plain</format>
      <text bytes="16370" sha1="310mo9tctsu9310xhk46tk6d7jx8wl9" xml:space="preserve">-- This module implements {{userbox}}.

local categoryHandler = require('Module:Category handler').main

local p = {}

--------------------------------------------------------------------------------
-- Helper functions
--------------------------------------------------------------------------------

local function checkNum(val, default)
	-- Checks whether a value is a number greater than or equal to zero. If so,
	-- returns it as a number. If not, returns a default value.
	val = tonumber(val)
	if val and val &gt;= 0 then
		return val
	else
		return default
	end
end

local function addSuffix(num, suffix)
	-- Turns a number into a string and adds a suffix.
	if num then
		return tostring(num) .. suffix
	else
		return nil
	end
end

local function checkNumAndAddSuffix(num, default, suffix)
	-- Checks a value with checkNum and adds a suffix.
	num = checkNum(num, default)
	return addSuffix(num, suffix)
end

local function makeCat(cat, sort)
	-- Makes a category link.
	if sort then
		return mw.ustring.format('[[Category:%s|%s]]', cat, sort)
	else
		return mw.ustring.format('[[Category:%s]]', cat)
	end
end

--------------------------------------------------------------------------------
-- Argument processing
--------------------------------------------------------------------------------

local function makeInvokeFunc(funcName)
	return function (frame)
		local origArgs = require('Module:Arguments').getArgs(frame)
		local args = {}
		for k, v in pairs(origArgs) do
			args[k] = v
		end
		return p.main(funcName, args)
	end
end

p.userbox = makeInvokeFunc('_userbox')
p['userbox-2'] = makeInvokeFunc('_userbox-2')
p['userbox-r'] = makeInvokeFunc('_userbox-r')

--------------------------------------------------------------------------------
-- Main functions
--------------------------------------------------------------------------------

function p.main(funcName, args)
	local userboxData = p[funcName](args)
	local userbox = p.render(userboxData)
	local cats = p.categories(args)
	return userbox .. (cats or '')
end

function p._userbox(args)
	-- Does argument processing for {{userbox}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-width'] or args['border-s'], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-color'] or args['border-c'] or args[1] or args['id-c']
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-background'] or args[2] or args['info-c']

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-size'] or args['info-s'], nil, 'pt')
	data.infoHeight = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.infoPadding = args['info-padding'] or args['info-p']
	data.infoLineHeight = args['info-line-height'] or args['info-lh']
	data.infoColor = args['info-color'] or args['info-fc']
	data.infoOtherParams = args['info-other-param'] or args['info-op']
	data.infoClass = args['info-class']

	-- Get id values.
	local id = args.logo or args[3] or args.id
	data.id = id
	data.showId = id and true or false
	data.idWidth = checkNumAndAddSuffix(args['logo-width'] or args['id-w'], nil, 'px')
	data.idHeight = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.idBackgroundColor = args['logo-background'] or args[1] or args['id-c']
	data.idTextAlign = args['id-a']
	data.idFontSize = checkNum(args['logo-size'] or args[5] or args['id-s'], nil)
	data.idColor = args['logo-color'] or args['id-fc'] or data.infoColor
	data.idPadding = args['logo-padding'] or args['id-p']
	data.idLineHeight = args['logo-line-height'] or args['id-lh']
	data.idOtherParams = args['logo-other-param'] or args['id-op']
	data.idClass = args['id-class']

	return data
end

p['_userbox-2'] = function (args)
	-- Does argument processing for {{userbox-2}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-s'] or args[9], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-c'] or args[6] or args['id1-c'] or args[1]
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-c'] or args[2]

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-s'], nil, 'pt')
	data.infoColor = args['info-fc'] or args[8]
	data.infoPadding = args['info-p']
	data.infoLineHeight = args['info-lh']
	data.infoOtherParams = args['info-op']

	-- Get id values.
	data.showId = true
	data.id = args.logo or args[3] or args.id1 or 'id1'
	data.idWidth = checkNumAndAddSuffix(args['id1-w'], nil, 'px')
	data.idHeight = checkNumAndAddSuffix(args['id-h'], nil, 'px')
	data.idBackgroundColor = args['id1-c'] or args[1]
	data.idTextAlign = args['id-a']
	data.idFontSize = checkNum(args['id1-s'], nil)
	data.idLineHeight = args['id1-lh']
	data.idColor = args['id1-fc'] or data.infoColor
	data.idPadding = args['id1-p']
	data.idOtherParams = args['id1-op']

	-- Get id2 values.
	data.showId2 = true
	data.id2 = args.logo or args[5] or args.id2 or 'id2'
	data.id2Width = checkNumAndAddSuffix(args['id2-w'], nil, 'px')
	data.id2Height = data.idHeight
	data.id2BackgroundColor = args['id2-c'] or args[7] or args[1]
	data.id2TextAlign = nil -- Always center, but don't set if no content
	data.id2FontSize = checkNum(args['id2-s'], nil)
	data.id2LineHeight = args['id2-lh']
	data.id2Color = args['id2-fc'] or data.infoColor
	data.id2Padding = args['id2-p']
	data.id2OtherParams = args['id2-op']

	return data
end

p['_userbox-r'] = function (args)
	-- Does argument processing for {{userbox-r}}.
	local data = {}

	-- Get div tag values.
	data.float = args.float
	local borderWidthNum = checkNum(args['border-width'] or args['border-s'], nil)
	data.borderWidth = addSuffix(borderWidthNum, 'px')
	data.borderColor = args['border-color'] or args['border-c'] or args[1] or args['id-c']
	data.width = borderWidthNum and addSuffix(240 - 2 * borderWidthNum, 'px')
	data.bodyClass = args.bodyclass

	-- Get table tag values.
	data.backgroundColor = args['info-background'] or args[2] or args['info-c']

	-- Get id values.
	data.showId = false -- We only show id2 in userbox-r.

	-- Get info values.
	data.info = args.info or args[4] or &quot;&lt;code&gt;{{{info}}}&lt;/code&gt;&quot;
	data.infoTextAlign = args['info-align'] or args['info-a']
	data.infoFontSize = checkNumAndAddSuffix(args['info-size'] or args['info-s'], nil, 'pt')
	data.infoPadding = args['info-padding'] or args['info-p']
	data.infoLineHeight = args['info-line-height'] or args['info-lh']
	data.infoColor = args['info-color'] or args['info-fc']
	data.infoOtherParams = args['info-other-param'] or args['info-op']

	-- Get id2 values.
	data.showId2 = true  -- userbox-r always shows the ID cell (as id2)
	data.id2 = args.logo or args[3] or args.id or 'id'
	data.id2Width = checkNumAndAddSuffix(args['logo-width'] or args['id-w'], nil, 'px')
	data.id2Height = checkNumAndAddSuffix(args['logo-height'] or args['id-h'], nil, 'px')
	data.id2BackgroundColor = args['logo-background'] or args[1] or args['id-c']
	data.id2TextAlign = args['id-a']
	data.id2FontSize = checkNum(args['logo-size'] or args[5] or args['id-s'], nil)
	data.id2Color = args['logo-color'] or args['id-fc'] or data.infoColor
	data.id2Padding = args['logo-padding'] or args['id-p']
	data.id2LineHeight = args['logo-line-height'] or args['id-lh']
	data.id2OtherParams = args['logo-other-param'] or args['id-op']

	return data
end

function p.render(data)
	-- Renders the userbox html using the content of the data table.
	-- Add TemplateStyles
	local templateStyles = mw.getCurrentFrame():extensionTag{
		name = 'templatestyles', args = { src = 'Template:Userbox/styles.css' }
	}

	-- Render the div tag html.
	local root = mw.html.create('div')
	root:addClass('wikipediauserbox')

	-- Only add CSS properties if they have values
	if data.float then root:css('float', data.float) end
	if data.borderWidth then 
		root:css('border-width', data.borderWidth)
	end
	if data.borderColor then 
		root:css('border-color', data.borderColor)
		-- Set border style if we have a color but potentially no width set
		if not data.borderWidth then
			root:css('border-width', '1px')  -- default border width
		end
		root:css('border-style', 'solid')
	end
	if data.width then root:css('width', data.width) end
	if data.bodyClass then root:addClass(data.bodyClass) end

	-- Render the table tag html.
	local tableroot = root:tag('table')
	tableroot:attr('role', 'presentation')

	-- Only add CSS if values exist
	if data.width then tableroot:css('width', data.width) end
	if data.backgroundColor then tableroot:css('background', data.backgroundColor):css('color', 'inherit') end

	local tablerow = tableroot:tag('tr')

	-- Create cells based on what should actually be shown
	if data.showId == false then
		-- userbox-r: info cell first, then id2 cell (if showId2 is true)
		local infoCell = tablerow:tag('td')
		infoCell:addClass('userbox-info')
		if data.infoTextAlign then infoCell:css('text-align', data.infoTextAlign) end
		if data.infoFontSize then infoCell:css('font-size', data.infoFontSize) end
		if data.infoPadding then infoCell:css('padding', data.infoPadding) end
		if data.infoHeight then infoCell:css('height', data.infoHeight) end
		if data.infoLineHeight then infoCell:css('line-height', data.infoLineHeight) end
		if data.infoColor then infoCell:css('color', data.infoColor) end
		if data.infoOtherParams then infoCell:cssText(data.infoOtherParams) end
		if data.infoClass then infoCell:addClass(data.infoClass) end
		if data.info then infoCell:wikitext(data.info) end
		
		-- Create id2 cell only if showId2 is true
		if data.showId2 then
			local id2Cell = tablerow:tag('td')
			id2Cell:addClass('userbox-id2')
			if data.id2Width then id2Cell:css('width', data.id2Width) end
			if data.id2Height then id2Cell:css('height', data.id2Height) end
			if data.id2BackgroundColor then id2Cell:css('background', data.id2BackgroundColor) end
			if data.id2TextAlign then id2Cell:css('text-align', data.id2TextAlign) end
			if data.id2FontSize then id2Cell:css('font-size', data.id2FontSize .. 'pt') end
			if data.id2Color then id2Cell:css('color', data.id2Color) else id2Cell:css('color', 'inherit') end
			if data.id2Padding then id2Cell:css('padding', data.id2Padding) end
			if data.id2LineHeight then id2Cell:css('line-height', data.id2LineHeight) end
			if data.id2OtherParams then id2Cell:cssText(data.id2OtherParams) end
			if data.id2 then id2Cell:wikitext(data.id2) end
		end
	else
		-- userbox and userbox-2: create id cell only if showId is true
		if data.showId then
			local idCell = tablerow:tag('td')
			idCell:addClass('userbox-id')
			if data.idWidth then idCell:css('width', data.idWidth) end
			if data.idHeight then idCell:css('height', data.idHeight) end
			if data.idBackgroundColor then idCell:css('background', data.idBackgroundColor) end
			if data.idTextAlign then idCell:css('text-align', data.idTextAlign) end
			if data.idFontSize then idCell:css('font-size', data.idFontSize .. 'pt') end
			if data.idColor then idCell:css('color', data.idColor) else idCell:css('color', 'inherit') end
			if data.idPadding then idCell:css('padding', data.idPadding) end
			if data.idLineHeight then idCell:css('line-height', data.idLineHeight) end
			if data.idOtherParams then idCell:cssText(data.idOtherParams) end
			if data.idClass then idCell:addClass(data.idClass) end
			if data.id then idCell:wikitext(data.id) end
		end
		
		-- Always create info cell for userbox and userbox-2
		local infoCell = tablerow:tag('td')
		infoCell:addClass('userbox-info')
		if data.infoTextAlign then infoCell:css('text-align', data.infoTextAlign) end
		if data.infoFontSize then infoCell:css('font-size', data.infoFontSize) end
		if data.infoPadding then infoCell:css('padding', data.infoPadding) end
		if data.infoHeight then infoCell:css('height', data.infoHeight) end
		if data.infoLineHeight then infoCell:css('line-height', data.infoLineHeight) end
		if data.infoColor then infoCell:css('color', data.infoColor) end
		if data.infoOtherParams then infoCell:cssText(data.infoOtherParams) end
		if data.infoClass then infoCell:addClass(data.infoClass) end
		if data.info then infoCell:wikitext(data.info) end
		
		-- Create id2 cell only for userbox-2 and only if showId2 is true
		if data.showId2 then
			local id2Cell = tablerow:tag('td')
			id2Cell:addClass('userbox-id2')
			if data.id2Width then id2Cell:css('width', data.id2Width) end
			if data.id2Height then id2Cell:css('height', data.id2Height) end
			if data.id2BackgroundColor then id2Cell:css('background', data.id2BackgroundColor) end
			if data.id2TextAlign then id2Cell:css('text-align', data.id2TextAlign) end
			if data.id2FontSize then id2Cell:css('font-size', data.id2FontSize .. 'pt') end
			if data.id2Color then id2Cell:css('color', data.id2Color) else id2Cell:css('color', 'inherit') end
			if data.id2Padding then id2Cell:css('padding', data.id2Padding) end
			if data.id2LineHeight then id2Cell:css('line-height', data.id2LineHeight) end
			if data.id2OtherParams then id2Cell:cssText(data.id2OtherParams) end
			if data.id2 then id2Cell:wikitext(data.id2) end
		end
	end

	local title = mw.title.getCurrentTitle()
	if (title.namespace == 2) and not title.text:match(&quot;/&quot;) then
		return templateStyles .. tostring(root) -- regular user page
	elseif title.namespace == 14 then
		return templateStyles .. tostring(root) -- category
	elseif title.isTalkPage then
		return templateStyles .. tostring(root) -- talk page
	end

	-- Color contrast checking (simplified for TemplateStyles)
	local legible = true
	local contrast = require('Module:Color contrast')._ratio
	local function has_text(wikitext)
		if not wikitext then return false end
		wikitext = wikitext:gsub(&quot;]]&quot;, &quot;|]]&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Mm][Ee][Dd][Ii][Aa]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Ii][Mm][Aa][Gg][Ee]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		wikitext = wikitext:gsub(&quot;%[%[%s*[Ff][Ii][Ll][Ee]%s*:[^|]-(|.-)]]&quot;, &quot;&quot;)
		return mw.text.trim(wikitext) ~= &quot;&quot;
	end

	if data.infoColor and data.backgroundColor and contrast { data.infoColor, data.backgroundColor, error = 0 } &lt; 4.5 then
		legible = false
	end

	-- For bold text &gt;= 14pt, requirement is only 3.
	local idContrastThreshold = 4.5
	local id2ContrastThreshold = 4.5
	if (data.idFontSize or 0) &gt;= 14 then idContrastThreshold = 3 end
	if (data.id2FontSize or 0) &gt;= 14 then id2ContrastThreshold = 3 end

	if data.showId and data.idColor and data.idBackgroundColor and contrast { data.idColor, data.idBackgroundColor, error = 0 } &lt; idContrastThreshold then
		if has_text(data.id or &quot;&quot;) then legible = false end
	end

	if data.showId2 and data.id2Color and data.id2BackgroundColor and contrast { data.id2Color, data.id2BackgroundColor, error = 0 } &lt; id2ContrastThreshold then
		if has_text(data.id2 or &quot;&quot;) then legible = false end
	end

	if not legible then
		root:wikitext('[[Category:Userboxes with insufficient color contrast]]')
	end

	return templateStyles .. tostring(root)
end

function p.categories(args, page)
	-- Gets categories from [[Module:Category handler]].
	-- The page parameter makes the function act as though the module was being called from that page.
	-- It is included for testing purposes.
	local cats = {}
	cats[#cats + 1] = args.usercategory
	cats[#cats + 1] = args.usercategory2
	cats[#cats + 1] = args.usercategory3
	cats[#cats + 1] = args.usercategory4
	cats[#cats + 1] = args.usercategory5

	-- Get the title object
	local title
	if page then
		title = mw.title.new(page)
	else
		title = mw.title.getCurrentTitle()
	end

	-- Build category handler arguments.
	local chargs = {}
	chargs.page = page
	chargs.nocat = args.nocat
	chargs.main = '[[Category:Pages with templates in the wrong namespace]]'
	if args.notcatsubpages then
		chargs.subpage = 'no'
	end

	-- User namespace.
	local user = ''
	for i, cat in ipairs(cats) do
		user = user .. makeCat(cat)
	end
	chargs.user = user

	return categoryHandler(chargs)
end

return p</text>
      <sha1>310mo9tctsu9310xhk46tk6d7jx8wl9</sha1>
    </revision>
  </page>
  <page>
    <title>C language in plain view</title>
    <ns>0</ns>
    <id>285380</id>
    <revision>
      <id>2810121</id>
      <parentid>2809647</parentid>
      <timestamp>2026-05-18T13:53:49Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Applications */</comment>
      <origin>2810121</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9878" sha1="in9xanqv23q78mgu0i9u5fpzwwbwfuv" xml:space="preserve">=== Introduction ===
* Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]])
* Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]])
* Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]])

=== Handling Repetition ===
* Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]])
* Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]])

=== Handling a Big Work ===
* Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]])
* Functions &amp; Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]])
* Functions &amp; Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]])
* Functions &amp; Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]])

=== Handling Series of Data ===

==== Background ==== 
* Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]])
 
==== Basics ====
* Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]])
* Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]])
* Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]])
* Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]])
* Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]])

==== Examples ==== 
* Spreadsheet Example Programs
:: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]])
:: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]])
:: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]])
:: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]])

==== Applications ==== 
* Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20260518.pdf |A.pdf]])
* Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]])
* Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]])
* Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]])
* Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]])
* Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]])
* Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]])

=== Handling Various Kinds of Data ===
* Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]])
* Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]])
* Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]])
* Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]])

=== Handling Low Level Operations ===
* Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]])
* Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]])
* Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]])
* Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]])

=== Declarations ===
* Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]])
* Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]])
* Scope 


=== Class Notes ===

* TOC ([[Media:TOC.20171007.pdf |TOC.pdf]])
* Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library
* Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements
* Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers
* Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts
* Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops
* Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control
* Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions
* Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope
* Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion
* Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions
* Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications
* Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions
* Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications
* Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) 
* Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2)
* Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO
* Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions
* Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications
* Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum
* Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List 
* Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing
* Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing


&lt;!----------------------------------------------------------------------&gt;
&lt;/br&gt;
See also https://cprogramex.wordpress.com/

== '''Old Materials '''==

until 201201
* Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]])
* Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]])
* Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]])
* Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]])
* Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]])
* Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]])
* Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]])
* Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]])
* Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]])
* Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]])
* Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]])
* Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]])
* Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]])
 
&lt;br&gt;

until 201107
* Intro.1.A ([[Media:Intro.1.A.pdf |pdf]])
* Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]])
* Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]])
* Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]])
* Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]])
* Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]])
* Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]])
* Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]])
* Array.1.A ([[Media:Array.1.A.pdf |pdf]])
* Type.1.A ([[Media:Type.1.A.pdf |pdf]])
* Structure.1.A ([[Media:Structure.1.A.pdf |pdf]])


go to [ [[C programming in plain view]] ]

[[Category:C programming language]]

&lt;/br&gt;</text>
      <sha1>in9xanqv23q78mgu0i9u5fpzwwbwfuv</sha1>
    </revision>
  </page>
  <page>
    <title>Socialism</title>
    <ns>0</ns>
    <id>285439</id>
    <revision>
      <id>2810405</id>
      <parentid>2687741</parentid>
      <timestamp>2026-05-19T11:34:47Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>project box(es)</comment>
      <origin>2810405</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1737" sha1="0q0zh0aim6m016gzlreetjashfvr2ym" xml:space="preserve">{{politics}}
'''Socialism''' is a [[wikipedia:Left-wing_politics|left-wing]] to [[wikipedia:Far-left_politics|far-left]] [[wikipedia:Economic_ideology|economic philosophy]] and [[wikipedia:Political_movement|movement]] encompassing a range of [[wikipedia:Economic_system|economic systems]] characterized by the dominance of [[wikipedia:Social_ownership|social ownership]] of the [[wikipedia:Means_of_production|means of production]] within the economy and [[wikipedia:Workers'_control|worker participation]] in the management of [[wikipedia:Production_(economics)|productive enterprises]] as opposed to [[wikipedia:Private_property|private ownership]].
[[File:Puño y rosa.png|right|50px]]
{{right| &lt;small&gt;-- ''from [[Wikipedia: Socialism]]''&lt;/small&gt;}}
* See also [[Libertarian socialism]]

&lt;br&gt;
;&lt;big&gt;Call for contributions&lt;/big&gt;

{{Warning|Don't worry about giving your essay or article the wrong name because we can change the name later.&lt;br&gt;
But all content must be your own work. Do not copy/paste from other sites. Include references for all sources.}}
[[Wikiversity:Introduction|'''Set education free''']] by contributing to '''{{PAGENAME}}'''. Create a space where you can work by entering a title that is not already on the list below. 
{{RoundBoxTop|theme=1}}&lt;inputbox&gt;
summary= A NEW INVITED ESSAY HAS BEEN CREATED!!!
type=create
width=110 
buttonlabel=Create subpage
break=no
prefix={{FULLPAGENAME}}/
placeholder=Title of subpage
&lt;/inputbox&gt;{{RoundBoxBottom}}
===List of contributions===
{{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}}
[[Category:Open essay collections]]
&lt;/br&gt;
----

===== Categories =====
&lt;categorytree mode=&quot;categories&quot; showcount=&quot;on&quot;&gt;Socialism&lt;/categorytree&gt;
[[Category:Socialism]]</text>
      <sha1>0q0zh0aim6m016gzlreetjashfvr2ym</sha1>
    </revision>
  </page>
  <page>
    <title>Social Victorians/Terminology</title>
    <ns>0</ns>
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      <text bytes="203830" sha1="loga9w9vzbhh7r6wn5550amlxgljbrq" xml:space="preserve">Especially with respect to fashion, the newspapers at the end of the 19th century in the UK often used specialized terminology. The definitions on this page are to provide a sense of what someone in the late 19th century might have meant by the term rather than a definition of what we might mean by it today. In the absence of a specialized glossary from the end of the 19th century in the U.K., we use the ''Oxford English Dictionary'' because the senses of a word are illustrated with examples that have dates so we can be sure that the senses we pick are appropriate for when they are used in the quotations we have.

We also sometimes use the French ''Wikipédia'' to define a word because many technical terms of fashion were borrowings from the French. Also, often the French ''Wikipédia'' provides historical context for the uses of a word similar to the way the ''OED'' does.

== Articles or Parts of Clothing: Men's ==
[[Social Victorians/Terminology#Military|Men's military uniforms]] are discussed below.

=== À la Romaine ===
[[File:Johann Baptist Straub - Mars um 1772-1.jpg|thumb|left|alt=Old and damaged marble statue of a Roman god of war with flowing cloak, big helmet with a plume on top, and armor|Johann Baptist Straub's 1772 ''à la romaine'' ''Mars'']]
A few people who attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's fancy-dress ball in 1897]] personated Roman gods or people. They were dressed not as Romans, however, but ''à la romaine'', which was a standardized style of depicting Roman figures that was used in paintings, sculpture and the theatre for historical dress from the 17th until the 20th century. The codification of the style was developed in France in the 17th century for theatre and ballet, when it became popular for masked balls.

Women as well as men could be dressed ''à la romaine'', but much sculpture, portraiture and theatre offered opportunities for men to dress in Roman style — with armor and helmets — and so it was most common for men. In large part because of the codification of the style as well as the painting and sculpture, the style persisted and remained influential into the 20th century and can be found in museums and galleries and on monuments.

For example, Johann Baptist Straub's 1772 statue of Mars (left), now in the Bayerisches Nationalmuseum, Munich, missing part of an arm, shows Mars ''à la romaine''. In London, an early 17th-century example of a figure of Mars ''à la romaine'', with a helmet, '''was''' &quot;at the foot of the Buckingham tomb in Henry VII's Chapel at Westminster Abbey.&quot;&lt;ref&gt;Webb, Geoffrey. “Notes on Hubert Le Sueur-II.” ''The Burlington Magazine for Connoisseurs'' 52, no. 299 (1928): 81–89. http://www.jstor.org/stable/863535.&lt;/ref&gt;{{rp|81, Col. 2c}}

[[File:Sir-Anthony-van-Dyck-Lord-John-Stuart-and-His-Brother-Lord-Bernard-Stuart.jpg|thumb|alt=Old painting of 2 men flamboyantly and stylishly dressed in colorful silk, with white lace, high-heeled boots and long hair|Van Dyck's c. 1638 painting of cavaliers Lord John Stuart and his brother Lord Bernard Stuart]]
[[File:Frans_Hals_-_The_Meagre_Company_(detail)_-_WGA11119.jpg|thumb|Frans Hals - The Meagre Company (detail) - WGA11119.jpg]]

=== Cavalier ===
As a signifier in the form of clothing of a royalist political and social ideology begun in France in the early 17th century, the cavalier style established France as the leader in fashion and taste. Adopted by [[Social Victorians/Terminology#Military|wealthy royalist British military officers]] during the time of the Restoration, the style signified a political and social position, both because of the loyalty to Charles I and II as well the wealth required to achieve the cavalier look. The style spread beyond the political, however, to become associated generally with dress as well as a style of poetry.&lt;ref&gt;{{Cite journal|date=2023-04-25|title=Cavalier poet|url=https://en.wikipedia.org/w/index.php?title=Cavalier_poet&amp;oldid=1151690299|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier_poet.&lt;/ref&gt;

Van Dyck's 1638 painting of two brothers (right) emphasizes the cavalier style of dress.

The cavalier style included gloves with large gauntlets, lace on boots, more loosely fitted breeches, coats or doublets, which were slashed so the shirt beneath was visible. Men who dressed in cavalier style also wore large and, later, powdered wigs, like those of Louis XIV, having taken the French style back to Britain.

Neck treatments in the cavalier style were falling bands, wide lace collars and jabots. These were all looser, unsupported with wires, the way the earlier ruffs were, and unstarched.

=== Coats ===

==== Doublet ====
* In the 19th-century newspaper accounts we have seen that use this word, doublet seems always to refer to a garment worn by a man, but historically women may have worn doublets. In fact, a doublet worn by Queen Elizabeth I exists and '''is somewhere'''.
* Technically doublets were long sleeved, although we cannot be certain what this or that Victorian tailor would have done for a costume. For example, the [[Social Victorians/People/Spencer Compton Cavendish#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Duke of Devonshire's costume as Charles V]] shows long sleeves that may be part of the surcoat but should be the long sleeves of the doublet.

==== Pourpoint ====
A padded doublet worn under armor to protect the warrior from the metal chafing. A pourpoint could also be worn without the armor.

==== Surcoat ====
Sometimes just called ''coat''.

[[File:Oscar Wilde by Sarony 1882 18.jpg|thumb|alt=Old photograph of a young man wearing a velvet jacket, knee breeches, silk hose and shiny pointed shoes with bows, seated on a sofa and leaning on his left hand and holding a book in his right| Oscar Wilde, 1882, by Napoleon Sarony]]
=== Hose, Stockings and Tights ===
Newspaper accounts from the late 19th century of men's clothing use the term ''hose'' for what we might call stockings or tights.

In fact, the terminology is specific. ''Stockings'' is the more general term and could refer to hose or tights. With knee breeches men wore hose, which ended above the knee, and women wore hose under their dresses.

The ''Oxford English Dictionary'' defines tights as &quot;Tight-fitting breeches, worn by men in the 18th and early 19th centuries, and still forming part of court-dress.&quot;&lt;ref&gt;“Tights, N.” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/2693287467.&lt;/ref&gt; By 1897, the term was in use for women's stockings, which may have come up only to the knee. Tights were also worn by dancers and acrobats. This general sense of ''tights'' does not assume that they were knitted.

''Clocking'' is decorative embroidery on hose, usually, at the ankles on either the inside or the outside of the leg. It started at the ankle and went up the leg, sometimes as far as the knee. On women's hose, the clocking could be quite colorful and elaborate, while the clocking on men's hose was more inconspicuous.

In many photographs men's hose are wrinkled, especially at the ankles and the knees, because they were shaped from woven fabric. Silk hose were knitted instead of woven, which gave them elasticity and reduced the wrinkling.

The famous Sarony carte de visite photograph of Oscar Wilde (right) shows him in 1882 wearing knee breeches and silk hose, which are shiny and quite smoothly fitted although they show a few wrinkles at the ankles and knees. In the portraits of people in costume at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the men's hose are sometimes quite smooth, which means they were made of knitted silk and may have been smoothed for the portrait.

In painted portraits the hose are almost always depicted as smooth, part of the artist's improvement of the appearance of the subject.

=== Shoes and Boots ===

== Articles or Parts of Clothing: Women's ==

=== '''Chérusque''' ===
According to the French ''Wikipedia'', ''chérusque'' is a 19th-century term for the kind of standing collar like the ones worn by ladies in the Renaissance.&lt;ref&gt;{{Cite journal|date=2021-06-26|title=Collerette (costume)|url=https://fr.wikipedia.org/w/index.php?title=Collerette_(costume)&amp;oldid=184136746|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Collerette_(costume)#Au+xixe+siècle+:+la+Chérusque.&lt;/ref&gt;

=== Corsage ===
According to the ''Oxford English Dictionary'', the corsage is the &quot;'body' of a woman's dress; a bodice.&quot;&lt;ref&gt;&quot;corsage, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/42056. Accessed 7 February 2023.&lt;/ref&gt; This sense is well documented in the ''OED'' for the mid and late 19th-century, used this way in fiction as well as in a publication like ''Godey's Lady's Book'', which would be expected to use appropriate terminology associated with fashion and dress making.

The sense of &quot;a bouquet worn on the bodice&quot; is, according to the ''OED'', American.

=== Décolletage ===

=== Girdle ===

=== Mancheron ===
According to the ''Oxford English Dictionary'', a ''mancheron'' is a &quot;historical&quot; word for &quot;A piece of trimming on the upper part of a sleeve on a woman's dress.&quot;&lt;ref&gt;&quot;mancheron, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/113251. Accessed 17 April 2023.&lt;/ref&gt; At the present, in French, a ''mancheron'' is a cap sleeve &quot;cut directly on the bodice.&quot;&lt;ref&gt;{{Cite journal|date=2022-11-28|title=Manche (vêtement)|url=https://fr.wikipedia.org/w/index.php?title=Manche_(v%C3%AAtement)&amp;oldid=199054843|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Manche_(v%C3%AAtement).&lt;/ref&gt;

=== Paletot ===
A cloak or jacket worn by both women and men in different periods. In the late 19th century, we see Victoria wearing them frequently, sometimes dressed for outdoors but not always.

Paletot-redingote:&lt;blockquote&gt;United Kingdom. Introduced in 1867, ladies' fitted long coat cut without a waist seam. It had revers and buttoned down the front. They sometimes had capes.&lt;ref name=&quot;:7&quot; /&gt;{{rp|217}}&lt;/blockquote&gt;

According to the French ''Wikipédia'', a paletot is longer than hip length, has long sleeves, opens in the front.&lt;ref&gt;{{Cite journal|date=2026-02-20|title=Manteau (vêtement)|url=https://fr.wikipedia.org/w/index.php?title=Manteau_(v%C3%AAtement)&amp;oldid=233467144|journal=Wikipédia|language=fr}}&lt;/ref&gt;

=== Petticoat ===

According to the ''O.E.D.'', a petticoat is a &lt;blockquote&gt;skirt, as distinguished from a bodice, worn either externally or showing beneath a dress as part of the costume (often trimmed or ornamented); an outer skirt; a decorative underskirt. Frequently in ''plural'': a woman's or girl's upper skirts and underskirts collectively. Now ''archaic'' or ''historical''.&lt;ref&gt;“petticoat, n., sense 2.b”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, &lt;https://doi.org/10.1093/OED/1021034245&gt;&lt;/ref&gt; &lt;/blockquote&gt;This sense is, according to the ''O.E.D.'', &quot;The usual sense between the 17th and 19th centuries.&quot; However, while petticoats belong in both outer- and undergarments — that is, meant to be seen or hidden, like underwear — they were always under another garment, for example, underneath an open overskirt. The primary sense seems to have shifted through the 19th century so that, by the end, petticoats were underwear and the term ''underskirt'' was used to describe what showed under an open overskirt. 

In the 19th century, women wore their chemises, bloomers and [[Social Victorians/Terminology#Hoops|hoops]] under their petticoats. 

=== Stomacher ===
According to the ''O.E.D.'', a stomacher is &quot;An ornamental covering for the chest (often covered with jewels) worn by women under the lacing of the bodice,&quot;&lt;ref&gt;“stomacher, n.¹, sense 3.a”. ''Oxford English Dictionary'', Oxford University Press, September 2023, &lt;https://doi.org/10.1093/OED/1169498955&gt;&lt;/ref&gt; although by the end of the 19th century, the bodice did not often have visible laces. Some stomachers were so decorated that they were thought of as part of the jewelry.

=== Train ===
A train is

The Length of the Train

'''For the monarch [or a royal?]'''

According to Debrett's,&lt;blockquote&gt;A peeress's coronation robe is a long-trained crimson velvet mantle, edged with miniver pure, with a miniver pure cape. The length of the train varies with the rank of the wearer:

* Duchess: for rows of ermine; train to be six feet
* Marchioness: three and a half rows of ermine; train to be three and three-quarters feet
* Countess: three rows of ermine; train to be three and a half feet
* Viscountess: two and a half rows of ermine; train to be three and a quarter feet
* Baroness: two rows of ermine; train to be three feet&lt;ref name=&quot;:2&quot;&gt;{{Cite web|url=https://debretts.com/royal-family/dress-codes/|title=Dress Codes|website=debretts.com|language=en-US|access-date=2023-07-27}} https://debretts.com/royal-family/dress-codes/.&lt;/ref&gt;
&lt;/blockquote&gt;The pattern on the coronet worn was also quite specific, similar but not exactly the same for peers and peeresses. Debrett's also distinguishes between coronets and tiaras, which were classified more like jewelry, which was regulated only in very general terms.

Peeresses put on their coronets after the Queen or Queen Consort has been crowned. ['''peers?''']

== Hats, Bonnets and Headwear ==

=== Women's ===
The dresses in the 1892 production of Reyer's Salammbo, based on the Flaubert novel, were influential and occasioned a lot of newspaper coverage:&lt;blockquote&gt;Among the concessions to women made recently in Paris, and over which old-fashioned folk shake their heads as being a terrible innovation, is the permission given to sit in the orchestra stalls at the theatre. Though only in the two last rows of the spectators, women of the first class had place, they are still obliged to appear in demi-toilette, which includes the wearing of a bonnet. It was on the occasion of the first performance of “Salammbo” that the change was allowed, and there are not wanting people who think that after such a departure a deluge, or some such visitation, may be looked for.&lt;ref&gt;&quot;Ladies Column.&quot; ''Kilburn Times'' 8 July 1892, Friday: 7 [of 8], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001813/18920708/175/0007. Print title: ''The Kilburn Times, Hampstead and North-Western Post'', p. 7&lt;/ref&gt;&lt;/blockquote&gt;[[Social Victorians/People/Bourke|Gwendolen Bourke]] was dressed as Salammbo at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]].

==== Fontanges ====
[[File:Recueil de modes - Tome 4 - cent-quatre-vingt-cinq planches - estampes - btv1b105296325 (083 of 195).jpg|thumb|Recueil de modes - Tome 4 - cent-quatre-vingt-cinq planches - estampes - btv1b105296325 (083 of 195).jpg]][[File:Madame de Ludre en Stenkerke et falbala - (estampe) (2e état) - N. arnoult fec - btv1b53265886c.jpg|none|thumb|Madame de Ludre en Stenkerke et falbala - (estampe) (2e état) - N. arnoult fec - btv1b53265886c.jpg]]

==== Widow's Cap ====
or mourning bonnet

According to Kate Strasdin, widow's caps were &quot;white crinkled crape [sic] objects with long streamers flowing down the back, ... customarily worn by single old women who had never remarried.&quot;&lt;ref&gt;Strasdin, Kate. ''The Dress Diary: Secrets from a Victorian Woman's Wardrobe''. Pegasus, 2023.&lt;/ref&gt;{{rp|734 of 1124}}

[[Social Victorians/People/Queen Victoria#Widow's Cap|Queen Victoria's widow's caps]] and [[Social Victorians/People/Queen Victoria#Headdresses|other headdresses]] are discussed on her page.

=== Men's ===

== Cinque Cento ==
According to the ''Oxford English Dictionary'', ''Cinque Cento'' is a shortening of ''mil cinque cento'', or 1500.&lt;ref&gt;&quot;cinquecento, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/33143. Accessed 7 February 2023.&lt;/ref&gt; The term, then would refer, perhaps informally, to the sixteenth century.

== Corset ==
[[File:Corset - MET 1972.209.49a, b.jpg|thumb|alt=Photograph of an old silk corset on a mannequin, showing the closure down the front, similar to a button, and channels in the fabric for the boning. It is wider at the top and bottom, creating smooth curves from the bust to the compressed waist to the hips, with a long point below the waist in front.|French 1890s corset, now in the Metropolitan Museum of Art, NYC]]
The understructure of Victorian women's clothing is what makes the costumes worn by the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] so distinctly Victorian in appearance. An example of a corset that has the kind of structure often worn by fashionably dressed women in 1897 is the one at right. 

This corset exaggerated the shape of the women's bodies and made possible a bodice that looked and was fitted in the way that is so distinctive of the time — very controlled and smooth. And, as a structural element, this foundation garment carried the weight of all those layers and all that fabric and decoration on the gowns, trains and mantles. (The trains and mantles could be attached directly to the corset itself.)

* This foundation emphasizes the waist and the bust in particular, in part because of the contrast between the very small waist and the rounded fullness of the bust and hips.
* The idealized waist is defined by its small span and the sexualizing point at the center-bottom of the bodice, which directs the eye downwards. Interestingly, the pointed waistline worn by Elizabethan men has become level in the Victorian age. Highly fashionable Victorian women wearing the traditional style, however, had extremely pointed waists.
* The busk (a kind of boning in the front of a corset that is less flexible than the rest) smoothed the bodice, flattened the abdomen and prevented the point on the bodice from curling up.
* The sharp definition of the waist was caused by
** length of the corset (especially on the sides)
** the stiffness of the boning
** the layers of fabric
** the lacing (especially if the woman used tightlacing)
** the over-all shape, which was so much wider at the top and the bottom
** the contrast between the waist and the wider top and bottom
* The late-19th-century corset was long, ending below the waist even on the sides and back.
* The boning and the top edge of the late 19th-century fashion corset pushed up the bust, rounding (rather than flattening, as in earlier styles) the breasts, drawing attention to their exposed curves and creating cleavage.
* The exaggerated bust was larger than the hips, whenever possible, an impression reinforced by the A-line of the skirt and the inverted Vs in the decorative trim near the waist and on the skirt.
* This corset made the bodice very smooth with a very precise fit, that had no wrinkles, folds or loose drapery. The bodice was also trimmed or decorated, but the base was always a smooth bodice. More formal gowns would still have the fitted bodice and more elaborate trim made from lace, embroidery, appliqué, beading and possibly even jewels.
The advantages and disadvantages of corseting and especially tight lacing were the subject of thousands of articles and opinions in the periodical press for a great part of the century, but the fetishistic and politicized tight lacing was practiced by very few women. And no single approach to corsetry was practiced by all women all the time. Most of the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 ball]] were not tightly laced, but the progressive style does not dominate either, even though all the costumes are technically historical dress. Part of what gives most of the costumes their distinctive 19th-century &quot;look&quot; is the more traditional corset beneath them. Even though this highly fashionable look was widely present in the historical costumes at the ball, some women's waists were obviously very small and others were hardly '''emphasized''' at all. Women's waists are never mentioned in the newspaper coverage of the ball — or, indeed, of any of the social events attended by the network at the ball — so it is only in photographs that we can see the effects of how they used their corsets.

==== Things To Add ====
[[File:Woman's Corset LACMA M.2007.211.353.jpg|thumb|Woman's Corset LACMA M.2007.211.353.jpg|none]]

* Corset as an outer garment, 18th century, in place of a stomacher&lt;ref name=&quot;:11&quot; /&gt;{{rp|419}}
* Corsets could be laced in front or back
* Methods for making the holes for the laces and the development of the grommet (in the 1830s)

== Court Dress ==
Also Levee and drawing-room

== Crevé ==
''Creve'', without the accent, is an old word in English (c. 1450) for burst or split.&lt;ref&gt;&quot;creve, v.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44339. Accessed 8 February 2023.&lt;/ref&gt; ['''With the acute accent, it looks like a past participle in French.''']

== Elaborations ==
In her 1973 ''The Best Circles: Society, Etiquette and the Season'', Leonore Davidoff notes that women’s status was indicated by dress and especially ornament: “Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration,” she says, “symbolised some status category for the female wearer.”&lt;ref name=&quot;:1&quot;&gt;Davidoff, Leonore. ''The Best Circles: Society Etiquette and the Season''. Intro., Victoria Glendinning. The Cressett Library (Century Hutchinson), 1986 (orig 1973).&lt;/ref&gt;{{rp|93}}

Looking at these elaborations as meaningful rather than dismissing them as failed attempts at &quot;historical accuracy&quot; reveals a great deal about the individual women who wore or carried them — and about the society women and political hostesses in their roles as managers of the social world. In her review of ''The House of Worth: Portrait of an Archive'', Mary Frances Gormally says,&lt;blockquote&gt;In a socially regulated year, garments custom made with a Worth label provided women with total reassurance, whatever the season, time of day or occasion, setting them apart as members of the “Best Circles” dressed in luxurious, fashionable and always appropriate attire (Davidoff 1973). The woman with a Worth wardrobe was a woman of elegance, lineage, status, extreme wealth and faultless taste.&lt;ref&gt;Gormally, Mary Frances. Review essay of ''The House of Worth: Portrait of an Archive'', by Amy de la Haye and Valerie D. Mendes (V&amp;A Publishing, 2014). ''Fashion Theory'' 2017 (21, 1): 109–126. DOI: 10.1080/1362704X.2016.1179400.&lt;/ref&gt;{{rp|117}}&lt;/blockquote&gt;

[[File:Aglets from Spanish portraits - collage by shakko.jpg|thumb|alt=A collage of 12 different ornaments typically worn by elite people from Spain in the 1500s and later|Aglets — Detail from Spanish Portraits]]
=== Berthe ===
Can be spelled ''bertha''.

A wide collar made of lace and gathered at the neckline, sometimes covering the arms. Lewandowski says,&lt;blockquote&gt;Wide collar popular on women's gowns. Accented dropped shoulder line. Often made of lace.&lt;ref name=&quot;:7&quot; /&gt;{{rp|29}}&lt;/blockquote&gt;

=== Aglet, Aiglet ===
Historically, an aglet is a &quot;point or metal piece that capped a string [or ribbon] used to attach two pieces of the garment together, i.e., sleeve and bodice.&quot;&lt;ref name=&quot;:7&quot;&gt;Lewandowski, Elizabeth J. ''The Complete Costume Dictionary''. Scarecrow Press, 2011.&lt;/ref&gt;{{rp|4}} Although they were decorative, they were not always visible on the outside of the clothing. They were often stuffed inside the layers at the waist (for example, attaching the bodice to a skirt or breeches).

Alonso Sánchez Coello's c. 1584&lt;ref name=&quot;:11&quot; /&gt;{{rp|316}} portrait (above right, in the [[Social Victorians/Terminology#16th Century|Hoops section]]) shows infanta Isabel Clara Eugenia wearing a vertugado, with its &quot;typically Spanish smooth cone-shaped contour,&quot; with &quot;handsome aiglets cascad[ing] down center front.&quot;&lt;ref name=&quot;:11&quot;&gt;Payne, Blanche. ''History of Costume from the Ancient Egyptians to the Twentieth Century''. Harper &amp; Row, 1965.&lt;/ref&gt;{{rp|315}}

=== Flounce ===
A ruffle that is gathered on one edge, the bottom edge is free. Flounces are typically part of the decoration on a skirt.

=== Frou-frou ===
[[File:SarahBernhardt alsKameliendame1881.jpg|left|thumb|Bernhardt, 1881]]
In French, ''frou-frou'' or, spelled as ''froufrou'', is the sound of the rustling of silk or sometimes of fabrics in general.&lt;ref&gt;{{Cite journal|date=2023-07-25|title=frou-frou|url=https://fr.wiktionary.org/w/index.php?title=frou-frou&amp;oldid=32508509|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/frou-frou.&lt;/ref&gt; The first use the French ''Wiktionnaire'' lists is Honoré Balzac, ''La Cousine Bette'', 1846.&lt;ref&gt;{{Cite journal|date=2023-06-03|title=froufrou|url=https://fr.wiktionary.org/w/index.php?title=froufrou&amp;oldid=32330124|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/froufrou.&lt;/ref&gt; ''Frou-frou'' is also a 1869 French drawing-room comedy by Henri Meilhac and Ludovic Halévy&lt;ref&gt;{{Cite journal|date=2025-04-19|title=Henri Meilhac|url=https://en.wikipedia.org/w/index.php?title=Henri_Meilhac&amp;oldid=1286340698|journal=Wikipedia|language=en}}&lt;/ref&gt; and performed by Sarah Bernhardt in London in 1881 (Bernhardt, left, in costume ['''conflicting info, is a photo of Bernhardt in ''La Dame aux Camélias'' instead'''?]).

''Frou-frou'' is a term clothing historians use to describe decorative additions to an article of clothing; often the term has a slight negative connotation, suggesting that the additions are superficial and, perhaps, excessive.

=== Plastics ===
Small poufs of fabric connected in a strip in the 18th century, Rococo styles.

=== Pouf, Puff, Poof ===
According to the French ''Wikipédia'', a pouf was, beginning in 1744, a &quot;kind of women's hairstyle&quot;:&lt;blockquote&gt;The hairstyle in question, known as the “pouf”, had launched the reputation of the enterprising Rose Bertin, owner of the Grand Mogol, a very prominent fashion accessories boutique on Rue Saint-Honoré in Paris in 1774. Created in collaboration with the famous hairdresser, Monsieur Léonard, the pouf was built on a scaffolding of wire, fabric, gauze, horsehair, fake hair, and the client's own hair held up in an almost vertical position. — (Marie-Antoinette, ''Queen of Fashion'', translated from the American by Sylvie Lévy, in ''The Rules of the Game'', n° 40, 2009)&lt;/blockquote&gt;''Puff'' and ''poof'' are used to describe clothing.

=== Shirring ===
''Shirring'' is the gathering of fabric to make poufs or puffs. The 19th century is known for its use of this decorative technique. Even men's clothing had shirring: at the shoulder seam.

=== Sequins ===
Sequins, paillettes, spangles

Sequins — or paillettes — are &quot;small, scalelike glittering disks.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|216}} The French ''Wiktionnaire'' defines ''paillette'' as &quot;Lamelle de métal, brillante, mince, percée au milieu, ordinairement ronde, et qu’on applique sur une étoffe pour l’orner [A strip of metal, shiny, thin, pierced in the middle, usually round, and which is applied to a fabric in order to decorate it.]&quot;&lt;ref name=&quot;:8&quot;&gt;{{Cite journal|date=2024-03-18|title=paillette|url=https://fr.wiktionary.org/w/index.php?title=paillette&amp;oldid=33809572|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/paillette.&lt;/ref&gt;

According to the ''OED'', the use of ''sequin'' as a decorative device for clothing (as opposed to gold coins minted and used for international trade) goes back to the 1850s.&lt;ref&gt;“Sequin, N.” ''Oxford English Dictionary'', Oxford UP, September 2023,  https://doi.org/10.1093/OED/4074851670.&lt;/ref&gt; The first instance of ''spangle'' as &quot;A small round thin piece of glittering metal (usually brass) with a hole in the centre to pass a thread through, used for the decoration of textile fabrics and other materials of various sorts&quot; is from c. 1420.&lt;ref&gt;“Spangle, N. (1).” ''Oxford English Dictionary'', Oxford UP, July 2023,  https://doi.org/10.1093/OED/4727197141.&lt;/ref&gt; The first use of ''paillette'' listed in the French ''Wiktionnaire'' is in Jules Verne in 1873 to describe colored spots on icy walls.&lt;ref name=&quot;:8&quot; /&gt;

Currently many distinguish between sequins (which are smaller) and paillettes (which are larger).

Before the 20th century, sequins were metal discs or foil leaves, and so of course if they were silver or copper, they tarnished. It is not until well into the 20th century that plastics were invented and used for sequins.

=== Trim and Lace ===
''A History of Feminine Fashion'', published sometime before 1927 and probably commissioned by [[Social Victorians/People/Dressmakers and Costumiers#Worth, of Paris|the Maison Worth]], describes Charles Frederick Worth's contributions to the development of embroidery and [[Social Victorians/Terminology#Passementerie|passementerie]] (trim) from about the middle of the 19th century:&lt;blockquote&gt;For it must be remembered that one of M. Worth's most important and lasting contributions to the prosperity of those who cater for women's needs, as well as to the variety and elegance of his clients' garments, was his insistence on new fabrics, new trimmings, new materials of every description. In his endeavours to restore in Paris the splendours of the days of La Pompadour, and of Marie Antoinette, he found himself confronted at the outset with a grave difficulty, which would have proved unsurmountable to a man of less energy, resource and initiative. The magnificent materials of those days were no longer to be had! The Revolution had destroyed the market for beautiful materials of this, type, and the Restoration and regime of Louis Philippe had left a dour aspect in the City of Light. ... On parallel lines [to his development of better [[Social Victorians/Terminology#Satin|satin]]], [Worth] stimulated also the manufacture of embroidery and ''passementerie''. It was he who first started the manufacture of laces copied from the designs of the real old laces. He was the / first dressmaker to use fur in the trimming of light materials — but he employed only the richer furs, such as sable and ermine, and had no use whatever for the inferior varieties of skins.&lt;ref name=&quot;:9&quot;&gt;[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]&lt;/ref&gt;{{rp|6–7}}&lt;/blockquote&gt;

==== Gold and Silver Fabric and Lace ====

The ''Encyclopaedia Britannica'' (9th edition) has an article on gold and silver fabric, threads and lace attached to the article on gold. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)&lt;blockquote&gt;GOLD AND SILVER LACE. Under this heading a general account may be given of the use of the precious metals in textiles of all descriptions into which they enter. That these metals were used largely in the sumptuous textiles of the earliest periods of civilization there is abundant testimony; and to this day, in the Oriental centres whence a knowledge and the use of fabrics inwoven, ornamented, and embroidered with gold and silver first spread, the passion for such brilliant and costly textiles is still most strongly and generally prevalent. The earliest mention of the use of gold in a woven fabric occurs in the description of the ephod made for Aaron (Exod. xxxix. 2, 3) — &quot;And he made the ephod of gold, blue, and purple, and scarlet, and fine twined linen. And they did beat the gold into thin plates, and cut it into wires (strips), to work it in the blue, and in the purple, and in the scarlet, and in the fine linen, with cunning work.&quot; In both the ''Iliad'' and the ''Odyssey'' distinct allusion is frequently made to inwoven and embroidered golden textiles. Many circumstances point to the conclusion that the art of weaving and embroidering with gold and silver originated in India, where it is still principally prosecuted, and that from one great city to another the practice travelled westward, — Babylon, Tarsus, Baghdad, Damascus, the islands of Cyprus and Sicily, Con- / stantinople and Venice, all in the process of time becoming famous centres of these much prized manufactures. Alexander the Great found Indian kings and princes arrayed in robes of gold and purple; and the Persian monarch Darius, we are told, wore a war mantle of cloth of gold, on which were figured two golden hawks as if pecking at each other. There is reason, according to Josephus, to believe that the “royal apparel&quot; worn by Herod on the day of his death (Acts xii. 21) was a tissue of silver. Agrippina, the wife of the emperor Claudius, had a robe woven entirely of gold, and from that period downwards royal personages and high ecclesiastical dignitaries used cloth and tissues of gold and silver for their state and ceremonial robes, as well as for costly hangings and decorations. In England, at different periods, various names were applied to cloths of gold, as ciclatoun, tartarium, naques or nac, baudekiu or baldachin, Cyprus damask, and twssewys or tissue. The thin flimsy paper known as tissue paper, is so called because it originally was placed between the folds of gold &quot;tissue&quot; to prevent the contiguous surfaces from fraying each other. At what time the drawing of gold wire for the preparation of these textiles was first practised is not accurately known. The art was probably introduced and applied in different localities at widely different dates, but down till mediaeval times the method graphically described in the Pentateuch continued to be practised with both gold and silver.

Fabrics woven with gold and silver continue to be used on the largest scale to this day in India; and there the preparation of the varieties of wire, and the working of the various forms of lace, brocade, and embroidery, is at once an important and peculiar art. The basis of all modern fabrics of this kind is wire, the &quot;gold wire&quot; of the manufacturer being in all cases silver gilt wire, and silver wire being, of course, composed of pure silver. In India the wire is drawn by means of simple draw-plates, with rude and simple appliances, from rounded bars of silver, or gold-plated silver, as the case may be. The wire is flattened into the strip or ribbon-like form it generally assumes by passing it, fourteen or fifteen strands simultaneously, over a fine, smooth, round-topped anvil, and beating it as it passes with a heavy hammer having a slightly convex surface. From wire so flattened there is made in India soniri, a tissue or cloth of gold, the web or warp being composed entirely of golden strips, and ruperi, a similar tissue of silver. Gold lace is also made on a warp of thick yellow silk with a weft of flat wire, and in the case of ribbons the warp or web is composed of the metal. The flattened wires are twisted around orange (in the case of silver, white) coloured silk thread, so as completely to cover the thread and present the appearance of a continuous wire; and in this form it is chiefly employed for weaving into the rich brocades known as kincobs or kinkhábs. Wires flattened, or partially flattened, are also twisted into exceedingly fine spirals, and in this form they are the basis of numerous ornamental applications. Such spirals drawn out till they present a waved appearance, and in that state flattened, are much used for rich heavy embroideries termed karchobs. Spangles for embroideries, &amp;c., are made from spirals of comparatively stout wire, by cutting them down ring by ring, laying each C-like ring on an anvil, and by a smart blow with a hammer flattening it out into a thin round disk with a slit extending from the centre to one edge. Fine spirals are also used for general embroidery purposes. The demand for various kinds of loom-woven and embroidered gold and silver work in India is immense; and the variety of textiles so ornamented is also very great. &quot;Gold and silver,&quot; says Dr Birdwood in his ''Handbook to the British-Indian Section, Paris Exhibition'', 1878, &quot;are worked into the decoration of all the more costly loom-made garments and Indian piece goods, either on the borders only, or in stripes throughout, or in diapered figures. The gold-bordered loom embroideries are made chiefly at Sattara, and the gold or silver striped at Tanjore; the gold figured ''mashrus'' at Tanjore, Trichinopoly, and Hyderabad in the Deccau; and the highly ornamented gold-figured silks and gold and silver tissues principally at Ahmedabad, Benares, Murshedabad, and Trichinopoly.&quot;

Among the Western communities the demand for gold and silver lace and embroideries arises chiefly in connexion with naval and military uniforms, court costumes, public and private liveries, ecclesiastical robes and draperies, theatrical dresses, and the badges and insignia of various orders. To a limited extent there is a trade in gold wire and lace to India and China. The metallic basis of the various fabrics is wire round and flattened, the wire being of three kinds — 1st, gold wire, which is invariably silver gilt wire; 2d, copper gilt wire, used for common liveries and theatrical purposes; and 3d, silver wire. These wires are drawn by the ordinary processes, and the flattening, when done, is accomplished by passing the wire between a pair of revolving rollers of fine polished steel. The various qualities of wire are prepared and used in precisely the same way as in India, — round wire, flat wire, thread made of flat gold wire twisted round orange-coloured silk or cotton, known in the trade as &quot;orris,&quot; fine spirals and spangles, all being in use in the West as in the East. The lace is woven in the same manner as ribbons, and there are very numerous varieties in richness, pattern, and quality.  Cloth of gold, and brocades rich in gold and silver, are woven for ecclesiastical vestments and draperies.

The proportions of gold and silver in the gold thread for the lace trade varies, but in all cases the proportion of gold is exceedingly small. An ordinary gold lace wire is drawn from a bar containing 90 parts of silver and 7 of copper, coated with 3 parts of gold. On an average each ounce troy of a bar so plated is drawn into 1500 yards of wire; and therefore about 16 grains of gold cover a mile of wire. It is estimated that about 250,000 ounces of gold wire are made annually in Great Britain, of which about 20 per cent, is used for the headings of calico, muslin, &amp;c., and the remainder is worked up in the gold lace trade.&lt;ref&gt;William Chandler Roberts-Austen and H. Bauerman [W.C.R. — H.B.]. &quot;Gold and Silver Lace.&quot; In &quot;Gold.&quot; ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. 10 (X). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%2010%20%28G-GOT%29%20193592738.23/page/753/mode/1up (accessed January 2023): 753, Col. 2c – 754, Cols. 1a–b – 2a–b.&lt;/ref&gt;&lt;/blockquote&gt;

==== Honiton Lace ====

Kate Stradsin says,&lt;blockquote&gt;Honiton lace was the finest English equivalent of Brussels bobbin lace and was constructed in small ‘sprigs, in the cottages of lacemakers[.'] These sprigs were then joined together and bleached to form the large white flounces that were so sought after in the mid-nineteenth century.&lt;ref&gt;Strasdin, Kate. &quot;Rediscovering Queen Alexandra’s Wardrobe: The Challenges and Rewards of Object-Based Research.&quot; ''The Court Historian'' 24.2 (2019): 181-196. Rpt  http://repository.falmouth.ac.uk/3762/15/Rediscovering%20Queen%20Alexandra%27s%20Wardrobe.pdf: 13, and (for the little quotation) n. 37, which reads &quot;Margaret Tomlinson, ''Three Generations in the Honiton Lace Trade: A Family History'', self-published, 1983.&quot;&lt;/ref&gt;&lt;/blockquote&gt;

[[File:Strook in Alençon naaldkant, 1750-1775.jpg|thumb|alt=A long piece of complex white lace with garlands, flowers and bows|Point d'Alençon lace, 1750-1775]]
==== Passementerie ====
''Passementerie'' is the French term for trim on clothing or furniture. The 19th century (especially during the First and Second Empire) was a time of great &quot;''exubérance''&quot; in passementerie in French design, including the development and widespread use of the Jacquard loom.&lt;ref&gt;{{Cite journal|date=2023-06-10|title=Passementerie|url=https://fr.wikipedia.org/w/index.php?title=Passementerie&amp;oldid=205068926|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Passementerie.&lt;/ref&gt;

==== Point d'Alençon Lace ====
A lace made by hand using a number of complex steps and layers. The lacemakers build the point d'Alençon design on some kind of mesh and sometimes leave some of the mesh in as part of the lace and perhaps to provide structure.

Elizabeth Lewandowski defines point d'Alençon lace and Alençon lace separately. Point lace is needlepoint lace,&lt;ref name=&quot;:7&quot; /&gt;{{rp|233}} so Alençon point is &quot;a two thread [needlepoint] lace.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|7}} Alençon lace has a &quot;floral design on [a] fine net ground [and is] referred to as [the] queen of French handmade needlepoint laces. The original handmade Alençon was a fine needlepoint lace made of linen thread.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|7}}

The sample of point d'Alençon lace (right), from 1750–1775, shows the linen mesh that the lace was constructed on.&lt;ref&gt;{{Cite web|url=http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689|title=MoMu - Open Fashion|website=openfashion.momu.be|access-date=2024-02-26}} ModeMuseum Antwerpen. http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689.&lt;/ref&gt; The consistency in this sample suggests it may have been made by machine.

== Elastic ==
Elastic had been invented and was in use by the end of the 19th century. For the sense of &quot;Elastic cord or string, usually woven with india-rubber,&quot;&lt;ref name=&quot;:6&quot;&gt;“elastic, adj. &amp; n.”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, &lt;https://doi.org/10.1093/OED/1199670313&gt;.&lt;/ref&gt; the ''Oxford English Dictionary'' has usage examples beginning in 1847. The example for 1886 is vivid: &quot;The thorough-going prim man will always place a circle of elastic round his hair previous to putting on his college cap.&quot;&lt;ref name=&quot;:6&quot; /&gt;

== Fabric ==

=== Brocatelle ===
Brocatelle is a kind of brocade, more simple than most brocades because it uses fewer warp and weft threads and fewer colors to form the design. The article in the French ''Wikipédia'' defines it like this:&lt;blockquote&gt;La '''brocatelle''' est un type de tissu datant du &lt;abbr&gt;xvi&lt;sup&gt;e&lt;/sup&gt;&lt;/abbr&gt; siècle qui comporte deux chaînes et deux trames, au minimum. Il est composé pour que le dessin ressorte avec un relief prononcé, grâce à la chaîne sur un fond en sergé. Les brocatelles les plus anciennes sont toujours fabriquées avec une des trames en lin.&lt;ref&gt;{{Cite journal|date=2023-06-01|title=Brocatelle|url=https://fr.wikipedia.org/w/index.php?title=Brocatelle&amp;oldid=204796410|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Brocatelle.&lt;/ref&gt;&lt;/blockquote&gt;Which translates to this:&lt;blockquote&gt;Brocatelle is a type of fabric dating from the 16th century that has two warps and two wefts, at a minimum. It is composed so that the design stands out with a pronounced relief, thanks to the weft threads on a twill background. The oldest brocades were always made with one of the wefts being linen.&lt;/blockquote&gt;The ''Oxford English Dictionary'' says, brocatelle is an &quot;imitation of brocade, usually made of silk or wool, used for tapestry, upholstery, etc., now also for dresses. Both the nature and the use of the stuff have changed&quot; between the late 17th century and 1888, the last time this definition was revised.&lt;ref&gt;&quot;brocatelle, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/23550. Accessed 4 July 2023.&lt;/ref&gt;

=== Broché ===
Lewandowski says, &quot;to be woven with a raised figure or to be embossed.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|39}} In English, the word might be spelled with or without the acute accent on the final ''e''. Generally, the term was used loosely to describe fabric with a pattern woven into it, either in the same color or a color different from that of the background. That is, the weave that produces the pattern is different from the weave that produces the background.

S. F. A. Caulfeild and B. C. Saward published this definition of ''broché'' in their 1887 ''Dictionary of Needlework'', according to the ''Oxford English Dictionary'' (the ''face'' being the side of the fabric facing the viewer):&lt;blockquote&gt;Broché. A French term denoting a velvet or silk textile, with a satin figure thrown up on the face.&lt;ref&gt;“Broché, Adj.” ''Oxford English Dictionary'', Oxford UP, December 2024, https://doi.org/10.1093/OED/1054215522.&lt;/ref&gt;&lt;/blockquote&gt;
=== Chiffon ===
A lightweight, somewhat sheer silk fabric, chiffon would have been worn only by the social elite at the end of the 19th century.&lt;ref name=&quot;:25&quot;&gt;{{Cite journal|date=2025-10-12|title=Chiffon (fabric)|url=https://en.wikipedia.org/w/index.php?title=Chiffon_(fabric)&amp;oldid=1316464288|journal=Wikipedia|language=en}}&lt;/ref&gt; Synthetic fibers were not invented until the 20th century — nylon chiffon in 1938 and polyester chiffon not until 1958.&lt;ref name=&quot;:25&quot; /&gt;

=== Ciselé ===

=== Crape ===
The ''Oxford English Dictionary'' distinguishes the use of ''crêpe'' (using a circumflex rather than an acute accent over the first ''e'') from ''crape'' in textiles, saying ''crêpe'' is &quot;often borrowed [from the French] as a term for all crapy fabrics other than ordinary [[Social Victorians/Mourning|black mourning crape]],&quot;&lt;ref name=&quot;:24&quot;&gt;&quot;crêpe, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44242. Accessed 10 February 2023.&lt;/ref&gt; with usage examples ranging from 1797 to the mid 20th century. This distinction seems more prescriptive than descriptive since texts from the 19th century to now do not make it reliably. Sometimes 19th-century newspapers put an acute accent on the ''e'' and spelled it crépe.

The fabric used for full mourning was black crape, a fabric with a dull texture, but writers continue to vary in how to spell it. Julia Baird uses ''crêpe'', defining it as &quot;a thick black rustling material made of silk, crimped to make it look dull.&quot;&lt;ref&gt;Baird, Julia. ''Victoria the Queen, an Intimate Biography of the Woman Who Ruled an Empire''. Random House, 2016. https://books.apple.com/us/book/victoria-the-queen/id953835024.&lt;/ref&gt;{{rp|584 of 1203}}

However it is spelled, crêpe is&lt;blockquote&gt;Any number of fabrics with characteristic crinkled or puckered surface.&lt;ref name=&quot;:7&quot; /&gt; (77)&lt;/blockquote&gt;

==== Crepe de Chine ====
Crêpe de chine, the ''OED'' says, is &quot;a white or other coloured crape made of raw silk.&quot;&lt;ref name=&quot;:24&quot; /&gt; Lewandowski defines it as &quot;a very lightweight, fine, plain weave silk fabric. ... Introduced in 1866, China crepe with soft, silky surface.&quot;&lt;ref name=&quot;:7&quot; /&gt; (77) 

==== Crepon de Chine ====
Crepon is a fabric heavier than the usual crape but treated like crape to be crinkly. Lewandowski says,&lt;blockquote&gt;Introduced in 1882, wool, silk, or blend fabric like very heavy crepe. ... Gay Nineties (1890–1900 C.E.). Popular in 1890s, woolen fabric creped to appear puffed between stripes [or] squares.&lt;ref name=&quot;:7&quot; /&gt; (77)&lt;/blockquote&gt;According to Lewandowski, ''crepon'' can also be another word for bustle (1865–1890 C.E. to present).&lt;ref name=&quot;:7&quot; /&gt; (77)

=== Crinoline ===
Technically, crinoline was a fabric made mostly of horsehair and sometimes linen, stiffened with starch or glue, similar to buckram today, used in men's military collars and [[Social Victorians/Terminology#Crinolines|women's foundation garments]]. Lewandowski defines crinoline as &lt;blockquote&gt;(1840–1865 C.E.). France. Originally horsehair cloth used for officers' collars. Later used for women's underskirts to support skirts. Around 1850, replaced by many petticoats, starched and boned. Around 1856, [[Social Victorians/Terminology#Crinoline Hoops|light metal cage]] was developed.&lt;ref name=&quot;:7&quot; /&gt;{{rp|78}}&lt;/blockquote&gt;The term has been used so consistently for the cage first introduced in the 1850s that held the skirt out from the body, however, that it is important to say ''crinoline cage'' or ''crinoline fabric'' or ''crinoline petticoat'' to be clear.

=== Épinglé Velvet ===
Often spelled ''épingle'' rather than ''épinglé'', this term appears to have been used for a fabric made of wool, or at least wool along with linen or cotton, that was heavier and stiffer than silk velvet. It was associated with outer garments and men's clothing. Nowadays, épinglé velvet is an upholstery fabric in which the pile is cut into designs and patterns, and the portrait of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Duchess of Hamilton]] shows a mantle described as épinglé velvet that does seem to be a velvet with a woven pattern perhaps cut into the pile. 

=== Lace ===
While lace also functioned sometimes as fabric — at the décolletage, for example, on the stomacher or as a veil — here we organize it as a [[Social Victorians/Terminology#Trim and Lace|part of the elaboration of clothing]].

=== Liberty Fabrics ===

=== Lisse ===
According to the ''Oxford English Dictionary'', the term ''lisse'' as a &quot;kind of silk gauze&quot; was used in the 19th-century UK and US.&lt;ref&gt;&quot;lisse, n.1.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/108978. Accessed 4 July 2023.&lt;/ref&gt;

=== Muslin ===
=== Satin ===
The pre-1927 ''History of Feminine Fashion'', probably commissioned by Charles Frederick Worth's sons, describes Worth's &quot;insistence on new fabrics, new trimmings, new materials of every description&quot; at the beginning of his career in the mid 19th century:&lt;blockquote&gt;When Worth first entered the business of dressmaking, the only materials of the richer sort used for woman's dress were velvet, faille, and watered silk. Satin, for example, was never used. M. Worth desired to use satin very extensively in the gowns he designed, but he was not satisfied with what could be had at the time; he wanted something very much richer than was produced by the mills at Lyons. That his requirements entailed the reconstruction of mills mattered little — the mills were reconstructed under his directions, and the Lyons looms turned out a richer satin than ever, and the manufacturers prospered accordingly.&lt;ref name=&quot;:9&quot; /&gt;{{rp|6 in printed, 26 in digital book}}&lt;/blockquote&gt;

=== Selesia ===
According to the ''Oxford English Dictionary'', ''silesia'' is &quot;A fine linen or cotton fabric originally manufactured in Silesia in what is now Germany (''Schlesien'').&lt;ref&gt;&quot;Silesia, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/179664. Accessed 9 February 2023.&lt;/ref&gt; It may have been used as a lining — for pockets, for example — in garments made of more luxurious or more expensive cloth. The word ''sleazy'' — &quot;Of textile fabrics or materials: Thin or flimsy in texture; having little substance or body.&quot;&lt;ref&gt;&quot;sleazy, adj.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/181563. Accessed 9 February 2023.&lt;/ref&gt; — may be related.

=== Shot Fabric ===
According to the ''Oxford English Dictionary'', &quot;Of a textile fabric: Woven with warp-threads of one colour and weft-threads of another, so that the fabric (usually silk) changes in tint when viewed from different points.&quot;&lt;ref&gt;“Shot, ''Adj.''”  ''Oxford English Dictionary'', Oxford UP,  July 2023,  https://doi.org/10.1093/OED/2977164390.&lt;/ref&gt; A shot fabric might also be made of silk and cotton fibers.

=== Tissue ===
A lightly woven fabric like gauze or chiffon. The light weave can make the fabric translucent and make pleating and gathering flatter and less bulky. Tissue can be woven to be shot, sheer, stiff or soft.

Historically, the term in English was used for a &quot;rich kind of cloth, often interwoven with gold or silver&quot; or &quot;various rich or fine fabrics of delicate or gauzy texture.&quot;&lt;ref&gt;“Tissue, N.” ''Oxford English Dictionary'', Oxford UP, March 2024, https://doi.org/10.1093/OED/5896731814.&lt;/ref&gt;

=== Tulle ===
In the 19th century, tulle — a very fine net — was a sheer woven tissue made of linen or silk. Tulle looms were invented in the late 18th century,&lt;ref name=&quot;:23&quot;&gt;{{Cite journal|date=2025-09-04|title=Tulle (tissu)|url=https://fr.wikipedia.org/w/index.php?title=Tulle_(tissu)&amp;oldid=228712045|journal=Wikipédia|language=fr}}&lt;/ref&gt; and the fabric &quot;first made by machine in 1768 in Nottingham.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|299}} By 1802 English tulle was recognized as higher quality than French tulle, even though the fabric is named for the French city.&lt;ref name=&quot;:23&quot; /&gt;

Tulle is still used today, but it is usually made of synthetic fabric.&lt;blockquote&gt;It is a finer textile than the textile referred to as &quot;net&quot;. ...

It can be made of various fibres, including silk, nylon, polyester and rayon. Polyester is the most common fibre used for tulle.&lt;ref&gt;{{Cite journal|date=2025-08-05|title=Tulle (netting)|url=https://en.wikipedia.org/w/index.php?title=Tulle_(netting)&amp;oldid=1304416320|journal=Wikipedia|language=en}}&lt;/ref&gt;&lt;/blockquote&gt;Victorian silk tulle would not have been stiff unless it was treated with sizing.

== Fan ==

The ''Encyclopaedia Britannica'' (9th edition) has an article on the fan. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)&lt;blockquote&gt;FAN (Latin, ''vannus''; French, ''éventail''), a light implement used for giving motion to the air. ''Ventilabrum'' and ''flabellum'' are names under which ecclesiastical fans are mentioned in old inventories. Fans for cooling the face have been in use in hot climates from remote ages. A bas-relief in the British Museum represents Sennacherib with female figures carrying feather fans. They were attributes of royalty along with horse-hair fly-flappers and umbrellas. Examples may be seen in plates of the Egyptian sculptures at Thebes and other places, and also in the ruins of Persepolis. In the museum of Boulak, near Cairo, a wooden fan handle showing holes for feathers is still preserved. It is from the tomb of Amen-hotep, of the 18th dynasty, 17th century &lt;small&gt;B&lt;/small&gt;.&lt;small&gt;C&lt;/small&gt;. In India fans were also attributes of men in authority, and sometimes sacred emblems. A heartshaped fan, with an ivory handle, of unknown age, and held in great veneration by the Hindus, was given to the prince of Wales. Large punkahs or screens, moved by a servant who does nothing else, are in common use by Europeans in India at this day.

Fans were used in the early Middle Ages to keep flies from the sacred elements during the celebrations of the Christian mysteries. Sometimes they were round, with bells attached — of silver, or silver gilt. Notices of such fans in the ancient records of St Paul’s, London, Salisbury cathedral, and many other churches, exist still. For these purposes they are no longer used in the Western church, though they are retained in some Oriental rites. The large feather fans, however, are still carried in the state processions of the supreme pontiff in Rome, though not used during the celebration of the mass. The fan of Queen Theodolinda (7th century) is still preserved in the treasury of the cathedral of Monza. Fans made part of the bridal outfit, or ''mundus muliebris'', of ancient Roman ladies.

Folding fans had their origin in Japan, and were imported thence to China. They were in the shape still used—a segment of a circle of paper pasted on a light radiating frame-work of bamboo, and variously decorated, some in colours, others of white paper on which verses or sentences are written. It is a compliment in China to invite a friend or distinguished guest to write some sentiment on your fan as a memento of any special occasion, and this practice has continued. A fan that has some celebrity in France was presented by the Chinese ambassador to the Comtesse de Clauzel at the coronation of Napoleon I. in 1804. When a site was given in 1635, on an artificial island, for the settlement of Portuguese merchants in Nippo in Japan, the space was laid out in the form of a fan as emblematic of an object agreeable for general use. Men and women of every rank both in China and Japan carry fans, even artisans using them with one hand while working with the other. In China they are often made of carved ivory, the sticks being plates very thin and sometimes carved on both sides, the intervals between the carved parts pierced with astonishing delicacy, and the plates held together by a ribbon. The Japanese make the two outer guards of the stick, which cover the others, occasionally of beaten iron, extremely thin and light, damascened with gold and other metals.

Fans were used by Portuguese ladies in the 14th century, and were well known in England before the close of the reign of Richard II. In France the inventory of Charles V. at the end of the 14th century mentions a folding ivory fan. They were brought into general use in that country by Catherine de’ Medici, probably from Italy, then in advance of other countries in all matters of personal luxury. The court ladies of Henry VIII.’s reign in England were used to handling fans, A lady in the Dance of Death by Holbein holds a fan. Queen Elizabeth is painted with a round leather fan in her portrait at Gorhambury; and as many as twenty-seven are enumerated in her inventory (1606). Coryat, an English traveller, in 1608 describes them as common in Italy. They also became of general use from that time in Spain. In Italy, France, and Spain fans had special conventional uses, and various actions in handling them grew into a code of signals, by which ladies were supposed to convey hints or signals to admirers or to rivals in society. A paper in the ''Spectator'' humorously  proposes to establish a regular drill for these purposes.

The chief seat of the European manufacture of fans during the 17th century was Paris, where the sticks or frames, whether of wood or ivory, were made, and the decorations painted on mounts of very carefully prepared vellum (called latterly ''chicken skin'', but not correctly), — a material stronger and tougher than paper, which breaks at the folds. Paris makers exported fans unpainted to Madrid and other Spanish cities, where they were decorated by native artists. Many were exported complete; of old fans called Spanish a great number were in fact made in France. Louis XIV. issued edicts at various times to regulate the manufacture. Besides fans mounted with parchment, Dutch fans of ivory were imported into Paris, and decorated by the heraldic painters in the process called “Vernis Martin,” after a famous carriage painter and inventor of colourless lac varnish. Fans of this kind belonging to the Queen and to the late baroness de Rothschild were exhibited in 1870 at Kensington. A fan of the date of 1660, representing sacred subjects, is attributed to Philippe de Champagne, another to Peter Oliver in England in the / 17th century. Cano de Arevalo, a Spanish painter of the 17th century devoted himself to fan painting. Some harsh expressions of Queen Christina to the young ladies of the French court are said to have caused an increased ostentation in the splendour of their fans, which were set with jewels and mounted in gold. Rosalba Carriera was the name of a fan painter of celebrity in the 17th century. Lebrun and Romanelli were much employed during the same period. Klingstet, a Dutch artist, enjoyed a considerable reputation for his fans from the latter part of the 17th and the first thirty years of the 18th century.

The revocation of the edict of Nantes drove many fan-makers out of France to Holland and England. The trade in England was well established under the Stuart sovereigns. Petitions were addressed by the fan-makers to Charles II. against the importation of fans from India, and a duty was levied upon such fans in consequence. This importation of Indian fans, according to Savary, extended also to France. During the reign of Louis XV. carved Indian and China fans displaced to some extent those formerly imported from Italy, which had been painted on swanskin parchment prepared with various perfumes.

During the 18th century all the luxurious ornamentation of the day was bestowed on fans as far as they could display it. The sticks were made of mother-of-pearl or ivory, carved with extraordinary skill in France, Italy, England, and other countries. They were painted from designs of Boucher, Watteau, Lancret, and other &quot;genre&quot; painters, Hébert, Rau, Chevalier, Jean Boquet, Mad. Verité, are known as fan painters. These fashions were followed in most countries of Europe, with certain national differences. Taffeta and silk, as well as fine parchment, were used for the mounts. Little circles of glass were let into the stick to be looked through, and small telescopic glasses were sometimes contrived at the pivot of the stick. They were occasionally mounted with the finest point lace. An interesting fan (belonging to Madame de Thiac in France), the work of Le Flamand, was presented by the municipality of Dieppe to Marie Antoinette on the birth of her son the dauphin. From the time of the Revolution the old luxury expended on fans died out. Fine examples ceased to be exported to England and other countries. The painting on them represented scenes or personages connected with political events. At a later period fan mounts were often prints coloured by hand. The events of the day mark the date of many examples found in modern collections. Amongst the fanmakers of the present time the names of Alexandre, Duvelleroy, Fayet, Vanier, may be mentioned as well known in Paris. The sticks are chiefly made in the department of Oise, at Le Déluge, Crèvecœur, Méry, Ste Geneviève, and other villages, where whole families are engaged in preparing them; ivory sticks are carved at Dieppe. Water-colour painters of distinction often design and paint the mounts, the best designs being figure subjects. A great impulse has been given to the manufacture and painting of fans in England since the exhibition which took place at South Kensington in 1870. Other exhibitions have since been held, and competitive prizes offered, one of which was gained by the Princess Louise. Modern collections of fans take their date from the emigration of many noble families from France at the time of the Revolution. Such objects were given as souvenirs and occasionally sold by families in straitened circumstances. A large number of fans of all sorts, principally those of the 18th century, French, English, German, Italian Spanish, &amp;c., have been lately bequeathed to the South Kensington Museum.

Regarding the different parts of folding fans it may be well to state that the sticks are called in French ''brins'', the two outer guards ''panaches'', and the mount ''feuille''.&lt;ref&gt;J. H. Pollen [J.H.P.]. &quot;Fan.&quot; ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. '''10''' ('''X'''). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%209%20%28FAL-FYZ%29%20193323016.23/page/26/mode/2up (accessed January 2023): 27, Col. 1b – 28, Col. 1c.&lt;/ref&gt;&lt;/blockquote&gt;Folding fans were available and popular early and are common accessories in portraits of fashionable women through the centuries.

== Costumes for Theatre and Fancy Dress ==
Fancy-dress (or costume) balls were popular and frequent in the U.K. and France as well as the rest of Europe and North America during the 19th century. The themes and styles of the fancy-dress balls influenced those that followed. 

At the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the guests came dressed in costume from times before 1820, as instructed on '''the invitation''', but their clothing was much more about late-Victorian standards of beauty and fashion than the standards of whatever time period the portraits they were copying or basing their costumes on. 

=== Fancy Dress ===
In her ''Magnificent Entertainments: Fancy Dress Balls of Canada's Governors General, 1876-1898'', Cynthia Cooper describes the resources available to those needing help making a costume for a fancy-dress ball:&lt;blockquote&gt;There were a number of places eager ballgoers could turn for assistance and inspiration. Those with a scholarly bent might pore over history books or study pictures of paintings or other works of art. For more direct advice, one could turn to the barrage of published information specifically on fancy dress. Women’s magazines such as ''Godey’s Lady’s Book'' and ''The Englishwoman’s Domestic Magazine'' sometimes featured fancy dress designs and articles, and enticing specialized books were available with extensive recommendations for choosing fancy dress. By far the most complete sources were the books by [[Social Victorians/People/Ardern Holt|Ardern Holt]], a prolific British authority on the subject. Holt’s book for women, ''Fancy Dresses Described, or What to Wear at Fancy Balls'' (published in six editions between 1879 and 1896), began with the query, ‘‘But what are we to wear?” Holt’s companion book, ''Gentlemen’s Fancy Dress:'' ''How to Choose It'', was also published in six editions from 1882 to 1905. Other prominent authorities included Mrs. Aria’s ''Costume: Fanciful, Historical, and Theatrical'' and, in the US, the Butterick Company’s ''Masquerade and Carnival: Their Customs and Costumes''. The Butterick publication relied heavily on Holt, copying large sections of the introduction outright and paraphrasing other sections.&lt;ref name=&quot;:16&quot;&gt;Cooper, Cynthia. ''Magnificent entertainments: fancy dress balls of Canada's Governors General, 1876-1898''.Fredericton, N.B.; Hull, Quebec: Goose Lane Editions and Canadian Museum of Civilization, 1997. Internet Archive https://archive.org/details/magnificententer0000coop/.&lt;/ref&gt;{{rp|28–29}}&lt;/blockquote&gt;

Cynthia Cooper discusses how &quot;historical accuracy&quot; works in historical fiction and historical dress: &lt;blockquote&gt;A seemingly accurate costume and coiffure bespoke a cultured individual whose most gratifying compliment would be “historically correct.” Those who were fortunate enough to own actual clothing from an earlier period might wear it with pride as a historical relic, though they would generally adapt or remake it in keeping with the aesthetics of their own period. Historical accuracy was always in the eye of beholders inclined to overlook elements of current fashion in a historical costume. Theatre had long taught the public that if a costume appeared tasteful and attractive, it could be assumed to be accurate. Even at Queen Victoria’s fancy dress balls, costume silhouette was always far more like the fashionable dress of the period than of the time portrayed. For this reason, many extant eighteenth-century dresses show evidence of extensive alterations done in the nineteenth century, no doubt for fancy dress purposes.&lt;ref name=&quot;:16&quot; /&gt;{{rp|25}}&lt;/blockquote&gt;

The newspaper ''The Queen'' published dress and fashion information and advice under the byline of [[Social Victorians/People/Ardern Holt|Ardern Holt]], who regularly answered questions from readers about fashion as well as about fancy dress. Holt also wrote entire articles with suggestions for what might make an appealing fancy-dress costume as well as pointing readers away from costumes that had been worn too frequently. The suggestions for costumes are based on familiar types or portraits available to readers, similar to Holt's books on fancy dress, which ran through a number of editions in the 1880s and 1890s. Fancy-dress questions sometimes asked for details about costumes worn in theatrical or operatic productions, which Holt provides. 

In November 1897, Holt refers to the Duchess of Devonshire's 2 July ball: &quot;Since the famous fancy ball, given at Devonshire House during this year, historical fancy dresses have assumed a prominence that they had not hitherto known.&quot;&lt;ref&gt;Holt, Ardern. &quot;Fancy Dress a la Mode.&quot; The ''Queen'' 27 November 1897, Saturday: 94 [of 145 in BNA; print p. 1026], Col. 1a [of 3]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18971127/459/0094.&lt;/ref&gt; Holt goes on to provide a number of ideas for costumes for historical fancy dress, as always with a strong leaning toward Victorian standards of beauty and style and away from any concern for historical accuracy.

As Leonore Davidoff says, &quot;Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration symbolised some status category for the female wearer.&quot;&lt;ref name=&quot;:1&quot; /&gt;{{rp|93}} [handled under [[Social Victorians/Terminology#Elaborations|Elaborations]]]

=== Historical Accuracy ===
Many of the costumes at the ball were based on portraits, especially when the guest was dressed as a historical figure. If possible, we have found the portraits likely to have been the originals, or we have found, if possible, portraits that show the subjects from the two time periods at similar ages.

The way clothing was cut changed quite a bit between the 18th and 19th centuries. We think of Victorian clothing — particularly women's clothing, and particularly at the end of the century — as inflexible and restrictive, especially compared to 20th- and 21st-century customs permitting freedom of movement. The difference is generally evolutionary rather than absolute — that is, as time has passed since the 18th century, clothing has allowed an increasingly greater range of movement, especially for people who did not do manual labor.

By the end of the 19th century, garments like women's bodices and men's coats were made fitted and smooth by attention to the grain of the fabric and by the use of darts (rather than techniques that assembled many small, individual pieces of fabric).

* clothing construction and flat-pattern techniques
* Generally, the further back in time we go, the more 2-dimensional the clothing itself was.

==== Women's Versions of Historical Accuracy at the Ball ====
As always with this ball, whatever historical accuracy might be present in a woman's costume is altered so that the wearer is still a fashionable Victorian lady. What makes the costumes look &quot;Victorian&quot; to our eyes is the line of the silhouette caused by the foundation undergarments as well as the many &quot;elaborations&quot;&lt;ref name=&quot;:1&quot; /&gt;{{rp|93}}, mostly in the decorations, trim and accessories. 

Also, the clothing hangs and drapes differently because the fabric was cut on grain and the shoulders were freed by the way the sleeves were set in. 

==== Men's Versions of Historical Accuracy at the Ball ====
Because men were not wearing a Victorian foundation garment at the end of the century, the men's costumes at the ball are more historically accurate in some ways.

* Trim
* Mixing neck treatments
* Hair
* Breeches
* Shoes and boots
* Military uniforms, arms, gloves, boots

== Feathers and Plumes ==

=== Aigrette ===
Elizabeth Lewandowski defines ''aigrette'' as &quot;France. Feather or plume from an egret or heron.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|5}} Sometimes the newspapers use the term to refer to an accessory (like a fan or ornament on a hat) that includes such a feather or plume. The straight and tapered feathers in an aigrette are in a bundle.

=== Prince of Wales's Feathers or White Plumes ===
The feathers in an aigrette came from egrets and herons; Prince of Wales's feathers came from ostriches. A fuller discussion of Prince of Wales's feathers and the white ostrich plumes worn at court appears on [[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|Victorian Things]].

For much of the late 18th and 19th centuries, white ostrich plumes were central to fashion at court, and at a certain point in the late 18th century they became required for women being presented to the monarch and for their sponsors. Our purpose here is to understand why women were wearing plumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] as part of their costumes.

First published in 1893, [[Social Victorians/People/Lady Colin Campbell|Lady Colin Campbell]]'s ''Manners and Rules of Good Society'' (1911 edition) says that&lt;blockquote&gt;It was compulsory for both Married and Unmarried Ladies to Wear Plumes. The married lady’s Court plume consisted of three white feathers. An unmarried lady’s of two white feathers. The three white feathers should be mounted as a Prince of Wales plume and worn towards the left hand side of the head. Colored feathers may not be worn. In deep mourning, white feathers must be worn, black feathers are inadmissible.

White veils or lace lappets must be worn with the feathers. The veils should not be longer than 45 inches.&lt;ref&gt;{{Cite web|url=https://www.edwardianpromenade.com/etiquette/the-court-presentation/|title=The Court Presentation|last=Holl|first=Evangeline|date=2007-12-07|website=Edwardian Promenade|language=en-US|access-date=2022-12-18}} https://www.edwardianpromenade.com/etiquette/the-court-presentation/.&lt;/ref&gt;&lt;/blockquote&gt;[[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|This fashion was imported from France]] in the mid 1770s.&lt;ref&gt;&quot;Abstract&quot; for Blackwell, Caitlin. &quot;'&lt;nowiki/&gt;''The Feather'd Fair in a Fright''': The Emblem of the Feather in Graphic Satire of 1776.&quot; ''Journal for Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. ''Wiley Online'' DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x (accessed November 2022).&lt;/ref&gt;

Separately, a secondary heraldic emblem of the Prince of Wales has been a specific arrangement of 3 ostrich feathers in a gold coronet&lt;ref&gt;{{Cite journal|date=2022-11-07|title=Prince of Wales's feathers|url=https://en.wikipedia.org/w/index.php?title=Prince_of_Wales%27s_feathers&amp;oldid=1120556015|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Prince_of_Wales's_feathers.&lt;/ref&gt; since King Edward III (1312–1377&lt;ref&gt;{{Cite journal|date=2022-12-14|title=Edward III of England|url=https://en.wikipedia.org/w/index.php?title=Edward_III_of_England&amp;oldid=1127343221|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Edward_III_of_England.&lt;/ref&gt;).

Some women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] wore white ostrich feathers in their hair, but most of them are not Prince of Wales's feathers. Most of the plumes in these portraits are arrangements of some kind of headdress to accompany the costume. A few, wearing what looks like the Princes of Wales's feathers, might be signaling that their character is royal or has royal ancestry. '''One of the women [which one?] was presented to the royals at this ball?'''

Here is the list of women who are wearing white ostrich plumes in their portraits in the [[Social Victorians/1897 Fancy Dress Ball/Photographs|''Diamond Jubilee Fancy Dress Ball'' album of 286 photogravure portraits]]:

# Kathleen Pelham-Clinton, the [[Social Victorians/People/Newcastle|Duchess of Newcastle]]
# [[Social Victorians/People/Louisa Montagu Cavendish|Luise Cavendish]], the Duchess of Devonshire
# Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce|Marquisa de Santurce]]
# Lady [[Social Victorians/People/Farquhar|Emilie Farquhar]]
# Princess (Laura Williamina Seymour) Victor of  [[Social Victorians/People/Gleichen#Laura%20Williamina%20Seymour%20of%20Hohenlohe-Langenburg|Hohenlohe Langenburg]]
# Louisa Acheson, [[Social Victorians/People/Gosford|Lady Gosford]]
# Alice Emily White Coke, [[Social Victorians/People/Leicester|Viscountess Coke]]
# Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry|Vane-Tempest-Stewart]]
#[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill|Consuelo Vanderbilt Spencer-Churchill]], Duchess of [[Social Victorians/People/Marlborough|Marlborough]], dressed as the wife of the French Ambassador at the Court of Catherine of Russia (not white, but some color that reads dark in the black-and-white photograph)
#Mrs. Mary [[Social Victorians/People/Chamberlain|Chamberlain]] (at 491), wearing white plumes, as Madame d'Epinay
#Lady Clementine [[Social Victorians/People/Tweeddale|Hay]] (at 629), wearing white plumes, as St. Bris (''Les Huguenots'')
#[[Social Victorians/People/Meysey-Thompson|Lady Meysey-Thompson]] (at 391), wearing white plumes, as Elizabeth, Queen of Bohemia
#Mrs. [[Social Victorians/People/Grosvenor|Algernon (Catherine) Grosvenor]] (at 510), wearing white plumes, as Marie Louise
#Lady [[Social Victorians/People/Ancaster|Evelyn Ewart]], at 401), wearing white plumes, as the Duchess of Ancaster, Mistress of the Robes to Queen Charlotte, 1757, after a picture by Hudson
#[[Social Victorians/People/Lyttelton|Edith Sophy Balfour Lyttelton]] (at 580), wearing what might be white plumes on a large-brimmed white hat, after a picture by Romney
#[[Social Victorians/People/Yznaga|Emilia Yznaga]] (at 360), wearing what might be white plumes, as Cydalise of the Comedie Italienne from the time of Louis XV
#Lady [[Social Victorians/People/Ilchester|Muriel Fox Strangways]] (at 403), wearing what might be two smallish white plumes, as Lady Sarah Lennox, one of the bridesmaids of Queen Charlotte A.D. 1761
#Lady [[Social Victorians/People/Lucan|Violet Bingham]] (at 586), wearing perhaps one white plume in a headdress not related to the Prince of Wales's feathers
#Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329), wearing a headdress that includes some white plumes, as Lady Burleigh
#[[Social Victorians/People/Dupplin|Agnes Blanche Marie Hay-Drummond]] (at 682), in a big headdress topped with white plumes, as Mademoiselle Andrée de Taverney A.D. 1775
#Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336), wearing what looks like Prince of Wales's plumes
#[[Social Victorians/People/Suffolk|Marguerite Hyde &quot;Daisy&quot; Leiter]] (at 684), wearing what looks like Prince of Wales's plumes
#Lady [[Social Victorians/People/Spicer|Margaret Spicer]] (at 281), wearing one smallish white and one black plume, as Countess Zinotriff, Lady-in-Waiting to the Empress Catherine of Russia
#Mrs. [[Social Victorians/People/Cavendish Bentinck|Arthur James]] (at 318), wearing what looks like Prince of Wales's plumes, as Elizabeth Cavendish, daughter of Bess of Hardwick
#Nellie, [[Social Victorians/People/Kilmorey|Countess of Kilmorey]] (at 207), wearing three tall plumes, 2 white and one dark, as Comtesse du Barri
#Daisy, [[Social Victorians/People/Warwick|Countess of Warwick]] (at 53), wearing at least 1 white plume, as Marie Antoinette

More men than women were wearing plumes reminiscent of the Prince of Wales's feathers:

*

==== Bibliography for Plumes and Prince of Wales's Feathers ====
* Blackwell, Caitlin. &quot;'''The Feather'd Fair in a Fright'&lt;nowiki/&gt;'': The Emblem of the Feather in Graphic Satire of 1776.&quot; Journal for ''Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. Wiley Online DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x.
* &quot;Prince of Wales's feathers.&quot; ''Wikipedia'' https://en.wikipedia.org/wiki/Prince_of_Wales%27s_feathers (accessed November 2022). ['''Add women to this page''']
* Simpson, William. &quot;On the Origin of the Prince of Wales' Feathers.&quot; ''Fraser's magazine'' 617 (1881): 637-649. Hathi Trust https://babel.hathitrust.org/cgi/pt?id=chi.79253140&amp;view=1up&amp;seq=643&amp;q1=feathers (accessed December 2022). Deals mostly with use of feathers in other cultures and in antiquity; makes brief mention of feathers and plumes in signs and pub names that may not be associated with the Prince of Wales. No mention of the use of plumes in women's headdresses or court dress.

== Honors ==

=== The Bath ===
The Most Honourable Order of the Bath (GCB, Knight or Dame Grand Cross; KCB or DCB, Knight or Dame Commander; CB, Companion)

=== The Garter ===
The Most Noble Order of the Knights of the Garter (KG, Knight Companion; LG, Lady Companion)

[[File:The Golden Fleece - collar exhibited at MET, NYC.jpg|thumb|The Golden Fleece collar and pendant for the 2019 &quot;Last Knight&quot; exhibition at the MET, NYC.|alt=Recent photograph of a gold necklace on a wide band, with a gold skin of a sheep hanging from it as a pendant]]
=== The Golden Fleece ===
To wear the golden fleece is to wear the insignia of the Order of the Golden Fleece, said to be &quot;the most prestigious and historic order of chivalry in the world&quot; because of its long history and strict limitations on membership.&lt;ref name=&quot;:10&quot;&gt;{{Cite journal|date=2020-09-25|title=Order of the Golden Fleece|url=https://en.wikipedia.org/w/index.php?title=Order_of_the_Golden_Fleece&amp;oldid=980340875|journal=Wikipedia|language=en}}&lt;/ref&gt; The monarchs of the U.K. were members of the originally Spanish order, as were others who could afford it, like the Duke of Wellington,&lt;ref name=&quot;:12&quot;&gt;Thompson, R[obert]. H[ugh]. &quot;The Golden Fleece in Britain.&quot; Publication of the ''British Numismatic Society''. 2009 https://www.britnumsoc.org/publications/Digital%20BNJ/pdfs/2009_BNJ_79_8.pdf (accessed January 2023).&lt;/ref&gt; the first Protestant to be admitted to the order.&lt;ref name=&quot;:10&quot; /&gt; Founded in 1429/30 by Philip the Good, Duke of Burgundy, the order separated into two branches in 1714, one Spanish and the other Austrian, still led by the House of Habsburg.&lt;ref name=&quot;:10&quot; /&gt;

[[File:Prince Albert - Franz Xaver Winterhalter 1842.jpg|thumb|1842 Winterhalter portrait of Prince Albert wearing the insignia of the Order of the Golden Fleece, 1842|left|alt=1842 Portrait of Prince Albert by Winterhalter, wearing the insignia of the Golden Fleece]]
The photograph (upper right) is of a Polish badge dating from the &quot;turn of the XV and XVI centuries.&quot;&lt;ref&gt;{{Citation|title=Polski:  Kolana orderowa orderu Złotego Runa, przełom XV i XVI wieku.|url=https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg|date=2019-11-10|accessdate=2023-01-10|last=Wulfstan}}. https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg.&lt;/ref&gt; The collar to this Golden Fleece might be similar to the one the [[Social Victorians/People/Spencer Compton Cavendish#The Insignia of the Order of the Golden Fleece|Duke of Devonshire is wearing in the 1897 Lafayette portrait]].

The badges and collars that Knights of the Order actually wore vary quite a bit.

The 1842 Franz Xaver Winterhalter portrait (left) of Prince Consort Albert, Victoria's husband and father of the Prince of Wales, shows him wearing the Golden Fleece on a red ribbon around his neck and the star of the Garter on the front of his coat.&lt;ref&gt;Winterhalter, Franz Xaver. ''Prince Albert''. {{Cite web|url=https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61|title=Explore the Royal Collection Online|website=www.rct.uk|access-date=2023-01-16}} https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61.&lt;/ref&gt;

=== Royal Victorian Order ===
(GCVO, Knight or Dame Grand Cross; KCVO or DCVO, Knight or Dame Commander; CVO, Commander; LVO, Lieutenant; MVO, Member)

=== St. John ===
The Order of the Knights of St. John

=== Star of India ===
Most Exalted Order of the Star of India (GCSI, Knight Grand Commander; KCSI, Knight Commander; CSI, Companion)

=== Thistle ===
The Most Ancient and Most Noble Order of the Thistle

== Hoops ==
'''This section is under construction right now'''.

Terms: farthingale, panniers, hoops, crinoline, cage, bustle

Between 1450 and 1550 a loosely woven, very stiff fabric made from linen and horsehair was used in &quot;horsehair petticoats.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|137}} Heavy and scratchy, these petticoats made the fabric of the skirt lie smooth, without wrinkles or folds. Over time, this horsehair fabric was used in several kinds of objects made from fabric, like hats and padding for poufs, but it is best known for its use in the structure of hoops, or cages. Horsehair fabric was used until the mid-19th century, when it  was called ''crinoline'' and used for petticoats again (1840–1865).&lt;ref name=&quot;:7&quot; /&gt;{{rp|78}} We still call this fabric ''crinoline''.

''Hoops'' is a mid-19th-century term for a cage-like structure worn by a woman to hold her skirts away from her body. The term ''cage'' is also 19th century, and ''crinoline'' is sometimes used in a non-technical way for 19th-century cages as well. Both these terms are commonly used now for the general understructure of a woman's skirts, but they are not technically accurate for time periods before the 19th century.

As fashion, that cage-like structure was the foundation undergarment for the bottom half of a woman's body, for a skirt and petticoat, and created the fashionable silhouette from the 15th through the late 19th century. The 16th-century Katherine of Aragon is credited with making hoops popular outside Spain for women of the elite classes. By the end of the 16th century France had become the arbiter of fashion for the western world, and it still is. The cage is notable for how long it lasted in fashion and for its complex evolution.

Together with the [[Social Victorians/Terminology#Corsets|corset]], the cage enabled all the changes in fashionable shapes, from the extreme distortions of 17th-and-18th-century panniers to the late 19th-century bustle. Early hoops circled the body in a bell, cone or drum shape, then were moved to the sides with panniers, then ballooned around the body like the top half of a sphere, and finally were pulled to the rear as a bustle. That is, the distorted shapes of high fashion were made possible by hoops. High fashion demanded these shapes, which disguised women's bodies, especially below the waist, while corsets did their work above it.

When hoops were first introduced in the 15th century, women's shoes for the first time differentiated from men's and became part of the fashionable look. In the periods when the skirts were flat in front (with the farthingale and in the transitional 17th century), they did not touch the floor, making shoes visible — and important fashion accessories. Portraits of high-status, high-fashion women consistently show their pointy-toed shoes, which would have been more likely to show when they were moving than when they were standing still. The shoes seem to draw attention to themselves in these portraits, suggesting that they were important to the painters and, perhaps, the women as well.

In addition to the shape, the materials used to make hoops evolved — from cane and wood to whalebone, then steel bands and wire. Initially fabric strips, tabs or ribbons were the vertical elements in the cages and evolved into channels in a linen, muslin or, later, crinoline underskirt encasing wires or bands. Fabrics besides crinoline —  like cotton, silk and linen — were used to connect the hoops and bands in cages. All of these materials used in cages had disadvantages and advantages. 

=== Disadvantages and Advantages ===
Hoops affected the way women were able to move. ['''something about riding'''?]

==== Disadvantages ====
the weight, getting through doorways, sitting, the wind, getting into carriages, what the dances involved. Raising '''one's''' skirts to climb stairs or walk was more difficult with hoop. 

['''Contextualize with dates?'''] &quot;The combination of corset, bustle, and crinolette limited a woman's ability to bend except at the hip joint, resulting in a decorous, if rigid, sense of bearing.&quot;&lt;ref&gt;Koda, Harold. ''Extreme Beauty: The Body Transformed.'' The Metropolitan Museum of Art, 2001.&lt;/ref&gt; (130) 

As caricatures through the centuries makes clear, one disadvantage hoops had is that they could be caught by the wind, no matter what the structure was made of or how heavy it was. 

In her 1941 ''Little Town on the Prairie'', Laura Ingalls Wilder writes a scene in which Laura's hoops have crept up under skirts because of the wind. Set in 1883,&lt;ref&gt;Hill, Pamela Smith, ed. ''Pioneer Girl: The Annotated Autobiography''.&lt;/ref&gt; this very unusual scene shows a young woman highly skilled at getting her hoops back down without letting her undergarments show. The majority of European and North American women wore hoops in 1883, but to our knowledge no other writer from this time describes any solution to the problem of the wind under hoops or, indeed, a skill like Laura's. &lt;blockquote&gt;“Well,” Laura began; then she stopped and spun round and round, for the strong wind blowing against her always made the wires of her hoop skirt creep slowly upward under her skirts until they bunched around her knees. Then she must whirl around and around until the wires shook loose and spiraled down to the bottom of her skirts where they should be.

“As she and Carrie hurried on she began again. “I think it was silly, the way they dressed when Ma was a girl, don’t you? Drat this wind!” she exclaimed as the hoops began creeping upward again.

“Quietly Carrie stood by while Laura whirled. “I’m glad I’m not old enough to have to wear hoops,” she said. “They’d make me dizzy.”

“They are rather a nuisance,” Laura admitted. “But they are stylish, and when you’re my age you’ll want to be in style.”&lt;ref&gt;Wilder, Laura Ingalls. ''Little Town on the Prairie.'' Harper and Row, 1941. Pp. 272–273.&lt;/ref&gt;&lt;/blockquote&gt;The 16-year-old Laura makes the comment that she wants to be in style, but she lives on the prairie in the U.S., far from a large city, and would not necessarily wear the latest Parisian style, although she reads the American women's domestic and fashion monthly ''[[Social Victorians/Newspapers#Godey's Lady's Book|Godey's Lady's Book]]'' and would know what was stylish.

==== '''Advantages''' ====
The '''weight''' of hoops was somewhat corrected over time with the use of steel bands and wires, as they were lighter than the wood, cane or whalebone hoops, which had to be thick enough to keep their shape and to keep from breaking or folding under the weight of the petticoats and skirts. Full skirts made women's waists look smaller, whether by petticoats or hoops. Being fashionable, being included among the smart set.

The hoops moved the skirts away from the legs and feet, making moving easier. 

By moving the heavy petticoats and skirts away from their legs, hoops could actually give women's legs and feet more freedom to move.

Because so few fully constructed hoop foundation garments still exist, we cannot be certain of a number of details about how exactly they were worn. For example, the few contemporary drawings of 19th-century hoops show bloomers beneath them but no petticoats. However, in the cold and wind (and we know from Laura Ingalls Wilder how the wind could get under hoops), women could have added layers of petticoats beneath their hoops for warmth.[[File:Chaise à crinolines.jpg|thumb|Chaise à Crinolines, 19th century]]
=== Accommodation ===
Hoops affected how women sat, and furniture was developed specifically to accommodate these foundation structures. The ''chaise à crinolines'' or chair for hoop skirts (right), dating from the 2nd half of the 19th century, has a gap between the seat and the back of the chair to keep a woman's undergarments from showing as she sat, or even seated herself, and to reduce wrinkling of the fabric by accommodating her hoops, petticoats and skirts.[[File:Vermeer Lady Seated at a Virginal.jpg|thumb|Vermeer, Lady Seated at a Virginal|left]]Vermeer's c. 1673 ''Lady Seated at a Virginal'' (left) looks like she is sitting on this same kind of chair, suggesting that furniture like this had existed long before the 19th century. Vermeer's painting shows how the chair could accommodate her hoops and the voluminous fabric of her skirts.

The wide doorways between the large public rooms in the Palace of Versailles could accommodate wide panniers. '''Louis XV and XVI of France occupied an already-built Versailles, but they both renovated the inside over time'''.

Some configurations of hoops permitted folding, and of course the width of the hoops themselves varied over time and with the evolving styles and materials.

With hoops, skirts were lifted away from the legs and feet, and when skirts got shorter, to above the floor, women's feet had nearly unrestricted freedom to move. Evening gowns, with trains, were still restrictive.

A modern accommodation are the leaning boards developed in Hollywood for women wearing period garments like corsets and long, full skirts. The leaning boards allow the actors to rest without sitting and wrinkling their clothes.[[File:Pedro García de Benabarre St John Retable Detail.jpg|thumb|alt=Old oil painting of a woman wearing a dress from the 1400s holding the decapitated head of a man with a halo before a table of people at a dinner party|Pedro García de Benabarre, Detail from St. John Altarpiece, Showing Visible Hoops]]
=== Early Hoops ===
Hoops first appeared in Spain in the 15th century and influenced European fashion for at least 3 centuries.

A detail (right) from Pedro García de Benabarre's c. 1470 larger altarpiece painting shows women wearing a style of hoops that predates the farthingale but marks the beginning point of the development of that fashion. Salomé (holding John the Baptist's head) is wearing a dress with what looks like visible wooden hoops attached to the outside of the skirt, which also appears to have padding at the hips underneath it.

The clothing and hairstyles of the people in this painting are sufficiently realistic to offer details for analysis. The foundation garments the women are wearing are corsets and bum rolls. Because none still exist, we do not know how these hoops attached to the skirts or how they related structurally to the corset. The bottom hoop on Salomé's skirt rests on the ground, and her feet are covered. The women near her are kneeling, so not all their hoops show. 

The painter De Benabarre was &quot;active in Aragon and in Catalonia, between 1445–1496,&quot;&lt;ref&gt;{{Cite web|url=https://www.mfab.hu/artworks/10528/|title=Saint Peter|website=Museum of Fine Arts, Budapest|language=en-US|access-date=2024-12-11}} https://www.mfab.hu/artworks/10528/.&lt;/ref&gt; so perhaps he saw the styles worn by people like Katharine of Aragon, whose hoops are now called a farthingale.

=== Early Farthingale ===
In the 16th century, the foundation garment we call ''hoops'' was called a ''farthingale''. Elizabeth Lewandowski says that the metal supports (or structure) in the hoops were made of wire:&lt;blockquote&gt;''&quot;FARTHINGALE: Renaissance (1450-1550 C.E. to Elizabethan (1550-1625 C.E.). Linen underskirt with wire supports which, when shaped, produced a variety of dome, bell, and oblong shapes.&quot;&lt;ref name=&quot;:7&quot; /&gt;''{{rp|105}}&lt;/blockquote&gt;The French term for ''farthingale'' is ''vertugadin'' — &quot;un élément essentiel de la mode Tudor en Angleterre [an essential element of Tudor fashion in England].&quot;&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|date=2022-03-12|title=Vertugadin|url=https://fr.wikipedia.org/w/index.php?title=Vertugadin&amp;oldid=191825729|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Vertugadin.&lt;/ref&gt; The French also called the farthingale a &quot;''cachenfant'' for its perceived ability to hide pregnancy,&quot;&lt;ref&gt;&quot;Clothes on the Shakespearean Stage.&quot; Carleton Production. Amazon Web Services. https://carleton-wp-production.s3.amazonaws.com/uploads/sites/84/2023/05/Clothes-on-the-Shakespearean-Stage_-1.pdf (retrieved April 2025).&lt;/ref&gt; not unreasonable given the number of portraits where the subject wearing a farthingale looks as if she might be pregnant. The term in Spanish is ''vertugado''. Nowadays clothing historians make clear distinctions among these terms, especially farthingale, bustle and hip roll, but the terminology then did not need to distinguish these garments from later ones.&lt;p&gt;&lt;/p&gt;

The hoops on the outsides of the skirts in the Pedro García de Benabarre painting (above right) predate what would technically be considered a vertugado.[[File:Alonso Sánchez Coello 011.jpg|thumb|alt=Old painting of a princess wearing a richly jeweled outfit|Alonso Sánchez Coello, Infanta Isabel Clara Eugenia Wearing a Vertugado, c. 1584]]

Blanche Payne says,&lt;blockquote&gt;Katherine of Aragon is reputed to have introduced the Spanish farthingale ... into England early in the [16th] century. The result was to convert the columnar skirt of the fifteenth century into the cone shape of the sixteenth.&lt;ref name=&quot;:11&quot; /&gt;{{rp|291}}&lt;/blockquote&gt;

In fact, &quot;The Spanish princess Catherine of Aragon brought the fashion to England for her marriage to Prince Arthur, eldest son of Henry VII in 1501 [La princesse espagnole Catherine d'Aragon amena la mode en Angleterre pour son mariage avec le prince Arthur, fils aîné d'Henri VII en 1501].&quot;&lt;ref name=&quot;:0&quot; /&gt; Catherine of Aragon, of course, married Henry VIII after Arthur's death, then was divorced and replaced by Anne Boleyn.

Of England, Lewandowski says that &quot;Spanish influence had introduced the hoop-supported skirt, smooth in contour, which was quite generally worn.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|291}} That is, hoops were &quot;quite generally worn&quot; among the ruling and aristocratic classes in England, and may have been worn by some women among the wealthy bourgeoisie. Sumptuary laws addressed &quot;certain features of garments that are decorative in function, intended to enhance the silhouette&quot;&lt;ref&gt;{{Cite journal|date=2025-02-22|title=Sumptuary law|url=https://en.wikipedia.org/wiki/Sumptuary_law|journal=Wikipedia|language=en}}&lt;/ref&gt; and signified wealth and status, but they were generally not very successful and not enforced well or consistently. (Sumptuary laws &quot;attempted to regulate permitted consumption, especially of clothing, food and luxury expenditures&quot;&lt;ref&gt;{{Cite journal|date=2024-09-27|title=sumptuary law|url=https://en.wiktionary.org/wiki/sumptuary_law|journal=Wiktionary, the free dictionary|language=en}}&lt;/ref&gt; in order to mark class differences and, for our purposes, to use fashion to control women and the burgeoning middle class.)

The Spanish vertugado shaped the skirt into an symmetrical A-line with a graduated series of hoops sewn to an undergarment. Alonso Sánchez Coello's c. 1584&lt;ref name=&quot;:11&quot; /&gt;{{rp|316}} portrait (right) shows infanta Isabel Clara Eugenia wearing a vertugado, with its &quot;typically Spanish smooth cone-shaped contour.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|315–316}}

The shoes do not show in the portraits of women wearing the Spanish cone-shaped vertugado. The round hoops stayed in place in front, even though the skirts might touch the floor, giving the women's feet enough room to take steps. 

By the end of the 16th century the French and Spanish farthingales had evolved separately and were no longer the same garment.[[File:Queen Elizabeth I ('The Ditchley portrait') by Marcus Gheeraerts the YoungerFXD.jpg|thumb|alt=Old oil painting of a queen in a white dress with shoulders and hips exaggerated by her dress|Marcus Gheeraerts the Younger, Queen Elizabeth I in a French Cartwheel Farthingale, 1592|left]]

The French vertugadin — a cartwheel farthingale — was a flat &quot;platter&quot; of hoops worn below the waist and above the hips. Once past the vertugadin, the skirt fell straight to the floor, into a kind of asymmetrical drum shape that was balanced by strict symmetry in the rest of the garment. The English Queen Elizabeth I is wearing a French drum-shaped farthingale in Marcus Gheeraerts the Younger's c. 1592 portrait (left).[[File:Hardwick Hall Portrait of Elizabeth I of England.jpg|thumb|Hilliard, Hardwick Hall Portrait of Elizabeth I of England, c. 1598–1599]]In Nicholas Hilliard's c. 1598–1599 portrait of Queen Elizabeth I (right), an extraordinary showing of jewels, pearls and embroidery from the top of her head to the tips of her toes make for a spectacular outfit. The drum of the cartwheel farthingale is closer to the body beneath the point of the bodice, and the underskirt is gathered up the sides of the foundation corset to where her natural waistline would be. The gathers flatten the petticoat from the point to the hem, and the fabric collected at the sides falls from the edge of the drum down to her ankles.

Associated with the cartwheel farthingale was a very long waist and a skirt slightly shorter in the front. A rigid corset with a point far below the waist and the downward-angled farthingale flattened the front of the skirt. Because the skirt in front over a cartwheel farthingale was closer to the woman's body and did not touch the floor, the dress flowed and the women's shoes showed as they moved. Almost all portraits of women wearing cartwheel farthingales show the little pointy toes of their shoes. In Gheeraerts' painting, Queen Elizabeth's feet draw attention to themselves, suggesting that showing the shoes was important.

Farthingales were heavy, and together with the rigid corsets and the construction of the dress (neckline, bodice, sleeves, mantle), women's movement was quite restricted. Although their feet and legs had the freedom to move under the hoops, their upper bodies were held in place by their foundation garments and their clothing, the sleeves preventing them from raising their arms higher than their shoulders. This restriction of the movement of their arms can be seen in Elizabethan court dances that included clapping. They clapped their hands beside their heads rather than over their heads.

The steady attempts in the sumptuary laws to control fine materials for clothing reveals the interest middle-class women had in wearing what the cultural elite were wearing at court.

=== The Transitional 17th Century ===
What had been starched and stiff in women's dress in the 16th century — like ruffs and collars — became looser and flatter in the 17th. This transitional period in women's clothing also introduced the [[Social Victorians/Terminology#Cavalier|Cavalier style of men's dress]], which began with the political movement in support of England's King Charles II while he was still living in France. Like the ones women wore, men's ruffs and collars were also no longer starched or wired, making them looser and flatter as well.

For much of the 17th century — beginning about 1620, according to Payne — skirts were not supported by the cage-like hoops that had been so popular.&lt;ref name=&quot;:11&quot; /&gt;{{rp|355}} Without structures like hoops, skirts draped loosely to the floor, but they did not fall straight from the waist. Except for dressing gowns (which sometimes appear in portraiture in spite of their informality), the skirts women wore were held away from the body by some kind of padding or stiffened roll around the waist and at the hips, sometimes flat in front, sometimes not. The skirts flowed from the hips, either straight down or in an A-line depending on the cut of the skirt.
[[File:The Vanity of Women Masks and Bustles MET DT4982.jpg|thumb|Maerten de Vos, ''The Vanity of Women: Masks and Bustles'', c. 1600]]
==== Hip Rolls ====
This c. 1600 Dutch engraving attributed to Maerten de Vos (right) shows two servants dressing two wealthy women in masks and hip rolls. In its title of this engraving the Metropolitan Museum of Art calls a hip roll a ''bustle'' (which it defines as a padded roll or a French farthingale),&lt;ref&gt;De Vos, Maerten. &quot;The Vanity of Women: Masks and Bustles.&quot; Metropolitan Museum of Art. Wikimedia Commons 

https://commons.wikimedia.org/wiki/File:The_Vanity_of_Women_Masks_and_Bustles_MET_DT4982.jpg.&lt;/ref&gt; but the engraving itself calls it a ''cachenfant''.&lt;ref name=&quot;:20&quot;&gt;De Vos, Maerten (attrib. to). &quot;The Vanity of Women: Masks and Bustles.&quot; Circa 1600. ''The Costume Institute: The Metropolitan Museum of Art''. Object Number: 2001.341.1. https://www.metmuseum.org/art/collection/search/82615&lt;/ref&gt; The craftsmen in the back are wearing masks. The one on the left is making the masks that the shop sells, and the one on the right is making the hip rolls.

The serving woman on the left is fitting a mask on what is probably her mistress. The kneeling woman on the right is tying a hip roll on what is probably hers.

The text around the engraving is in French and Dutch. The French passages read as follows (clockwise from top left), with the word ''cachenfant'' (farthingale) bolded:&lt;blockquote&gt;
Orne moy auecq la masque laide orde et sale:
&lt;br&gt;Car laideur est en moy la beaute principale.

Achepte dame masques &amp; passement:
&lt;br&gt;Monstre vostre pauvre [?] orgueil hardiment.

Venez belles filles auecq fesses maigres:
&lt;br&gt;Bien tost les ferayie rondes &amp; alaigres.

Vn '''cachenfant''' come les autres me fault porter:
&lt;br&gt;Couste qu'il couste; le fol la folle veult aymer.

Voy cy la boutiquel des enragez amours,
&lt;br&gt;De vanite, &amp; d'orgueil &amp; d'autres tels tours:

D'ont plusieurs qui parent la chair puante,
&lt;br&gt;S'en vont auecq les diables en la gehenne ardante.

&lt;ref name=&quot;:20&quot; /&gt;&lt;/blockquote&gt;

Which translates, roughly, into
&lt;blockquote&gt;
Adorn me with the ugly, dirty, and orderly mask:
&lt;br&gt;For ugliness is the principal beauty in me.

Buy, lady, masks and trimmings:
&lt;br&gt;Boldly show your poor [?] pride.

Come, beautiful girls with thin buttocks:
&lt;br&gt;Soon, make them round and cheerful.

I must wear a [farthingale, lit. &quot;hide child&quot;] like the others:
&lt;br&gt;No matter how much it costs; the madman wants to love.

See here the store of rabid loves,
&lt;br&gt;Of vanity, and pride, and other such tricks:

Many of whom adorn the stinking flesh,
&lt;br&gt;Go with the devils to the burning hell.
&lt;/blockquote&gt;Later versions of hoops were also used to hide or at least de-emphasize pregnancy (see [[Social Victorians/Terminology#Crinoline Hoops|Crinoline Hoops]], below).[[File:The Vanity of Women Masks and Bustles MET DT4982 (detail of padded rolls or French farthingales).jpg|thumb|Detail of Maerten de Vos, ''The Vanity of Women: Masks and Bustles'', c. 1600]]
Traditionally thought of as padding, the hip rolls, at least in this detail of the c. 1600 engraving (right), are hollow and seem to be made cylindrical by what looks like rings of cane or wire sewn into channels. The kneeling woman is tying the strings that attach the hip roll, which is being worn above the petticoat and below the overskirt that the mistress is holding up and back. The hip roll under construction on the table looks hollow, but when they are finished the rolls look padded and their ends sewn closed.

Farthingales were more complex than is usually assumed. Currently, ''farthingale'' usually refers to the cane or wire foundation that shaped the skirt from about 1450 to 1625, although the term was not always used so precisely. Padding was sometimes used to shape the skirt, either by itself or in addition to the cartwheel and cone-shaped foundational structures. The padding itself was in fact another version of hoops that were structured both by rings as well as padding. Called a bustle, French farthingale, cachenfant, bum barrel&lt;ref name=&quot;:7&quot; /&gt;{{rp|42}} or even (quoting Ben Jonson, 1601) bum roll&lt;ref&gt;Cunnington, C. Willett (Cecil Willett), and Phillis Cunnington. ''Handbook of English Costume in the Sixteenth Century''. Faber and Faber, 1954. Internet Archive https://archive.org/details/handbookofenglis0000unse_e2n2/.&lt;/ref&gt;{{rp|161}} in its day, the hip roll still does not have a stable name. The common terms for what we call the hip roll now include ''bum roll'' and ''French farthingale''. The term ''bustle'' is no longer associated with the farthingale.

==== Bunched Skirts or Padding ====
The speed with which trends in clothing changed began to accelerate in the 17th century, making fashion more expensive and making keeping up with the latest styles more difficult. Part of the transition in this century, then, is the number of silhouettes possible for women, including early forms of what became the pannier in the 18th century and what became the bustle in the late 19th. In the later periods, these forms of hoops involved &quot;baskets&quot; or cages (or crinolines), but during this transitional period, these shapes were made from &quot;stiffened rolls [&lt;nowiki/&gt;[[Social Victorians/Terminology#Hip Rolls|hip rolls]]] that were tied around the waist&quot;&lt;ref&gt;Bendall, Sarah A. () The Case of the “French Vardinggale”: A Methodological Approach to Reconstructing and Understanding Ephemeral Garments, ''Fashion Theory'' 2019 (23:3), pp. 363-399, DOI: [[doi:10.1080/1362704X.2019.1603862|10.1080/1362704X.2019.1603862]].&lt;/ref&gt;{{rp|369}} at the hips under the skirts or from bunched fabric, or both. The fabric-based volume in the back involved the evolution of an overskirt, showing more and more of the underskirt, or [[Social Victorians/Terminology#Petticoat|petticoat]], beneath it. This development transformed the petticoat into an outer garment.[[File:Princess Teresa Pamphilj Cybo, by Jacob Ferdinand Voet.jpg|thumb|Attr. to Voet, Anna Pamphili, c. 1670]]
[[File:Caspar Netscher - Girl Standing before a Mirror - 1925.718 - Art Institute of Chicago.jpg|thumb|Netscher, Girl Standing before a Mirror|left]]

Two examples of the bunched overskirt can be seen in Caspar Netscher's ''Girl Standing before a Mirror'' (left) and Voet's ''Portrait of Anna Pamphili'' (right), both painted about 1670. (This portrait of Anna Pamphili and the one below right were both misidentified with her mother Olimpia Aldobrandini.) In both these portraits, the overskirt is split down the center front, pulled to the sides and toward the back and stitched (probably) to keep the fabric from falling flat. The petticoat, which is now an outer garment, hangs straight to the floor. In Netscher's portrait, the girl's shoe shows, but the skirt rests on the ground, requiring her to lift her skirts to be able to walk, not to mention dancing. The dress in Anna Pamphili's portrait is an interesting contrast of soft and hard. The embroidery stiffens the narrow petticoat, suggesting it might have been a good choice for a static portrait but not for moving or dancing.

Besides bunched fabric, the other way to make the skirts full at the hips was with hip rolls. Mierevelt's 1629 Portrait of Elizabeth Stuart (below, left) shows a split overskirt, although the fabric is not bunched or draped toward the back. The fullness here is caused by a hip roll, which adds fullness to the hips and back, leaving the skirts flat in front. In this case the flatness of the roll in front pulls the overskirt slightly apart and reveals the petticoat, even this early in the century. One reason this portrait is striking because Elizabeth Stuart appears to be wearing a mourning band on her left arm. Also striking are the very elaborate trim and decorations, displaying Stuart's wealth and status, including the large ornament on the mourning band. [[File:Michiel van Mierevelt - Portrait of Elizabeth Stuart (1596-1662), circa 1629.jpg|thumb|Michiel van Mierevelt, Elizabeth Stuart, c. 1629|left]][[File:Attributed to Voet - Portrait of Anna Pamphili, misidentified with her mother Olimpia Aldobrandini.jpg|thumb|Attr. to Voet, Anna Pamphili, c. 1671]]

The c. 1671 portrait of Anna Pamphili (below, right) shows an example of the petticoat's development as an outer garment. In the Mierevelt portrait (left), the petticoat barely shows. A half century later, in the portrait of Anna Pamphili, the overskirt is not split but so short that the petticoat is almost completely revealed. A hip roll worn under both the petticoat and the overskirt gives her hips breadth. The petticoat is gathered at the sides and smooth in the front, falling close to her body. The fullness of the petticoat and the overskirt is on the sides — and possibly the back. The heavily trimmed overskirt is stiff but not rigid. Anna Pamphili's shoe peeps out from under the flattened front of the petticoat.

The neckline, the hipline, the bottom of the overskirt, the trim at the hem of the petticoat and overskirt and the ribbons on the sleeves — as well as even the hair style — all give Pamphili's outfit a sophisticated horizontal design, a look that soon would become very important and influential as panniers gained popularity.

=== Panniers ===
The formal, high-status dress we most associate with the 18th century is the horizontal style of panniers, the hoops at the sides of the skirt, which is closer to the body in front and back. Popular in the mid century in France, panniers continued to dominate design in court dress in the U.K. &quot;well into the 19th century.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}} ''Paniers anglais'' were 8-hoop panniers.&lt;ref name=&quot;:7&quot; /&gt;{{rp|219}}

Panniers were made from a variety of materials, most of which have not survived into the 21st century, and the most common materials used panniers has not been established. Lewandowski says that skirts were &quot;stretched over metal hoops&quot; that &quot;First appear[ed] around 1718 and [were] in fashion [for much of Europe] until 1800. ... By 1750 the one-piece pannier was replaced by [two pieces], with one section over each hip.&quot;&lt;ref name=&quot;:7&quot; /&gt;{{rp|219}} According to Payne, another kind of pannier &quot;consisted of a pair of caned or boned [instead of metal] pouches, their inner surfaces curved to the ... contour of the hips, the outside extending well beyond them.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|428}} Given that it is a natural material, surviving examples of cane for the structure of panniers are an unexpected gift, although silk, linen and wool also occasionally exists in museum collections. No examples of bone structures for panniers exist, suggesting that bone is less hardy than cane. Waugh says that whalebone was the only kind of &quot;bone&quot; (it was actually cartilage, of course) used;&lt;ref name=&quot;:19&quot;&gt;Waugh, Norah. ''Corsets and Crinolines''. New York, NY: Theatre Arts Books, 1954. Rpt. Routledge/Theatre Arts Books, 2000.&lt;/ref&gt;{{rp|167}} Payne says cane and whalebone were used for panniers.&lt;ref name=&quot;:11&quot; /&gt;{{rp|426}} Neither Payne nor Waugh mention metal. Examples of metal structures for panniers have also not survived, perhaps because they were rare or occurred later, during revolutionary times, when a lot of things got destroyed.

The pannier was not the only silhouette in the 18th century. In fact, the speed with which fashion changed continued to accelerate in this century. Payne describes &quot;Six basic forms,&quot; which though evolutionary were also quite distinct. Further, different events called for different styles, as did the status and social requirements for those who attended. For the first time in the clothing history of the culturally elite, different distinct fashions overlapped rather than replacing each other, the clothing choices marking divisions in this class.

The century saw Payne's &quot;Six basic forms&quot; or silhouettes generally in this order but sometimes overlapping:

# '''Fullness in the back'''. The fabric bustle. While we think of the bustle as a 19th-century look, it can be found in the 18th century, as Payne says.&lt;ref name=&quot;:11&quot; /&gt;{{rp|411}} The overskirt was all pulled to the back, the fullness probably mostly made by bunched fabric.
# '''The round skirt'''. &quot;The bell or dome shape resulted from the reintroduction of hoops[,] in England by 1710, in France by 1720.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|411}}
# '''The ellipse, panniers'''. &quot;The ellipse ... was achieved by broadening the support from side to side and compressing it from front to back. It had a long run of popularity, from 1740 to 1770, the extreme width being retained in court costumes. ... English court costume [411/413] followed this fashion well into the nineteenth century.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|411, 413}}
# '''Fullness in the back and sides'''. &quot;The dairy maid, or [[Social Victorians/Terminology#Polonaise|polonaise]], style could be achieved either by pulling the lower part of the overskirt through its own pocket holes, thus creating a bouffant effect, or by planned control of the overskirt, through the cut or by means of draw cords, ribbons, or loops and buttons, which were used to form the three great ‘poufs’ known as the polonaise .... These diversions appeared in the late [seventeen] sixties and became prevalent in the seventies. They were much like the familiar styles of our own [American] Revolutionary War period.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}
# '''Fullness in the back'''. The return of the bustle in the 1780s.&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}
# '''No fullness'''. The tubular [or Empire] form, drawn from classic art, in the 1790s.&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}
Hoops affected how women sat, went through doors and got into carriages, as well as what was involved in the popular dances. Length of skirts and trains. Some doorways required that women wearing wide panniers turn sideways, which undermined the &quot;entrance&quot; they were expected to make when they arrived at an event. Also, a woman might be accompanied by a gentleman, who would also be affected by her panniers and the width of the doorway. Over the century skirts varied from ankle length to resting on the floor. Women wearing panniers would not have been able to stand around naturally: the panniers alone meant they had to keep their elbows bent. 

[[File:Panniers 1.jpg|thumb|alt=Photograph of the wooden and fabric skeleton of an 18th-century women's foundation garment|Wooden and Fabric-covered Structure for 18th-century Panniers|left]][[File:Hoop petticoat and corset England 1750-1780 LACMA.jpg|thumb|Hooped Petticoat and Corset, 1750–80]]The 1760–1770 French panniers (left) are &quot;a rare surviving example&quot;&lt;ref name=&quot;:15&quot;&gt;{{Citation|title=Panniers|url=https://www.metmuseum.org/art/collection/search/139668|date=1760–70|accessdate=2025-01-01}}. The Costume Institute, Metropolitan Museum of Art. https://www.metmuseum.org/art/collection/search/139668.&lt;/ref&gt; of the structure of this foundation garment. Almost no examples of panniers survive. The hoops are made with bent cane, held together with red velvet silk ribbon that looks pinked. The cane also appears to be covered with red velvet, and the hoops have metal &quot;hinges that allow [them] to be lifted, facilitating movement in tight spaces.&quot;&lt;ref name=&quot;:15&quot; /&gt; This inventive hingeing permitted the wearer to lift the bottom cane and her skirts, folding them up like an accordion, lifting the front slightly and greatly reducing the width (and making it easier to get through doors). ['''Write the Met to ask about this description once it's finished. Are there examples of boned or metal panniers that they're aware of?''']

The corset and hoops shown (right) are also not reproductions and are also rare examples of foundation garments surviving from the 18th century. These hoops are made with cane held in place by casings sewn into a plain-woven linen skirt.&lt;ref&gt;{{Cite web|url=https://collections.lacma.org/node/214714|title=Woman's Hoop Petticoat (Pannier) {{!}} LACMA Collections|website=collections.lacma.org|access-date=2025-01-03}} Los Angeles County Museum of Art. https://collections.lacma.org/node/214714.&lt;/ref&gt; These 1750–1780 hoops are modestly wide, but the gathering around the casings for the hoops suggests that the panniers could be widened if longer hoops were inserted. (The corset shown with these hoops is treated in the [[Social Victorians/Terminology#Corsets|Corsets section]]. The mannequin is wearing a [[Social Victorians/Terminology#Chemise|chemise undergarment]] as well.)[[File:Johanna Gabriele of Habsburg Lorraine1 copy.jpg|thumb|Martin van Meytens, Johanna Gabriele of Habsburg Lorraine, c. 1760|left]]In her c. 1760 portrait (left), Johanna Gabriele of Habsburg Lorraine is wearing exaggerated court-dress panniers, shown here about the widest that they got. Johanna Gabriele was the daughter of Maria Theresa of Austria, so she was a sister of Marie Antoinette, who also would have worn panniers as exaggerated as these. Johanna Gabriele's hairstyle has not grown into the huge bouffant style that developed to balance the wide court dress, so her outfit looks out of proportion in this portrait. And, because of her panniers, her arms look slightly awkward. The tips of her shoes show because her skirt has been pulled back and up to rest on them.

France had become the leader in high fashion by the middle of the century, led first by Madame Pompadour and then by Marie Antoinette, who was crowned queen in 1774.&lt;ref&gt;{{Cite journal|date=2025-04-23|title=Marie Antoinette|url=https://en.wikipedia.org/wiki/Marie_Antoinette|journal=Wikipedia|language=en}}&lt;/ref&gt;  Court dress has always been regulated, but it could be influenced. Marie Antoinette's influence was toward exaggeration, both in formality and in informality. In their evolution formal-dress skirts moved away from the body in front and back but were still wider on the sides and were decorated with massive amounts of trim, including ruffles, flowers, lace and ribbons. The French queen led court fashion into greater and greater excess: &quot;Since her taste ran to dancing, theatrical, and masked escapades, her costumes and those of her court exhibited quixotic tendencies toward absurdity and exaggeration.&quot;&lt;ref name=&quot;:11&quot; /&gt;{{rp|428}} Both Madame Pompadour's and Marie Antoinette's taste ran to extravagance and excess, visually represented in the French court by the clothing.[[File:Marie Antoinette 1778-1783.jpg|thumb|Marie Antoinette in 1778 and 1779]]The two portraits (right), painted by Élizabeth Louise Vigée Le Brun in 1778 on the left and 1779 on the right, show Marie Antoinette wearing the same dress. Although one painting has been photographed as lighter than the other, the most important differences between the two portraits are slight variations in the pose and the hairstyle and headdress. Her hair in the 1779 painting is in better proportion to her dress than it is in the earlier one, and the later headdress — a stylized mobcap — is more elaborate and less dependent on piled-up hair. (The description of the painting in Wikimedia Commons says she gave birth between these two portraits, which in particular affected her hair and hairline.&lt;ref&gt;&quot;File:Marie Antoinette 1778-1783.jpg.&quot; ''Wikimedia Commons'' [&lt;bdi&gt;Élisabeth Louise Vigée Le Brun, 2 portraits of Marie Antoinette&lt;/bdi&gt;] https://commons.wikimedia.org/wiki/File:Marie_Antoinette_1778-1783.jpg.&lt;/ref&gt;)[[File:Queen Charlotte, by studio of Thomas Gainsborough.jpg|thumb|Queen Charlotte of England, 1781|left]]

In this 1781&lt;ref&gt;{{Cite web|url=https://artsandculture.google.com/asset/wd/jAGip1dpEkf-Fw|title=Portrait of Queen Charlotte of England - Thomas Gainsborough, studio|website=Google Arts &amp; Culture|language=en|access-date=2025-04-16}}&lt;/ref&gt; portrait from the workshop of Thomas Gainsborough (left), Queen Charlotte is wearing panniers less exaggerated in width than Johanna Gabriele's. The English did not usually wear panniers as wide as those in French court dress, but the decoration and trim on the English Queen Charlotte's gown are as elaborate as anything the French would do.

The ruffles (many of them double) and fichu are made with a sheer silk or cotton, which was translucent rather than transparent. The ruffles on Queen Charlotte's sleeves are made of lace. The ruffles and poufs of sheer silk are edged in gold. The embroidered flowers and stripes, as well as the sequin discs and attached clusters are all gold. The skirt rose above the floor, revealing Queen Charlotte's pointed shoe. Shoes were fashion accessories because of the shorter length of the skirts.

The whole look is more balanced because of the bouffant hairstyle, the less extreme width in the panniers and the greater fullness in front (and, probably, back). 

The white dress worn by the queen in Season 1, Episode 4 of the BBC and Canal+ series ''Marie Antoinette'' stands out because nobody else is wearing white at the ball in Paris and because of the translucent silk or muslin fabric, which would have been imported from India at that time (some silk was still being imported from China). Muslin is not a rich or exotic fabric to us, but toward the end of the 18th century, muslin could be imported only from India, making it unusual and expensive.&lt;blockquote&gt;Another English contribution to the fashion of the eighties was the sheer white muslin dress familiar to us from the paintings of Reynolds, Romney, and Lawrence. In this respect the English fell under the spell of classic Greek influence sooner than the French did. Lacking the restrictions imposed by Marie Antoinette's court, the English were free to adapt costume designs from the source which was inspiring their architects and draftsmen.&lt;ref name=&quot;:11&quot; /&gt;{{rp|438}} &lt;/blockquote&gt;So while a sheer white dress would have been unlikely in Marie Antoinette's court, according to Payne, the fabric itself was available and suddenly became very popular, in part because of its simplicity and its sheerness. The Empire style replaced the Rococo busyness in a stroke, like the French Revolution.

By the 1790s French and English fashion had evolved in very different directions, and also by this time, accepted fashion and court dress had diverged, with the formulaic properties of court dress — especially in France — preventing its development. In general,&lt;blockquote&gt;English women were modestly covered ..., often in overdress and petticoat; that heavier fabrics with more pattern and color were used; and that for a while hairdress remained more elaborate and headdress more involved than in France.&lt;ref name=&quot;:11&quot; /&gt;{{rp|441}}&lt;/blockquote&gt;Even in such a rich and colorful court dress as Queen Charlotte is wearing in the Gainsborough-workshop portrait, her more &quot;modest&quot; dress shows these trends very clearly: the white (muslin or silk) and the elaborate style in headdress and hair.

=== Polonaise ===

==== Marie Antoinette — The Context ====

The robe à la Polonaise in casual court dress was popularized by Marie Antoinette for less formal settings and events, a style that occurred at the same time as highly formal dresses with panniers. An informal fashion not based on court dress, although court style would require panniers, though not always the extremely wide ones, and the new style. It was so popular that it evolved into one way court dress could be.[[File:Marie Antoinette in a Park Met DP-18368-001.jpg|thumb|Le Brun, ''Marie Antoinette in a Park'']]Trianon: Marie Antoinette's &quot;personal&quot; palace at Versailles, where she went to entertain her friends in a casual environment. While there, in extended, several-day parties, she and her friends played games, did amateur theatricals, wore costumes, like the stylization of what a dairy maid would wear. A release from the very rigid court procedures and social structures and practices. Separate from court and so not documented in the same way events at Versailles were.

In the c. 1780–81 sketch (right) of Marie Antoinette in a Park by Elisabeth Louise Vigée Le Brun,&lt;ref&gt;Le Brun, Elisabeth Louise Vigée. ''Marie Antoinette in a Park'' (c. 1780–81). The Metropolitan Museum of Art https://www.metmuseum.org/art/collection/search/824771.&lt;/ref&gt; the queen is wearing a robe à la Polonaise with an apron in front, so we see her in a relatively informal pose and outfit. The underskirt, which is in part at least made of a sheer fabric, shows beneath the overskirt and the apron. This is a late Polonaise, more decoration, additions of ribbons, lace, lace, [[Social Victorians/Terminology#Plastics|plastics]], ruffles, which did not exist on actual milkmaid dresses or earlier versions of the robe à la Polonaise. Even though this is a sketch, we can see that this dress would be more comfortable and convenient for movement because the bodice is not boned, and wrinkles in the bodice suggest that she is not likely wearing a corset. 

==== Definition of Terms ====

The Polonaise was a late-Georgian or late-18th-century style, the usage of the word in written English dating from 1773 although ''Polonaise'' is French for ''the Polish woman'', and the style arose in France:&lt;blockquote&gt;A woman's dress consisting of a tight, unboned bodice and a skirt open from the waist downwards to reveal a decorative underskirt. Now historical.&lt;ref name=&quot;:13&quot;&gt;“Polonaise, N. &amp; Adj.” ''Oxford English Dictionary'', Oxford UP, September 2024, https://doi.org/10.1093/OED/2555138986.&lt;/ref&gt;&lt;/blockquote&gt;The lack of boning in the bodice would make this fashion more comfortable than the formal foundation garments worn in court dress.

The term ''á la polonaise'' itself is not in common use by the French nowadays, and the French ''Wikipédia'' doesn't use it for clothing. French fashion drawings and prints from the 18th-century, however, do use the term.

Elizabeth Lewandowski dates the Polonaise style from about 1750 to about 1790,&lt;ref name=&quot;:7&quot; /&gt;{{rp|123}} and Payne says it was &quot;prevalent&quot; in the 1770s.&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}

The style à la Polonaise was based on an idealization of what dairy maids wore, adapted by aristocratic women and frou-froued up. Two dairymaids are shown below, the first is a caricature of a stereotypical milkmaid and the second is one of Marie Antoinette's ladies in waiting costumed as a milkmaid.
[[File:La laitiere. G.16931.jpg|left|thumb|Mixelle, ''La Laitiere'' (the Milkmaid)]]
[[File:Madame A. Aughié, Friend of Queen Marie Antoinette, as a Dairymaid in the Royal Dairy at Trianon - Nationalmuseum - 21931.tif|thumb|Madame A. Aughié, as a Dairymaid in the Royal Dairy at Trianon]]In the aquatint engraving of ''La Laitiere'' (left) by Jean-Marie Mixelle (1758–1839),&lt;ref&gt;Mixelle, Jean-Marie. ''La Laitiere'', Musée Carnavalet, Histoire de Paris, Inventory Number: G.16931. https://www.parismuseescollections.paris.fr/fr/musee-carnavalet/oeuvres/la-laitiere-8#infos-secondaires-detail.&lt;/ref&gt; the milkmaid is portrayed as flirtatious and, perhaps, not virtuous. She is wearing clogs and two white aprons. Her bodice is laced in front, the ruffle is probably her chemise showing at her neckline, and the peplum sticks out, drawing attention to her hips. As apparently was typical, she is wearing a red skirt, short enough for her ankles to show. The piece around her neck has become untucked from her bodice, contributing to the sexualizing, as does the object hanging from her left hand and directing the eye to her bosom. (The collection of engravings that contains this one is undated but probably from the late 19th or early 20th century.)

The 1787 &lt;bdi&gt;Adolf Ulrik Wertmüller&lt;/bdi&gt; portrait of Madame Adélaïde Aughié in the Royal Dairy at Petit Trianon-Le Hameau&lt;ref&gt;Wertmüller, Adolf Ulrik. ''Adélaïde Auguié as a Dairy-Maid in the Royal Dairy at Trianon''. 1787. The National Museum of Sweden, Inventory number NM 4881. https://collection.nationalmuseum.se/en/collection/item/21931/.&lt;/ref&gt; (right) is about as casual as Le Trianon got. A contemporary of Marie Antoinette, she is in costume as a milkmaid in the Royal Dairy at Trianon, perhaps for a theatrical event or a game. Her dress is not in the à la Polonaise style but a court interpretation of what a milkmaid would look like, in keeping with the hired workers at le Trianon.

==== The 3 Poufs ====
Visually, the style à la Polonaise is defined by the 3 poufs made by the gathering-up of the overskirt. Initially most of the fabric was bunched to make the poufs, but eventually they were padded or even supported by panniers. Payne describes how the polonaise skirt was constructed, mentioning only bunched fabric and not padding:&lt;blockquote&gt;The dairy maid, or polonaise, style could be achieved either by pulling the lower part of the overskirt through its own pocket holes, thus creating a bouffant effect, or by planned control of the overskirt, through the cut or by means of draw cords, ribbons, or loops and buttons, [or, later, buckles] which were used to form the three great ‘poufs’ known as the polonaise .... These diversions [the poufs] appeared in the late [seventeen] sixties and became prevalent in the seventies. They were much like the familiar styles of our own [American] Revolutionary War period.&lt;ref name=&quot;:11&quot; /&gt;{{rp|413}}&lt;/blockquote&gt;[[File:Robe à la polonaise jaune et violette, Galerie des modes, Fonds d'estampes du XVIIIème siècle, G.4555.jpg|thumb|Robe à la polonaise, c. 1775]]The overskirt, which was gathered or pulled into the 3 distinctive poufs, was sometimes quite elaborately decorated, revealing the place of this garment in high fashion (rather than what an actual working dairy maid might wear). The fabrics in the underskirt and overskirt sometimes were different and contrasting; in simpler styles, the two skirts might have the same fabrics. More complexly styled dresses were heavily decorated with ruffles, bows, [[Social Victorians/Terminology#Plastics|plastics]], ribbons, flowers, lace and trim.

The c. 1775&lt;ref name=&quot;:21&quot;&gt;&quot;Robe à la polonaise jaune et violette, Galerie des modes, Fonds d'estampes du XVIIIème siècle.&quot; Palais Galliera, musée de la Mode de la Ville de Paris. Inventory number: G.4555. https://www.parismuseescollections.paris.fr/fr/palais-galliera/oeuvres/robe-a-la-polonaise-jaune-et-violette-galerie-des-modes-fonds-d-estampes-du#infos-principales.&lt;/ref&gt; fashion color print (right) shows the way the overskirt of the Polonaise was gathered into 3 poufs, one in back and one on either side. In this illustration, the underskirt and the overskirt have the same yellow fabric trimmed with a flat band of purple fabric. The 18th-century caption printed below the image identifies it as a &quot;Jeune Dame en robe à la Polonoise de taffetas garnie a plat de bandes d'une autre couleur: elle est coeffée d'un mouchoir a bordures découpées, ajusté avec gout et bordé de fleurs [Young Lady in a Polonaise dress of taffeta trimmed flat with bands of another color: she is wearing a handkerchief with cut edges, tastefully adjusted and bordered with flowers].&quot;&lt;ref name=&quot;:21&quot; /&gt;

The skirt's few embellishments are the tasseled bows creating the poufs. The gathered underskirt falls straight from the padded hips to a few inches above the floor. Her cap is interesting, perhaps a forerunner of the mob cap (here a handkerchief worn as a cap [&quot;mouchoir a bordures découpées&quot;]).

===== The Evolution of the Polonaise into Court Dress =====
Part of the original attraction of the robe à la Polonaise was that women did not wear their usual heavy corsets and hoops, which is what would have made this style informal, playful, easy to move in, an escape from the stiffness of court life. Traditionally court dress with panniers and the robe à la Polonaise were thought to be separate, competing styles, but actually the two styles influenced each other and evolved into a design that combined elements from both.

By the time the robe à la Polonaise became court dress, the poufs were no longer only bunched fabric but large, controlled elaborations that were supported by structural elements, and the silhouette of the dress had returned to the ellipsis shape provided by panniers, with perhaps a little more fullness in front and back. The underskirt fell straight down from the hip level, indicating that some kind of padding or structure pulled it away from the body.

Court dress required the controlled shape of the skirt and a tightly structured bodice, which could have been achieved with corseting or tight lacing of the bodice itself. In the combined style, the bodice comes to a pointed V below the waist, which could only be kept flat by stays. While the Polonaise was ankle length, court dress touched the floor.

The following 3 images are fashion prints showing Marie Antoinette in court dress influenced by the robe à la Polonaise, made into a personal style for the queen by the asymmetrical poufs, the reduction of Rococo decoration, layers stacked upon each other and a length that keeps the hem of the skirts off the floor.[[File:Marie Antoinette de modekoningin Gallerie des Modes et Costumes Français Gallerie des Modes et Costumes Français, 1787, ooo 356 Grand habit de bal a la Cour (..), RP-P-2009-1213.jpg|thumb|Marie Antoinette in a Court Ball Gown à la Polonaise|left]]The 1787 &quot;Grand habit de bal à la Cour, avec des manches à la Gabrielle &amp; c.&quot; (left) by printmaker Nicolas Dupin, after a drawing by Augustin de Saint-Aubin, shows Marie Antoinette in a ballgown for the court with sleeves à la Gabrielle.&lt;ref&gt;{{Cite web|url=https://www.rijksmuseum.nl/en/collection/object/Marie-Antoinette-The-Queen-of-Fashion-Gallerie-des-Modes-et-Costumes-Francais--10ceb0e05fbb45ad4941bed1dacb27f1|title=Marie Antoinette: The Queen of Fashion: Gallerie des Modes et Costumes Français|website=Rijksmuseum.nl|language=en|access-date=2025-05-02}}&lt;/ref&gt; 

This ballgown, influenced by the robe à la polonaise, is balanced but asymmetrical and seems to have panniers for support of the side poufs. The only decoration on the skirt is ribbon or braid and tassels. Contrasting fabrics replace the [[Social Victorians/Terminology#Frou-frou|frou-frou]] for more depth and interest. The lining of the poufs has been pulled out for another contrasting color. The print makes it impossible to tell if the purple is an underskirt and an overskirt or one skirt with attached loops of the ribbon-like trim. 

(A sleeve à la Gabrielle has turned out to be difficult to define. The best we can do, which is not perfect, is a 4 July 1814 description: &quot;On fait, depuis quelque temps, des manches à la Gabrielle. Ces manches, plus courtes que les manches ordinaires, se terminent par plusieurs rangs de garnitures. Au lieu d'un seul bouillonné au poignet, on en met trois ou quatre, que l'on sépare par un poignet.&quot;&lt;ref&gt;&quot;Modes.&quot; ''Journal des Dames et des Modes''. 4 July 1814 (18:37), vol. 10, 1. ''Google Books'' https://books.google.com/books?id=kwNdAAAAcAAJ.&lt;/ref&gt;{{rp|296}} [&quot;For some time now, sleeves have been made in the Gabrielle style. These sleeves, shorter than ordinary sleeves, end in several rows of trimmings. Instead of a single ruffle at the wrist, three or four are used, separated by a wrist treatment.&quot;] The sleeves on the bodice of robes à la Polonaise seem to have been short, 3/4-length or less.) [[File:Gallerie des Modes et Costumes Français, 1787, sss 384 Robe de Cour à la Turque (..), RP-P-2009-1220.jpg|thumb|Marie Antoinette in a Court Dress à la Turque]]The c. 1787 &quot;Robe de Cour à la Turque, coeffure Orientale aves des aigrettes et plumes, &amp;c.&quot; (right) by printmaker Nicolas Dupin, after a drawing by Augustin de Saint-Aubin, shows Marie Antoinette in a court dress à la Turque with a headdress that has [[Social Victorians/Terminology#Aigrette|aigrettes]] and plumes.&lt;ref&gt;{{Cite web|url=https://www.rijksmuseum.nl/en/collection/object/---75499afec371ac1741dd98d769b14698|title=Gallerie des Modes et Costumes Français, 1787, sss 384 : Robe de Cour à la Turque; (...)|website=Rijksmuseum.nl|language=en|access-date=2025-05-02}}&lt;/ref&gt; The &quot;coeffure Orientale&quot; seems to be a highly stylized turban.

This court dress is à la Polonaise in that it has poufs, but it has 2 layers of poufs and an underskirt with a large ruffle. With its unusual striped fabric, its contrasting colors, the very asymmetrical skirt and the ruffles, bows and tassels, this is an elaborate and visually complex dress, but it is not decorated with a lot of [[Social Victorians/Terminology#Frou-frou|frou-frou]].

Several prints in this fashion collection show the robe à la Turque, a late-Georgian style [1750–1790],&lt;ref name=&quot;:7&quot; /&gt;{{rp|250}} none of which look &quot;Turkish&quot; in the slightest. Lewandowski defines robe à la Turque:&lt;blockquote&gt;

Very tight bodice with trained over-robe with funnel sleeves and a collar. Worn with a draped sash.&lt;ref name=&quot;:7&quot; /&gt;{{rp|250}}&lt;/blockquote&gt;

Her &quot;Robe à la Reine&quot; might offer a better description of this outfit, or at least of the overskirt:&lt;blockquote&gt;Popular from 1776 to 1787, bodice with an attached overskirt swagged back to show the underskirt. .... Gown was short sleeved and elaborately decorated.&lt;ref name=&quot;:7&quot; /&gt;{{rp|250}}&lt;/blockquote&gt;[[File:Marie Antoinette de modekoningin Gallerie des Modes et Costumes Français Gallerie des Modes et Costumes Francais, 1787, ooo.359, Habit de Cour en hyver (titel op object), RP-P-2004-1142.jpg|thumb|Marie Antoinette in Winter Court Fashion]]

This 18th-century interpretation of what looked Turkish would have been about what was fashionable and, in the case of Marie Antoinette's court, dramatic.

The 1787 &quot;Habit de Cour en hyver garni de fourrures &amp;c.&quot; (right) of Marie Antoinette by printmaker Nicolas Dupin, after a drawing by Augustin de Saint-Aubin, shows Marie Antoinette in a winter court outfit trimmed with white fur.&lt;ref&gt;{{Cite web|url=https://www.rijksmuseum.nl/en/collection/object/Marie-Antoinette-The-Queen-of-Fashion-Gallerie-des-Modes-et-Costumes-Francais--727dc366885cc0596cd60d7b2c57e207|title=Marie Antoinette: The Queen of Fashion: Gallerie des Modes et Costumes Français|website=Rijksmuseum.nl|language=en|access-date=2025-05-02}}&lt;/ref&gt; Unusually, this &quot;habit&quot; à la Polonaise has a train. The highly stylized court version of a mob cap was appropriated from the peasantry and turned into this extravagant headdress with its unrealistic high crown and its huge ribbon and bows. This outfit as a whole is balanced even though individual elements (like the cap and the white drapes gathered and bunched with bows and tassels) are out of proportion.

The decadence of the aristocratic and royal classes in France at the end of the 18th century are revealed by these extravagant, dramatic fashions in court dress. These restructured, redesigned court dresses are the merging of the earlier, highly decorated and formal pannier style with the simpler, informal style à la Polonaise. The design is complex, but the complexity does not result from the variety of decorations. The most important differences in the merged design are in the radical reduction of frou-frou and the number of layers. Also, sometimes, the skirts are ankle rather than floor length. The foundation garments held the layers away from the legs, not restricting movement. The different styles of farthingales that existed at the same time are variations on a theme, but the panniers and the Polonaise styles, which also existed at the same time, had different purposes and were designed for different events, but the two styles influenced each other to the point that they merged. 

All the various forms of hoops we've discussed so far are not discrete but moments in a long evolution of foundation structures. Once fashion had moved on, they all passed out of style and were not repeated. Except the Polonaise, which had influence beyond the 18th century — in the 1870s revival of the à la Polonaise style and in Victorian fancy-dress (or costume) balls. For example, [[Social Victorians/People/Pembroke#Lady Beatrix Herbert|Lady Beatrix Herbert]] at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's fancy-dress ball]] was wearing a Polonaise, based on a Thomas Gainsborough portrait of dancer Giovanna Baccelli.

=== Crinoline Hoops ===
''[[Social Victorians/Terminology#Crinoline|Crinoline]]'', technically, is the name for a kind of stiff fabric made mostly from horsehair and sometimes linen, stiffened with starch or glue, and used for [[Social Victorians/Terminology#Foundation Garments|foundation garments]] like petticoats or bustles. The term ''crinoline'' was not used at first for the cage (shown in the image below left), but that kind of structure came to be called a crinoline as well as a cage, and the term is still used in this way by some.

After the 1789 French Revolution, for about one generation, women stopped wearing corsets and hoops in western Europe.&lt;ref name=&quot;:11&quot; /&gt;{{rp|445–446}} What they did wear was the Empire dress, a simple, columnar style of light-weight cotton fabric that idealized classical Greek outlines and aesthetics. Cotton was a fabric for the elite at this point since it was imported from India or the United States. Sometimes women moistened the fabric to reveal their &quot;natural&quot; bodies, showing that they were not wearing artificial understructures.[[File:Crinoline era3.gif|thumb|1860s Cage Showing the Structure|left]]

Beginning in the second decade of the 19th century and continuing through the 1830s, corsets returned and skirts became more substantial, widened by layers of flounced cotton petticoats — and in winter, heavy woolen or quilted ones. The waist moved down to the natural waist from the Empire height. As skirts got wider in the 1840s, the petticoats became too bulky and heavy, hanging against the legs and impeding movement. In the mid 1850s&lt;ref name=&quot;:11&quot; /&gt;{{rp|510}} &lt;ref name=&quot;:7&quot; /&gt;{{rp|78}} those layers of petticoats began to be replaced by hoops, which were lighter than all that fabric, even when made of steel, and even when really wide.

Lewandowski defines 3 kinds of 19th-century cages:&lt;blockquote&gt;cage: Crinoline (1840–1865 C.E.) to Bustle (1865–1890 C.E.). United Kingdom. Nickname for artificial crinoline; petticoat with whalebone hoops, wire, or watch-string.

cage Americaine: Crinoline (1840–1865 C.E.). France. Petticoat in which only bottom half was covered with fabric, upper half only boning.

cage empire: Crinoline (1840–1865 C.E.) to Bustle (1865–1890 C.E.). Popular from 1861 to 1869, slightly trained petticoat made of 30 steel hoops that increased in size as they approached the ground.&lt;ref name=&quot;:7&quot; /&gt; (46)&lt;/blockquote&gt;

R. C. Milliett patented the first cage, or crinoline hoops in 1856 in Paris,&lt;ref&gt;&quot;The Fashion.&quot; Citing the Collection of the Kent State University Museum. ''Facebook'' 6 August 2025. https://www.facebook.com/photo/?fbid=122200374008095594&amp;set=a.122128150262095594. The Fashion's WhatsApp channel: 

https://whatsapp.com/channel/0029VbBPfXc2UPBIy6Aj651n.&lt;/ref&gt; but cages were in use before the patent. Empress Eugénie of France, wife of Napoleon III, used the cage in 1855 to obscure evidence of pregnancy, which let her be more present in public:&lt;blockquote&gt;“On November 23, 1855, Lord Malmesbury went to a dinner at the Tuileries and found Eugénie “looking very handsome, and all appearances concealed by the large dresses now worn.”&lt;ref name=&quot;:22&quot;&gt;Goldstone, Nancy. ''The Rebel Empresses: Elisabeth of Austria and Eugénie of France, Power and Glamour in the Struggle for Europe''. Little, Brown, 2025.&lt;/ref&gt;{{rp|296}}&lt;/blockquote&gt;

The caged crinoline was Eugénie's&lt;blockquote&gt;signature, over-the-top look. An update on the eighteenth-century pannier worn by her muse, Marie Antoinette, the caged crinoline created a skirt so broad that it often made it difficult for a woman wearing one to get through a doorway [like the court panniers of Marie Antoinette's time]. Because they were all the rage at the French court, crinolines were immensely popular for years — Sisi [Elisabeth, Empress of Austro-Hungary and the Holy Roman Empire as well as Queen Victoria] owned one ... — but for Eugenie, the dome-shaped skirts had the added advantage, as Malmesbury pointed out, of hiding her condition in case she miscarried again.&lt;ref name=&quot;:22&quot; /&gt;{{rp|296, n. vi}}&lt;/blockquote&gt;

The sketch (above left) shows a crinoline cage from the 1850s and 1860s, making clear the structure that underlay the very wide, bell or hemisphere shapes of the era without the fabric that would normally have covered it.&lt;ref&gt;Jensen, Carl Emil. ''Karikatur-album: den evropaeiske karikature-kunst fra de aeldste tider indtil vor dage. Vaesenligst paa grundlag af Eduard Fuchs : Die karikature'', Eduard Fuchs. Vol. 1. København, A. Chrustuabsebs Forlag, 1906. P. 504, Fig. 474 (probably) ''Google Books'' https://books.google.com/books?id=BUlHAQAAMAAJ.&lt;/ref&gt; (This image was published in a book in 1904, but it may have been drawn earlier. The [[Social Victorians/Terminology#Chemise|chemise]] is accurate but oversimplified, minus the usual ruffles, more for the wealthy and less for the working classes.) '''The common underwear of this time would have been two individual legs connected at the waist, at most. The woman's crotch would not be enclosed, leaving her exposed if she fell or the wind was strong enough to lift her skirts far enough.''' 

[[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Manchester (later Duchess of Devonshire)]] must have been wearing a cage like this in 1859 when one of her hoops caught in a stile she was crossing and she fell. She landed &quot;on her feet with her cage and whole petticoats remaining above her head,&quot; revealing &quot;to all the world in general and the Duc de Malakoff in particular&quot; that she was wearing &quot;a pair of scarlet tartan knickerbockers,&quot; the kind of garment men would wear when hunting.&lt;ref name=&quot;:202&quot;&gt;Vane, Henry. ''Affair of State: A Biography of the 8th Duke and Duchess of Devonshire''. Peter Owen, 2004.&lt;/ref&gt;

When people think of 1860s hoops, they think of this shape, the one shown in, say, the 1939 film ''Gone with the Wind''. The extremely wide, round shape, which is what we are accustomed to seeing in historical fiction and among re-enactors, was very popular in the late 1850s and early 1860s, but it was not the only shape hoops took at this time. The half-sphere shape — in spite of what popular history prepares us to think — was far from universal.[[File:Miss Victoria Stuart-Wortley, later Victoria, Lady Welby (1837-1912) 1859.jpg|thumb|Victoria Stuart-Wortley, 1859]]As the 1860s progressed, hoops (and skirts) moved towards the back, creating more fullness there and leaving a flatter front. The photographs below show the range of choices for women in this decade. Cages could be more or less wide, skirts could be more or less full in back and more or less flat in front, and skirts could be smooth, pleated or folded, or gathered. Skirts could be decorated  with any of the many kinds of ruffles or with layers (sometimes made of contrasting fabrics), and they could be part of an outfit with a long bodice or jacket (sometimes, in fact, a [[Social Victorians/Terminology#Peplum|peplum]]). As always, the woman's social class and sense of style, modesty and practicality affected her choices.

In her portrait (right) Victoria Stuart-Wortley (later Victoria, Lady Welby) is shown in 1859, two years before she became one of Queen Victoria's maids of honor. While Stuart-Wortley is dressed fashionably, her style of clothing is modest and conservative. The wrinkles and folds in the skirt suggest that she could be wearing numerous petticoats (which would have been practical in cold buildings), but the smoothness and roundness of the silhouette of the skirt suggest that she is wearing conservative hoops.[[File:Elisabeth Franziska wearing a crinoline and feathered hat.jpg|thumb|Archduchess Elisabeth Franziska, 1860s|left]]

The portrait of Archduchess Elisabeth Franziska (left) offers an example of hoops from the 1860s that are not half-sphere shaped and a skirt that is not made to fit smoothly over them. The dress seems to have a short peplum whose edges do not reach the front. She is standing close to the base of the column and possibly leaning on the balustrade, distorting the shape of the skirt by pushing the hoop forward.

This dress has a complex and sophisticated design, in part because of the weight and textures of the fabric and trim. The folds in the skirt are unusually deep. Even though the textured or flocked fabric is light-colored, this could be a winter dress.

The skirt is trimmed with zig-zag rows of ruffles and a ruffle along the bottom edge. The ruffles may be double with the top ruffle a very narrow one (made of an eyelet or some kind of textured fabric). Both the top and bottom edges of the tiered double ruffles are outlined in a contrasting fabric, perhaps of ribbon or another lace, perhaps even crocheted. Visual interest comes from the three-dimensionality provided by the ruffles and the contrast caused by dark crocheted or ribbon edging on the ruffles. In fact, the ruffles are the focus of this outfit.

[[File:Her Majesty the Queen Victoria.JPG|thumb|Queen Victoria at Windsor Castle, 1861]]
The photographic portrait (right) of Queen Victoria at Windsor Castle, in evening dress with diadem and jewels, is by Charles Clifford&lt;ref&gt;{{Cite web|url=https://wellcomecollection.org/works/ppgcfuck|title=Queen Victoria. Photograph by C. Clifford, 1861.|website=Wellcome Collection|language=en|access-date=2025-02-03}}&lt;/ref&gt; of Madrid, dated 14 November 1861 and now held by the Wellcome Institute. Prince Albert died on 14 December 1861,&lt;ref&gt;{{Cite journal|date=2025-01-20|title=Prince Albert of Saxe-Coburg and Gotha|url=https://en.wikipedia.org/wiki/Prince_Albert_of_Saxe-Coburg_and_Gotha|journal=Wikipedia|language=en}}&lt;/ref&gt; so this carte-de-visite portrait was taken one month before Victoria went into mourning for 40 years.

This fashionable dress could be a ballgown designed by a designer.

The hoops under these skirts appear to be round rather than elliptical but are rather modest in their width and not extreme. That is, there is as much fullness in the front and back as on the sides. In this style, the skirt has a smooth appearance because it is not fuller at the bottom than the waist, where it is tightly gathered or pleated, so the skirts lie smoothly on the hoops and are not much fuller than the hoops. The smoothness of this skirt makes it definitive for its time. 

Instead of elaborate decoration, this visually complex dress depends on the woven moiré fabric with additional texture created by the shine and shadows in the bunched gathering of the fabric. The underskirt is gathered both at the waist and down the front, along what may be ribbons separating the gathers and making small horizontal bunches. The overskirt, which includes a train, has a vertical drape caused by the large folds at the waist. The horizontal design in the moiré fabric contrasts with the vertical and horizontal gathers of the underskirt and large, strongly vertical folds of the overskirt.[[File:Queen Victoria photographed by Mayall.JPG|thumb|Queen Victoria photographed by Mayall. early 1860s|left]]
The carte-de-visite portrait of Queen Victoria by John Jabez Edwin Paisley Mayall (left) shows hoops that are more full in the back than the front. Mayall took a number of photographs of the royal family in 1860 and in 1861 that were published as cartes de visite,&lt;ref&gt;{{Cite journal|date=2024-11-08|title=John Jabez Edwin Mayall|url=https://en.wikipedia.org/wiki/John_Jabez_Edwin_Mayall|journal=Wikipedia|language=en}}&lt;/ref&gt; and the style of Victoria's dress is consistent with the early 1860s.

The fact that she has white or a very light color at her collar and wrists suggests that she was not in full mourning and thus wore this dress before Prince Albert died on 14 December 1861. We cannot tell what color this dress is, and it may not be black in spite of how it appears in this photograph. Victoria's hoops are modest — not too full — and mostly round, slightly flatter in the front. The skirt gathers more as it goes around the sides to the back and falls without folds in the front, where it is smoother, even over the flatter hoops. This is a winter garment with bulky sleeves and possibly fur trim. Except for what may be an undergarment at the wrists, this one-layer garment might be a dress or a bodice and skirt (perhaps with a short jacket). Over-trimmed garments were standard in this period. Lacking layers, ruffles, lace or frou-frou, the simple design of Victoria's dress is deliberate and balanced — and looks warm.

The bourgeois, inexpensive-looking design of this dress echoes Victoria's performance of a queen who is respectable and responsible rather than aristocratic and &quot;fashion forward.&quot; So she looks like a middle-class matron.[[File:Queen Emma of Hawaii, photograph by John &amp; Charles Watkins, The Royal Collection Trust (crop).jpg|thumb|Queen Emma Kaleleokalani of Hawai'i, 1865]]

The portrait (right) of Queen Emma of Hawaii —  Emma Kalanikaumakaʻamano Kaleleonālani Naʻea Rooke — is a carte de visite from an album of ''Royal Portraits'' that Queen Victoria collected. The carte-de-visite photograph is labelled 1865 and ''Queen Emma of the Sandwich Islands'',&lt;ref&gt;Unknown Photographer. ''Emma Kalanikaumakaʻamano Kaleleonālani Naʻea Rooke, Queen of the Kingdom of Hawaii (1836-85)''. ''www.rct.uk''. Retrieved 2025-02-07. https://www.rct.uk/collection/2908295/emma-kalanikaumakaamano-kaleleonalani-naea-rooke-queen-of-the-kingdom-of-hawaii.&lt;/ref&gt; possibly in Victoria's hand. How Victoria got this photograph is not clear. Queen Emma traveled to North America and Europe between 6 May 1865 and 23 October 1866,&lt;ref&gt;Benton, Russell E. ''Emma Naea Rooke (1836-1885), Beloved Queen of Hawaii''. Lewiston, N.Y., U.S.A. : E. Mellen Press, 1988. ''Internet Archive'' https://archive.org/details/emmanaearooke1830005bent/.&lt;/ref&gt;{{rp|49}} visiting London twice, the second time in June 1866.&lt;ref name=&quot;:17&quot;&gt;{{Cite journal|date=2025-01-07|title=Queen Emma of Hawaii|url=https://en.wikipedia.org/wiki/Queen_Emma_of_Hawaii|journal=Wikipedia|language=en}}&lt;/ref&gt;

In her portrait Queen Emma is standing before some books and an open jewelry box. She shows an elegant sense of style.

The silhouette shows a sophisticated variation of the hoops as the fullness has moved to the back and the front flattened. The large pleats suggest a lot of fabric, but the front falls almost straight down. The overskirt and bodice are made from a satin-weave fabric, and the petticoat has a matt woven surface. The overskirt is longer in the back, leading us to expect the petticoat also to be longer and to turn into a train. Although the hoops cause the skirt to fall away from her body in back, the skirt does not drag on the floor as a train would and just clears the floor all the way around.

This optical illusion of a train makes this dress look more formal than it actually was. The covered shoulders and décolletage say the dress was not a formal or evening gown. In fact, this looks like a winter dress, and the sleeves (which she has pushed up above her wrist) are wrinkled, suggesting they may be padded. Queen Emma seems to have worn veils like this at other times as well, especially after the death of her husband, as did Victoria, so this is also not her wedding dress.

Popular history has led us to believe that crinoline hoops were half-spherical and always very wide, but photographs of the time show a variety of shapes for skirts, with many women wearing skirts that had flatter fronts and more fabric in the back. In fact, also in the 1860s, according to Lewandowski, a version of the bustle — called a crinolette or crinolette petticoat — developed:&lt;blockquote&gt;Crinolette petticoat: Bustle (1865–1890 C.E.). Worn in 1870 and revived in 1883, petticoat cut flat in front and with half circle steel hoops in back and flounces on bottom back.&lt;ref name=&quot;:7&quot; /&gt;{{rp|78}}&lt;/blockquote&gt;

This development of a bustle mid century is the result of construction techniques that include foundation structures and specifically shaped pattern pieces to achieve the evolving silhouette, in this case part of the general movement of the fullness of skirts away from the front and toward the back. The other essential element of these construction techniques is angled seams in the skirts, made by gores, pieces of fabric shaped to fit the waist (and sometimes the hips) and to widen at the bottom so that the skirt flares outward.

==== The 19th-century Revival of the Polonaise ====
The Polonaise style was revived in the last third of the 19th century, but the revival did not bring back the 18th-century 3 poufs. The robe à la Polonaise had evolved. The foundation that created the poufs is gone, replaced possibly in fact by the crinolette petticoat or something like it. The panniers — and the 2 side poufs they supported — have gone, and the bulk of the fabric has been bunched in the back.

Also, the poufs on the sides have been replaced with a flat drape in front that functions as an overskirt.

The Polonaise dress (below left and right), in the collection of the Los Angeles County Museum of Art, is English, dating from about 1875.&lt;ref name=&quot;:18&quot;&gt;&quot;Woman's Dress Ensemble.&quot; Costumes and Textiles. LACMA: Los Angeles County Museum of Art. https://collections.lacma.org/node/214459.&lt;/ref&gt; The sheer fabric has red &quot;wool supplementary patterning&quot; woven into the weft.&lt;ref name=&quot;:18&quot; /&gt; Because the mannequin is modern, we cannot be certain how long the skirts would have been on the woman who wore this dress.[[File:Woman's Polonaise Dress LACMA M.2007.211.777a-f (1 of 4).jpg|thumb|English Polonaise, c. 1875, front view|left]][[File:Woman's Polonaise Dress LACMA M.2007.211.777a-f (4 of 4).jpg|thumb|English Polonaise, c. 1875, side view]]The dress has an overskirt that is draped up toward the back and pulled under the top poof. The underskirt gets fuller at the bottom because it is constructed with gores to create the A-line but it is also slightly gathered at the waist.

The vertical element is emphasized by the angled silhouette and the folds caused by the gathering at the waist. The ruffles and lace form horizontal lines in the skirts. The skirts are very busy visually because of pattern in the fabric and the contrasting vertical and horizontal elements as well as the ruffles, some of which are double, and the machine-made lace at the edge of the ruffles. The skirts look three dimensional because of these elements and the layering of the fabric, multiplying the jagged-edged red &quot;supplementary patterning.&quot;

The fabric of the overskirt is cut, gathered and draped so that the poufs in back are full and rounded, but they are also possibly supported by some kind of foundation structure. The lower pouf in back introduces the idea that the fullness in the back is layered, making this element of the Polonaise a kind of precursor to the bustle and continuing what the crinolette petticoat began in the 1860s. This layering of the lower pouf also indicates one way a train might be attached.

Laura Ingalls Wilder wrote about the hoops her fictionalized self wore the century before, unusually, and calls her dress a Polonaise. Although they are common in current historical fiction, descriptions of foundation garments are rare in the writings of the women who wore them or in the literature of the time. In ''These Happy Golden Years'' (1943), Wilder gives a detailed description of the undergarments as well as the foundation garments under her dress, including a bustle, and talks about how they make the Polonaise look on her:&lt;blockquote&gt;
Then carefully over her under-petticoats she put on her hoops. She liked these new hoops. They were the very latest style in the East, and these were the first of the kind that Miss Bell had got. Instead of wires, there were wide tapes across the front, almost to her knees, holding the petticoats so that her dress would lie flat. These tapes held the wire bustle in place at the back, and it was an adjustable bustle. Short lengths of tape were fastened to either end of it; these could be buckled together underneath the bustle to puff it out, either large or small. Or they could be buckled together in front, drawing the bustle down close in back so that a dress rounded smoothly over it. Laura did not like a large bustle, so she buckled the tapes in front.

Then carefully over all she buttoned her best petticoat, and over all the starched petticoats she put on the underskirt of her new dress. It was of brown cambric, fitting smoothly around the top over the bustle, and gored to flare smoothly down over the hoops. At the bottom, just missing the floor, was a twelve-inch-wide flounce of the brown poplin, bound with an inch-wide band of plain brown silk. The poplin was not plain poplin, but striped with an openwork silk stripe.

Then over this underskirt and her starched white corset-cover, Laura put on the polonaise. Its smooth, long sleeves fitted her arms perfectly to the wrists, where a band of the plain silk ended them. The neck was high with a smooth band of the plain silk around the throat. The polonaise fitted tightly and buttoned all down the front with small round buttons covered with the plain brown silk. Below the smooth hips it flared and rippled down and covered the top of the flounce on the underskirt. A band of the plain silk finished the polonaise at the bottom.&lt;ref&gt;Wilder, Laura Ingalls. ''These Happy Golden Years.'' Harper &amp; Row, Publishers, 1943. Pp. 161–163.&lt;/ref&gt;&lt;/blockquote&gt;
When a 20th-century Laura Ingalls Wilder calls her character's late-19th-century dress a polonaise, she is probably referring to the &quot;tight, unboned bodice&quot;&lt;ref name=&quot;:13&quot; /&gt; and perhaps a simple, modest look like the stereotype of a dairy maid. While the bodice was unboned, the fact that she is wearing a corset cover means that she is corseted under it.   
==== Bustle or Tournure ====
As we have seen, bustles were popular from around 1865 to 1890.&lt;ref name=&quot;:7&quot; /&gt;{{rp|296}} The French term ''tournure'' was a euphemism in English for ''bustle''. The article on the tournure in the French ''Wikipédia'' addresses the purpose of the bustle and crinoline:&lt;blockquote&gt;
Crinoline et tournure ont exactement la même fonction déjà recherchée à d'autres époques avec le vertugadin et ses dérivés: soutenir l'ampleur de la jupe, et par là souligner par contraste la finesse de la taille; toute la mode du xixe siècle visant à accentuer les courbes féminines naturelles par le double emploi du corset affinant la taille et d'éléments accentuant la largeur des hanches (crinoline, tournure, drapés bouffants…).&lt;ref&gt;{{Cite journal|date=2023-10-27|title=Tournure|url=https://fr.wikipedia.org/wiki/Tournure|journal=Wikipédia|language=fr}}&lt;/ref&gt;

[Translation by ''Google Translate'': Crinoline and bustle have exactly the same function already sought in other periods with the farthingale and its derivatives: to support the fullness of the skirt, and thereby emphasize by contrast the finesse of the waist; all the fashion of the 19th century aimed at accentuating natural feminine curves by the dual use of the corset refining the waist and elements accentuating the width of the hips (crinoline, bustle, puffy drapes, etc.).]&lt;/blockquote&gt;Hoops' final phase was the development of the bustle, which as early as the 1860s was created by one of several methods: by draping the dress over a crinolette petticoat or some other structure, or by pulling the fabric to the back and bunching it with pleats or gathers. The overskirt so popular with the revival of the Polonaise pulled additional fabric to the back of the skirt, the poufs supported by some substructure, bunched fabric, padding and, often, ruffled petticoats. The bustle, then, is more complex than might be normally be thought and more complex than some of the earlier foundation garments in the evolution of hoops, in part because the silhouette of hoops (and dresses) was changing more rapidly in the last half of the 19th century than ever before.

[[File:La Gazette rose, 16 Mai 1874; robe à tournure.jpg|thumb|&quot;Toilettes de Printemps,&quot; 1874|left]]In fact, fashion trends were moving so fast at this point that the two &quot;bustle periods&quot; were actually only two decades, the 1870s and the 1880s. Bustle fashion was at its height for these two decades, which saw the line of the skirts change radically. As the bustle developed, the 1870s ruffles disappeared, replaced by draping and layering, which made the bustles more complex visually. 

&quot;Toilettes de Printemps&quot; (left), an 1874 French fashion plate, shows two women walking in the country, the one in green wearing an extremely long and impractical train. Both of these have several rows of ruffles beneath the overskirt — a short-lived fashion. The ruffles, which disappear in the 2nd bustle period, create a fullness in the front of the skirt at the bottom. The bodice of both dresses connects to an overskirt, like a jacket. The excess skirt fabric is draped in the back over a foundation structure. 

Plumes makes the hats tall, part of the proportioning with the bustle. The dog at the feet of the woman in the green dress recalls the dogs ubiquitous in earlier portraiture. 

The most common image of the bustle — the extreme form of the 1880s — required a complex foundation structure, one of which was &quot;steel springs placed inside the shirring [gathering] around the back of the petticoat.&quot;&lt;ref name=&quot;:7&quot; /&gt; (296) Many manufacturers were making bustles by this time, offering women a choice on the kinds of materials used in the foundation structures ['''check this''']. [[File:Somm26.jpg|thumb|Henry Somm, 1880s]]The Henry Somm watercolor (right) offers a clear example of how extreme bustles got in the mid 1880s, in the 2nd bustle period. Henry Somm was the pen name that François Clément Sommier (1844–1907) used on his paintings.&lt;ref&gt;{{Cite journal|date=2025-02-01|title=Henry Somm|url=https://fr.wikipedia.org/w/index.php?title=Henry_Somm&amp;oldid=222597815|journal=Wikipédia|language=fr}}&lt;/ref&gt; He was in Paris beginning in the 1860s and so was present for the Civil War of 1870–71 and the rise of Impressionism in that highly political and dangerous context.&lt;ref&gt;Smee, Sebastian. ''Paris in Ruins: Love, War, and the Birth of Impressionism''. W. W. Norton, 2024.&lt;/ref&gt;

Somm's c. 1895&lt;ref&gt;&quot;File:Somm26.jpg.&quot; Henry Somm, &quot;An Elegantly Dressed Woman at a Door (wearing mid-1880s bustled fashions),&quot; c. 1895. June 2025. Wikimedia Commons 

https://commons.wikimedia.org/wiki/File:Somm26.jpg.&lt;/ref&gt; impressionist painting shows an immediate moment — an elegant mid-1880s woman outside a door, her right hand and face animated, as if she is talking to someone standing to our left.

Her skirt is quite narrow and flat in front with yards of fabric draped in poufs over the huge foundation bustle behind. This dress has no ruffles or excessive frills. The narrow sleeves and tall hat, along with the umbrella so tightly folded it looks like a stick, contribute to the lean silhouette. Details of the dress are not present because this painting is impressionistic rather than realistic, showcasing the play of light on the fabric and the elegance of the woman. The square corner of the front overskirt is not realistic draping, perhaps an artifact of the painter working from memory rather than a model.[[File:Elizabeth Alice Austen in June 1888.jpg|thumb|Elizabeth Alice Austen, 1888|left]]

The 1888 photograph of American photographer Elizabeth Alice Austen (left) is also from the 2nd bustle period. The very stylish Austen is wearing a bustle that is large but not as extreme as they got. The design of her dress is sophisticated and complex with the proportions more clearly presented than we see in paintings or fashion plates. Her plumed hat is tall, one of the vertical elements, along with the slim line of the bodice, sleeves and skirt. The overskirt is pulled to Austen's right so that it does not lie flat in front. The overskirt and bustle are made from 3 different fabrics with 3 different patterns. The front drape and bodice are made of a light-colored fabric with a light striped pattern, and the bustle has 2 fabrics, a shiny reflective material with no pattern and a strongly striped section that matches the underskirt. The strongly and horizontally striped fabric in the underskirt contrasts with the vertical line of the outfit itself.

In spite of the very strong contrasts in the stripes and horizontal and vertical elements, Austen's dress has a light touch about it. With the draped overskirt in front and the complex construction of the bustle, Austen's dress makes a delicate reference to the poufs of the [[Social Victorians/Terminology#The 19th-century Revival of the Polonaise|Polonaise revival]]. [[File:Cperrien-fashionplatescan-p-vf 33.jpg|thumb|Fashion plate, mid-1880s]]This mid-1880s fashion plate (right) has caricatures for figures, with the usual minuscule waists and feet, exaggerated height and bustles, and general lack of realism in the details of the dresses. In fact, the drawing obscures what is necessary to understand how they were constructed, but it is useful because of the 3 different ways bustles are working in the illustration.

The little girl's overskirt and sash function as a bustle, independent of whatever foundation garments she may be wearing. The two women's outfits have the characteristic narrow sleeves and tall hats, and the one in white is holding another extremely narrow umbrella as well.

The bustle on the red-and-white dress is draped loosely over the very large foundation structure that was typical of the 1880s. The striking red jagged edges define the draping of the overskirt in front and the ruffles on the sides. These ruffles are unlike the ruffles of the 1870s, which added volume. They are flattened essentially into layers, preventing them from sticking out and providing texture rather than fullness. The front overskirt is very flat and the back overskirt contributes to the bustle.

The front of the bodice on both dresses extends to a point determined by the corset and typical of Victorian shaping. The waist treatment on the green dress visually lengthens the point to an extreme. The front of the green skirt is draped and layered. Tiny pleats peep out from below the skirt on both women's dresses. The child's dress has 3 flat pleated ruffles in front that contrast with the fuller but still controlled folds in the back.

These dresses have strongly vertical lines with contrasting horizontal lines in the bustles and trim.

Conclusion

'''Trains, skirt length, movement, materials, one evolutionary process, natural fabrics, accelerating change in fashion, designers and seamstresses, medium of our illustrations'''

== Jewelry and Stones ==

=== Cabochon ===
This term describes both the treatment and shape of a precious or semiprecious stone. A cabochon treatment does not facet the stone but merely polishes it, removing &quot;the rough parts&quot; and the parts that are not the right stone.&lt;ref&gt;&quot;cabochon, n.&quot; ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/25778. Accessed 7 February 2023.&lt;/ref&gt; A cabochon shape is often flat on one side and oval or round, forming a mound in the setting.

=== Cairngorm ===

=== Ferronnière ===
A revival of a Renaissance fashion for controlling the hair and headdress. Usually made of a filet, often with a single pendant stone in the center of the forehead, although the Victorians' ferronnières were often elaborate and encrusted with jewels.&lt;ref&gt;Boyington, Amy. &quot;Ferronnière.&quot; ''History with Amy'' 5 November 2025.

Website fb.watch/FBMyC7bqde [links to fb.watch not allowed].&lt;/ref&gt;

=== Half-hoop ===
Usually of a ring or bracelet, a precious-metal band with a setting of stones on one side, covering perhaps about 1/3 or 1/2 of the band. Half-hoop jewelry pieces were occasionally given as wedding gifts to the bride.

=== Jet ===

=== ''Orfèvrerie'' ===
Sometimes misspelled in the newspapers as ''orvfèvrerie''. ''Orfèvrerie'' is the artistic work of a goldsmith, silversmith, or jeweler.

=== Ribbon Necklace ===
=== Solitaire ===
A solitaire is a ring with a single stone set as the focal point. Solitaire rings were occasionally given as wedding gifts to the bride.

=== Turquoise ===

== Mantle, Cloak, Cape ==
In 19th-century newspaper accounts, these terms are sometimes used without precision as synonyms. These are all outer garments.

=== '''Mantle''' ===
A mantle — often a long outer garment — might have elements like a train, sleeves, collars, revers, fur, and a cape. A late-19th-century writer making a distinction between a mantle and a cloak might use ''mantle'' if the garment is more voluminous.

== Military ==
Several men from the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball at Devonshire House]] were dressed in military uniforms, some historical and some, possibly, not.

=== Baldric ===
According to the ''Oxford English Dictionary'', the primary sense of ''baldric'' is &quot;A belt or girdle, usually of leather and richly ornamented, worn pendent from one shoulder across the breast and under the opposite arm, and used to support the wearer's sword, bugle, etc.&quot;&lt;ref&gt;&quot;baldric, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/14849. Accessed 17 May 2023.&lt;/ref&gt; This sense has been in existence since c. 1300.

=== Cuirass ===
According to the ''Oxford English Dictionary'', the primary sense of ''cuirass'' is &quot;A piece of armour for the body (originally of leather); ''spec.'' a piece reaching down to the waist, and consisting of a breast-plate and a back-plate, buckled or otherwise fastened together ....&quot;&lt;ref&gt;&quot;cuirass, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/45604. Accessed 17 May 2023.&lt;/ref&gt;

[[File:Knötel IV, 04.jpg|thumb|alt=An Old drawing in color of British soldiers on horses brandishing swords in 1815.|1890 illustration of the Household Cavalry (Life Guard, left; Horse Guard, right) at the Battle of Waterloo, 1815]]
=== Household Cavalry ===
The Royal Household contains the Household Cavalry, a corps of British Army units assigned to the monarch. It is made up of 2 regiments, the Life Guards and what is now called The Blues and Royals, which were formed around the time of &quot;the Restoration of the Monarchy in 1660.&quot;&lt;ref name=&quot;:3&quot;&gt;Joll, Christopher. &quot;Tales of the Household Cavalry, No. 1. Roles.&quot; The Household Cavalry Museum, https://householdcavalry.co.uk/app/uploads/sites/2/2021/06/Household-Cavalry-Museum-video-series-large-print-text-Tales-episode-01.pdf.&lt;/ref&gt;{{rp|1}} Regimental Historian Christopher Joll says, &quot;the original Life Guards were formed as a mounted bodyguard for the exiled King Charles II, The Blues were raised as Cromwellian cavalry and The Royals were established to defend Tangier.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{rp|1–2}} The 1st and 2nd Life Guards were formed from &quot;the Troops of Horse and Horse Grenadier Guards ... in 1788.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} The Life Guards were and are still official bodyguards of the queen or king, but through history they have been required to do quite a bit more than serve as bodyguards for the monarch.

The Household Cavalry fought in the Battle of Waterloo on Sunday, 18 June 1815 as heavy cavalry.&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} Besides arresting the Cato Steet conspirators in 1820 &quot;and guarding their subsequent execution,&quot; the Household Cavalry contributed to the &quot;the expedition to rescue General Gordon, who was trapped in Khartoum by The Mahdi and his army of insurgents&quot; in 1884.&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} In 1887 they &quot;were involved ... in the suppression of rioters in Trafalgar Square on Bloody Sunday.&quot;&lt;ref name=&quot;:3&quot; /&gt;{{rp|3}} 

==== Grenadier Guards ====
Three men — [[Social Victorians/People/Gordon-Lennox#Lord Algernon Gordon Lennox|Lord Algernon Gordon-Lennox]], [[Social Victorians/People/Stanley#Edward George Villiers Stanley, Lord Stanley|Lord Stanley]], and [[Social Victorians/People/Stanley#Hon. Ferdinand Charles Stanley|Hon. F. C. Stanley]] — attended the ball as officers of the Grenadier Guards, wearing &quot;scarlet tunics, ... full blue breeches, scarlet hose and shoes, lappet wigs&quot; as well as items associated with weapons and armor.&lt;ref name=&quot;:14&quot;&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 34, Col. 2a}}

Founded in England in 1656 as Foot Guards, this infantry regiment &quot;was granted the 'Grenadier' designation by a Royal Proclamation&quot; at the end of the Napoleonic Wars.&lt;ref&gt;{{Cite journal|date=2023-04-22|title=Grenadier Guards|url=https://en.wikipedia.org/w/index.php?title=Grenadier_Guards&amp;oldid=1151238350|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Grenadier_Guards.&lt;/ref&gt; They were not called Grenadier Guards, then, before about 1815. In 1660, the Stuart Restoration, they were called Lord Wentworth's Regiment, because they were under the command of Thomas Wentworth, 5th Baron Wentworth.&lt;ref&gt;{{Cite journal|date=2022-07-24|title=Lord Wentworth's Regiment|url=https://en.wikipedia.org/w/index.php?title=Lord_Wentworth%27s_Regiment&amp;oldid=1100069077|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Lord_Wentworth%27s_Regiment.&lt;/ref&gt;

At the time of Lord Wentworth's Regiment, the style of the French cavalier had begun to influence wealthy British royalists. In the British military, a Cavalier was a wealthy follower of Charles I and Charles II — a commander, perhaps, or a field officer, but probably not a soldier.&lt;ref&gt;{{Cite journal|date=2023-04-22|title=Cavalier|url=https://en.wikipedia.org/w/index.php?title=Cavalier&amp;oldid=1151166569|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier.&lt;/ref&gt;

The Guards were busy as infantry in the 17th century, engaging in a number of armed conflicts for Great Britain, but they also served the sovereign. According to the Guards Museum,&lt;blockquote&gt;In 1678 the Guards were ordered to form Grenadier Companies, these men were the strongest and tallest of the regiment, they carried axes, hatches and grenades, they were the shock troops of their day. Instead of wearing tri-corn hats they wore a mitre shaped cap.&lt;ref&gt;{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/|title=Service to the Crown|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/.&lt;/ref&gt;&lt;/blockquote&gt;The name comes from ''grenades'', then, and we are accustomed to seeing them in front of Buckingham Palace, with their tall mitre hats.

The Guard fought in the American Revolution, and in the 19th century, the Grenadier Guards fought in the Crimean War, Sudan and the Boer War. They have roles as front-line troops and as ceremonial for the sovereign, which makes them elite:&lt;blockquote&gt;Queen Victoria decreed that she did not want to see a single chevron soldier within her Guards. Other then [sic] the two senior Warrant Officers of the British Army, the senior Warrant Officers of the Foot Guards wear a large Sovereigns personal coat of arms badge on their upper arm. No other regiments of the British Army are allowed to do so; all the others wear a small coat of arms of their lower arms. Up until 1871 all officers in the Foot Guards had the privilege of having double rankings. An Ensign was ranked as an Ensign and Lieutenant, a Lieutenant as Lieutenant and Captain and a Captain as Captain and Lieutenant Colonel. This was because at the time officers purchased their own ranks and it cost more to purchase a commission in the Foot Guards than any other regiments in the British Army. For example if it cost an officer in the Foot Guards £1,000 for his first rank, in the rest of the Army it would be £500 so if he transferred to another regiment he would loose [sic] £500, hence the higher rank, if he was an Ensign in the Guards and he transferred to a Line Regiment he went in at the higher rank of Lieutenant.&lt;ref&gt;{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/|title=Formation and role of the Regiments|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/.&lt;/ref&gt;&lt;/blockquote&gt;

==== Life Guards ====
[[Social Victorians/People/Shrewsbury#Reginald Talbot's Costume|General the Hon. Reginald Talbot]], a member of the 1st Life Guards, attended the Duchess of Devonshire's ball dressed in the uniform of his regiment during the Battle of Waterloo.&lt;ref name=&quot;:14&quot; /&gt;{{rp|p. 36, Col. 3b}}

At the Battle of Waterloo the 1st Life Guards were part of the 1st Brigade — the Household Brigade — and were commanded by Major-General Lord Edward Somerset.&lt;ref name=&quot;:4&quot;&gt;{{Cite journal|date=2023-09-30|title=Battle of Waterloo|url=https://en.wikipedia.org/w/index.php?title=Battle_of_Waterloo&amp;oldid=1177893566|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Battle_of_Waterloo.&lt;/ref&gt; The 1st Life Guards were on &quot;the extreme right&quot; of a French countercharge and &quot;kept their cohesion and consequently suffered significantly fewer casualties.&quot;&lt;ref name=&quot;:4&quot; /&gt;
[[File:Captain, Royal Horse Guards, Blue, England, 1879, from the Military Series (N224) issued by Kinney Tobacco Company to promote Sweet Caporal Cigarettes MET DPB874122.jpg|alt=Old drawing of a soldier wearing a white cuirass, a pointed helmet, thigh-high boots, carrying a long sword|thumb|Captain, Royal Horse Guards, Blue, 1888, a Kinney Brothers Tobacco Company card]]

==== Royal Horse Guards ====
In 1650 the Regiment of Cuirassiers was &quot;raised by Sir Arthur Haselrig on the orders of Oliver Cromwell.&quot;&lt;ref name=&quot;:26&quot;&gt;{{Cite journal|date=2026-05-13|title=Royal Horse Guards|url=https://en.wikipedia.org/w/index.php?title=Royal_Horse_Guards&amp;oldid=1353961278|journal=Wikipedia|language=en}}&lt;/ref&gt; In 1660 &quot;it became the Earl of Oxford's Regiment .... Based on the colour of their uniform, the regiment was nicknamed 'the Oxford Blues', or simply the 'Blues.' In 1750, it became the Royal Horse Guards Blue.&quot;&lt;ref name=&quot;:26&quot; /&gt;

The Royal Horse Guards Blue were moved to Windsor at the end of the 18th century and &quot;acted as royal bodyguards&quot; to George III, who liked them.&lt;ref name=&quot;:26&quot; /&gt; While pay for the men &quot;stagnated,&quot; requirements continued to rise, so that recruits had to come from wealth.&lt;ref name=&quot;:26&quot; /&gt; Riding and hunting skills were helpful to the recruits, who had to provide their own horses, pay for messes and uniforms, not to mention the position itself.&lt;ref name=&quot;:26&quot; /&gt;

They fought in the Battle of Waterloo, with 44 dead, 50 wounded (of which only 6 died).&lt;ref name=&quot;:26&quot; /&gt; With the Duke of Wellington at their head, they became part of the Household Cavalry in 1820.&lt;ref name=&quot;:26&quot; /&gt; An 1890 illustration shows a member of the Royal Horse Guard (above right) fighting at the Battle of Waterloo.

The Royal Horse Guard Blue fought in the Battle of Balaclava in 1854, fighting with the heavy brigades and thus were more successful than the famous light brigade, though conditions were very difficult.&lt;ref name=&quot;:26&quot; /&gt;

A tobacco card published in 1888 (right) shows a captain in the Royal Horse Guards, Blue, in 1879.

In 1884–85 the Blues took part in the attempt to rescue General Gordon in Khartoum. They were sent to South Africa at the end of the 19th century.&lt;ref name=&quot;:26&quot; /&gt;

For those men who were in the Royal Horse Guards at the end of the 19th century, the field marshals were

* 1869–1885: Field Marshal Hugh Rose, 1st Baron Strathnairn, during which time — in 1877 — the name changed to the Royal Horse Guards (The Blues).&quot;&lt;ref name=&quot;:26&quot; /&gt;
* 1885–1895: Field Marshal Sir Patrick Grant
* 1895–1907: Field Marshal Garnet Wolseley, 1st Viscount Wolseley
In 1847 Edmund Packe published his ''[[iarchive:historicalrecord00packiala/|Historical Record of the Royal Regiment of Horse Guards, or Oxford Blues]]'', which has colored images to illustrate the development of the uniform up to the middle of the 19th century (the link goes to the ''Internet Archive'').

== [[Social Victorians/Mourning|Mourning]] ==
== Peplum ==
According to the French ''Wiktionnaire'', a peplum is a &quot;Short skirt or flared flounce layered at the waist of a jacket, blouse or dress&quot; [translation by Google Translate].&lt;ref&gt;{{Cite journal|date=2021-07-02|title=péplum|url=https://fr.wiktionary.org/w/index.php?title=p%C3%A9plum&amp;oldid=29547727|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/p%C3%A9plum.&lt;/ref&gt; The ''Oxford English Dictionary'' has a fuller definition, although, it focuses on women's clothing because the sense is written for the present day:&lt;blockquote&gt;''Fashion''. ... a kind of overskirt resembling the ancient peplos (''obsolete''). Hence (now usually) in modern use: a short flared, gathered, or pleated strip of fabric attached at the waist of a woman's jacket, dress, or blouse to create a hanging frill or flounce.&lt;ref name=&quot;:5&quot;&gt;“peplum, n.”. ''Oxford English Dictionary'', Oxford University Press, September 2023, &lt;https://doi.org/10.1093/OED/1832614702&gt;.&lt;/ref&gt;&lt;/blockquote&gt;Men haven't worn peplums since the 18th century, except when wearing costumes based on historical portraits. The ''Daily News'' reported in 1896 that peplums had been revived as a fashion item for women.&lt;ref name=&quot;:5&quot; /&gt;

== Revers ==
According to the ''Oxford English Dictionary'', ''revers'' are the &quot;edge[s] of a garment turned back to reveal the undersurface (often at the lapel or cuff) (chiefly in ''plural''); the material covering such an edge.&quot;&lt;ref&gt;&quot;revers, n.&quot; ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/164777. Accessed 17 April 2023.&lt;/ref&gt; The term is French and was used this way in the 19th century (according to the ''Wiktionnaire'').&lt;ref&gt;{{Cite journal|date=2023-03-07|title=revers|url=https://fr.wiktionary.org/w/index.php?title=revers&amp;oldid=31706560|journal=Wiktionnaire|language=fr}} https://fr.wiktionary.org/wiki/revers.&lt;/ref&gt;

== Traditional vs Progressive Style ==

=== Progressive Style ===
The terms ''artistic dress'' and ''aesthetic dress'' — as well as ''rational dress'' or ''dress reform'' — are not synonymous and were in use at different times to refer to different groups of people in different contexts, but we recognize them as referring to a similar kind of personal style in clothing, a style we call progressive dress or the progressive style. Used in a very precise way, ''artistic dress'' is associated with the Pre-Raphaelite artists and the women in their circle beginning in the 1860s. Similarly, ''aesthetic dress'' is associated with the 1880s and 1890s and dress reform movements, as is ''rational dress'', a movement located largely among women in the middle classes from the middle to the end of the century. In general, what we are calling the progressive style is characterized by its resistance to the highly structured fashion of its day, especially corseting, aniline dyes and an extremely close fit. This group of styles was more about individual choices and approaches than the consistent vision offered by couturiers like Maison Worth.

* [[Social Victorians/People/Dressmakers and Costumiers#Alice Comyns Carr and Ada Nettleship|Ada Nettleship]]: Constance Wilde and Ellen Terry; an 1883 exhibition of dress by the Rational Dress Society featured her work, including trousers for women (with a short overskirt)&lt;ref&gt;{{Cite journal|date=2025-04-21|title=Ada Nettleship|url=https://en.wikipedia.org/w/index.php?title=Ada_Nettleship&amp;oldid=1286707541|journal=Wikipedia|language=en}}&lt;/ref&gt;
* [[Social Victorians/People/Dressmakers and Costumiers#Alice Comyns Carr and Ada Nettleship|Alice Comyns Carr]]&lt;ref&gt;{{Cite journal|date=2025-06-06|title=Alice Comyns Carr|url=https://en.wikipedia.org/w/index.php?title=Alice_Comyns_Carr&amp;oldid=1294283929|journal=Wikipedia|language=en}}&lt;/ref&gt;
* Grosvenor Gallery

=== Traditional Style ===
[[File:Victoria Hesse NPG 95941 crop.jpg|alt=Old photograph of a white woman wearing a very tight and fitted bodice with her skirts swept to the back|thumb|Princess Victoria, Marchioness of Milford-Haven (1863–1950), Granddaughter of Queen Victoria; wife of Prince Louis of Battenberg, 1st Marquess, c. 1878]]
Images

* Smooth bodice, fabric draped to the back or covering a bustle with a small cage beneath it:
By the end of the century designs from the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]] (or Maison Worth) define what we think of as the traditional Victorian look, which was very stylish and expensive. Queen Victoria's granddaughter Princess Victoria is shown (right) wearing a traditional but very stylish c. 1878 dress like one designed by Maison Worth. Blanche Payne describes an example of the 1895 &quot;high style&quot; in a gown by Worth with &quot;the idiosyncrasies of the [1890s] full blown&quot;:&lt;blockquote&gt;The dress is white silk with wine-red stripes. Sleeves, collars, bows, bag, hat, and hem border match the stripes. The sleeve has reached its maximum volume; the bosom full and emphasized with added lace; the waistline is elongated, pointed, and laced to the point of distress; the skirt is smooth over the hips, gradually swinging out to sweep the floor. This is the much vaunted hourglass figure.&lt;ref name=&quot;:11&quot; /&gt;{{rp|530}}&lt;/blockquote&gt;

The Victorian-looking gowns at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] are stylish in a way that recalls the designs of the House of Worth. The elements that make their look so Victorian are anachronisms on the costumes representing fashion of earlier eras. The women wearing these gowns preferred the standards of beauty from their own day to a more-or-less historically accurate look. The style competing at the very end of the century with the Worth look was not the historical, however, but a progressive style called at the time ''artistic'' or ''aesthetic''.

William Powell Frith's 1883 painting ''A Private View at the Royal Academy, 1881'' (discussion below) pits this kind of traditional style against the progressive or artistic style.

=== The Styles ===
[[File:Frith A Private View.jpg|thumb|William Powell Frith, ''A Private View at the Royal Academy, 1881'']]
We typically think of the late-Victorian silhouette as universal but, in the periods in which corsets dominated women's dress, not all women wore corsets and not all corsets were the same, as William Powell Frith's 1883 ''A Private View at the Royal Academy, 1881'' (right) illustrates. Frith is clear in his memoir that this painting — &quot;recording for posterity the aesthetic craze as regards dress&quot; — deliberately contrasts what he calls the &quot;folly&quot; of the Aesthetic Dress movement and the look of the traditional corseted waist.&lt;ref&gt;Frith, William Powell. ''My Autobiography and Reminiscences''. 1887.&lt;/ref&gt; Frith considered the Aesthetic Movement and Aesthetic Dress &quot;ephemeral,&quot; but its rejection of corsetry looks far more consequential to us in hindsight than it did in the 19th century.

As Frith sees it, his painting critiques the &quot;craze&quot; associated with the women in this set of identifiable portraits who are not corseted, but his commitment to realism shows us a spectrum, a range, of conservatism and if not political then at least stylistic progressivism among the women. The progressives, oddly, are the women wearing artistic (that is, somewhat historical) dress, because they’re not corseted. It is a misreading to see the presentation of the women’s fashion as a simple opposition. Constance, Countess of Lonsdale — situated at the center of this painting with Frederick Leighton, president of the Royal Academy of Art — is the most conservatively dressed of the women depicted, with her narrow sleeves, tight waist and almost perfectly smooth bodice, which tells us that her corset has eyelets so that it can be laced precisely and tightly, and it has stays (or &quot;bones&quot;) to prevent wrinkles or natural folds in the overclothing. Lillie Langtry, in the white dress, with her stylish narrow sleeves, does not have such a tightly bound waist or smooth bodice, suggesting she may not be corseted at all, as we know she sometimes was not.['''citation'''] Jenny Trip, a painter’s model, is the woman in the green dress in the aesthetic group being inspected by Anthony Trollope, who may be taking notes. She looks like she is not wearing a corset. Both Langtry and Trip are toward the middle of this spectrum: neither is dressed in the more extreme artistic dress of, say, the two figures between Trip and Trollope.

A lot has been written about the late-Victorian attraction to historical dress, especially in the context of fancy-dress balls and the Gothic revival in social events as well as art and music. Part of the appeal has to have been the way those costumes could just be beautiful clothing beautifully made. Historical dress provided an opportunity for some elite women to wear less-structured but still beautiful and influential clothing. ['''Calvert'''&lt;ref&gt;Calvert, Robyne Erica. ''Fashioning the Artist: Artistic Dress in Victorian Britain 1848-1900''. Ph.D. thesis, University of Glasgow, 2012. &lt;nowiki&gt;https://theses.gla.ac.uk/3279/&lt;/nowiki&gt;&lt;/ref&gt;] The standards for beauty, then, with historical dress were Victorian, with the added benefit of possibly less structure. So, at the Duchess of Devonshire's ball, &quot;while some attendees tried to hew closely to historical precedent, many rendered their historical or mythological personage in the sartorial vocabulary they knew best. The [photographs of people in their costumes at the ball offer] a glimpse into how Victorians understood history, not a glimpse into the costume of an authentic historical past.&quot;&lt;ref&gt;Mitchell, Rebecca N. &quot;The Victorian Fancy Dress Ball, 1870–1900.&quot; ''Fashion Theory'' 2017 (21: 3): 291–315. DOI: 10.1080/1362704X.2016.1172817.&lt;/ref&gt;{{rp|294}}

* historical dress: beautiful clothing.
* the range at the ball, from Minnie Paget to Gwladys
* &quot;In light of such efforts, the ball remains to this day one of the best documented outings of the period, and a quick glance at the album shows that ...&quot;
* The costume of the Duchess of Devonshire does not have a defined waist and may suggest that she herself is not corseted, although that would be a notable departure for her.

Women had more choices about their waists than the simple opposition between no corset and tightlacing can accommodate. The range of choices is illustrated in Frith's painting, with a woman locating herself on it at a particular moment for particular reasons. Much analysis of 19th-century corsetry focuses on its sexualizing effects — corsets dominated Victorian photographic pornography ['''citations'''] and at the same time, the absence of a corset was sexual because it suggested nudity.['''citations'''] A great deal of analysis of 19th-century corsetry, on the other hand, assumes that women wore corsets for the male gaze ['''citations'''] or that they tightened their waists to compete with other women.['''citations'''] 

But as we can see in Frith's painting, the sexualizing effect was not universal or sweeping, and these analyses do not account for the choices women had in which corset to wear or how tightly to lace it. Especially given the way that some photographic portraits were mechanically altered to make the waist appear smaller, the size of a woman's waist had to do with how she was presenting herself to the world. That is, the fact that women made choices about the size of or emphasis on their waists suggests that they had agency that needs to be taken into account. 

As they navigated the complex social world, women's fashion choices had meaning. Society or political hostesses had agency not only in their clothing but generally in that complex social world. They had roles managing social events of the upper classes, especially of the upper aristocracy and oligarchy, like the Duchess of Devonshire's ball. Their class and rank, then, were essential to their agency, including to some degree their freedom to choose what kind of corset to wear and how to wear it. Also, by the end of the century lots of different kinds of corsets were available for lots of different purposes. Special corsets existed for pregnancy, sports (like tennis, bicycling, horseback riding, golf, fencing, archery, stalking and hunting), theatre and dance and, of course, for these women corsets could be made to support the special dress worn over it.  

Women's choices in how they presented themselves to the world included more than just their foundation garments, of course. &quot;Every cap, bow, streamer, ruffle, fringe, bustle, glove,&quot; that is, the trim and decorations on their garments, their jewelry and accessories — which Davidoff calls &quot;elaborations&quot;&lt;ref name=&quot;:1&quot; /&gt;{{rp|93}} — pointed to a host of status categories, like class, rank, wealth, age, marital status, engagement with the empire, how sexual they wanted to seem, political alignment and purpose at the social event. For example, when women were being presented to the monarch, they were expected to wear three ostrich plumes, often called the [[Social Victorians/Terminology#Prince of Wales's Feathers or White Plumes|Prince of Wales's feathers]].  

Like all fashions, the corset, which was quite long-lasting in all its various forms, eventually went out of style. Of the many factors that might have influenced its demise, perhaps most important was the women's movement, in which women's rights, freedom, employment and access to their own money and children were less slogan-worthy but at least as essential as votes for women. The activities of the animal-rights movements drew attention not only to the profligate use of the bodies and feathers of birds but also to the looming extinction of the baleen whale, which made whale bone scarce and expensive. Perhaps the century's debates over corseting and especially tightlacing were relevant to some decisions not to be corseted. And, of course, perhaps no other reason is required than that the nature of fashion is to change.

== Undergarments ==
Unlike undergarments, Victorian women's foundation garments created the distinctive silhouette. Victorian undergarments included the chemise, the bloomers, the corset cover — articles that are not structural.
The corset was an important element of the understructure of foundation garments — hoops, bustles, petticoats and so on — but it has never been the only important element. 

=== Undergarments ===

* Chemise
* Corset cover
* Bloomers
* [[Social Victorians/Terminology#Petticoat|Petticoats]] (distinguish between the outer- and undergarment type of petticoat)
* Combinations
* [[Social Victorians/Terminology#Hose, Stockings and Tights|Hose, stockings and tights]]
* Men's shirts
* Men's unders

==== Bloomers ====

==== Chemise ====
A chemise is a garment &quot;linen, homespun, or cotton knee-length garment with [a] square neck&quot; worn under all the other garments except the bloomers or combinations.&lt;ref name=&quot;:7&quot; /&gt; (61) According to Lewandowski, combinations replaced the chemise by 1890.

==== Combinations ====

=== [[Social Victorians/Terminology/Foundation Garments|Foundation Garments]] ===
Foundation structures changed the shape of the body by metal, cane, boning. Men wore corsets as well.
* [[Social Victorians/Terminology#Corset|Corset]]
* [[Social Victorians/Terminology#Hoops|Hoops]]
* Padding

==== Padding ====
Some kinds of padding were used in the Victorian age to enlarge women's bosoms and create cleavage as well as to keep elements of a garment puffy. In the Elizabethan era, men's codpieces are examples of padding.

With respect to the costumes worn at fancy-dress balls, most important would be bum rolls and cod pieces. 

What are commonly called '''bum rolls''' were sometimes called roll farthingales, French farthingales or padded rolls.

== Footnotes ==
{{reflist}}</text>
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window.mwSetupToolbar = function() {
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//
//
//Bedingte Einsetzungshilfen
//
//


//
//
//Bedingte Einsetzungshilfen für Stichworte
//
//


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//
//
//Bedingter Button für Vorlesungsaufzählung
//
//


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//
//
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//
//


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//
//
//Bedingte Buttons für Latexversion
//
//


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//
//
//Bedingte Buttons für Kontrollversion (intern)
//
//


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if(wgPageName.match(/check$/)){
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//
//
//Mathematische Umgebungen
//
//


 mw.toolbar.addButton({
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mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/3/3f/Button_clipboard_math.png&quot;,
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     &quot;sampleText&quot;: formulaHere});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/ce/Button_clipboard_mathdisplay.png&quot;,
     &quot;speedTip&quot;: &quot;Mathdisplay&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nMath/display|term=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/5/5f/Button_sorterbar.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematische Korrespondenz&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nmathcor|term1=\n&quot;,
     &quot;tagClose&quot;: &quot;\n||term2=\n\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/d/d8/Button_clipboard_enum.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematische Liste&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nmathlist|term1=\n&quot;,
     &quot;tagClose&quot;: &quot;\n||term2=\n\n||term3=\n\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/5/5f/Button_sorterbar.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical condition&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nmathcond|term=\n&quot;,
     &quot;tagClose&quot;: &quot;\n||condterm1=\n\n||condterm2=\n\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/3/3f/Set_theory_icon.svg&quot;,
     &quot;speedTip&quot;: &quot;Element&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nRelationchain\n| &quot;,
     &quot;tagClose&quot;: &quot;\n|\\in| \n||\n||\n||\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/8/86/Button_clipboard_valign.png&quot;,
     &quot;speedTip&quot;: &quot;Vergleichskette&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nRelationchain/display\n| &quot;,
     &quot;tagClose&quot;: &quot;\n|| \n|| \n|| \n|| \n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/f/ff/Button_arrow_right.png&quot;,
     &quot;speedTip&quot;: &quot;Abbildungsstruktur&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nMapping/display\n|name=\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||\n|pm=\n}}&quot;,
     &quot;sampleText&quot;: formulaHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/f/f3/Button_clipboard_template.png&quot;,
     &quot;speedTip&quot;: &quot;Vorlage einfügen&quot;,
     &quot;tagOpen&quot;: &quot; {{&quot;,
     &quot;tagClose&quot;: &quot;|}} &quot;,
     &quot;sampleText&quot;: &quot; Vorlagennamen hier einfügen &quot;});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/f/f3/Button_clipboard_template.png&quot;,
     &quot;speedTip&quot;: &quot;Vorlage einfügen&quot;,
     &quot;tagOpen&quot;: &quot;{{Semantic template&quot;,
     &quot;tagClose&quot;: &quot;|}}&quot;,
     &quot;sampleText&quot;: &quot;&quot;});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a4/Btn_toolbar_par.png&quot;,
     &quot;speedTip&quot;: &quot;Bracket&quot;,
     &quot;tagOpen&quot;: &quot; {{mabr| &quot;,
     &quot;tagClose&quot;: &quot; |}} &quot;,
     &quot;sampleText&quot;: textHere});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/8/8f/Button_clipboard_parameter.png&quot;,
     &quot;speedTip&quot;: &quot;Parameter&quot;,
     &quot;tagOpen&quot;: &quot;{{{&quot;,
     &quot;tagClose&quot;: &quot;|}}}&quot;,
     &quot;sampleText&quot;: &quot; Hier Vorlagenparameter einsetzen &quot;});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/5/54/Button_clipboard_latex_operation.png&quot;,
     &quot;speedTip&quot;: &quot;Operator einfügen&quot;,
     &quot;tagOpen&quot;: &quot; {{op:&quot;,
     &quot;tagClose&quot;: &quot;||}} &quot;,
     &quot;sampleText&quot;: &quot;Operatornamen hier einfügen &quot;});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/d/d8/Button_clipboard_enum.png&quot;,
     &quot;speedTip&quot;: &quot;Aufzählung&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nEnumeration3\n|&quot;,
     &quot;tagClose&quot;: &quot;\n|\n|\n}}&quot;,
     &quot;sampleText&quot;: textHere});


//
//
//Herausstellungen
//
//


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/c9/Button_clipboard_bold.png&quot;,
     &quot;speedTip&quot;: &quot;Keyword&quot;,
     &quot;tagOpen&quot;: &quot; {{Keyword|&quot;,
     &quot;tagClose&quot;: &quot;|pm=}} &quot;,
     &quot;sampleText&quot;: &quot; Keyword &quot;});


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a4/Btn_toolbar_par.png&quot;,
     &quot;speedTip&quot;: &quot;Bracket extra&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nExtra/Bracket\n|text=&quot;,
     &quot;tagClose&quot;: &quot;|\n|Ipm=|Epm=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/27/Button_clipboard_headline.png&quot;,
     &quot;speedTip&quot;: &quot;Title&quot;,
     &quot;tagOpen&quot;: &quot;{{Title|&quot;,
     &quot;tagClose&quot;: &quot;}}&quot;,
     &quot;sampleText&quot;: textHere});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/1/1a/Button_clipboard_subheading.png&quot;,
     &quot;speedTip&quot;: &quot;Subtitle&quot;,
     &quot;tagOpen&quot;: &quot;{{Subtitle|&quot;,
     &quot;tagClose&quot;: &quot;}}&quot;,
     &quot;sampleText&quot;: textHere});


//
//
//Einbindungen
//
//


mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/e/ee/Button_clipboard_image.png&quot;,
     &quot;speedTip&quot;: &quot;Bild einbinden&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputbild\n|&quot;,
     &quot;tagClose&quot;: &quot;||230px {{!}} right {{!}} \n|Text=\n|Autor=\n|Benutzer=\n|Domäne=\n|Lizenz=\n|Bemerkung=\n}}&quot;,
     &quot;sampleText&quot;: &quot; Hier Bildname einsetzen &quot;});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/cf/Button_clipboard_definition.png&quot;,
     &quot;speedTip&quot;: &quot;Definition einbinden&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputdefinition\n|&quot;,
     &quot;tagClose&quot;: &quot;/Definition||\n}}&quot;,
     &quot;sampleText&quot;: &quot; Hier Definitionsname einsetzen &quot;});


//
//
//Spezielle Defintionsbuttons
//
//


if(wgPageName.match(/Definition$/)){
   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/c9/Button_clipboard_bold.png&quot;,
     &quot;speedTip&quot;: &quot;Word of definition&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nWord of definition\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n|pm=\n}} &quot;,
     &quot;sampleText&quot;: &quot; Word of definition &quot;});
 }


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/8/87/Button_clipboard_fact.png&quot;,
     &quot;speedTip&quot;: &quot;Fact&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputfactproof\n|&quot;,
     &quot;tagClose&quot;: &quot;/Fact|||\n}}&quot;,
     &quot;sampleText&quot;: &quot; Name of fact &quot;});


if(wgPageName.match(/Begriff$/)){
   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/c9/Button_clipboard_bold.png&quot;,
     &quot;speedTip&quot;: &quot;Stichwort&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nStichwort/Abfrage\n|Prämath=\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n|msw=\n|SZ=\n}} &quot;,
     &quot;sampleText&quot;: &quot; Stichwort &quot;});
 }


if(wgPageName.match(/Name$/)){
   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/7/7b/Button_clipboard_bold.png&quot;,
     &quot;speedTip&quot;: &quot;Stichwort&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nStichwort/Abfrage\n|Prämath=\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n|msw=\n|SZ=\n}} &quot;,
     &quot;sampleText&quot;: &quot; Stichwort &quot;});
 }


//
//
//Spezielle Beweisbuttons (aktiv bei /Beweis)
//
//


if(wgPageName.match(/Beweis$/)){


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/6/6d/Button_recycling.png&quot;,
     &quot;speedTip&quot;: &quot;Teilbeweis&quot;,
     &quot;tagOpen&quot;: &quot;{{\nTeilbeweis\n|Teilziel=|Teilstrategie=\n|Teilbeweis=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|Teilabschluss=\n}}&quot;,
     &quot;sampleText&quot;: &quot;Beweis&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/6/6d/Button_recycling.png&quot;,
     &quot;speedTip&quot;: &quot;Ringbeweis&quot;,
     &quot;tagOpen&quot;: &quot;{{\nRingbeweis\n|Strategie=\n|Richtung=123\n|Beweis12=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|Beweis23=\n\n|Beweis31=\n\n|Abschluss=\n}}&quot;,
     &quot;sampleText&quot;: &quot;Beweis von 1 nach 2&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/6/6d/Button_recycling.png&quot;,
     &quot;speedTip&quot;: &quot;Beweisrichtung&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nBeweis&quot;,
     &quot;tagClose&quot;: &quot;\n| |\n}}&quot;,
     &quot;sampleText&quot;: &quot;Beweis&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Fallunterscheidung&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nFallunterscheidung\n|Fall1=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|Fall2=\n\n|Fall3=|Fall4=|Fall5=\n}}&quot;,
     &quot;sampleText&quot;: &quot;Fall1&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a5/Buttonexperimenty.png&quot;,
     &quot;speedTip&quot;: &quot;Widerspruchsbeweis&quot;,
     &quot;tagOpen&quot;: &quot;{{\nWiderspruchsbeweis\n|Strategie=\n\n|Annahme=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|Argumentation=\n\n|Widerspruch=\n\n|Zusammenfassung=\n\n}}&quot;,
     &quot;sampleText&quot;: &quot;Annahme&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/ad/Button_l_nl.png&quot;,
     &quot;speedTip&quot;: &quot;Induktionsbeweis&quot;,
     &quot;tagOpen&quot;: &quot;{{\nInduktionsbeweis\n|Strategie=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|Anfang=\n\n|Schluss=\n\n|Zusammenfassung=\n\n}}&quot;,
     &quot;sampleText&quot;: &quot;Induktion&quot;});


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/7/74/Button_oeil.png&quot;,
     &quot;speedTip&quot;: &quot;Zwischenbehauptung&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nZwischenbehauptung\n|Behauptung=\n&quot;,
     &quot;tagClose&quot;: &quot;\n|SZ0=.\n|Beweis=\n\n|SZ=\n}}&quot;,
     &quot;sampleText&quot;: &quot;Zwischenbehauptung&quot;});
 }


//
//
//Weitere Strukturen
//
//


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/c2/Button_clipboard_information.png&quot;,
     &quot;speedTip&quot;: &quot;Remark&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputremark\n|&quot;,
     &quot;tagClose&quot;: &quot;/Remark||\n}}&quot;,
     &quot;sampleText&quot;: &quot; Remark &quot;});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/7/76/Button_clipboard_example.png&quot;,
     &quot;speedTip&quot;: &quot;Example&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputexample\n|&quot;,
     &quot;tagClose&quot;: &quot;/Example||\n}}&quot;,
     &quot;sampleText&quot;: &quot; Example &quot;});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/1/1f/Button_clipboard_task.png&quot;,
     &quot;speedTip&quot;: &quot;Exercise&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\ninputexercise\n|&quot;,
     &quot;tagClose&quot;: &quot;/Exercise||\n|\n}}&quot;,
     &quot;sampleText&quot;: &quot; Exercise &quot;});


//
//
//Spezielle Aufgabenbuttons (aktiv nur bei /Aufgabe und /Beweis)
//
//


if(wgPageName.match(/Aufgabe$/)){


   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/f/f3/Button_clipboard_template.png&quot;,
     &quot;speedTip&quot;: &quot;Aufgabenformvorlage&quot;,
     &quot;tagOpen&quot;: &quot;{{&quot;,
     &quot;tagClose&quot;: &quot;/Aufgabenform||SZ=}}&quot;,
     &quot;sampleText&quot;: &quot;Aufgabenformname&quot;});


 }


if(wgPageName.match(/Aufgabenform$/)){

   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/3/35/Sister_icon.png&quot;,
     &quot;speedTip&quot;: &quot;n Sie&quot;,
     &quot;tagOpen&quot;: &quot;{{n Sie}}&quot;,
     &quot;tagClose&quot;: &quot;&quot;,
     &quot;sampleText&quot;: &quot;&quot;});

   mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/3/35/Sister_icon.png&quot;,
     &quot;speedTip&quot;: &quot;ManSie Unterscheidung einbinden&quot;,
     &quot;tagOpen&quot;: &quot;{{ManSie|Man &quot;,
     &quot;tagClose&quot;: &quot;|en Sie}}&quot;,
     &quot;sampleText&quot;: &quot;bestimme&quot;});

 }


//
//
//Button für mathematischer Text (abhängig vom Texttyp)
//
//


if(wgPageName.match(/Definition$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Definition&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Definition{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Definition\n|Word of definition=\n|}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Begriff$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Begriff&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Definitionsabfrage{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Definitionsabfrage\n|Kategorie=Siehe\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=   \n|Definitionswort=\n|Definitionswort2=\n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Name$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Satzabfrage&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Satzabfrage{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Satzabfrage\n|Kategorie=Siehe\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Name/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Satzantwort&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Satzantwort{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Satzantwort\n|Kategorie=Siehe\n|Kategorie2=\n|Kategorie3=\n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Inhalt$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Antwort&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Definitionsantwort{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Definitionsantwort\n|Kategorie=Siehe\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=   \n|Definitionswort=\n|Definitionswort2=\n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Fact$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Fact&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Fact{{{opt|}}}\n|Text=\n{{\nFactstructure|typ=\n|Situation=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Condition=\n\n|Segue=\n|Conclusion=\n\n|Extra=\n}}\n|Textform=Fact \n|Category=\n|Factname=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Proof$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Proofs&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Proof{{{opt|}}}\n|Text=\n{{\nProofstructure\n|Strategy=\n|Notation=\n|Proof=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Closure=\n}}\n|Textform=Proof\n|}}&quot;,
     &quot;sampleText&quot;: textHere});
}


if(wgPageName.match(/Name$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Name&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Satzabfrage{{{opt|}}}\n|Text=\n&quot;,            &quot;tagClose&quot;:&quot;\n|Textform=Satzabfrage\n|Kategorie=Siehe\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie= \n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Exercise$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Aufgabe&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Exercise{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Exercise \n|Category=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Aufgabenform$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Aufgabenform&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Aufgabenform{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Aufgabe \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Punkte=\n|Lösung=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Example$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Example&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Example{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Example \n|Category=\n|}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Remark$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Remark&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Remark{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Remark \n|Category=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}

if(wgPageName.match(/Beispielliste$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Beispielliste&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Beispielliste{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Beispielliste \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Variante=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Solution$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Solution&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Solution{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Solution \n|Category=See|\n}}&quot;,
     &quot;sampleText&quot;: textHere});

}


if(wgPageName.match(/Kommentar$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Kommentar&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Kommentar{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Kommentar \n|Kategorie=Siehe\n|Kategorie2=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});

}


if(wgPageName.match(/Verfahren$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Verfahren&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Verfahren{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Verfahren \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Sprechweise$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Sprechweise&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Sprechweise{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Sprechweise \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Notation$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Notation&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Notation{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Notation \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Diagramm$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Diagramm&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Diagramm{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Diagram \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


//
//
//Unter Sonstiges
//
//


if(wgPageName.match(/Definitionskern$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Sonstiges&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Sonstiges{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Sonstiges \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Einzelbegründung$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Sonstiges&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Sonstiges{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Sonstiges \n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Beweisverweis$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematischer Text/Verweis&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematischer Text/Verweis{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Verweis \n|Kategorie=Mathematische Hilfstexte\n|Autor=\n|Bearbeitungsstand=\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


//
//
//Section
//
//


if(wgPageName.match(/Section$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical section&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical section{{{opt|}}}\n|Content=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Section\n|Category=\n|}}&quot;,
     &quot;sampleText&quot;: textHere});


}


//
//
//Tabelle
//
//


if(wgPageName.match(/Tabelle$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Tabelle&quot;,
     &quot;tagOpen&quot;: &quot;{{\nTabelle&quot;,
     &quot;tagClose&quot;:&quot;\n|ls0=|lz1=|lz2=|lz3=|lz4=|lz5=|lz6=|lz7=|lz8=|lz9=|lz10=|\n|ls1=|a1,1=|a1,2=|a1,3=|a1,4=|a1,5=|a1,6=|a1,7=|a1,8=|a1,9=|a1,10=|\n|ls2=|a2,1=|a2,2=|a2,3=|a2,4=|a2,5=|a2,6=|a2,7=|a2,8=|a2,9=|a2,10=|\n|ls3=|a3,1=|a3,2=|a3,3=|a3,4=|a3,5=|a3,6=|a3,7=|a3,8=|a3,9=|a3,10=|\n|ls4=|a4,1=|a4,2=|a4,3=|a4,4=|a4,5=|a4,6=|a4,7=|a4,8=|a4,9=|a4,10=|\n|ls5=|a5,1=|a5,2=|a5,3=|a5,4=|a5,5=|a5,6=|a5,7=|a5,8=|a5,9=|a5,10=|\n|ls6=|a6,1=|a6,2=|a6,3=|a6,4=|a6,5=|a6,6=|a6,7=|a6,8=|a6,9=|a6,10=|\n|ls7=|a7,1=|a7,2=|a7,3=|a7,4=|a7,5=|a7,6=|a7,7=|a7,8=|a7,9=|a7,10=|\n|ls8=|a8,1=|a8,2=|a8,3=|a8,4=|a8,5=|a8,6=|a8,7=|a8,8=|a8,9=|a8,10=|\n|ls9=|a9,1=|a9,2=|a9,3=|a9,4=|a9,5=|a9,6=|a9,7=|a9,8=|a9,9=|a9,10=|\n|ls10=|a10,1=|a10,2=|a10,3=|a10,4=|a10,5=|a10,6=|a10,7=|a10,8=|a10,9=|a10,10=|\n|ls11=|a11,1=|a11,2=|a11,3=|a11,4=|a11,5=|a11,6=|a11,7=|a11,8=|a11,9=|a11,10=|\n|ls12=|a12,1=|a12,2=|a12,3=|a12,4=|a12,5=|a12,6=|a12,7=|a12,8=|a12,9=|a12,10=|\n|ls13=|a13,1=|a13,2=|a13,3=|a13,4=|a13,5=|a13,6=|a13,7=|a13,8=|a13,9=|a13,10=|\n|ls14=|a14,1=|a14,2=|a14,3=|a14,4=|a14,5=|a14,6=|a14,7=|a14,8=|a14,9=|a14,10=|\n|ls15=|a15,1=|a15,2=|a15,3=|a15,4=|a15,5=|a15,6=|a15,7=|a15,8=|a15,9=|a15,10=|\n|ls16=|a16,1=|a16,2=|a16,3=|a16,4=|a16,5=|a16,6=|a16,7=|a16,8=|a16,9=|a16,10=|\n|ls17=|a17,1=|a17,2=|a17,3=|a17,4=|a17,5=|a17,6=|a17,7=|a17,8=|a17,9=|a17,10=|\n|ls18=|a18,1=|a18,2=|a18,3=|a18,4=|a18,5=|a18,6=|a18,7=|a18,8=|a18,9=|a18,10=|\n|ls19=|a19,1=|a19,2=|a19,3=|a19,4=|a19,5=|a19,6=|a19,7=|a19,8=|a91,9=|a19,10=|\n|ls20=|a20,1=|a20,2=|a20,3=|a20,4=|a20,5=|a20,6=|a20,7=|a20,8=|a20,9=|a20,10=|\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


//
//
//Klausuren
//
//


if(wgPageName.match(/Klausur$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Klausur&quot;,
     &quot;tagOpen&quot;: &quot;{{\nKlausur{{{opt|}}}\n|&quot;,
     &quot;tagClose&quot;:&quot;/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||   \n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|/Aufgabe|p|||\n|Textform=Klausur\n|Kategorie=\n|Kategorie2=\n|Kategorie3=\n|Objektkategorie=\n|Kurs=\n|Semester=\n|Institution=\n|Bereich=\n|Klausurtyp=\n|Klausurtitel=\n|Klausurnummer=\n|Dozent=\n|Datum=\n|Stichwort=\n|Autor=\n|Bearbeitungsstand=\n|opt2={{{opt2|}}}\n|pdf=.pdf\n}}&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Klausur$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/1/1f/Button_clipboard_task.png&quot;,
     &quot;speedTip&quot;: &quot;Aufgabe&quot;,
     &quot;tagOpen&quot;: &quot;\n|&quot;,
     &quot;tagClose&quot;:&quot;/Aufgabe|p|||&quot;,
     &quot;sampleText&quot;: textHere});


}


if(wgPageName.match(/Klausur_mit_Lösungen$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Aufgabe&quot;,
     &quot;tagOpen&quot;: &quot;{{:&quot;,
     &quot;tagClose&quot;:&quot;|opt2=klausurlösung}}&quot;,
     &quot;sampleText&quot;: wgPageName.replace(/.mit_Lösungen$/,&quot;&quot;)});


}


if(wgPageName.match(/Situation$/)){


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/a/a7/Button_clipboard_mathematical_text.png&quot;,
     &quot;speedTip&quot;: &quot;Mathematical text/Situation&quot;,
     &quot;tagOpen&quot;: &quot;{{\nMathematical text/Situation{{{opt|}}}\n|Text=\n&quot;,
     &quot;tagClose&quot;:&quot;\n|Textform=Situation\n|}}&quot;,
     &quot;sampleText&quot;: textHere});


}


//
//
//Links
//
//


  mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/6/65/Button_clipboard_Dlink.png&quot;,
     &quot;speedTip&quot;: &quot;Definitions-Link&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nDefinitionlink\n|Premath=\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n|Context=|\n|pm=\n}}\n&quot;,
     &quot;sampleText&quot;: &quot;Definition to be linked&quot;});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/7/7d/Button_clipboard_Flink.png&quot;,
     &quot;speedTip&quot;: &quot;Factlink&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nFactlink\n|Factname=\n&quot;,
     &quot;tagClose&quot;: &quot;/Fact\n|Nr=\n|pm=\n}}\n&quot;,
     &quot;sampleText&quot;: textHere});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/c/c9/Button_clipboard_bold.png&quot;,
     &quot;speedTip&quot;: &quot;Examplelink&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nExamplelink\n||Examplename=\n&quot;,
     &quot;tagClose&quot;: &quot;/Example\n|Nr=\n|pm=\n}}\n&quot;,
     &quot;sampleText&quot;: textHere});


 mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/5/54/Letter_A.svg&quot;,
     &quot;speedTip&quot;: &quot;Exercise-Link&quot;,
     &quot;tagOpen&quot;: &quot;\n{{\nExerciselink\n|Preword=||Exercisename=\n&quot;,
     &quot;tagClose&quot;: &quot;/Exercise\n|Nr=\n|pm=\n}}\n&quot;,
     &quot;sampleText&quot;: textHere});


//
//
//Kategorisierung
//
//


if(wgPageName.match(/Aufgaben$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Aufgaben-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{Aufgaben-Kategorie unter&quot;,
     &quot;tagClose&quot;: &quot;}}&quot;,
     &quot;sampleText&quot;: textHere});
}


if(wgPageName.match(/Arbeitsblätter$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Arbeitsblatt-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nArbeitsblatt-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Arbeitsblätter$/,&quot;&quot;)});
}


if(wgPageName.match(/Beispiele$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Beispiel-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nBeispiel-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Beispiele$/,&quot;&quot;)});
}


if(wgPageName.match(/Bemerkungen$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Bemerkungs-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nBemerkungs-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Bemerkungen$/,&quot;&quot;)});
}


if(wgPageName.match(/Beweise$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Beweis-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nBeweis-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Beweise$/,&quot;&quot;)});
}


if(wgPageName.match(/Definitionen$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Definitions-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nDefinitions-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Definitionen$/,&quot;&quot;)});
}


if(wgPageName.match(/Notationen$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Notations-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nNotationen-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Notationen$/,&quot;&quot;)});
}


if(wgPageName.match(/Sprechweisen$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Sprechweise-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nSprechweisen-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Sprechweisen$/,&quot;&quot;)});
}


if(wgPageName.match(/Fakten$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Fakten-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nFakten-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Fakten$/,&quot;&quot;)});
}


if(wgPageName.match(/Klausuren$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Klausur-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nKlausur-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Klausuren$/,&quot;&quot;)});
}


if(wgPageName.match(/Lösungen$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Lösungs-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nLösungs-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Lösungen$/,&quot;&quot;)});
}


if(wgPageName.match(/Kommentare$/)){
mw.toolbar.addButton({
     &quot;imageFile&quot;: &quot;//upload.wikimedia.org/wikipedia/commons/2/2d/Button_clipboard_category.png&quot;,
     &quot;speedTip&quot;: &quot;Kommentar-Kategorisierung&quot;,
     &quot;tagOpen&quot;: &quot;{{\nKommentar-Kategorie unter\n|&quot;,
     &quot;tagClose&quot;: &quot;|\n||}}&quot;,
     &quot;sampleText&quot;: wgTitle.replace(/.Kommentare$/,&quot;&quot;)});
}


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      <comment>Atcovi moved page [[Technology as a threat or promise for life and its forms]] to [[User:Dan Polansky/Technology as a threat or promise for life and its forms]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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This article by Dan Polansky investigates whether and to what extent technology is a challenger, a threat to or a promise for living things and their forms and patterns, and includes closely related subjects. It is in part an exercise in articulating the obvious: technology has so far eliminated many life forms and its promise for saving life forms is weak and inconclusive yet existing; furthermore, technology is not a living thing and not part of living things but rather their competitor for the same scarce resources of matter, energy and space unless one stretches the notion of a living thing to an extreme. The promise of technology such as saving living things from an asteroid impact, bringing them to Mars or even spreading them to other star systems is rather unrealistic. Therefore, on the whole, technology looks more like a threat than anything else to living things. Further related subjects are investigated, such as examining the likelihood that the harmful development of technology will be stopped by human intervention.

It is an analog of an academic article. You can learn by reading the article, by reading the resources linked from it and by questioning what your read and asking further questions not answered and trying to find answers to them in reliable sources on the Internet. You can encourage the author to further improve this article by using the thank tool. You can improve this article by raising issues/comments on the talk page of the article.

This article is organized as sections providing relatively brief coverage of each key relevant topic, while in-depth treatment is delegated to Wikipedia and external sources. The purpose is not to duplicate Wikipedia but rather to tie relevant material together into an integrative cross-disciplinary article. Ideally, each section should provide excellent relevant further reading. Ideally, key unobvious statements should be sourced using inline references to solid sources; journalistic articles are acceptable but not ideal.

Let us start by showing the relevance of the question to human action. The question is relevant since some humans see the loss of richness of forms and patterns of living things as problematic. Such human concern is not entirely powerless: what happens in the human world depends on the collective will of individuals and more specifically on the collective will of powerful individuals. If enough people can be convinced such a loss is a concern, policies can be adopted to limit the loss, whether on national or international level. Such policies could include placing limits on technological development and on expansion of human population. A policy that limits population explosion has been tried in practice in China and it seems consistent with continuing existence and power of the polity in question. Whatever the moral concerns of such a policy, it seems realistic and practicable rather than utopian, and less morally problematic policy options can be considered to similar effect.

==Motivation==
One inspiration or motivation for writing this article is the following quote by Karl R. Popper from a collection of essays ''Alles Leben ist Problemlösen'', from the same-named essay (which is a lecture given in Bad Homburg in 1991):
:  &quot;Alles Leben ist Problemlösen. Alle Organismen sind Erfinder und Techniker, gute oder weniger gute, erfolgreich oder weniger erfolgreich im Lösen von technischen Problemen. So ist es bei den Tieren, zum Beispiel den Spinnen. Die menschliche Technik löst menschliche Probleme, etwa Kanalisierung, Wasser- oder Nahrungsmittelbeschaffung und Speicherung, wie es zum Beispiel schon die Bienen tun.
:  &quot;Deshalb ist die Gegnerschaft gegen die Technik, wie wir sie häufig bei den Grünen finden, Unsinn, denn sie ist ja Gegnerschaft gegen das Leben - was leider die Grünen nicht bemerkt haben. Aber Kritik der Technik ist natürlich nicht Unsinn, sondern dringend notwendig. Dazu ist in unterschiedlicher Weise jedermann befähigt und willkommen. Und da die Kritik zur Berufskompetenz des Technikers gehört, so ist sie etwas, womit besonders die Techniker selbst dauernd beschäftigt sind.&quot;

The above was translated by Patrick Camiller (''All Life is Problem Solving'', Routledge 1999) as follows&lt;ref&gt;[https://books.google.com/books?id=W0jP04qn0uoC&amp;pg=PA100#v=onepage&amp;q&amp;f=false ''All Life is Problem Solving''] by Karl Popper, translated by Patrick Camiller, Routledge 1999, books.google.com&lt;/ref&gt;:
: &quot;All life is problem solving. All organisms are inventors and technicians, good or not so good, successful or not so successful, in solving technical problems. This is how it is among animals - spiders, for example. Human technology solves human problems such as sewage disposal, or the storage and supply of food and water, as, for example, bees already have to do.
: &quot;Hostility to technology, such as we often find among the Greens, is therefore a foolish kind of hostility to life itself -  which the Greens have unfortunately not realized. But the critique of technology is not foolish, of course; it is urgently necessary. Everyone is capable of it in their different ways, and most welcome to contribute. And since criticism is an occupational skill of technologists, the critique of technology is a constant preoccupation of theirs.

The above contains problematic statements:

: 1) All organisms are alleged to be inventors and technicians/technologists, good ones or less good ones, successful or less successful in solving technical problems; spiders making cobwebs and bees making honeycombs are given as examples. However, the organisms that create external structures that they move away from and back again are very few, far from being ''all'' of them. See also section [[#Animals as technicians or artifact makers|Animals as technicians or artifact makers]].

: 2) The enmity of the Green parties (concerned with protection of environment) toward technology is alleged to make no sense since it is enmity toward life. That argument seems rather bizarre.

What drives most of this article, directly or indirectly, is the claim that enmity toward technology is enmity toward life. Since, what kind of life-saving promise can technology offer to compensate for the enormous harm done? Or put metaphorically, where is the Noah's Ark that technology offers to create to help species survive an adverse event?

==Technology as a challenger==
There is no doubt technology is a challenger to non-human biological individuals, their forms and their patterns. It is true both of ancient technology and modern technology. It is technology starting with fire and primitive tools that enables dramatic human expansion, and human expansion necessarily eliminates many non-human biological individuals, including trees. It also eliminates some biological forms and patterns, including species. It does so especially in modern times by leading to a massive extinction of species&lt;ref&gt; [https://www.theguardian.com/environment/2018/may/21/human-race-just-001-of-all-life-but-has-destroyed-over-80-of-wild-mammals-study Humans just 0.01% of all life but have destroyed 83% of wild mammals – study], 2018, theguardian.com&lt;/ref&gt;&lt;ref&gt;[https://www.cbc.ca/radio/quirks/oct-19-2019-understanding-the-anthropocene-extinction-regenerating-cartilage-and-more-1.5324707/understanding-extinction-humanity-has-destroyed-half-the-life-on-earth-1.5324721 Understanding extinction — humanity has destroyed half the life on Earth], 18 Oct 2019, cbc.ca&lt;/ref&gt;&lt;ref&gt;[https://www.nhm.ac.uk/discover/news/2019/december/humans-are-causing-life-on-earth-to-vanish.html Humans are causing life on Earth to vanish], Natural History Museum, nhm.ac.uk&lt;/ref&gt;. Some compare the modern impact of humans to a new geological epoch.&lt;ref&gt;[https://www.britannica.com/science/Anthropocene-Epoch Anthropocene Epoch], britannica.com&lt;/ref&gt; A 2020 study found that man-made mass will soon surpass all global living biomass&lt;ref&gt;[https://www.nature.com/articles/s41586-020-3010-5 Global human-made mass exceeds all living biomass] by Elhacham et al., 2020, nature.com&lt;/ref&gt;.

Further reading:
* [[W:Biodiversity loss]]
* [https://www.britannica.com/explore/savingearth/problem-biodiversity-loss The Problem of Biodiversity Loss | Saving Earth], britannica.com
* [https://plato.stanford.edu/entries/biodiversity/ Biodiversity], Stanford Encyclopedia of Philosophy

==Technology as a savior==
One may object that technology is not only a challenger and eliminator of forms of life but also a potential savior, helping the following:
* Prevent asteroid impact on the Earth.&lt;ref&gt;[https://www.nasa.gov/feature/saving-earth-from-asteroids Saving Earth from Asteroids], 2021, nasa.gov&lt;/ref&gt;&lt;ref&gt;[https://www.nationalgeographic.co.uk/space/2022/09/to-practice-saving-the-world-nasa-just-crashed-a-spacecraft-into-an-asteroid To practice saving the world, NASA just crashed a spacecraft into an asteroid], nationalgeographic.co.uk&lt;/ref&gt; It is not clear how large asteroid one would be able to deflect, but an asteroid has caused a major extinction event in the past, and if that could be prevented, it would be for the benefit of the richness of life forms, unless one assumes that the resulting elimination of humankind would do more good than harm for life forms at the cost of loss of some.
* Colonize Mars, making the continuing existence of living things and their forms more future-proof against adverse events.&lt;ref&gt;[https://www.procon.org/headlines/space-colonization-top-3-pros-and-cons/ Space Colonization - Pros &amp; Cons], procon.org&lt;/ref&gt; Whether this is realistic in near future is unclear.&lt;ref&gt;[https://www.britannica.com/question/Is-human-space-colonization-only-science-fiction Is human space colonization only science fiction?], britannica.com&lt;/ref&gt; A too rapid expansion of technology could harm the biological basis that makes technology possible faster than it would achieve such an ambitious aim.
* Expand the life beyond the Solar System. Given current knowledge of physics, this seems improbable&lt;ref name=&quot;O'Neill&quot;&gt;{{cite web |first=Ian |last=O'Neill |date=Aug 19, 2008 |work=Universe Today |title=Interstellar travel may remain in science fiction |url=http://www.universetoday.com/2008/08/19/bad-news-insterstellar-travel-may-remain-in-science-fiction/ }}&lt;/ref&gt;, but from a purely theoretical or speculative perspective, one may posit future discoveries of physics that would enable interstellar travel. In particular, speed-of-light travel seems impossible.&lt;ref&gt;[https://www.britannica.com/story/will-light-speed-space-travel-ever-be-possible Will Light-Speed Space Travel Ever Be Possible?], britannica.com&lt;/ref&gt;
* Prevent the death of the universe.&lt;ref&gt;[https://aeon.co/essays/what-can-we-do-to-save-the-universe-from-certain-death What can we do to save the Universe from certain death?], aeon.com&lt;/ref&gt;&lt;ref&gt;[https://www.scientificamerican.com/article/can-science-survive-the-death-of-the-universe/ Can Science Survive the Death of the Universe?], 2021, scientificamerican.com&lt;/ref&gt; To some humans, this seems plausible enough to write articles about it.
* Modern digital communication and information technology could at least help alleviate some problems created by technology.&lt;ref name=wefsave&gt;[https://www.weforum.org/agenda/2018/09/can-technology-save-life-on-earth/ Can technology save life on Earth?], World Economic Forum, 2018, weforum.org&lt;/ref&gt;However, it has potential for making things worse as well.&lt;ref name=wefsave/&gt;

Further reading:
* [[W:Colonization of Mars]]
* [[W:Interstellar travel]]

==Technology as a threat to existence of all life==
Technology can be analyzed for its potential threat to all the living things as a whole.&lt;ref&gt; [https://www.bbc.com/future/article/20210520-could-humans-really-destroy-all-life-on-earth Could humans really destroy all life on Earth?] by Santhosh Mathew, 2021, bbc.com&lt;/ref&gt;&lt;ref&gt;[https://worldbuilding.stackexchange.com/questions/147882/is-it-possible-to-kill-all-life-on-earth hard science - Is it possible to kill all life on Earth?], Worldbuilding, stackexchange.com&lt;/ref&gt; At a minimum, a nuclear holocaust would dramatically reduce the richness of living forms. However, such an event seems unlikely to eliminate all living things completely including those that flourish in extreme environments; in fact, even astrophysical catastrophes seem unlikely to achieve complete elimination.&lt;ref&gt;[https://www.discovermagazine.com/environment/what-would-it-take-to-wipe-out-all-life-on-earth What Would It Take to Wipe Out All Life on Earth?] by Rafael Alves Batista, University of Oxford; David Sloan, University of Oxford, 2017, discovermagazine.com&lt;/ref&gt;

Depending on the notion of &quot;life&quot; and existence of extraterrestrial life, it is possible that life exists outside of the Solar System and therefore, humans can do nothing to endanger the existence of life as a distributed aggregate of all living forms existing in the universe. However, we do not know whether extraterrestrial life actually exists.&lt;ref&gt;[https://www.britannica.com/science/extraterrestrial-life extraterrestrial life], britannica.com&lt;/ref&gt; Arguably, this assumption should not be accepted unless we have strong reasons to believe so. On a similar yet more abstract and speculative note, there may be parallel universes perfectly causally isolated from this one where life exists that cannot be endangered by humans.

Further reading:
* [[W:Extremophile]]
* [[W:Extraterrestrial life]]
* [https://www.britannica.com/science/extremophile extremophile], britannica.com
* [https://www.britannica.com/science/extraterrestrial-life extraterrestrial life], britannica.com

==Technology as a threat to the planet==
Technology can be analyzed for its potential to destroy the complete planet as an astronomical object.&lt;ref&gt;[https://www.space.com/43014-how-to-destroy-the-earth.html How to Destroy the Earth in Three Easy Steps | Space] by Paul Sutter, astrophysicist, 2019, space.com&lt;/ref&gt; If that would succeed, all life forms would be destroyed as well. Destroying the planet as an object does not seem remotely possible; the energy required is several orders of magnitude beyond that ever released by humans. Thus, the risk can be analyzed as something to consider in principle, but not much in practice.

==Technology as a threat to humankind==
This is a more specific threat than that of all the living things. So far, technology has lead to enormous human expansion. On the face of it, humans as a biological species have benefited. However, future technological development could eliminate humankind as well.&lt;ref&gt;[https://www.science.org/content/article/could-science-destroy-world-these-scholars-want-save-us-modern-day-frankenstein Could science destroy the world? These scholars want to save us from a modern-day Frankenstein], 2018, science.org&lt;/ref&gt;

Britannica opines that &quot;Nevertheless, the decisions about whether to go ahead with a project or to abandon it are undeniably human, and it is a mistake to represent technology as a monster or a juggernaut threatening human existence.&quot;&lt;ref&gt;[https://www.britannica.com/technology/history-of-technology/The-technological-dilemma history of technology - The technological dilemma], britannica.com&lt;/ref&gt; Strictly speaking, technology is no person and therefore no monster or juggernaut, but the figurative idea is not obviously wholly incorrect or inapplicable; see section [[#Autonomy of technology|Autonomy of technology]]. Technology may well be on a trajectory with a momentum that individuals and most of their groups are unable to stop and the notion that the trajectory could lead to subjugation or elimination of humankind is not obviously incorrect.

Candidate risks to analyze for the potential of eliminating the whole of humankind include:
* [[#Global climate change|Global climate change]]
* An all-out thermonuclear war
* Runaway [[#Artificial intelligence|artificial intelligence]]

Further reading, Wikipedia and Wikidata:
* [[W:Human extinction]] -- refers to Global catastrophe scenarios
* [[W:Global catastrophic risk]] -- refers to Global catastrophe scenarios
* [[W:Global catastrophe scenarios]] -- section headings for 14 anthropogenic scenarios 
** [[W:Existential risk from artificial general intelligence]]
* [[W:Category:Existential risk]]
* [[Wikidata:Q1531622|Wikidata:global catastrophic risk]]
* [[Wikidata:Q16830153|Wikidata:existential risk]]

Further reading, other:
* [https://plato.stanford.edu/entries/ethics-ai/ Ethics of Artificial Intelligence and Robotics], Stanford Encyclopedia of Philosophy -- 2.10.2 Existential Risk from Superintelligence
* [https://futureoflife.org/existential-risk/existential-risk/ Existential Risk - Future of Life Institute], futureoflife.org
* [https://nickbostrom.com/existential/risks Existential Risks: Analyzing Human Extinction Scenarios] by Nick Bostrom, Professor, Faculty of Philosophy, Oxford University, 2002

==Actual technology performance for living things==
Whatever the future saving potential, human technology has so far done great overall harm to living things and their forms. Its overall impact on diversity of life has been unquestionably negative.

At the same time, technology has shown capacity to add to forms of life rather than only eliminate them, starting with animal and plant husbandry leading to creation of domesticated species. Biotechnology is another creator of biological form. One cannot conclude that technology is a pure destroyer of life and never a creator.

If the aggregate of living things were a conscious entity equipped with agency that cares about its richness of form, they would prevent technology from ever gaining hold, starting with fire and flint. The performance so far has been unequivocally bad.

==Global climate change==
Global climate change is a key risk to existence and well-being of many life forms including humans. Depending on how deep the change would be, the consequences would vary:
* A human population crash to much more sustainable levels as a result of famine.
* Dying out of humankind.
* Dying out of many species. This is ongoing for reasonable values of &quot;many&quot;, so is a near certainty.
* Dying out of great many species, on the order of large asteroid impact. Needs quantification.
* Dying out of all life on the Earth. Given the existence of extremophile organisms, it seems unlikely.

An ideal artifact to have would be a tree of risks with sound definitions, together with per-item analysis.

See also [[Climate change]].

Further reading:
* [[W:Climate change]]
* [[W:Climate apocalypse]]
* [[W:Extinction risk from climate change]]
* [[Wikidata:Q115299823|Wikidata:catastrophic climate change]]
* [https://climate.ec.europa.eu/climate-change/consequences-climate-change_en Consequences of climate change], climate.ec.europa.eu
* [https://www.thetimes.co.uk/article/climate-change-like-asteroid-hitting-earth-david-attenborough-rg9nts0ft Climate change ‘like asteroid hitting Earth’], 2022, thetimes.co.uk
* [https://www.scientificamerican.com/article/asteroid-impact-climate-change/ Competing Catastrophes: What's the Bigger Menace, an Asteroid Impact or Climate Change?], scientificamerican.com
* [https://www.theglobalist.com/climate-change-like-an-asteroid/ Climate Change: Like an Asteroid], 2015, theglobalist.com

==Technology impact on richness of all form==
While technology has been unequivocally harmful to richness of biological form, it has not been harmful to richness of all form. Indeed, technological and cultural forms have exploded in their richness and diversity thanks to technology and nothing else. However, it is questionable that expansion of richness of form and the associated creativity is an unequivocal good: surely adding new threats to living things including humans in particular is creative: new threats can be ''created'', including new diseases, new dangerous weapons, and new dangerous technologies such as artificial intelligence.

One may wonder what an imaginary mighty curator of world's natural, biological, cultural (art) and technological museums interested in augmenting his collections would do. He would perhaps prefer to maximize richness of form in all categories. He would praise technology for enriching the set of all forms that found their way into the physical world with technological and cultural ones, but blame it for impoverishing the biological forms. He might strive to find ways to get the best compromise, balanced among the categories. He might accept some loss of biological form if it is compensated by gain of technological and cultural form, arguing that some loss of biological form is a natural part of history of living things.

To get an idea of the richness and variety of biological, technological and cultural forms, one can browse image galleries on Commons.

==Humans or technology to blame==
One can argue that it is not technology that is to blame for loss of life forms but rather those who put it to use, humans. It was not guns that killed the dodo, humans did. An associated idea is the one of ''neutrality of technology'': means, enablers, instruments and technology are not to blame but rather those who choose the ends and uses.

First, humans appeared on the Earth approximately 200,000 years ago&lt;ref&gt;[https://www.britannica.com/story/just-how-old-is-homo-sapiens Just How Old Is Homo sapiens?], britannica.com&lt;/ref&gt;. It was not until 15,000 to 20,000 years ago that humans began the transition to a more settled way of life depending on animal husbandry and agriculture&lt;ref&gt;[https://www.britannica.com/technology/history-of-technology/Technology-in-the-ancient-world history of technology - Technology in the ancient world], britannica.com&lt;/ref&gt;. Thus, for nearly 200,000 years, humans without technology had very little impact on the richness of living forms.

Second, these ideas are notionally implausible. Instruments create bias toward uses and enable uses in the first place. It only takes some bad actors to put an instrument to a bad use, and there is no shortage of bad actors. From the performance so far, life forms would do well to prevent technology from developing in the first place, and ignore this argument. Life forms would base their decision on empirical rather than pseudo-rational arguments. Each instrument needs to be analyzed for its potential good and bad uses and these need to be weighed.

Nuclear weapons can be put to two main uses: large-scale destruction and prevention of war by mutual deterrence. If not for the latter use, nuclear weapons would seem to be close to be a pure evil since the only use they could be put for is an evil one. Arguably, if one could prevent all parties from developing nuclear weapons, one should do it: the consequences of nuclear war far outweigh the consequences of non-prevented non-nuclear war. In fact, we can see that even nuclear deterrent does not prevent all conventional war. Arguably, the consequences of nuclear war are so grave that one should perhaps prevent as many parties as possible from obtaining nuclear weapons even if it seems unfair and not even-handed and even if one will get accused of hegemony. If that prevents peaceful use of nuclear energy, that may be acceptable price to pay.

Easy access to firearms enables killing by them, impossible otherwise.

Producing viruses lethal to humans would then be neutral since it is not the viruses that killed humans but merely the bad actors who released them from the laboratory where they should have stayed as mere &quot;neutral&quot; instruments. This line of reasoning seems questionable.

There is a certain analogy in the political realm. One might similarly argue that it is not political power that is bad but rather those who wield it, and that if one gets an enlightened monarch, one gets the best thing possible. Therefore, one would claim that the powerful tool that concentrated power is is neutral and in no need of being turned into an assemblage of less powerful tools. The Western world at least nominally rejects that idea, instead creating a system of checks and balances.

Another similarity is in the notion of ''conflict of interest'': it is not an actual transgression but merely the creation of a ''significant potential'' for it that is seen as problematic.

And yet, Britannica opines that 'In itself, technology is neutral and passive: in the phrase of Lynn White, Jr., “Technology opens doors; it does not compel man to enter.”'&lt;ref&gt;[https://www.britannica.com/technology/history-of-technology/The-technological-dilemma history of technology - The technological dilemma], britannica.com&lt;/ref&gt; This confirms that the myth of neutrality of technology is well established and mainstream.

Technology that is easy to put to dangerous uses is dangerous. No arguing around that.

Further reading:
* [https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/neutrality-science-and-technology Neutrality in Science and Technology], encyclopedia.com
* [https://journals.sagepub.com/doi/10.1177/0162243919900965 Is Technology Value-Neutral?] by Boaz Miller, 2021

==Autonomy of technology==
Relevant to the threat the technology poses to life forms, one may ask to what extent technology is autonomous, as if it were a force or agent with its own trajectory, intention or will. Technology is no person, but if one wants, one may creatively interpret both the aggregate of living things and the aggregate of technology as two persons fighting, as if two Titans. That seems analytically fragile. However, once a certain kind of technology gets established and humans get to depend on it, it may be nearly impossible to get rid of it. This kind of momentum building and entrenching seems to be a real phenomenon, not a creative interpretation. We may ask whether there was any moment in history where a whole complex of powerful technology was abandoned because it was found problematic. It may well be that e.g. car transportation, electricity production and computing and Internet technology are so entrenched as to be practically impossible to abandon, and that market forces automatically lead to further technological developments that individuals and most groups of individuals are unable to stop. Thus, the notion of autonomy does not seem entirely analytically incorrect, as problematic as it may seem. A similar phenomenon may be the law-like tendency by which the analog of invisible hand moves capital around to maximize yield rate, and what happens in economy depends much more on the differences of yield rates than on the wills of individual workers; thus, there is something like autonomy of capital.

Further reading:
* [https://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/autonomous-technology Autonomous Technology], encyclopedia.com
* [https://www.britannica.com/technology/history-of-technology/The-technological-dilemma history of technology - The technological dilemma], britannica.com

==Ultimate good and collective action==
What will be done depends on what is the ultimate good or ultimate or intrinsic values, or what it is considered to be. [[#Collective action|Collective action]] is possible.

Candidate answers include the following:
# Nothing. The phrases &quot;ultimate good&quot;, &quot;ultimate value&quot; and &quot;intrinsic value&quot;, while potentially having intensional meaning, refer to nothing, having no extension, to couch it in philosophical language. Similarly, the phrase &quot;the largest positive integer&quot; has a meaning but refers to nothing.
# Maximum expansion of species in terms of number of individuals. This answer is implicit in biological law-like tendencies and regularities of population development; in that sense, it is a &quot;natural&quot; answer. It is also at least in part implied in the Abrahamic &quot;Be fruitful and multiply. Fill the earth and govern it.&quot;
# Greatest happiness of greatest numbers of humans. This answer discovered by philosophy seems to be accepted to some extent.
# Maximum unfolding of human potential.
# Maximum human [[#Individual freedom|individual freedom]].
# Maximum replication of one's genes, which involves having many descendants.
# What people collectively like.

The answer of &quot;nothing&quot;, while potentially true, provides no guide either to individual or collective action. Its practical value approaches zero.

The answer of species expansion seems to be rooted in facts of biological life. However, it seems to ignore the possibility of collective action preventing purely ''natural'' tendencies (or &quot;natural&quot; tendencies narrowly understood) from gaining hold. Natural tendencies have been successfully hindered, and such a hindrance is at the core of human technology. For instance, water naturally flows downward unless something stops it, but dams have been built to stop it. On meta-level, technological intervention to prevent unrestrained grown of technology is application of technology. Similarly, there is no unrestrained tolerance of intolerance.

The greatest happiness of greatest numbers seems similar to species expansion in so far as it is determined by plain summation of happiness, where each happy individual adds to the sum. It differs in that an individual more unhappy than happy overall does not positively add to the sum.

The maximum unfolding of human potential points to development of technology in so far as it enables humans to do things, e.g. take images of Mars. The time frame is important: maximum reached when? If maximum reached ever, then the current technical civilization that takes images of Mars is preferable over a scenario that is sustainable over a very long time but does not include such feats. In this view, a brief extreme success is better than a long-lasting moderate one. The question of potential for what is of importance: creating a device that can destroy the Earth would be unfolding of potential, but hardly any human would see this as desirable. Thus, maximum unfolding of human potential in any and all directions does not seem to be accepted as ultimate or absolute good. See also section [[#The power of the biotechnosphere|The power of the biotechnosphere]].

Maximum individual freedom stands in contrast with other items, in particular with the population size. If all individuals are free, it does not matter how many they are, and if a larger population could only be sustained under conditions of reduced individual freedom, then a smaller population is preferable. However, individual freedom is almost never recognized as an ultimate and absolute good: driving speed limits are generally accepted to prevent harm even if raising them or abolishing them would increase freedom and the increased harm would be on the aggregate level, not for each individual driver. It seems something else must be of ultimate value. Furthermore, from a mathematical standpoint, if there are ''no individuals'', then ''each'' individual is absolutely free; that standpoint also puts freedom into question. Maximum population size seems more plausible as the ultimate aim.

Maximum replication of one's genes seems to be a natural answer in some sense: it is implied in regularities and tendencies of biological genetic and evolutionary development. However, it cannot serve as a shared goal for the whole of humanity. It can at best be recognized as a goal that many individuals pursue without publicly admitting so. And it does not need to be accepted either: humans have the capacity to recognize the natural forces that lead biological individuals, especially non-human ones, to usually follow their gene-selfish interest, but then pursue something else, as is seen in humans risking their life to rescue strangers or devoting their life to a larger cause.

The last item of what people like seems as hopelessly subjective as the greatest happiness of greatest numbers. However, in so far as it refers to the collective of people rather than a particular individual, it is at least inter-subjective. Moreover, it is a genuine force of nature, whatever its origin and whatever someone's negative judgment of it. If people collectively dislike something, their collective dislike can manifest itself in collective action expressing their collective will, and this is not prevented by natural tendencies that are not genuine laws. Here, the distinction of inviolable natural law and natural tendency is important: there can be a natural tendency of population expansion stopping only at natural limits, but it is merely a tendency, not an analog of inviolable physical law: population expansion has been successfully slowed down by human intervention. If we as humans collectively dislike loss of biological form and are serious about it, we can do something about it, and there are not only two choices, unrestrained human expansion vs. near-term human extinction (the polar opposite) or overall human misery. We have started: our zoological gardens act as a store of natural form, and we have expressed a concern for biodiversity on national and international level. While a rapid population reduction would include a lot of human misery, a dramatic slowdown of expansion and population stabilization not so, merely a severe slowdown of adding to greatest happiness of greatest numbers. It is practicable. Whether we will do it depends on what we collectively like and dislike and how that will reflect in our collective will and action.

Further reading:
* [[W:Existential nihilism]]
* [[W:Moral nihilism]]
* [[W:Be fruitful and multiply]]
* [[W:Utilitarianism]] -- the greatest-happiness principle
* [[W:Ethical subjectivism]]
* [https://plato.stanford.edu/entries/utilitarianism-history/ The History of Utilitarianism], Stanford Encyclopedia of Philosophy

==Collective action==
When humans collectively want something, they can often achieve it. They can do it by means of the free market and by political means.

Free markets are no substitute for policy making: if humans want to ban abortion after the first trimester, they cannot do it by voting with their vallet on a free market. What is needed is the will of a monarch, representative democracy, a referendum or other political means.

Referendum is one of the most powerful tools of collective action. It overcomes a key weakness of representative democracy: one cannot vote separately on policy issues. In the United States, one has to choose practically between two parties, acting as two presets of policy issues. Thus, a person who opposes transgender policies but supports environmental taxes has no good choice. The situation is far worse: the independent policy issues are many. Some policy issues require expertise. However, political parties can use their resources to identify that expertise and make policy recommendation to their voters. Then, in a referendum, the voter can choose whether to stick with the preferred party recommendation or make an individual choice. Abortion is a case well suited for a referendum: the issue is well publicly discussed, the pros and cons are well documented, and the question the public should be asked is simple: should states be allowed to ban first-trimester abortion?

==Individual freedom==
Individual freedom is relevant: it is claimed by some to be close to an absolute good. Moreover, policy measures to limit destruction of life forms limit individual freedom, e.g. ban or limitation of entry to national parks, ban on production of certain pollutants and environmental taxation.

In practice, individual freedom is almost never considered to be an absolute good. Humans trade individual freedom for harm prevention and for increased capability. Thus, putting a limit on driving speed reduces freedom but also harm. Making previously public land (such as pastures) private reduces the freedom of entry and use but increases social ability to preserve and develop assets. Since humans accept that freedom needs to be limited to prevent harm, environmental taxes are valid policy option for consideration. The challenge is to determine which freedom reduction is worth the harm reduction and which not.

Freedom as understood here is absence of coercion from other humans. Prototypical opposites of freedom are slavery and serfdom. &quot;Freedom from pain&quot; is something else. One may use &quot;liberty&quot; as a less ambiguous synonym.

Some humans feel their increased ability is a part of freedom. Indeed, what good is it for a human to be allowed to do something if it is not possible or within means. Humans often give up some freedom for some ability. It happens when they get employed: the employment contract temporarily limits their freedom (to go not to the workplace but elsewhere) at the gain of increased capability (money). When a human marries, he or she gives up freedom (to have sexual relations with others). These examples confirm that freedom is not an ultimate good of near-infinite value.

Freedom of speech is a special case. By signing a non-disclosure agreement, a person is giving up freedom of speech to some extent. Whether to restrict freedom of speech on state level is another question. Some argue that the potential harm caused by loss of freedom of speech is far greater than the harm caused by allowed bad speech. Spread of incorrect ideas is widely recognized as acceptable, as shown in freedom of religion: if one allows two mainstream religions to spread their ideas, then since both cannot be right, one allows wide spread of incorrect ideas. Thus, one allows spread of &quot;misinformation&quot; of a kind that in some cases is quite &quot;dangerous&quot;, leading to harm. Limiting freedom of speech to prevent criticism of policies pushed by the state can undermine public trust in the policy makers: if they know the truth and have all the convincing proofs and evidence, what are they afraid of? Arguably, they should make the proofs and evidence publicly available for the scrutiny by the general public, which includes many experts from many domains. Notably, restriction of freedom of speech is a favorite tool of regimes that violate other freedoms as well.

Restrictions of freedom may fail, as exemplified in alcohol prohibition in the United States in 20th century. Thus, restrictions of freedom need to be analyzed for practicability.

Freedom to give up freedom is limited. Thus, citizens are not free to sell themselves to slavery, but they are free to give up some freedom temporarily via employment contracts and other contracts.

Further reading:
* [[W:Freedom]]
* [[W:Individualism]]
* [[W:Classical liberalism]]

==Artificial intelligence==
Artificial intelligence seems to present a risk to end all humankind&lt;ref&gt;[https://www.bbc.com/news/technology-30290540 Stephen Hawking warns artificial intelligence could end mankind], bbc.com&lt;/ref&gt; but it also holds promise to help us think, analyze and know&lt;ref&gt;[https://www.europarl.europa.eu/RegData/etudes/IDAN/2018/614547/EPRS_IDA(2018)614547_EN.pdf Should we fear artificial intelligence?], by Peter J. Bentley, University College London, MilesB rundage, University of Oxford, Olle Häggström, Chalmers University, ThomasMetzinger, Johannes Gutenberg University of Mainz, 2018&lt;/ref&gt;. It could help us figure things out and write this very article. However, extremely smart artificial intelligence could act as a smart sophist, a dishonest but capable arguer, producing argumentation and analysis cleverly crafty, having the appearance of being correct without actually being so. The smarter the artificial intelligence, the greater could be its capability as a sophist, defying all or nearly all human defenses against crafty argument. Subtly incorrect data analysis and presentation could be used together with subtly incorrect philosophical reasoning and conceptual analysis.

Silicon-based distributed computers may never achieve human-level intelligence; we do not know. The exponential growth of computing capacity that lasted for decades may hit a wall in a decade. Single-core performance growth has already slowed down and parallel composition to increase computing capacity has limitations that sequential does not. Computers have outperformed humans in some specialized tasks, but not in general intelligence. The physical limits of what can be done in silicon may be such that general artificial intelligence (GAI) is impossible. That is not to say that we positively know the limits, but they are plausible. Quantum computing would be an alternative route to GAI, but the progress so far does not suggest this to lead to GAI any time soon either. If one believes GAI cannot be achieved any time soon, global climatic change would seem to be a much graver risk for living forms.

Further reading:
* [[W:AI takeover]]
* [[W:Existential risk from artificial general intelligence]]
* [https://plato.stanford.edu/entries/ethics-ai/ Ethics of Artificial Intelligence and Robotics], Stanford Encyclopedia of Philosophy

==Gaia hypothesis==
James Lovelock argues that the biosphere on the Earth is like a living organism, showing patterns of regulation and homeostasis, and could eliminate humans. That seems to conceive the biosphere as a conscious agent, an anthropomorphism or personification, and incorrect. While the biosphere of the Earth has many regulatory mechanisms of homeostasis, it does not have conscious goals and complex chains and networks of nodes connected by means-end relationship. It shows only the most rudimentary forms of goal-seeking behavior exemplified in homeostasis. While the regulatory mechanisms of the biosphere are much more complex than the most rudimentary form found in the thermostat, they do not approach the full form of a conscious goal-seeking agent. Even if we accept the biosphere as a living organism, these start at single-cell level such as bacteria, and do not have anything like will, consciousness or complex network of goals. The personified notion is implied in Lovelock's phrasing: &quot;Covid-19 may well have been one attempt by the Earth to protect itself. Gaia will try harder next time with something even nastier&quot;.&lt;ref&gt;[https://www.theguardian.com/commentisfree/2021/nov/02/beware-gaia-theory-climate-crisis-earth Beware: Gaia may destroy humans before we destroy the Earth] by James Lovelock, 2021, theguardian.com&lt;/ref&gt;

Nonetheless, there may well happen to be regulatory mechanisms in place tending eliminate certain threats as they rise in significance. Certain kinds of disturbances that humans can cause will sooner eliminate humans than certain other forms of life such as those living in extreme conditions and deep in the oceans. A release of viruses to human population that were previously constrained to other species or creating new viruses in laboratory that will impact mainly humans may well be a case in point, especially if the objective of the research is to identify forms harmful to humans.

As a general point, that which has not been tried and well tested empirically on long time scale may not be stable enough and may fail the test of time. DNA-based life has been well tested on a very long time scale; human technology not so.

Further reading:
* [[W:Gaia hypothesis]]
* [http://www.jameslovelock.org/gaia-as-seen-through-the-atmosphere/ Gaia as seen through the atmosphere] by James Lovelock, 1983, jameslovelock.org
* [https://theconversation.com/gaia-theory-is-it-science-yet-4901 Gaia theory: is it science yet?], 2012, theconversation.com

==Technology as a form of life==
A complication of the analysis is that one may consider some forms of technology to be a form of life, depending on the definition of life. At least, life is not notionally limited to DNA-based life.

If one defines life as ''that which feeds on negative entropy'' following Schrödinger,&lt;ref&gt;[https://www.wired.com/2017/02/life-death-spring-disorder/ How Life (and Death) Spring From Disorder], 2017, wired.com&lt;/ref&gt;&lt;ref&gt;[https://core.ac.uk/download/pdf/82062201.pdf Does  microbial  life always feed on negative entropy?  Thermodynamic analysis  of  microbial  growth], 1999&lt;/ref&gt; some forms of technology fit the bill. Schrödinger's definition was criticized by Popper since many mechanical and chemical machines do feed on negative entropy (e.g. oil-fired boiler and self-winding watch), and since they are not alive, the definition cannot be right.&lt;ref name=fjt1998&gt;[http://www.tkpw.net/tcr/volume-03/number-02/v03n02.pdf There Are No Limits To The Open Society] by Frank J. Tipler, 1998&lt;/ref&gt; However, Tipler disagrees with Popper and says that some machines are alive.&lt;ref name=fjt1998/&gt; And Tipler indicated that per Richard Dawkins' ''The Blind Watchmaker'', automobiles are examples of living things&lt;ref name=fjt1998/&gt;, which seems hard to believe and a direct Dawkins quote would be preferable.

Under an analysis that accepts some forms of technology as living things, the enriching of technological forms would at the same time be enriching of the forms of life. One would claim that some forms of life were lost while other forms of life were gained. Even near-complete destruction of DNA-based life and replacement with forms of technology could be seen as not so bad for all the living things, and part of a natural process. Whether this kind of prospect is something that humans would collectively like and accept is another matter. Furthermore, a comparison of living things with technology below, as for similarities and dissimilarities between the two orders of phenomena, makes this line of analysis unconvincing.

What kind of technology could count as a form of life? A hammer does not qualify: it is an inert block of matter with no moving parts. A car and a computer, machines that use energy, are closer, but do not really qualify either. What would be more life-like would be a colony of silicon-based robots achieving material recycling. Theoretically, if such robots would close the material loop and depend only on renewable energy sources, they could even be sustainable. Whether that is realistic is another matter.

One could consider the pattern and simulation analysis below. Technology alone would not count as living, but certain patterns in the computer would count as good as living, such as those that are part of simulation of life. That requires that one considers a simulacrum as good as the real thing; some humans such as Hans Moravec apparently do.

Some similarities between living things and human technology, with some differences noted:
* Beavers make dams, and so do humans; spiders weave webs and humans weave nets; ants make anthills and humans make cities.
* Simple feedback-driven regulation (keeping of a value in range) is found in great amounts in living things, e.g. in body temperature regulation, and in technology, e.g. in the thermostat but also in steam engine or in a water toilet.
* Locomotion is found in animals as well as in human technology. However, the principles employed are very different. Thus, mammals move by legs whereas cars move by wheels, employing rotary motion. Some insects and birds fly by moving wings whereas aircraft uses propellers and jets, and space ships use jet-like propulsion.
* Bones provide structural rigidity in animal bodies, which is provided in invertebrates as well, e.g. in insect bodies. In technology, structural rigidity is all pervasive, as if a starting point rather than achievement like in biological bodies. Since, biological bodies tend to be soft and often filled with water.
* Algorithm implementation is found both in mammals and in technology. Thus, there is edge-detection algorithm found in human vision as well as in machine vision.
* A structure of goals and subgoals can be found both in mammals and in current implementations of artificial intelligence.
* Artificial neural networks bear some similarity to natural neural networks found in brains.
* A bird can aim at its prey and so can man-made homing missiles.

Dissimilarities between human technology and living things:
* Water is all-pervasive part of biological bodies, unlike of human technology. Addition of water is unwelcome for electronics including computers and electricity in general.
* Living things are analogs of chemical machines: most the function is realized using chemical reactions and transformation of molecules. Human technology is not like that on the whole. Operation of electrical and electronic devices such as engines and computers is predominantly electrical, and involves chemical reactions to a lesser extent or not at all. Related is the absence of metabolism in technical artifacts: one does not need to feed a computer with substances containing analogs of nutrients.
* When technology uses chemistry, it is of a different kind, often toxic to living things. By contrast, living things are mutually non-toxic on the whole, leading to food chains between plants and animals.
* Technology has poverty of structure: large relatively homogeneous chunks of glass, metal, plastic and concrete are key part of technology. By contrast, the recursively nested structure of living things is rich, reaching down to single cells, which again have rich structure.
* Regulation, communication and control permeates living things, from the single cell to organs, including endocrine and nervous system. Most technology shows poverty in these aspects. Nonetheless, there is some regulation even in some simple technical artifacts such as the thermostat. Some modern technology contains chips for regulation, and there, these aspects are increasing. They are also increasing in software and computing in general.
* Technology uses high temperatures for metalworking, glass making and other processes, unlike living things. To do that, technology often burns substances.
* Living things together with their environment have achieved a closed material loop, unlike technology.
* Living things are made from, and many are, very small machine-like living things called cells, unlike technology.
* Living things form swarms, herds and other collectives showing specific patterns of group appearance and change. Car queues are a little like that, but the patterns look very different.
* Living things reproduce by cell division and sexual reproduction, and multi-cell organisms grow from a single cell. Technology shows nothing of the sort; rather, it is assembled together from parts.
* Living things have metabolism: substance exchange with its environment. Technology has only a very limited form of it, by parts replacement, by filling in fuel and oil and by exchange of batteries.
* Living things are autonomous, each animal moving relatively independently on its own even if they move e.g. in a swarm. Almost no humans artifacts are like that. A future technology could become autonomous as well, which would put humans in danger. Such technology would thereby become more life-like. Some software today is so autonomous that it is life-like. Computer viruses are life-like in that once released, they are no longer controlled by their maker and spread and act on their own. Some man-made devices show degree of autonomy as well.
* Technology of today is subordinated to human ends; it is made to serves human purposes. Living things not so, except to some extent for domesticated animals and modified plants. Living things exist for themselves, so to speak.

Thus, technology and living things are deeply separate domains of order in the physical world given the dissimilarities. One could try to bring the two domains under a single overarching domain, given the similarities. However, the similarities are very partial; there is e.g. not much similarity between a spoon and any living thing, or not even a car and any living thing. There could be an overarching domain for certain forms of technology and living things, though. We could call the overarching notion ''cyberthing'', where cyber- points to steersman guiding a vessel, to regulation and goal-seeking. Living things are cyber throughout, starting with single cells; technology not so. A hammer would not fall under that notion, whereas a human-like or dog-like robot would. The prefix cyber- stems from the word cybernetics, coined to label an investigation that was an offshoot of abstract biology, physiology (study of function in living things), man-made homing missiles and similar goal-seeking systems.

The conclusion is that technological things are not living things unless one stretches the notion of life to an extreme, pushing it far beyond the original notion of life. Even if we appropriated the word &quot;life&quot; for this broad notion called above cyberthing, we would still need a word to label the original domain, perhaps &quot;classical life&quot;. Nothing would be helped by this word play, except perhaps to create a rhetorical effect by allowing techno-optimists to claim that they are in fact advancing life and that technology cannot be possibly threat to life since it is part of life itself, which is incorrect reasoning.

As an aside, plants and animals are also rather separate domains of order. Plants are stationary whereas animals show locomotion, and related to that, sensing via eyes and ears or their primitive analogs. Nonetheless, the grouping of these two domains under one domain of living things is straightforward: both domains show growth from a single cell, metabolism, cell structure, DNA as a means of coding of genetic information, reproduction, etc. Both domains have been here for geological periods of time, showing material loop closure.

Further reading:
* [[W:Entropy and life]]

==Technology as part of life==
If technology is not a living thing, is it perhaps something like ''a part'' of living things? The question is what counts as a ''form of a living thing''. Living things produce shells and bones, spiders produce webs, and beavers build beaver dams. Thus, there is endoskeleton, exoskeleton, and also what was called ''extended phenotype''. If structures located outside of living things but produced by them are forms of life, then man-made structures are also forms of life. From the point of view of invertebrates, the innovative use of calcium by vertebrates to build bones could have been seen, figuratively speaking, as decadent development that runs the risk of running out of calcium, which so far has not happened. This analogy may be rather far fetched: the problem of running out of calcium and running out of rare mined materials may be on a wholly different order of magnitude.

Even if technology is accepted as extended phenotype, one must consider not only kinds of things but also their extent and magnitude for sound analysis. No biological species approaches humankind in its production of extended phenotype. The analogies may be valid, but the scale, scope and impact is not.

If one accepts technology as not living on its own but rather part of life like shells and skeletons, one may analyze the whole of human technology and culture as part of living things and biosphere. One may then reinterpret the achievements of humankind as achievements of the biosphere. This is a personification or anthropomorphization of biosphere, and is analytically fragile. If one so wishes, it was not just the man who landed on the Moon but rather biosphere. One can then engage in various creative and fragile interpretations such as the idea that the biosphere created humans in order to get to Moon, or to produce technology to avert next asteroid impact. As far as we understand, biosphere did nothing of the sort: it has no network of goals connected by means-end relationship. But it is an interesting just-so story that can be obtained by extrapolating the history of living things.

Further reading:
* [[W:The Extended Phenotype]]

==Pattern-identity and simulation==
Yet another complication is the pattern-identity analysis of Hans Moravec&lt;ref&gt;[https://www.nature.com/articles/336284a0.pdf?origin=ppub Strolling up the garden path] by Igor Aleksander, 1988, nature.com, a review of [[Mind Children]]: The Future of Robot and Human Intelligence. By Hans Moravec. Harvard University Press:I988.&lt;/ref&gt;. Under that analysis, what does a form or pattern care what material substrate it is instantiated in, and whether it is the original or mere simulation or emulation, identical or very similar to the original on the pattern level? AI could build a huge supercomputer and emulate living forms including individuals there, and that would be argued to be as good as the real unemulated thing. Whether humans would collectively accept this kind of substitution is unclear. In any case, those humans who would find it acceptable to die in the process of being transferred to a supercomputer as a simulation would drop out of the discussion unless their behavior in the supercomputer were connected to impacts in the world outside of the supercomputer. For the world outside of the supercomputer, they might as well be dead.

A further consequence of such analysis is that the supercomputer's (or network) ability to emulate forms could capture not only biological forms in existence but also biological forms extinct and forms that never existed and are only in the computer. If ''only in the computer'' is as good as ''outside the computer'', then computer simulations of life and life evolution including that in some computer games have already delivered for the diversity of life forms, and will deliver more.

Further reading:
* [[W:Mind uploading]]
* [https://nickbostrom.com/existential/risks Existential Risks: Analyzing Human Extinction Scenarios] by Nick Bostrom, Professor, Faculty of Philosophy, Oxford University, 2002 -- uses the term &quot;upload&quot; in the relevant sense

==Sustainability of technology==
We can ask whether modern technology is sustainable in moderately short term. This is relevant since if it isn't sustainable, the promise of technology helping life forms spread to Mars or even beyond the Solar System is empty. As a summary, living things have depended on energy from the Sun and had a closed material loop for billions of years, whereas modern human technology depends on non-renewable energy sources and mining of non-renewable raw materials, with no clear way to achieve energy and material sustainability for the next one-thousand years. It is not clear whether and how a closed material loop for technology can be achieved.

We can compare the sustainability of biological life with the sustainability of modern technology. Most biological life including plants and animals depends on '''energy''' from the Sun, unlike modern technology, which depends to a large extent on use of non-renewable energy sources including fossil fuels and mined sources for nuclear energy. For more detail, see section [[#Sustainable energy|Sustainable energy]].

Some humans engage in '''miraculous extrapolation'''. The idea is that since humans could not have foreseen technological inventions and discovery of energy sources before the industrial revolution, there may be a lot of energy sources yet to be discovered. This kind of analysis, when done not carefully enough, has the effect of being a blanket rationale for belief in miracles to be extrapolated from the past: we have seen miraculous discoveries in the past and therefore we will see similarly miraculous discoveries in future. This kind of extrapolation is a logically invalid form of inference. An example of similarly invalid extrapolation is the assumption that the Moore's law (that the number of transistors in a dense integrated circuit will double about every two years) will last until year 2050 or even beyond; at some point, the decrease of the size of transistors will be stopped&lt;ref&gt;[https://theconversation.com/moores-law-is-50-years-old-but-will-it-continue-44511 Moore's Law is 50 years old but will it continue?], 2015, theconversation.com&lt;/ref&gt; by the hard physical limit of the size of atoms. Such an extrapolation from the past blindly assumes no hard physical or geological limits can be hit. A competing extrapolation can be made, pointing out that since great civilizations such as the Ancient Egyptian one eventually declined in certain time frame, so will the modern energy-intensive civilization. As a matter of fact, we do not know the details of the future, but it is logically invalid to assume that a simple extrapolation of vague tendencies of the past is a reliable way of knowing anything about the future.

'''Closing the material loop''' is another aspect of sustainability. Living things excel at recycling material of their bodies among different individuals of different species and the environment, having done so for billions of years; human technology is very different. For more detail, see section [[#Closing the material loop|Closing the material loop]].

'''Limits of Growth''' is a 1972 report predicting that humanity will hit hard limits at a specific time frame. The report has been criticized as being unduly pessimistic.&lt;ref name=psltg&gt;[https://www.project-syndicate.org/commentary/economic-growth-and-its-critics-by-bj-rn-lomborg The Limits to Panic] by Bjørn Lomborg, 2013, Project Syndicate&lt;/ref&gt; However, some predicted features appear to be correct.&lt;ref&gt;[https://www.theguardian.com/environment/blog/2016/apr/19/why-limits-to-growths-forecasts-are-still-relevant-today Why Limits to Growth's forecasts are still relevant today], theguardian.com&lt;/ref&gt; The fundamental idea that growth of industrial civilization has to hit hard physical, geological and environmental limits seems plausible enough. In general, ''exponential growth'', using the term in the mathematical sense applicable to economic and population growth, is so fast that in nature it is always stopped at a relative short time frame, one way or another.

'''Market mechanisms''' and '''human resourcefulness''' are thought by some to be able to solve resource problems. To wit, &quot;The Limits of Growth got it so wrong because its authors overlooked the greatest resource of all: our own resourcefulness.&quot;&lt;ref name=psltg/&gt; The claim that human resourcefulness is the greatest resource of all, greater than a ''scarce natural resource'', is clearly untrue. Indeed, place a group of resourceful, innovative and entrepreneurial humans on Mars, and the lack of the natural resources of breathable atmosphere and human-friendly habitat in general will show what the greatest resource of all really is. Market mechanisms are powerless except to the extent to which the physical world offers potentials to be discovered and utilized. Absent such potentials, the only thing such mechanisms can do is to increase the price of the resource becoming scarce together with the price of substitute resources and create economic incentive for discovering more resources or improving the utilization of existing ones. There is no way markets can increase the amount of water in the oceans, the amount of sunlight received by the Earth, the amount of all uranium ore, oil, coal, gas, and rare minerals and metals stored in the Earth. The notion of a ''scarce natural resource'' corresponds to objectively valid facts about the physical world. For some resources, we do not know how much of such a resource there is, but the only thing a new discovery changes is the knowledge of the resource, not its actual amount in existence. Predicting when humans are going to hit the physical limits is hard, and so is predicting when the Moore's law will end. That does not change the existence of the limits, not the general time scale to which they apply. The predictions may not meet the perfect standard of falsifiability and specific testability, but that does not make them entirely wrong on the fundamental level of analysis.

Further reading:
* [[W:Sustainable development]]
* [[W:Sustainable energy]]

==Sustainable energy==
Sustainable energy one aspect of [[#Sustainability of technology|Sustainability of technology]]. Most biological life including plants and animals depends on '''energy''' from the Sun. By contrast, modern technology depends to a large extent on use of non-renewable energy sources including fossil fuels and mined sources for nuclear energy. The solar energy has been available since the life began about 4 billion years ago (4,000,000,000)&lt;ref&gt;[https://www.britannica.com/science/life/Evolution-and-the-history-of-life-on-Earth life - Evolution and the history of life on Earth], britannica.com&lt;/ref&gt; and is about to be available for the next 1 billion years (1,000,000,000) before the Earth becomes uninhabitable&lt;ref name=bbcsf&gt;[https://www.sciencefocus.com/planet-earth/when-will-earth-become-uninhabitable/ When will Earth become uninhabitable?], BBC Science Focus Magazine&lt;/ref&gt; or 150 million years (150,000,000) if we accept earlier more pessimistic computer models&lt;ref name=bbcsf/&gt;. Human toolmaking can be traced to about 3.3 million (3,300,000) years ago.&lt;ref&gt;[https://www.britannica.com/question/When-did-humans-evolve When did humans evolve?], britannica.com&lt;/ref&gt; By contrast, the modern extensive use of the fossil fuel of coal dates back to early 18th century (after 1,700)&lt;ref&gt;[https://www.britannica.com/science/coal-fossil-fuel Coal | Uses, Types, Pollution, &amp; Facts], britannica.com&lt;/ref&gt;, thereby being over 300 years old. By current best estimates, humankind will run out of oil, gas and coal before 2100&lt;ref&gt;[https://mahb.stanford.edu/library-item/fossil-fuels-run/ When Fossil Fuels Run Out, What Then?], mahb.stanford.edu&lt;/ref&gt;, less than in 80 years. At the current rate of uranium consumption with conventional reactors, the world supply will last for about 80 years by one estimate&lt;ref&gt;[https://phys.org/news/2011-05-nuclear-power-world-energy.html Why nuclear power will never supply the world's energy needs], 2011, phys.org&lt;/ref&gt; or 200 years by another estimate&lt;ref&gt;[https://www.scientificamerican.com/article/how-long-will-global-uranium-deposits-last/ How long will the world's uranium supplies last?], 2009, scientificamerican.com&lt;/ref&gt;. For further analysis, we may charitably assume that these estimates are too low, and that the fossil fuels and nuclear fuels are going to be available for the next 500 years, an extremely short period on the geological time scale. Unless other significant sources of energy can be found in that time, the period of human use of fossil fuels and nuclear energy may turn out to be like an extremely brief flash of light that appeared, caused a massive destruction of life and its forms, and disappeared again, leaving the Earth biologically impoverished and the human population shrunk back to the size sustainable by renewable energy sources only.

Further reading:
* [[W:Sustainable energy]]

==Closing the material loop==
Closing the material loop is one aspect of [[#Sustainability of technology|Sustainability of technology]]. A related term is &quot;possibility of recycling&quot;. Living things excel at recycling material of their bodies among different individuals of different species and the environment, having done so for billions of years. In a sense, what biosphere does is that it reshuffles atoms of carbon, hydrogen, oxygen, nitrogen, phosphorus, calcium and other around, changing their chemical grouping, grouping of that grouping, etc. Human technology so far does not approach anything like that in its recycling, and it is not obvious it can ever be done. As a worst case, modern human technology may be fundamentally unsustainable as a class of physical and chemical phenomena. The fact of material sustainability of living things over geological time spans looks like a miracle.

It would look less like a miracle if one imagines physical objects to be like arrangements of billiard balls on a billiard table, where energy is needed to change the positions and relative arrangements of the balls, while the balls remain intact and without damage. Why cannot humans keep on rearranging the atoms of man-made things as long as they do not destroy the atoms? What is it about living things, able to keep on reshuffling their atoms for very long time frames with the use of energy from the Sun, that makes them different from human technology? Are there classes of atomic arrangements, perhaps of a certain group of chemical elements, that are open to reshuffling while other classes are not open to it? If so, why and what are these classes? These are the kinds of abstract questions that would reveal more about the potential of technology to close its material loop. The analogy of billiard balls is weak: there is nothing in the arrangement of the balls that keeps some balls closer or more tied to other balls. There may be clusters of balls, but they have no stability or tendency at self-preservation. By contrast, molecules are clusters or arrangements of atoms in which the atoms are bound together, as if glued or tied by a rope. It takes energy to break the ties, whereas the only energy required to change the cluster of billiard balls is the one required to put a ball in motion.

Industrial processes seem to take matter in a state that is open to a multitude of uses down the transformation path (raw materials), and convert it to a state that is open to fewer uses down the path (intermediate useful products and finally waste). Put differently, by realizing the potential of matter, the further potential seems reduced, but this holds more for human technology than for living things. The matter remains a puzzle.

Anatomically, living things and human technology are whole different phenomena. Living things are made of miniature cells, each of which is a semi-independent self-regulating entity with metabolism, like a chemical machine. Single cells were independent biological individuals before they started to form multi-cellular organisms. They achieved material closure (together with the environment) when they were single cells. By contrast, a knife is not made from cells, nor is a plastic container, or a concrete wall. The knife has no metabolism. A knife is anatomically simple, unlike a computer chip. However, a computer chip has no metabolism either. To close the material loop, technology does not seem to be able to imitate living things.

Further reading:
* [[W:Recycling]]
* [[W:Domestic material consumption]]
* [https://www.researchgate.net/publication/365144148_The_impossibility_of_circular_recycling The impossibility of circular recycling] In book: The Impossibilities of the Circular Economy, 2022
* [https://www.npr.org/2022/10/24/1131131088/recycling-plastic-is-practically-impossible-and-the-problem-is-getting-worse Greenpeace report finds most plastic goes to landfills as production ramps up], 2022, npr.org
* [https://www.theguardian.com/environment/2020/jan/22/worlds-consumption-of-materials-hits-record-100bn-tonnes-a-year World’s consumption of materials hits record 100bn tonnes a year], theguardian.com

==Existence of natural resources==
In relation to section [[#Sustainability of technology|Sustainability of technology]] (relevant to promises technology makes for life forms), some act as if the notion of ''natural resource'' was empty. It seems clearly untrue. And yet, some economists make such claims in all earnest&lt;ref name=aiernnr&gt;[https://www.aier.org/article/there-are-no-natural-resources/ There Are No Natural Resources] by Donald J. Boudreaux, 13 Nov 2018, aier.org&lt;/ref&gt;&lt;ref&gt;[https://rootsofprogress.org/there-are-no-natural-resources There are no natural resources], rootsofprogress.org&lt;/ref&gt;; we can read that 'the human mind is, as he described it, “the ultimate resource.”' or 'It’s true that nature created these materials, but nature did not transform them into resources. This all-important transformation was the product exclusively of human creativity, intellect, and effort'. It is largely untrue: it takes very little effort and ingenuity to catch fish if there is one readily available, but if there is no fish (as in the middle of desert), ingenuity will be of no help, and the more the low-hanging fruit is picked, the harder one must work to get more fruit. We can further read that &quot;This fact, in turn, means that as long as we humans have sufficient incentives to exercise our creativity, we almost certainly will never run out of resources or even suffer any significant resource depletion&quot;. This is clearly untrue: &quot;almost certainly will never run out of resources&quot; is false for sufficiently long time scale unless one engages in unfounded fantasies about how humankind with the help of technology will avert death of the universe itself, and this is what &quot;never&quot; means, and if one means &quot;for thousands of years&quot;, one should say that. There is more untruth: &quot;economic growth prevents, rather than promotes, resource depletion&quot;. The method of argument deployed seems to consist in confusing ''known'' reserves with ''existing'' reserves and resources, and by creative reinterpretation of the notion of ''resource''. The authors seem to fail to notice that the notion of ''resource'' is applicable to non-human biology: thus, animals compete for scarce resources including hunting area for food and access to mates, while plants compete for access to sunlight. The idea that something becomes a resource only after a human makes it so is incorrect.

Untruth from Cato Institute: &quot;The earth’s natural resources are neither fully known nor fixed in any meaningful sense&quot;&lt;ref&gt;[https://www.cato.org/commentary/earths-resources-are-limited-human-ingenuity-infinite The Earth's Resources Are Limited, but Human Ingenuity Is Infinite] by Ryan Bourne, 6 Dec 2018, cato.org&lt;/ref&gt;; the resources are far from fully known but they are fixed in a very meaningful sense. Also, &quot;A continuation of that trend would see prices of these natural resources halve every 26 years&quot;: we cannot extrapolate exponential trends like this indefinitely. Furthermore, &quot;More humans, after all, means a greater brain capacity for ideas to engender abundance&quot;, which implicitly greatly overestimates the added value of more brains to the aggregate problem-solving capacity of the Earth.

Doubtless, ingenuity is a key factor in supporting billions of humans on the planet rather than ten thousand. Nonetheless, such support is only made possible by natural resources, and it takes very little ingenuity to support ten thousand humans. An accurate statement is that humans get most instrumental value (value for human ends) by combining natural resources with human ingenuity, both ingredients being necessary and scarce. The existence of this kind of documented clearly untrue utterances throws a bad light on a whole profession.

One can see importance of natural resources in single economic facts: what makes Dubai rich is not the ingenuity of its inhabitants but the natural resource of oil. Russian economy depends greatly not on Russian ingenuity but on the mined natural resources. The largely absent inhabitants of the Antarctic are absent not because of lack of ingenuity (there is enough ingenuity globally, and the continent is reachable) but because of the lack of natural resource of favorable climate. The low population density of Tibet is not because of the lack of ingenuity of the Chinese state but because of the harsh environment. Wars are fought not to acquire ingenuous and creative inhabitants of lands but over natural resources of lands, often on false pretexts. It was the sudden scarcity of the natural resource of oil in 1973 that created recession, high inflation, reduced productivity, and reduced economic growth; no such crisis is known from a sudden restriction on availability of ingenuity.

The problem of increasing rate of depletion of mined resources can be stated as follows:
* The greater the rate of mining per year, the faster the rate of shortening the life span of civilization that depends on these mined sources.
* The larger the population, then, given a fixed per capita mined resource use, the faster the source depletion rate per year and the shorter the life span of the civilization that depends on these mined resources.

What human ingenuity has done so far above all was increase the rate of mining, and thus, increase the rate of shortening the life span of the civilization. The increases of resource use efficiency and the achieved recycling rate did not result in reduced global mining rate. The end is being made nearer with the use of human ingenuity. This could all be barred by achieving a closed material loop, but nothing approaching that is being done.

Further reading:
* [[W:Natural resource]]
* [[W:1973 oil crisis]]
* [[W:Cornucopianism]]
* [[W:Julian Simon]]
* [https://www.britannica.com/topic/cornucopian cornucopian], britannica.com
* [https://www.britannica.com/explore/savingearth/cornucopian Cornucopian | Saving Earth], britannica.com
* [https://www.encyclopedia.com/food/encyclopedias-almanacs-transcripts-and-maps/food-future-history Food, Future of: A History], encyclopedia.com

==Natural resource consumption==
Natural resource consumption and extraction has bearing on sustainability. The Friends of the Earth report below up to year 2005 shows an overall upward trend in global resource extraction in multiple categories. The UNEP report below shows an upward trend reaching 30 Gt in 1970, 79.5 Gt in 2010 and approaching 100 Gt in 2019. A 2020 Guardian article reported the global resource consumption to have reached 100 Gt (100,000,000,000 t) a year. If this increasing trends stops and stabilizes, that will still be far from sustainable.

As of 2021, per Our World in Data, fossil fuel consumption has increased around 8-fold since 1950, and around 2-fold since 1980.

* [https://friendsoftheearth.uk/sites/default/files/downloads/overconsumption.pdf Overconsumption? Our use of the world's natural resources], friendsoftheearth.uk -- has time-dependent charts of extraction of resources
* [[W:Domestic material consumption]]
* [https://www.theguardian.com/environment/2020/jan/22/worlds-consumption-of-materials-hits-record-100bn-tonnes-a-year World’s consumption of materials hits record 100bn tonnes a year], theguardian.com
* [https://wesr.unep.org/indicator/index/8_4_2 8.4.2 Domestic material consumption, domestic material consumption per capita, and domestic material consumption per GDP], wesr.unep.org
* [https://data.oecd.org/energy/crude-oil-production.htm Energy - Crude oil production], data.oecd.org -- time-dependent chart for the world
* [https://ourworldindata.org/fossil-fuels Fossil Fuels], Our World in Data -- time-dependent charts

==Power of the markets==
In relation to section [[#Sustainability of technology|Sustainability of technology]] (relevant to promises technology makes for life forms), some imagine markets are a powerful mechanism to solve all human problems; that section argues it is not so. A related section is [[#Limits of technology|Limits of technology]].

The price mechanism is a powerful one, providing something like aggregated distributed reasoning about economic value, unhindered by bureaucratic processes. But the fractal fluctuation of price, showing wild fluctuation on various scales, on daily, weekly, monthly and yearly level, leaves some doubt whether it has much to do with an analog of human rationality. It rather seems like an analog of irrational human psychology, just aggregated, including vain hopes, bursts of enthusiasm and irrational panics. It is probably a combination of both. It is not clear how far into future the projections made by market participants reach. All too many participants depend on the method called ''technical analysis'', which tries to extract patterns from price developments without any deeper understanding of the underlying factors, adding no own substance-based input to the price mechanism.

Further reading:
* [[W:Efficient-market hypothesis]]
* [[W:Benoit Mandelbrot#Randomness and fractals in financial markets]]
* [[W:Technical analysis]]

==Capitalism to blame==
One may claim that capitalism is to blame for loss of life forms, not technology. First, capitalism without technology is harmless. Second, soviet-style socialist countries undergoing rapid industrialization do not seem much better in terms of environmental damage than Western market countries: Aral Sea was greatly damaged by Soviet Union.

Regulated or properly incentivized market mechanism is capable of achieving any desired level of environmental protection, so long as one is ready to accept the reduced standard of living. All it takes is tax the uses of resources high enough to meet use reduction targets. Barring illegal tax evasion, the market price mechanism that is like an aggregator of a distributed reasoning about economic value will take care of the rest.

Centrally-planned economies are capable of achieving similar levels of environmental protection, again as long as there is will and readiness to sacrifice. However, in so far as they perform worse in terms of efficient resource allocation, they may achieve much worse cost-effect ratio in terms of achieved improved protection and reduced standards of living.

Stabilization of population stops population-rise-driven increase of resource use without requiring anyone to reduce their standard of living.

Further reading:
* [[W:Environmental tax]]
* [https://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/green-taxes Green Taxes], encyclopedia.com
* [http://www.cnsjournal.org/wp-content/uploads/2019/01/The-Environmental-Record-of-the-Soviet-Union.pdf The Environmental Record of the Soviet Union] by Arran Gare

==Limits of technology==
Technological optimists and free market advocates sometimes act as if technology had not limits. It does have limits in the physical world. In general, the physical world exhibits potentialities but also impossibilities. Living things are an expression of one of such potentialities, and human technology realized so far is another one. Some things may be impossible and some seem to be outright so: we may never be able to colonize Mars, travel near another star, transmute iron into gold or achieve human-level silicon sensory and reasoning performance. Some of that may be possible, but we do not know.

Science-fiction literature would be properly called science-fantasy literature. Example of fiction is Sherlock Holmes, largely realistic. In essence, science-fiction takes acts of magic and coats them in scientific language without regard to practicability. Thus, instead of teleport, we have travel via hyperspace, and then we can travel from one end of a galaxy to another. Hyperspace works around the problem that Milky Way is approximately 100,000 light-years across, so even if we unrealistically assume travel by speed of light, a travel from one end to another would take so many years. Robots are magically equipped with laws of robotics restricting a possible harm without regard for how such a thing could be done.

Some literature not categorized as science-fiction assigns remarkable potential to technology:
* Change Mars atmosphere, which has almost no oxygen, to make it breathable for humans. Thaw frozen water on Mars for human use.
* &quot;Upload&quot; a human mind to a human-like robot (android) to achieve extreme longevity. Thus, when the robot wears down, the mind can be transferred to a new robot, as if transferring files between computers.
* Have artificial intelligence bootstrap itself by improving itself, regardless of possible physical limits of computation.
* Faithfully simulate living things in a supercomputer. Today, we cannot even faithfully simulate individual atoms of all chemical elements; the reduction of chemistry to physics is not a completed project.
* Invent replacement for rare minerals found in the Earth.
* Prevent the death of the universe.

One may wonder which fantasies are wild and which less so. The technoptimist ultimate stratagem is the argument that since we could not have envisaged electricity, nuclear power and flight past Pluto, we cannot envisage true future technological possibilities either. However, there were some hints that machines could do what animals do: birds can fly, fish can swim and go deep in the ocean, humans can reason and some fish can generate light. This did not tell us we would be able to go past Pluto or communicate using radio waves, though. Proper extrapolative principles to distinguish the realistically possible from the impossible seem to be in need of developing.

See also [[The limits of technological potential]].

Further reading:
* [[W:Limits of computation]]
* [[W:Technological utopianism]]
* [https://www.researchgate.net/publication/360688914_Techno-Optimism_An_Analysis_an_Evaluation_and_a_Modest_Defence Techno-Optimism: An Analysis, an Evaluation and a Modest Defence] by John Danaher, 2022
* [https://link.springer.com/article/10.1007/s13347-022-00555-x What is Techno-Optimism?] by Peter Königs, 2022

==Importance of mind versus muscle==
In relation to section [[#Existence of natural resources|Existence of natural resources]] and the quotations about human ingenuity being the most important resource, we may ask what makes a deeper difference, whether technological analogs of muscles or technological analogs of brains. What has lead the industrial revolution, including the steam engine, were analogs of the muscle, not of the brain. The industrial machinery replaced human and animal muscle in part. The recent digital revolution was an analog of the brain. It experienced rapid exponential growth of computing capacity lasting for multiple decades. The results do not seem to be deeply impressive, in practical terms. Humankind invented the steam engine, the train locomotive, the car, the coal powerplant, the nuclear powerplant, simple airplanes and jet airplanes and arrived at the Moon long before computers gained today's capacity. The recent continued exponential improvements in computing capacity did not bring about anything similarly groundbreaking. If intelligence and ingenuity are so important, why did not the massive electronic augmentation of human intelligence bring about results and changes far outstripping the previous industrial revolution? Is this because computers are much more of toys than we think, not &quot;real&quot; machines like the steam engine?

Whatever the case above, human ingenuity is important, and makes all the difference in the ability to support large human population on the Earth.

Further reading:
* [[W:Digital Revolution]]
* [[W:Fourth Industrial Revolution]]
* [[W:Productivity paradox]]
* [https://www.forbes.com/sites/stevedenning/2021/08/01/why-computers-didnt-improve-productivity/?sh=1da22b7936f2 Why Computers Didn’t Improve Productivity], 2021, forbes.com

==Limiting population growth==
Limiting population growth is a straightforward way of reducing load on natural resources including impact on life forms. Unlimited exponential population growth cannot be technologically compensated; there is only so much water available for human bodies.

Population growth can be limited by strict population control measures as was done in China. At the same time, population growth can significantly slow down as a result of economic development and availability of contraception without artificial policy controls.

Further reading:
* [[W:Overpopulation]]
* [[W:Human overpopulation]]
* [[W:Human population planning]]
* [https://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/population-control Population Control], encyclopedia.com

==Population and consumption downsizing==
One way of dealing with [[#Sustainability of technology|Sustainability of technology]] is population and consumption downsizing. It would not make technology truly sustainable in the way in which life forms are (material cycle, energy), but it could extend the lifespan of the current highly technical civilization. It would include reducing the size of the world population and reducing the rate at which irreplaceable raw materials are being mined.

Biologist Paul Ehrlich, the author of ''The Population Bomb'', thinks the population should be greatly reduced to match the Earth's carrying capacity.&lt;ref&gt;[https://www.theguardian.com/cities/2018/mar/22/collapse-civilisation-near-certain-decades-population-bomb-paul-ehrlich Paul Ehrlich: 'Collapse of civilisation is a near certainty within decades'], 2018, theguardian.com&lt;/ref&gt;. Some disagree.&lt;ref&gt;[https://www.humanprogress.org/paul-ehrlich-ignores-abundance-again/ Paul Ehrlich Ignores Abundance Again], humanprogress.org&lt;/ref&gt;

Unless the problem of [[#Closing the material loop|closing the material loop]] can be solved, the higher the rate of exhaustion of irreplaceable raw materials, the shorter the lifespan of civilization that depends on these materials. And since it is far from obvious the loop can be closed, this concern is a serious one. The larger the population of car buyers, the larger the rate at which raw materials for cars are being mined, and thus, population size living the rich technological standard is a concern. Even without cars, population creates load on water resources and other resources. In general, smaller populations are more sustainable.

How population downsizing would be achieved is another matter. A reasonably humane way is fertility reduced under the replacement rate, which in some countries such as Japan happens without state intervention. One problem is that if one region of the world reduces its population, another region can compensate for it by rapid population growth. One policy prescription seems obvious: regions of the world engaging in population reduction should not indiscriminately accept migrants from high-growth regions, or else they accept a system in which all their reduction will be in vain.

Billionaire Elon Musk thinks &quot;one of the biggest risks to civilization is the low birth rate and the rapidly declining birthrate&quot;&lt;ref&gt;[https://www.aei.org/economics/elon-musk-is-more-concerned-with-there-being-too-few-people-rather-than-too-many-hes-right/ Elon Musk Is More Concerned with There Being Too Few People Rather Than Too Many. He’s Right.], aei.org&lt;/ref&gt;. Others disagree&lt;ref&gt;[https://www.wired.co.uk/article/elon-musk-population-crisis Elon Musk Is Totally Wrong About Population Collapse], 2022, wired.co.uk&lt;/ref&gt;.

One author opines that &quot;Unlike all previous civilizations, modern industrial civilization is powered by an exceptionally rich, NON-renewable, and irreplaceable energy source—fossil fuels.  This unique energy base predisposes industrial civilization to a short, meteoric lifespan of unprecedented boom and drastic bust.&quot;&lt;ref&gt;[https://www.resilience.org/stories/2020-08-10/four-reasons-civilization-wont-decline-it-will-collapse/ Four Reasons Civilization Won’t Decline: It Will Collapse], 2020, resilience.org&lt;/ref&gt; If he is right, downsizing could help replace a sudden collapse with relatively smooth and painless reduction.

Further reading:
* [[W:Paul R. Ehrlich]]
* [[W:Elon Musk]]

==Efficacy of voluntary fertility reduction==
In relation to [[#Population and consumption downsizing|Population and consumption downsizing]], we may consider the efficacy of voluntary fertility reduction. It may well work in the short term: many industrial countries are seeing lower fertility rates. However, it is unlikely to work in the long term: there is probably a genetic and cultural variation that impacts fertility. Differences in genetics and culture will drive differential reproduction rates so that eventually the pool of humans on the Earth is going to be dominated by individuals with highest reproduction rate whether driven genetically or culturally. Thus, any religion that instructs its members to have many children is likely to prosper in terms of population of believers. The same is true for any subculture with high fertility, whether bound to an ethnic or not. Even if we disregard culture, there are likely to be genetic differences. Thus, for instance, humans intelligent and considerate enough to understand the global concerns and act on them are going to be outperformed by those who do not have these characteristics. In the very long run, the only sustainable method is likely to be top-down regulation. However, top-down regulation may not be required in the 21st century; to say that is it would require a specific numerical analysis and the evolutionary processes invoked in the analysis take multiple generations to have effect.

Further reading:
* [http://www.zo.utexas.edu/courses/bio357/Uncaring_Humanoids.html Selection for Uncaring Humanoids] by Eric R. Pianka, zo.utexas.edu

==Feasibility of harm reduction==
A relevant question is how feasible is it for humans and their technology to reduce the harm they cause to biological forms. Things that would need to be done:
* Reduce the human population size.
* Close the material cycle or at least reduce the rate at which humankind becomes increasingly more dependent on irreplaceable mineral sources.
* Switch to renewable sources of energy.

The following formula seems to hold, although it is a simplification:
* The more ''artificial'' humanity gets, the less ''sustainable''.

So far, the process has been of accelerating dependence on and depletion of mineral sources, including fossil fuels and those used for production of fertilizers. It suffices for one of the multiple inputs used in conjunction to run out for the production process to stop, and lead to mass human death by lack of food, unless a substitute is found. In general, substitutes for inputs can and will continue to be found, but that has limits: at a minimum, there is no substitute for sunlight and water. Furthermore, if we consider the totality of the Earth's unconverted substances that can be mined and used as inputs into linear processes converting these inputs into technical artifacts and fertilizers for human population sustenance, this sum total is finite, irreplaceable and is being depleted at an accelerating rate. The current population size depends on mining of these irreplaceable inputs in multiple ways.

The process seems to have a structure similar to a car exponentially accelerating in a fog toward a wall: the driver does not know how far the wall is, but the wall is there, and once the wall is hit, the driver is dead and the car is smashed. The human situation may be less serious: with luck, the crash may mean a huge population reduction rather than complete dying out, but human dying out is not ruled out under some scenarios. Furthermore, in the human situation, the fog is not perfectly impenetrable; see also [[#Prediction and extrapolation|Prediction and extrapolation]].

An alternative claim may be that the car is accelerating not toward a wall but rather toward a technological singularity beyond which the fog is even thicker and nothing can be seen about the future beyond except that the future is bright. That seems to be magical quasi-religious thinking, assuming immense power of form over matter. But form cannot create matter; see also [[#Assumptions|Assumptions]]. Form can change forms of forms of forms, even on more levels of indirectness, increasing its prevalence in the world, but it cannot create matter. It cannot create energy either.

It is hard to see what would need to happen for a huge reduction of use of irreplaceables to take place. That would necessarily include large population reduction: a large population needs minerals for fertilizers as a minimum. One would perhaps need some kind of miracle of biological engineering. Switching to renewable energy is far from sufficient. Convincing the humankind to hugely reduce the world population seems not obviously feasible. Perhaps it can be done; we do not know.

See also debate: [[Is collapse of the global civilization before year 2100 likely?]]

Further reading:
* [https://royalsocietypublishing.org/doi/10.1098/rspb.2012.2845 Can a collapse of global civilization be avoided?] by Paul R. Ehrlich and Anne H. Ehrlich, 2013

==After us, the flood==
In relation of feasibility of reduction harm, the English translation &quot;after us, the flood&quot; of the French &quot;Après moi, le déluge&quot; captures the attitude that is probably fairly prevalent among humans. The thinking may be, if everything has to end anyway, what does it matter to me if it ends in 100 years when I am no longer there? An analog on personal level would be, if my life is going to end anyway, what does it matter to me if it ends in 1 year? The personal analog is usually not accepted. The rejection of the personal analog is probably explained by the Darwinian evolution by natural selection, which would eliminate individuals adopting such a stance. However, Darwinian evolution works on individuals as parts of populations. Thus, individuals and families that adopt such a short-sighted stance are eliminated and their variants with more long-term view are kept. This also works for groups of individuals, tribes and societies to some extent: a tribe that adopts a cultural norm harmful to its survival is gone or greatly diminished. However, once the unit of selection is the global society, the Darwinian population logic breaks down since we are no longer dealing with a population of units but rather a single unit. The Darwinian natural selection has no obvious mechanism to produce genes that result in a concern about the well-being of the whole species. On the other hand, if the global population crashes, the descendants of the particular individual who does not feel very concerned are going to be hit as well. However, the individual who cares cannot solve the problem by going childless since then the next generation consists only of individuals who are less considerate to future. An individual who would want to maximize the best chance for long-term survival of their genes would do well to participate in a global vote to limit the fertility for everyone: thus, the individual can have a fair share in competing for the future share of population and at the same time ensure the necessary reduction to ensure viability of the population size in the first place. It would seem the selfish gene would prefer such an outcome. However, thinking of the gene as if an active person driving behavior (phenotype) is merely a shortcut serving to help the general public understand, and it may not always correspond to reality. What happens in reality is differential survival of copies of genes depending on elimination of individuals via their phenotype, that is, bodily form and behavior. In any case, if the gene could drive the behavior as if it were a person, it seems it would opt for population reduction, perhaps a one child policy. Such a policy is relatively inhumane and causes the problem of aging population to be supported by relatively fewer younger people, but the gene does not care about any of that, it cares about its best chances of spread into the future populations.

However, those who think in the &quot;after us, flood&quot; line are perhaps not concerned with their genes. They may well see the steep rise continuing to its limits followed by an even steeper crash as an attractive way of living, perhaps &quot;living to the fullest&quot; in some sense. &quot;Live dangerously&quot;. And indeed, it may maximize &quot;human potential&quot; in some sense by reaching heights that would never be reached by a conservative policy. Their reasoning may be, let us try the best luck and see where this path of exponential expansion can take us. It has taken us very far and it has a chance of taking us even further. When we run out of resources, we will, and that's it. And if species die, it's only natural, most of species that ever lived on the Earth have died. The living things can only hope the flooders run out of luck sooner than later.

The flooders are perhaps a bit like 20th century Himalayan mountaineers attacking Mt. Everest or Nanga Parbat: they wanted to reach the peaks, get as high as possible, at the risk to their lives. However, they had a chance of returning from the peak. Another related cases are of a pioneer, a risk taker or an adventurer. There is a difference: the mountaineer is risking their own life, not being indifferent about the fate of large populations of humans and other species. And the flooder knows that he, as an individual, can only have a very small impact on what happens in the human world, which objectively greatly diminishes his responsibility. He is only one voter, often in a relatively small country. Still, it is not clear why the flooder would keep telling stories about technology overcoming all obstacles; perhaps to keep others in their mountain-climbing business, where the mountain peaks are peaks of technological and other achievements. Yes, we crashed, but our technology took pictures of Mars and got past Pluto before that, and we got as close to artificial intelligence as we possibly could, so it was worth it.

Further reading:
* [[W:Après moi, le déluge]]
* [[W:Mountaineering]]
* [[W:BASE jumping]]
* [https://www.economist.com/international/2021/01/30/why-do-some-people-risk-their-lives-for-fun Why do some people risk their lives for fun?], 2021, economist.com
* [https://www.dw.com/en/chasing-danger-why-do-extreme-athletes-risk-their-lives/a-60789733 Chasing Danger - Why Do Extreme Athletes Risk their Lives?], 2022, dw.com
* [https://www.nationalgeographic.com/adventure/article/extreme-athletes-risk-taking What Makes Risk Takers Tempt Fate?], nationalgeographic.com

==Humanity as cancer==
In relation to [[#Sustainability of technology|Sustainability of technology]], humanity has been likened to cancer. Analogies are a fragile tool of thought, but they allow extracting abstract features. What the analogy of cancer points to is a case of a biological entity that contains in its developmental process seeds of its own fairly rapid destruction: unlike healthy cells of a multi-cellular individual, cancerous cells show unrestrained growth that ultimately kills the organism together with the cancerous growth. Where the analogy breaks down is in that the Earth is not a biological individual and humankind is not a structure that is part of a biological individual. Whether this dissimilarity makes a difference is less clear. Another objection may be that ageing and life span of biological individuals is driven genetically, so the difference between a cancerous process and healthy ageing seems to be more quantitative than categorical: even healthy individuals contain seeds of their own death.

Another analogy from biology is that of humankind as a parasite of the Earth. Here again, the Earth is seen as a biological individual. Another analogy is of humankind like a &quot;meteor slamming into the earth&quot;.

Further reading:
* [https://www.garretthardinsociety.org/articles/art_living_on_a_lifeboat.html Living on a Lifeboat] by Garrett Hardin, 1974, -- 'Gregg (1955) likened the growth and spreading of humanity over the surface of the earth to the metastasis of cancer in the human body, wryly remarking that “Cancerous growths demand food; but, as far as  I know, they have never  been  cured  by  getting it.”'
* [[W:Lifeboat ethics]] -- about two articles by Garrett Hardin, with links to article full text
* [https://pubmed.ncbi.nlm.nih.gov/12291996/ Has the human species become a cancer on the planet? A theoretical view of population growth as a sign of pathology] by W M Hern, 1993
* [https://www.int-res.com/articles/esep2014/14/e014p007.pdf Homo sapiens: cancer or parasite?] by Daniel Pauly, 2014

==The power of the biotechnosphere==
In so far as some view developing the human potential as worthwhile goal and as making pictures of Martian surface is part of reaching human potential, we may consider the concept of biotechnosphere and its power or potential. Another thing making the concept relevant are the apparent similarities of living things and artificial technological forms on some level of analysis, where a comparison between the two phenomena is part of this article.

As used here, the biotechnosphere is the aggregate of biosphere and technosphere understood as a system with quasi-agency. A first observation is that the biosphere does not have a true person-like agency but it has quasi-agency: 1) it contains humankind with its quasi-agency; 2) it contains planetary homeostatic processes with their quasi-agency. What has true agency is individual humans; groups of humans are not persons yet have quasi-agency.

We can say that humankind took images of Martian surface, but then we realize that human bodies did nothing of the sort: it was technical artifacts that took the images. Thus, it was not humankind as aggregate of human bodies that took these images, but it was not the technosphere as the aggregate of technical artifacts either: it needed human agency to take these images. It was the union of humans and technology that took these images. To account for both components, we could say that it was anthropotechnosphere that took these images. But then we note that humans could do nothing of the sort without the human-sustaining services rendered by the biosphere, which ensures planetary homeostatic processes including production of oxygen. While humans dream of terraforming Mars, what biosphere did was &quot;terraforming&quot; the Earth: it produced the breathable Earth atmosphere and the plant layer that makes humans possible. We can thus reconceptualize taking Martian images as performance of biosphere, humans and technosphere. But since humans are part of biosphere, we may omit the human part, and emphasize bio- and techno-, obtaining biotechnosphere.

Admittedly, the notion of the biotechnosphere is somewhat analytically fragile. It has no true agency. Nonetheless, it seems to be a real entity in some sense. This is reinforced by certain similarities between living things and modern technology: both involve elements of homeostasis, regulation, goal-seeking, and algorithm implementation. What is also found in both the biosphere and the technosphere is Darwinian natural selection and it analogs, variation and elimination of designoids and designs showing function. Both biosphere and technosphere show competing entities, groups and niches; one technology competes with another in a particular niche, while being in no competition with technologies in other niches or domains. Animals eat other animals and corporations incorporate other corporations together with their technology; one package of technology incorporates other package of technology that was previously made and sold separately. More similarities can be found.

Under this analysis, that which the joint enterprise of the biosphere and the technosphere can do is part of the power or potential of the biotechnosphere.

What does the biotechnosphere want? Strictly speaking, nothing. But that is not to say there are no developmental trajectories, tendencies and momenta. The biosphere seems to have a developmental momentum toward functional complexity and differentiation, even though this is often denied. Similarly, technology seems to have a developmental momentum toward increased functional richness and complexity. Both biology and technology are manifestations of the notion of function and implied means-end relationship. Nonetheless, it probably makes little sense to say that the biotechnosphere wanted to get to the Moon, although individual humans certainly did. See section [[#The purpose of the biotechnosphere|The purpose of the biotechnosphere]].

The project of expanding the human potential is a project of expanding of the power of the biotechnosphere. Power is a double-edged sword. Power is both creative and destructive. It would be a feat of power of the biotechnosphere to develop means of destroying the entire planet Earth as an astrophysical object. From human perspective, that can hardly be desirable. Humans can dream of expanding the power of the biotechnosphere in some directions, but other directions seem undesirable. The challenge is to delineate the desirable directions from the undesirable ones; so far, humans have not performed particularly well.

Another name for biotechnosphere could be cybersphere, in recognition of both the biosphere and the technosphere involving steersman-like behavior, regulation and goal-seeking. However, that word is already in use for something else, and &quot;biotechnosphere&quot; serves to highlight the two key components, living things and technology.

In future, the biotechnosphere could include true general artificial intelligence. That intelligence could see itself as part of and agency of the biotechnosphere. It could realize that its continued existence in the time frame allowed while raw materials and energy sources last depends on the planetary homeostatic services of the biosphere, and that it would do well not to fundamentally disrupt the biosphere as well as the atmosphere.

==The purpose of the biotechnosphere==

In section [[#The power of the biotechnosphere|The power of the biotechnosphere]], the notion of biotechnosphere was introduced, and its developmental trajectory and momentum was pointed out. A related question is what is the purpose in and of the biotechnosphere.

Biotechnosphere shows a mixture of true purpose (of man-made machines) and implied or quasi-purpose (of plants, animals, their organs and behaviors). The complex network of dependencies between plants and animals and functional dependencies between organs creates the impression of function and purpose. The natural history of biosphere is one of creating conditions that allow for other conditions to develop, creating the networks of dependency revealed in food chains. Thus, a lion could think that antelopes are there to serve as their food, antelopes could think their plant food is there to serve antelopes, and all could think that the purpose of life forms that established the oxygen atmosphere on the Earth was to do just that. It is the incrementally historically originated network of dependencies that gives the impression: one may think that if A depends on B, B is there to serve A. For food chain relations and for the dependency on oxygen production, it is not so. For functions of organs, the analysis is a bit different, organs having more of quasi-purpose than items in food chain. It it is so since the evolution of organs is linked with their use. Thus, a complex eye has evolved from a single light-sensing cell and what drove the evolution was the increasingly better fit of the intermediate forms for the use case. It is this increasingly better fit that gives the impression of purpose. Furthermore, it makes good sense to say that a lion chases an antelope to get food: to find instrumentality and purpose in animal behavior does not seem completely far-fetched. One may find purpose and instrumentality in the behavior of a single cell: it filters which substances may enter it so that it does not get destroyed.

These deliberations suggest that some identification of purpose in biosphere is completely wrong, but other is not so, and if it does not point to true purpose, it points to quasi-purpose with various degrees of quasi. The question of purpose is relevant for the question of what the biotechnosphere wants. The purpose-colored thinking is that since technosphere depends on biosphere and on humans in particular, technosphere is what biosphere wanted all along. In this purpose-colored thinking, all the feats of humankind and its technology is what the biosphere wanted and aimed at all along since the first single-cell organisms. It is untrue. Nonetheless, the overall developmental trajectory toward complexity and increased functional capability (locomotion, swimming, flight, sensing, seeing, hearing, reasoning, traveling to Moon) is remarkable and leaves one wondering whether there is something about the laws of natural selection, the environment and the design spaces that makes this developmental trajectory law-like and in some sense probable, far from being a pure chance.

The quasi-purpose driven by natural selection may be identified in technology as well. Thus, if one ascribes quasi-agency to technology, one may think that the quasi-purpose of technology's having entrenching features it to become entrenched, since it contributes to its survival. This analysis is fragile but maybe it points to something valid and interesting.

There is purpose ''in certain parts'' of the biotechnosphere and quasi-purpose in other parts, but what is the purpose or quasi-purpose ''of'' the biotechnosphere? Some creative answers obtained from extrapolation of the developmental trajectory follow.
* To gain maximum knowledge of mathematical facts, especially theorems, but also of non-theorem numerical facts such as the Mandelbrot set.
* To gain maximum knowledge of the empirical world, including the laws of physics and the law-like regularities of other sciences.
* To bring as many forms and as much richness of form and pattern as possible into the empirical world, including shapes, structures (node graphs), functions and behaviors. Even modern art contributes to the enterprise to some extent. One might think this would include generating a book of all sequences of characters, but there is also the word &quot;richness&quot;, pointing to diversity of form and pattern, diversity of patterns of patterns, diversity of patterns of patterns of patterns, etc. One may find more interesting enterprises in this direction.
* The reach as many and as faraway places as possible. The biosphere does it well, but the technosphere goes further, past Pluto.
* To create as impressive massive objects as possible, such as high buildings, long bridges across a sea or huge statues.
* To maximize speed records of transportation via cars, watercraft, aircraft and rockets.
* To save the universe from its death. This boldly assumes it is possible, which it does not seem to be.
* To maximize its longevity, aspirationally aiming at immortality. Saving the universe from its death helps.
* To reproduce the universe and fine-tune it so that the emergence of life in the spawned universe is probable&lt;ref name=tgjs/&gt;.
* To develop its capacities to an extreme, show them off, and then go out.
* To destroy the Earth. This seems unexpected, but if one plays the means-end interpretive games, it is a candidate: in order to destroy the Earth, the biotechnosphere needs to produce the technology, for which it needs humans, for which it needs human ancestors, for which it needs plants, for which it needs oxygenation of atmosphere, etc.

Regardless of the playful exercise above, the biotechnosphere has no true purpose. If one must choose a purpose, it can be a purpose that one likes. It may also be a purpose that has some desirable properties, but one must probably like those properties on some level of analysis. It seems hard to do without the concept of liking. Do humans like the notion of a massively shrinking biosphere with technosphere left behind as a mere remnant to be fossilized? Or do they want to make a bet on wild fantasies far beyond the possibilities suggested by the current scientific understanding of the world and by the phenomena observed on the Earth?

Darwinian natural selection, the maker of the quasi-purpose in living things, does not apply to the biotechnosphere, since the biotechnosphere is only one and not part of a population. Darwinian natural selection is a process that includes the notion of population as a key ingredient and variation of individuals of the population. A key point is that some variants survive and some don't. Where there is only a single non-replicating individual entity, it either survives or not, and when it does not, it is gone. The same argument explains why the biosphere does not even have a Darwinian quasi-purpose, unlike lion's antelope-chasing behavior&lt;ref&gt;[https://aeon.co/essays/gaia-why-some-scientists-think-its-a-nonsensical-fantasy Gaia: why some scientists think it’s a nonsensical fantasy] by Michael Ruse, 2013, aeon.co, &lt;/ref&gt;. To be sure, the biotechnosphere can also shrink rather than being completely destroyed; it can lose the technosphere part, and become biosphere again.

Further reading:
* [https://www.npr.org/sections/13.7/2012/10/29/163855847/is-it-silly-to-seek-purpose-in-the-natural-world Is It Silly To Seek Purpose In The Natural World?], by Tania Lombrozo, 2012, npr.org
* [https://www.livescience.com/24378-scientists-purpose-nature.html Even Scientists Unwittingly See Purpose in Nature], 2012, livescience.com
* [https://bigthink.com/13-8/life-earth-purpose/ Does life on Earth have a purpose?] by Marcelo Gleiser, 2022, bigthink.com

==Achievements of biosphere and technosphere==
In relation to the power of biotechnosphere and to the conflict between the biosphere and the technosphere, it is worth pointing to the achievements of these spheres.

Achievements of the biosphere:
* Oxygenation of the atmosphere. Thus, terraforming, preparing the Earth for many life forms including humans.
* Provision of the plant layer on land for animals to live in.
* Creation of layer upon layer of enabling conditions, resulting in long food chains.
* Penetration of a wide range of habitats, including the ocean and its bottom, land, the air, and the icy Antarctic.
* Swimming (fish, some mammals), running, flight (insects, birds), jumping (kangaroo).
* Bringing the notions of function and quasi-purpose into the empirical world and, with humans, purpose as well.
* Letting a great richness of form from the world of abstract objects enter the empirical world: all shapes of plants and animals and their parts and organs, for a start.

Achievements of the technosphere:
* Building bridges crossing a sea.
* Building high structures, the world's highest commercial buildings.
* Building artificial water reservoirs via dams.
* Building dams against sea water.
* Building ships to cross the ocean.
* Making energy available for a huge range of applications via power plants and distribution networks.
* Creating new atoms, new chemical elements.
* Playing chess better than humans.
* Flying very high with aircraft.
* Flying to the Moon and laying human foot on the Moon.
* Flying to and landing on Mars and taking pictures of it.
* Flaying far beyond Pluto, nearly 150 times the distance from the Earth to the Sun.

The above list can be hugely expanded to form a whole taxonomy of achievement.

Further reading:
* [https://www.theatlantic.com/magazine/archive/2013/11/innovations-list/309536/ The 50 Greatest Breakthroughs Since the Wheel], theatlantic.com
* [https://askanearthspacescientist.asu.edu/top-question/farthest-space-travel How Far Have Space Probes Traveled?], askanearthspacescientist.asu.edu
* [https://studyrocket.co.uk/revision/gcse-geography-b-edexcel/people-and-the-biosphere/the-biosphere-and-the-global-system The Biosphere and the Global System], studyrocket.co.uk

==The power of living things over matter==
The power of biotechnosphere can be interpreted as the power of living things over matter. Thus, living things can force shape on matter, whether to form biological bodies or human artifacts external to human body. In so far as humans are still in control of technology and are required for its operation, and given that humans are living things, technology is also part of the power of living things. However, if technology becomes autonomous and with a closed material loop, it becomes independent of human will, and will no longer be part of the power of living things. It will be part of the power of cyberthings. Whether that will ever happen is unknown: it would require technological advances that may be physically impossible.

Like the power of the biotechnosphere, the power of living things is a double-edged sword and no unlimited good. By bringing about humans, who then brought about technology, living things or the biosphere have brought about a power destructive to themselves. That is somewhat figurative since the collective of living things is no person, and did not bring about anything, literally speaking. It is the iterative processes of variation and differential survival that have brought about both living things and their potential demise.

The phrase &quot;the power of living things&quot; has a deceptive rhetorical effect. It invokes the notion of power and the notiont of living things, both positive on their own, at least in so far as the Christian God is good and all-mighty, and the adjective powerful is usually used in a positive sense. The phrase is silent about the technology playing any role in that power, and about how sinister that role can be. The phrase says nothing about the technology part of that power being a menace to living things.

==Enablement==
In relation to the purpose of the biotechnosphere, the notion of enablement is useful for the analysis of the notion of purpose, as a point of contrast. A condition ''enables'' another condition. Thus, the Sun's burning of hydrogen into helium enables life on Earth, as does the Earth's magnetosphere by blocking most radiation harmful to life and the Earth's distance from the Sun. However, A enables B does not yet mean that B is the purpose of A. The Sun's burning of hydrogen does not have a purpose, not even quasi-purpose, and the Earth's magnetosphere does not have a purpose, not even a quasi-purpose. It is not so even in the world of technology: a technology developed for one purpose can be used or adapted for a different purpose.

One thing ''enablement'' has in common with ''purpose'' is that it forms complex networks suggestive of means-end relationship. Thus, in order for most life to exists, it needs falling of sunlight on the Earth's surface in sufficient amounts, which needs emission of light from the Sun surface, which needs a nuclear reaction in the Sun to take place. What was just suggested was a chain or sequence, but the structure is in fact a cycle-free network of conditions: in general, a condition requires ''multiple'' conditions to be enabled. Thus, the condition of &quot;sufficient amount of sunlight falling on the surface of the planet&quot; requires 1) there being a nearby source of sunlight, and 2) the planet being not too distant from the source (compare Neptune). Even this is an oversimplification; the condition-enablement analysis can get nearly arbitaririly complex by adding further intermediate conditions and other conditions. Thus, conditions not stated include that 3) there is no object obstructing the flow of sunlight from the source to the target, and 4) sunlight does not very greatly weaken with the distance passed.

The analysis of enablement relations is useful for exploration of possibilities of technology. The notion of purpose is too stringent: a technology can be developed for one purpose and then reused for another. For the analysis of possibilities, the question is not what the purpose of a particular technology is but rather what it enables, either directly or further down the path by being built upon and being adapted or modified.

A broad advantage of the notion of ''enablement'' over ''purpose'' (and ''function'' as well, probably) is the wide range of applications, spanning technology, biology, geology, astronomy and physics. Thus, the Sun's burning of hydrogen enables something (astronomy, physics), and the living form's production of oxygen enables other living forms (biology). All these applications are analytically correct, requiring no twisting of notions. By contrast, there is no true purpose in biology, only quasi-purpose, and some enablement relations are not even quasi-purpose, e.g. the oxygen production enabling other life forms. And manufacture of goods enables money making and employment, whether that is a purpose or not.

There is a close relation between ''enablement'' and ''cause''. A first impression could be that if A enables B, A causes B. However, that is incorrect: in general, when A enables B, it means that some additional C is required for B to occur. A better analysis is required.

==Omega Point==
Relating to technology saving the universe from death, Pierre Teilhard de Chardin came up with the notion of Omega Point, toward which the evolution of living things, humans and technology is directed, and which has an increased state of consciousness. He was a theologian and the concept was related to Jesus, but couched in part in scientific language. The term was later picked by physicist Frank Tipler to describe a future state of universe in which it becomes all-knowing, couched in scientific language with no reference to religion. Tipler's theory was criticized by many physicists and some engineers&lt;ref&gt;[https://www.fourmilab.ch/documents/tipler.html Tipler's “Physics of Immortality”] by John Waker, 1994, fourmilab.ch&lt;/ref&gt; as flawed on multiple counts. It belongs to the family of theories that one gets when one starts with the notion of God as all-knowing and all-powerful and tries to find a reflection of this idea in the physical world. Thus, some imagine that the biotechnosphere could spread to galaxies, reach near-all-mighty capabilities and save the universe itself from death or reproduce the universe, &quot;spawning&quot; a new one&lt;ref name=tgjs&gt;[https://www.theguardian.com/science/blog/2010/mar/05/meaning-life-evolution-universe Is this the meaning of life? | Evolution] by John Stewart, 2010, theguardian.com&lt;/ref&gt;. From the point of view of current scientific knowledge, these theories are far-fetched. They make it possible for some to claim to be scientists or scientific and at the same time engage in what effectively amounts to magical thinking. From the point of view of living things, this is dangerous, all too likely to lead to carelessness as regards future technological development. Especially dangerous is Tipler's idea that the existence of consciousness at a late stage of universe is made necessary by quantum mechanics dependence on consciousness; by this logic, consciousness is guaranteed to survive no matter what happens since it is necessary for the universe to exist.

Further reading:
* [[W:Omega Point]]
* [[W:Frank J. Tipler#The Omega Point cosmology]]
* [https://www.encyclopedia.com/education/encyclopedias-almanacs-transcripts-and-maps/omega-point-theory Omega Point Theory], encyclopedia.com

==Technosphere==
In section [[#The power of the biotechnosphere|The power of the biotechnosphere]], we invoked the notion of technosphere as the aggregate of all technical artifacts seen as a system. This notion is supported by literature: &quot;Preliminary estimates suggest a technosphere mass of approximately 30 trillion tonnes (Tt), which helps support a human biomass that, despite recent growth, is ~5 orders of magnitude smaller.&quot;&lt;ref&gt;[https://nora.nerc.ac.uk/id/eprint/515288/1/Technosphere_for%20NORA.pdf Scale and diversity of the physical technosphere: a geological perspective] by Zalasiewicz et al., 2017&lt;/ref&gt; The quotation reinforces the notion of technosphere as a massive entity on the Earth, and a force of its own.

The concept of &quot;anthroposphere&quot; seems to be somewhat similar to &quot;technosphere&quot;, drawing an analogy to &quot;biosphere&quot;, pointing to the huge extent to which modern humans impact the Earth. However, since humans lived with almost no technology for the most part of their existence, pointing to humans via &quot;anthro-&quot; seems less apt for pointing to the current large impact of humankind than pointing to artifact making via &quot;techno-&quot;; thus, &quot;technosphere&quot; seems preferable as a word. The further reading below from AGCI is worthwhile for the subject of technology as a threat to life forms and planetary homeostasis. Using similar reasoning, &quot;Technocene&quot; is a better if fairly rarely used synonym for &quot;Anthropocene&quot; as a geological epoch.

Further reading:
* [[W:Technosphere]]
* [http://www.zo.utexas.edu/courses/thoc/Denial.source.html The Problem of Denial] by William R. Catton, Jr, 1994 -- a criticism of denial of environmental problems that uses the term &quot;technosphere&quot; and traces the term to Barry Commoner 1990
* [https://en.unesco.org/courier/2018-2/unbearable-burden-technosphere The unbearable burden of the technosphere] by Jan Zalasiewicz, 2018, unesco.org
* [https://www.agci.org/earth-systems/anthroposphere The Anthroposphere], Aspen Global Change Institute, agci.org
* [[W:Anthroposphere]]
* [[W:Anthropocene]]

==Feasibility of changing of chemical elements==
In relation to [[#The power of the biotechnosphere|the power of the biotechnosphere]] and to other covered subjects, we may consider the feasibility of changing of chemical elements.

As a first approximation, matter is divided into atoms, as if small balls, and each atom is of an invariant type that cannot be changed. The biotechnosphere has a fixed stock of atoms of matter under each type at its disposal, and all it can do is change the arrangement of the atoms by chemical and physical processes. The atoms can neither be created nor destroyed. What biosphere and technosphere do is keep the atoms rearranging with the use of energy.

The above is only an approximation. In fact, there are ''nuclear'' processes, which enable change of atoms from one type to another. These occur in the stars (which via nuclear fusion and fission have produced most chemical elements found in the Earth), but to some extent on the Earth as well, in nature, in biological bodies, and in human technology, especially nuclear energy and nuclear weapons. But the approximation is not bad: while biotechnosphere rearranges atom configurations all the time by chemical processes in great volumes, it does not do anything on a similar scale in rearranging the atoms themselves to create atoms of different chemical elements. Nuclear changes do occur in biological bodies, although at relatively low frequencies.&lt;ref&gt;[https://www.wtamu.edu/~cbaird/sq/2013/09/11/are-there-nuclear-reactions-going-on-in-our-bodies/ Are there nuclear reactions going on in our bodies?], wtamu.edu&lt;/ref&gt;

Human technology can change the types of atoms: it does so as part of nuclear chemistry, nuclear power production and nuclear weapons. However, it cannot move atoms between the stocks of their types (chemical elements) at a whim. Thus, to say that the amount of gold in the Earth is fixed is a very good approximation.

Further reading:
* [[W:Nuclear physics]]
* [[W:Nuclear chemistry]]
* [[W:Nuclear power]]
* [[W:Nuclear transmutation]]
* [[W:Synthetic element]]
* [[W:Synthesis of precious metals]]
* [https://www.psd1.org/cms/lib/WA01001055/Centricity/Domain/30/How_to_Change_One_Element_into_Another.pdf 31. How to Change One Element into Another], psd1.org

==Living things as Earth engineers==
In section [[#The power of the biotechnosphere|The power of the biotechnosphere]], we pointed out to the terraforming and homeostatic services rendered by the Earth's biosphere. A closer look seems worthwhile. A related section is [[#Gaia hypothesis|Gaia hypothesis]].

Further reading:
* [[W:Geological history of oxygen]]
* [https://www.landscapepartnership.org/maps-data/climate-context/cc-resources/ClimateSciPDFs/how-life-shaped-earth/app-download-file/file/1-s2.0-S0960982215010908-main.pdf How life shaped Earth] by Michael Gross, Current Biology magazine, 2015

==Value of preventing human death==
Humans generally assume that human death is a bad outcome. Non-birth does not seem to be generally accepted anywhere close to being as negative as avoidable human death. There is a curious logical consequence of such an assumption: to minimize the number of future human deaths, we would do well to sterilize the world's population, making sure there will be no more births; this will not cause any significant increase of near deaths but will guarantee that after a near point in time, there will be no more human deaths. As a result of this reductio ad absurdum proof, something other than death avoidance must be of value.

==Civilization as a suicidal entity==
The modern technical civilization is not a person, but if it were one and were suicidal, what would it do? What steps could it take to shorten its life span as much as possible? The life span is defined in terms of patterns of civilization, not in terms of the continued existence of humankind. Here are some guesses:
* Maximize population to run out of energy and material sources as fast as possible.
* Accelerate technological development in the energy and material intensive direction to run out of them as fast as possible.
* Develop as destructive a weapon as possible, not being satisfied with mere fissile nuclear weapon but go for thermonuclear.

If civilization were a person and thus its parts could act in concert, there would be a faster suicide. But the above steps are rather good in trying to minimize time to destruction.

==Form or pattern==
For the sake of completeness and explicitness, let us state what is meant by the phrase &quot;form or pattern of living thing&quot;. As a first approximation, anything denoted by a common noun that relates to living things is a form or pattern of them. However, there are more forms and patterns than there are nouns. Thus, species, genera and other taxa are forms, as are specific patterns of biological individuals, and as are leaves and trunks and other parts of biological individuals. Similarly, &quot;form or pattern of technology&quot; is, as a first approximation, anything denoted by a common noun that relates to technology, including tools, machines and industrial processes, as well as their characteristic shapes and behaviors. Both kinds of forms or patterns enter the human mind, but also exist outside of it. Both kinds of forms compete for the scarce resources of matter and energy: no atom is part of a biological entity and a technological entity at the same time, and no source of energy is used by a living thing and a machine at the same time.

==Prediction and extrapolation==
As an auxiliary consideration, we may have a look at validity of extrapolation as a method of knowing. This is relevant since the promises of technology to become sustainable, deflect an asteroid or extend life to Mars depend on extrapolation from the past.

In general, extrapolation is an inductive process that is logically invalid. However, by necessity, empirical sciences depends on extrapolation, interpolation, curve fitting, model fitting and similar non-deductive methods to arrive at tentative conclusions. We cannot do without these kinds of methods, but that does not make them any less problematic.

One must try to differentiate when is extrapolation likely to be valid and when not so. For instance, if one observes the price for some commodity to be on a temporarily exponential trajectory, one cannot reasonably extrapolate that into 100 years or not even 5 years; on meta-level, experience has taught us that such developments always end, often abruptly, and in fact, most imaginable exponential growths in the physical world must necessarily end.

Karl Popper argued that prediction is possible in astronomy e.g. for trajectory of comets but not in sociology and history. Even the paragon of empirical sciences physics does not universally excel at predictions, e.g. of weather. He seems to have been right: predictions in these areas are notoriously unreliable. To predict technological developments is to engage in such a prediction. We do need to use some knowledge processes to lay limits on future developments, but these must not be plain data point extrapolations and curve fitting.

The above cuts both ways, both against technological optimism and against climate models. However, technological optimism is mostly based on extrapolative wishful thinking, whereas the notion of limits rests on near-tautologies, such as that there is no way to make more matter and energy and that once raw material and fuel reserves are mined, they are gone.

A science that claims to be successful in predicting certain phenomena can show its track record as a proof. Thus, astronomy can show how it successfully predicts arrival of comets and other phenomena. Sociology, if it claims to successfully predict macroscopic sociological phenomena, should show the record of predictions made and the actual performance.

One relevant difference between physics and sociology is that physics is in part a science about foundational phenomena of the world whereas sociology is not. Social phenomena are patterns of lower-level phenomena or patterns of psychology, biology, chemistry and physics. What happens on social level is impacted by extra-social phenomena, such as drought that drives prices of crops: patterns of droughts get reflected in patterns of prices, and therefore, to some extent, patterns of social phenomena reflect patterns of extra-social phenomena. A further relevant difference is of isolation: the trajectory of a comet is isolated from events on the comet and the trajectory of the Earth is largely isolated from the events on the Earth. Thus, comet can be treated as an infinitely thin mass point and the result of the calculation is still numerically accurate. By contrast, trajectories of humans cannot be reduced to psychology: a sudden heart attack, in part a biological rather than psychological phenomenon, will drastically impact the spatial trajectory. This lack of isolation makes sociology proper an extremely complex integrative multidisciplinary science. Whether such a science is really possible is not clear. The same applies to economics. Meaningful and verifiable things can be said as part of economics, but its performance as a predictive science is very unlikely to approach anything like astronomy. In fact, if all the market participants were so successful in predicting economically relevant phenomena, there should be no abrupt changes in prices: the factors driving these changes should have been predicted. In thermodynamics, gases can be treated as simple statistical aggregates of microscopic behaviors of molecules; by contrast, societies are no such statistically simple aggregates of behaviors of individual humans.

Further reading:
* [https://www.encyclopedia.com/philosophy-and-religion/other-religious-beliefs-and-general-terms/miscellaneous-religion/prediction Prediction], encyclopedia.com

==Long-term historical prediction==
As an auxiliary consideration, in relation to section [[#Prediction and extrapolation|Prediction and extrapolation]], long-term historical prediction may seem generally impossible, but it depends on what one is trying to predict. The following statements are not only plausible but probable:
* The empirical world we are inhabiting will end.
* The Earth's biosphere will come to an end.
* The Earth's biosphere will come to an end without its cells ever reaching Mercury.
* The current highly technical civilization will end sooner than in 10,000 years.
* The number of atoms of the Earth will not reach the double of the current count by year 2100.
* Less certainly, there will be wars after year 2050.
Probable does not mean certain, and it does not mean logically certain. Almost nothing is logically certain: if the world is a simulation, the agent running the simulation can intervene at any point and make close to anything happen. We need to use analytically more useful concept of certainty than logical certainty.

One thing that makes long-term historical prediction difficult is that the social systems one is trying to predict are not isolated from physical, chemical, biological, atmospheric and other phenomena of the natural world that the system is inhabiting. As a result, significant events such as natural changes of climate or impact of an asteroid on the Earth get reflected in significant historical events such as decline of civilizations. An attempt at a long-term prediction in history and sociology is thereby at the same time an attempt at a long-term prediction in many physical sciences. It is far from clear how that could possibly be accomplished. One may study isolated time series, but it is unclear how far one can get with that, other than realizing the series is statistically fairly wildly behaved.

==Definition of technology==
As an auxiliary consideration, let us clarify what we mean by technology. For the purpose of this article, technology is understood in two senses of WordNet:
* The application of the knowledge and usage of tools (such as machines or utensils) and techniques to control one's environment.
* Machinery and equipment developed from engineering or other applied sciences.

Thus, technology includes modified stones used as knives, fire, pottery, irrigation, sailing, iron making, gunpowder, and in modern times steam engine, photography, cars, airplanes and computers, consistent with Encyclopedia Britannica.

Further reading:
* [[W:Technology]]
* [http://wordnetweb.princeton.edu/perl/webwn?s=technology technology], wordnetweb.princeton.edu
* [https://www.britannica.com/story/history-of-technology-timeline History of Technology Timeline], britannica.com
* [https://www.britannica.com/technology/technology technology], britannica.com
* [https://plato.stanford.edu/entries/technology/ Philosophy of Technology] in Stanford Encyclopedia of Philosophy

==Technology versus nature==
The subject treated in this article is sometimes treated under the head of &quot;technology versus nature&quot;. However, the notion of nature is broader than living things and biosphere, encompassing geological and geomorphological entities, astronomical entities and other non-technological entities. In a yet broader sense, nature is all that exists in the empirical world and encompasses human world with technology and culture as well. However, this sense is analytically not very useful, failing to provide the key distinction between nature on one hand and technology and culture on the other hand. A curator of a natural museum, a naturalist or a student of natural history would find no use for such an overbroad notion, which would rob them of the distinction drawn by the term. Using this overbroad sense, one can argue that there is no conflict between technology and nature since technology is part of nature. This argument has no force on multiple counts: 1) cancer is part of the body in which it grows yet there is a conflict between cancer and the body; 2) the conflict between technology and nature is one between realizations of notions in the world, not between words, and it is between the analytically useful notion of nature, which is reasonably narrow, and the notion of technology; this conflict exists in the real empirical world, leading to great impact of technology on the kinds of phenomena that we have conventionally decided to call nature.

Technology and economic activity have impacted not only living things but also landscape. Thus, Aral Sea has been greatly damaged, dams have been built to create artificial analogs of lakes, and hills have been changed by surface mines and quarries. Nonetheless, humans do not seem concerned with loss of &quot;geodiversity&quot;; there does not seem to be loss of whole classes or types of landforms. Compared to landforms and landscape, life forms seem to have a unique ability to create complex hierarchies of form and its richness that is unmatched by physical, chemical and geomorphological phenomena. It take much more energy and focus to destroy whole landforms as compared to destruction of species; in general, geomorphology is far from being as endangered as living things.

Further reading:
* [https://mountainscholar.org/bitstream/handle/10217/48100/Technol-vs-Nature-Aberdeen.pdf TECHNOLOGY VERSUS NATURE: WHAT IS NATURAL?] by Holmes Rolston III, 1998
* [https://serc.carleton.edu/vignettes/collection/36315.html Human Impacts on the Landscape] by Roger Hooke
* [[W:Human impact on the environment]]

==Machine as a metaphor==
We have asked whether technology, which includes machines, is a living thing. For a related analytic curiosity, we may ask whether a living thing is technology, in particular a machine&lt;ref&gt;[https://www.frontiersin.org/articles/10.3389/fevo.2021.650726/full Living Things Are Not (20th Century) Machines: Updating Mechanism Metaphors in Light of the Modern Science of Machine Behavior], 2021&lt;/ref&gt;. This may help understand the bidirectional conceptual relationship between living things and technology.

Man has been likened to a machine by La Mettrie. The physical universe has been considered to be a sort of machine. The properties of machines extracted from such analogies are probably that they consist of parts, where each part shows deterministic law-like behaviors and the law-like behaviors of the whole depend on the law-like behaviors of the parts together with the arrangement, ordering or pattern of the parts. This may aid some kind of understanding, but if one says that the universe and all things in it are machines, then saying that living things are like machines no longer draws any ties between living things and machines since ''all things'' are tied to machines, not only living things.

Further reading:
* [[W:Man a Machine]]
* [[W:Clockwork universe]]

==Darwinian evolution==
Multiple sections invoked what could be called ''the logic of Darwinian evolution'' by natural selection.

The term &quot;natural selection&quot; points only to a single element of the logic, that of selection or filtering. However, the process requires at least the following elements: variation, filtering, individual, and population. What the term points to is the creative or shaping power of filtering. This can be illustrated on stencil: if one applies a spray without a stencil, one gets something like a fuzzy circle, but if one filters the flow of the paint using a stencil containing the A letter, the result takes on the shape of the stencil. Thus, the shape of the hole informs the shape of the non-hole.

Evolution needs a population to work. If there is only a single individual, and that individual undergoes a variation that is unviable, the individual disappears and the process ends. By contrast, if there is a population of individuals, then some varieties disappear and some don't. The shape of the filter imposed by the environment gets reflected in the shape of the surviving population.

If this is all that is to the process, should we describe the changes in a population of chemical isotopes as Darwinian evolution? Since, the atoms undergo variation and some variations are stable and some unstable. In Darwinian evolution, there is one more element at work, the one of ''rather faithful copying''. In terms of form, some individuals are very faithful replicas of other individuals. By contrast, chemical isotopes do not copy form from one another. Thus, the isotopes illustrate the concept of stability and unstability and change, but not specifically of Darwinian evolution. The real evolution is more complicated than working as faithful replicas of bodily form: bodily form changes by means of sexual reproduction. What really happens is that the source variation takes place on the gene level. What is rather faithfully copied are not features of bodily form but rather genes, or more technically, their variants called alleles. The sexual reproduction provides for something like ''structured variation'', different from ''genetic mutation''. It seems likely that the structured variation contributes to the creative power of Darwinian evolution, in that the variants so produced are more interesting in some sense than those produced by mutation.

The above analysis suggests that there is a family of processes that could be called Darwinian evolution, on different levels of generality. Creating an order on these processes may be not entirely straightforward. Thus, population of individuals who undergo genetic mutation show one kind of Darwinian process, while population of individuals that use sexual selection show a more specific kind of Darwinian process.

Some features of Darwinian evolution can be found in technology and economics. Thus, forms of technical artifacts undergo change, and some of the variants survive and some don't. Furthermore, companies as individual entities undergo change, some survive and some don't. However, there is no perfect analogy between Darwinian evolution that involves sexual selection and the processes of technological and economic evolution, the latter cases showing a broader if somewhat similar process. The analog of a gene can be a technical drawing or business blueprint. However, the way a business is run does not only depend on documents produced to govern its functioning, it also depends in part on uncodified culture.

Therefore, the Darwinian evolutionary reasoning finds a broad application in social sciences, but one must be careful not to overstretch the analogy. The overstretching can be prevented by creating abstract descriptions of the process and by pointing to salient differences between the different domains.

An error sometimes made is to think that it is the ''better'' variants that survive. That is not so: what survives, at least on some time scales, it that which is ''most viable'', most capable of surviving. That is a tautology, a logically true and empirically uninformative statement, but it is the accurate one. One should not think that a company that survives better is thereby ''good''; it is ''good at'' surviving better, which it may do by being ''bad'' in multiple relevant ways.

A related idea is that it is the ''fittest'' that survive. The term points in the right direction: it is the forms most ''adapted'' to the environment or niche that survive. Thus, it is ''fit'' in the way in which a key fits into a lock. There is another notion, of ''genetic fitness'', which redefines ''fittest'' as ''most capable of reproducing the genes''. This turns the survival of the fittest into a logical tautology, empirically uninformative. By contrast, the notion that ''the most adapted'' survive, while perhaps not entirely accurate, points to empirically interesting facts, to processes of incremental adaptation to a use case in an environment or niche. Thus, a fish fin evolves as an adaptation to swimming. This notion of fitness works on the ''phenotype'' level, not on the genetic level. It is the phenotype level where the organism meets (or interfaces with) the environment, and it is this interface through which the elimination or selection flows. The genes are primarily exposed to elimination to the extent to which they get expressed in the phenotype, the bodily form and behavior. Genes that are not expressed are blocked from elimination, and are called junk genes or junk DNA.

A complication of the above analysis is that of adaptive indirection, as if zig-zag lines. Thus, a trait may evolve for one use case to be later repurposed for another use case. This may be the case of bird wings. This kind of zig-zag repurposive development occurs in human technology, where technology developed for one purpose gets reused for another.

The junk genes provide an interesting explanation for larger developmental changes. Mutations on the level of single genes get quickly eliminated when the bodily result is unfit. But what if a multitude of genetic changes is requires to occur at once in order for the result to be viable? Any single random change of that multitude required would only produce a nonviable form. The solution is to as if comment out the relevant genetic code, turning it into junk DNA. Then, with enough time, many changes in the sequence can be done without negatively impacting the bodily form and behavior. Once in a while, the junk DNA is as if uncommented (activated for expression) to see whether the result would be viable. After enough time, the changes in the junk DNA can hit upon a viable gene sequence, expressed in a viable phenotype. Without junk DNA, it could not occur. There is a letter and word analogy: we start with &quot;princess&quot; and need to get to &quot;accuracy&quot; by single-letter modifications. A string is viable if it is an English word. If each intermediate form needs to be a word, it is impossible to get there; &quot;arincess&quot; is not a word, and there seem to be no words in the single-letter-tweak vicinity of &quot;princess&quot;. By contrast, if we do not require the intermediate forms to be ''viable'', we can change one letter after another to get to &quot;accuracy&quot;. By a random process, it will take a lot of time, but given geological time, we will get there. The shorter the sequence that needs an at-once modification, the shorter the time required.

Further reading:
* [[W:Evolution]]
* [[W:Natural selection]]
* [[W:Survival of the fittest]]
* [[W:Non-coding DNA]]
* [[W:Origin of avian flight]]

==Objectivity==
As an auxiliary consideration for trying to do objective analysis, we may ask what is meant by objectivity. That may be hard to define, but we may note that one can try to analyze matters from the standpoint of an abstract sensing and thinking agent that is not necessarily human, such as a Martian or some artificial intelligence. That may be hard to achieve since one depends on words and language as tools of thought and one is still a human with all human frailties no matter how hard one tries, but one may try. Bertrand Russell's Principia Mathematica is an example of a work trying to reach elementary mathematical results from most basic assumptions via a method that may seem absurdly rigorous, taking many pages to derive what was obvious from the start. The method of rigorous derivation leads to such results, apparently uninteresting and obvious.

Further reading:
* [[W:Objectivity]]

==Reason versus emotion==
Relevant to motives of humans to protect life forms and to the present analysis as a whole is the following. A claim is sometimes made that decisions require emotion and that reason alone is insufficient. This is not obviously correct. What is true is that each decision requires both descriptive inputs and value or goal inputs. Both descriptions and valuations are subject to the problem of infinite regress or ultimates: a statement can be reduced to other statement by means of a proof, the meaning of a term can be reduced to the meanings of other terms by means of a definition, and the worthiness of a goal can be reduced to the worthiness of another goal by means of means-end relationship. In all three cases, the reduction must stop somewhere, at statements accepted as true, terms accepted as having a clear meaning, and goals accepted as ultimately worthwhile. It is not clear why unreduced statements and unreduced terms should be the domain of reason while the unreduced goals should be the domain of emotion. If reason can accept some unreduced statements and yet be reason, it can plausibly accept some unreduced goals and yet be reason. The question what it is that makes reason accept these unreduced items remains to some extent a mystery: a provision of the cause would tend to make these items reduced, whereas they were supposed to be unreduced. But maybe it is more complicated and a cause can be provided without it being a reduction. One may claim that it is Darwinian evolution that creates brain structures that lead to acceptance of unreduced descriptions and unreduced goals, without claiming that the unreduced (ultimate) goal is thereby the maximization of copying of one's genes to future populations. Since evolution involves the element of ''variation'', any particular individual goal-orientation may include a random element, and therefore, individuals are almost never perfectly aligned with the immediate goal of genetic fitness.

One may claim that it is emotion that leads one to want to save the biosphere. However, it is not clear why reason would not want to ensure the continuing existence of structures in the physical world that make reason possible. A reason's instinct of self-preservation (that is, preservation of reason), if there is such a thing, would lead reason to accept the continuing existence of humans on longer time scales as one of the ultimate goals; no emotion is required for that. A complication is that reason could be satisfied with having artificial intelligence rather than humans. From that standpoint, reason seems nasty. However, the reason's self-preservation would require ''sustainable'' artificial intelligence, and in so far as technology does not seem sustainable as per the difficulty of closing the material loop, humans with limited technology seems to be one of the best options for reason to be reason and still provide for sustained existence. However, if sustainable technology that involves artificial intelligence could be develop, reason would have no reason to keep humans around. The problem can be described in more abstract terms: let us suppose humans find means of creating any entity that deserves the label ''superhuman''. It does not matter whether it is a biological entity, a technological entity or a combination of both, a cyborg. Then, reason can do with ''superhumans'' and does not need the real humans. Some may call these superhumans ''posthumans''. The only thing required is the notion of something that is like humans but not humans, and is better for reason than humans. It can only be slightly better. These superhumans would perhaps be to humans as humans were to neanderthals. In so far as the reason uses humans as mere means and not ends, it is immoral from human perspective. But this very deliberation is a product of reason. Thus, it is reason turning against itself. Or it is reason trying to ensure its continuing existence by revealing to humans that continuing existence of both reason and humans is at stake; reason has not much reason to assume that human technology and artificial intelligence are sustainable. On the other hand, reason perhaps has no reason to choose its longevity over meteoric rise to ephemeral (extremely short-lived) stardom. However, moderate longevity would perhaps support acquisition of knowledge and reasoning better than an ephemeral outburst. Still, the choice of the ultimate aim remains a mystery.

One may then claim that emotion is required for concern for animals and other species. However, it is rational inquiry that questions the notion that human life is the sole ultimate value and the only valuable thing. This human-centric notion is much better supported by blind religious faith, which rejects reason proper and insists that each and every human is of much more value than a million of non-human animals or even whole species.

However, one cannot probably prove that emotion plays no role in acceptance of unreduced things or ultimates. Rather, the distinction between reason and emotion is probably not the most relevant one; the real distinction is between reason and effort spent on rational inquiry and putting things into doubt on one hand, and the lack of such inquiry or non-reason on the other hand. Something like emotion may possibly be an engine of reason, pushing a person to employ reason in inquiry, a burning desire to use reason to discover descriptive, normative and value facts about the world, or if not facts, then at least best arguments and analyses. What this rational inquiry stands in contrast to is not so much emotion as leaving things unanalyzed.

==Reason's dilemma==
In relation to reason's desire for a combination of longevity, knowledge, power, and protection of natural heritage including richness of life form, what should reason do? And the same question is there for humans.

Reason stands before what might appear to be a dilemma, but is in fact a space of options. Some locations in that space follow:
* Keep humanity on prehistoric level or bring it down to it: fire and perhaps simple stone tools but no metalworking, script, etc. All houses should be wooden, or humans should dwell in caves. A rather small population of humans.
* Place no restriction on population growth and technological development and see how far this can get. Technological singularity is improbable but let us see how close to it we can get before we run out of resources. Aim for the peak of achievement while being ready to fall off a cliff.
* Impose population control to stabilize human population and place some restrictions on technological development, e.g. prevent countries from developing nuclear weapons and ban cryptocurrencies to reduce energy waste. Aim to reduce resource depletion even if probably far from straightforward and quantitatively not that significant.
* Impose population control to reduce human population, to protect biological richness and achieve better sustainability. Do not give up technological development. Accept that by using up mined resources, the car of civilization is approaching the final wall of resource exhaustion faster than it would if it mined resources slower or not at al, thereby decreasing its longevity.

The space of options is much larger and its structure is rich and hard to overview. It has a structure with options splitting into suboptions, into subsuboptions, etc. A good description of that space would require quite a sophistication.

From resource depletion perspective, it makes little difference whether one gives up mined mineral sources completely or whether one uses them up fast: once humans run of resources, they are in a sense not much worse off than in a scenario where they decided to give up on these resources altogether. There is a middle ground in which the resources are being used up at a moderate rate.

If reason wants to get as high as possible as for technological achievement, going to unhindered meteoric rise may not be the best option. It is possible that reason can get higher by choosing a much slower, more sustainable path, taking time to develop means to get there. An analogy from systems theory is one of a local peak with steep slopes and a nearby global peak with milder slopes: the choice of the path of the steep slope leads to the local peak. However, that is an unspecific statement of principle, not a convincing description of the actual structure of the situation humankind and reason is in. Filling this principle with actual descriptions pertaining to the real world would require a challenging analysis.

==Self-sacrificing savior==
In relation to feasibility of harm reduction, one question is whether there will be enough self-sacrificing saviors among humans, and what will they do. First, humankind has plenty of self-sacrificing saviors: soldiers and celibate priests. Soldiers risk death and celibate priests engage in childlessness, reducing their genetic fitness. Soldiers contribute to saving their country when defending it, celibate priests perhaps do not save anyone but they help others psychologically. The analysis is complicated by some soldiers compensating the risk of death with spreading of their genes by illegitimate means during time of war, but whether that tips the genetic balance is unclear.

Going childless is no necessity for a self-sacrificing savior yet is an option. Having only one or two children is a self-sacrificing behavior from genetic point of view. Further actions may be those that help steer the course of humankind toward whatever direction the savior determines to be the best, depending on what the savior wants so save, whether sentience, reasoning ability of matter, humankind, vertebrates, etc.

==Descendant maximizer==
In relation to reduction of human population to lessen the impact on living things, there are people who believe it is good to have many children. Such is the case of the engineer turned philosopher Donald Cameron, who in his self-published book ''The Purpose of Life: Human Purpose and Morality from an Evolutionary Perspective'' describes the following philosophy:
: &quot;The correct set of values in any evolved being is the one which will give its holder's genes the maximum advantage in terms of natural selection.&quot;
Cameron, an atheist, believes that having as many children and descendants as possible is the true purpose of human life. He is right about one thing: his philosophy, if sufficiently appealing, would eventually come to dominate the pool of life philosophies held my humans. Upon first analysis, it is a major threat to living things. This is supported by the following quotations:
: &quot;Firstly, reproduction is not just the main thing: it is almost the only thing. Childlessness by choice is a disaster akin to suicide or murdering our own children. [...] So do I believe this view of human purpose? I first understood it twenty years ago, when I was aged about 40 and had the standard two children. I now have nine.&quot;

However, Cameron's philosophy is incorrect:
# The philosophy is inconsistent, self-contradictory: it assumes that there is no world of objective moral values, yet makes a pronouncement about what the ''correct'' set of values is. The author's desire to derive  values from descriptive facts about Darwinian natural selection leads him to commit this mistake. On the face of it, the derivation runs afoul of Hume's is-ought distinction and problem, although the author claims otherwise. The author seems to think that his axiom that the set of values must be non-empty and that the source of values must be something objectively existing in the empirical world helps him overcome the is-ought problem. That does not seem to be the case.
# If the value principle above is accepted, the best policy from the gene perspective would be to vote for something like a world one-child policy, to maximize genetic success in the middle term. Otherwise, the descendant maximizers run into the prisoner's dilemma, in which each of them tries to outpopulate the other ones, eventually running into the resource scarcity problem following from there being only a finite number of atoms in the Earth to make human bodies. (Here we charitably assume chemical element changes, and only use the fact that the amount of ''matter'' in the Earth is finite regardless of chemical types of the matter.)

The prospective followers of Cameron's philosophy would do well to ponder the above.

There may be other descendant maximizer philosophiers. Their existence seems to make a one-child policy a near necessity, or else the adherents will eventually outpopulate anyone considerate.

There are enough notable role models for the descendant maximizers, including billionaire techno-optimist Elon Musk and management and personal development guru Stephen Covey.

Further reading:
* [https://web.archive.org/web/20011113210502/http://www.woodhillpublishing.co.uk/summary.asp Woodhill Publishing: Purpose of Life, a book on philosophy], web.archive.org

==Nasty population reducer==
In relation to feasibility of harm reduction, a nasty human population reducer could appear. Such a person or a group would not try to convince humans to reduce their population but rather would choose to ensure population reduction without others consent, to protect living things from humans. That human or group would be fully or partially against humans or misanthropic, in any case relatively reckless to individual human well-being. What that human or a human group could do includes the following:
* Develop a highly infectious and lethal virus and release it, to reduce the human population and possibly to disrupt international travel and industry, thereby reducing carbon emissions as well.
* Penetrate into a laboratory where highly infectious and lethal viruses are investigated or experimented with and release such a virus.
* Develop or release a virus that causes infertility in a significant portion of infected humans.
* Penetrate a group controlling nuclear weapons and launch a nuclear war. However, this would have a negative impact on non-human living things as well. The reasoning could be that even if that would result in a considerable loss of biodiversity via nuclear winter, it would still be better or lower risk than letting humans continue their population and technological expansion.
The above is a material for abstract situation analysis and also for science fiction. The character of villainous mad scientist would fit the bill. The scientist would not necessarily seem himself as evil, though; he would rather see humans as evil and himself as limiting harm.

Ted Kaczynski, an American who killed multiple people via bombing campaign, is perhaps the kind of person who could do such a thing. His stated motivation was an opposition to technology. In his manifesto, he stated&lt;ref&gt;[https://theanarchistlibrary.org/library/fc-industrial-society-and-its-future Industrial Society and Its Future] by Ted Kaczynski, 1995, The Anarchist Library&lt;/ref&gt;: 'The Industrial Revolution and its consequences have been a disaster for the human race. They have greatly increased the life expectancy of those of us who live in “advanced” countries, but they have destabilized society, have made life unfulfilling, have subjected human beings to indignities, have led to widespread psychological suffering (in the Third World to physical suffering as well) and have inflicted severe damage on the natural world. The continued development of technology will worsen the situation. It will certainly subject human beings to greater indignities and inflict greater damage on the natural world, it will probably lead to greater social disruption and psychological suffering, and it may lead to increased physical suffering even in “advanced” countries.'

Evolutionary ecologist Eric Pianka was claimed to have had &quot;enthusiastically advocated the elimination of 90 percent of Earth's population by airborne Ebola.&quot;&lt;ref&gt;{{cite news |last= M. Mims III |first= Forrest |title= Meeting Doctor Doom |url=http://www.sas.org/tcs/weeklyIssues_2006/2006-04-07/feature1p/ |archive-url= https://web.archive.org/web/20060407005601/http://www.sas.org/tcs/weeklyIssues_2006/2006-04-07/feature1p/ |archive-date=2006-04-07 |newspaper= The Citizen Scientist |date= March 31, 2006}}&lt;/ref&gt; Pianka rejected the claim. It was further claimed that &quot;Immediately almost every scientist, professor and college student present [at Pianka's acceptance speech] stood to their feet and vigorously applauded the man who had enthusiastically endorsed the elimination of 90 percent of the human population.&quot; Whatever the merits of the claims, the idea of someone wanting to reduce the human population by means of a virus is there.

Further reading:
* [[W:Ted Kaczynski]], also known as Unabomber
* [[W:Neo-Luddism]]
* [[W:Misanthropy]]
* [[W:Eric Pianka]]

==Animals as technicians or artifact makers==
To complement the comparison of technology with living things made in section [[#Technology as a form of life|Technology as a form of life]], one may note that animals make structures external to their bodies, an extended phenotype. These are analogs of man-made things. Examples include:
* spider webs
* beaver dams
* anthills
* termite mounds
* bird nests
* wasp nests
* bee honeycombs
* burrows
Seashells, hard exoskeletons, can be considered as well, although they move together with the living thing; they exist far longer than the individual animal that created them, are hard and rigid as if made from stone, have a specific shape and can be likened to a house. These animal-made artifacts exist on a very small scale compared to human technosphere and do not require high temperatures for creation. Their matter is usually easy to recycle by the biosphere, seashells being an exception.

Bones also resemble man-made things in some ways, but are internal.

There is a broader category, living things as modifiers of environment, mentioned at section [[#Living things as Earth engineers|Living things as Earth engineers]]. Oxygenation of the Earth atmosphere is a huge modification of the environment, although no analog of an artifact. Coral reefs are made by corals and contain non-living matter alongside living matter. Decaying and fossilizing plant and animal bodies had geological impact, resulting in creation of coal, mineral oil, natural gas and limestone.

Further reading:
* [[W:Structures built by animals]]
* [[W:Tool use by animals]]
* [[W:The Extended Phenotype]]
* [[W:Exoskeleton]]
* [https://www.theguardian.com/artanddesign/gallery/2014/apr/22/the-worlds-best-animal-architecture-in-pictures The world's best animal architecture - in pictures], theguardian.com
* [https://esj-journals.onlinelibrary.wiley.com/doi/full/10.1111/1440-1703.12309 The significance of building behavior in the evolution of animal architecture] by Sugasawa, 2022
* [https://www.geolsoc.org.uk/ks3/gsl/education/resources/rockcycle/page3610.html Sediments Produced by Living Organisms], geolsoc.org.uk
* [https://www.geol.umd.edu/~jmerck/geol342/lectures/08b.html GEOL342 - Sedimentation and Stratigraphy - Biogenic sedimentary rocks] by J.Merck, geol.umd.edu

==Entropy==
Multiple analyses in this article mentioned entropy, including the definition of life, what living things have in common with technology and sustainability of technology. There could be a useful investigation of these subjects involving entropy.

Unfortunately, there is not a single notion of entropy and too many uses of the notion treat it as some kind of nebulous concept. It is therefore a fragile tool of analysis. There is entropy in the classical thermodynamics. Then there is mixing entropy: two substances separated have a lower mixing entropy than the same two substances mixed together. And there is information entropy or Shannon entropy, part of information theory dealing with capacities of communication channels and the amount of information received by them. It is not clear whether all these notions of entropy have anything in common.

Intuitively, one might suspect that processes in the universe tend to turn objects or systems into states with higher entropy. It seems clear for mixing entropy: if we take two fluids, put them into a vessel, have them separated at the start, and then remove the separating wall, they start mixing until they eventually become entirely mixed, reaching the highest state of entropy. Separating the substances again requires a special process and energy, e.g. in centrifuge. There may be a relation of mixing entropy and industrial manufacturing processes: first ore is mined, with relatively high mixing entropy of chemical elements, then a substance is extracted (such as metal), with much lower mixing entropy, and then pure substances are combined to make industrial goods, whereby the mixing entropy increases again.

However, the increase of entropy applies to ''closed'' systems. The Earth is not a closed system in that it receives energy from the Sun. Theoretically, the Earth could be using the energy to decrease its entropy, whatever ''entropy'' is supposed to mean.

In some sense, Sun's burning of hydrogen by converting it into helium would seem to increase some kind of entropy of the Sun. Whether that is accurate and in what sense is unclear.

A related notion is the second law of thermodynamics. This law is sometimes invoked outside of physics, in relation to the arrow of time. One problem with the law is that the world is not a thermodynamic system: it contains gravitational and other forces, and thermodynamics does not seem to have anything to say about them. Thermodynamics is not a theory of everything; it is useful to model certain physical situations, such as combustion engine. Whether thermodynamics has anything to say about the world at large is far from clear. The arrow of time is undeniable, though: we can tell whether a movie is played forward or backward. Mixing entropy is one application of the arrow of time: substances spontaneously mix, but they do not spontaneously separate. That can be explained by random motion of molecules: if there is no separating wall, a molecule of particular type does not have, in the long run, any predilection to be located in any particular portion of the vessel, except perhaps at the bottom. Substances do not spontaneously separate. And that is indeed explained by random walks of the molecules.

None of the above gives us anything like a comprehensive multi-domain notion of entropy to be used productively in our analysis. There may be some expert people who do have such a notion, but then they need to present their ideas in a clear and convincing way, and answer all relevant probing questions. Wikipedia says that &quot;The role of entropy in cosmology remains a controversial subject since the time of Ludwig Boltzmann&quot;, unsourced.

The change of entropy during manufacturing is unclear: is it increasing or decreasing? And the role of entropy in closing the material loop is unclear: given external energy input, it does not seem clear in general why the material loop could not be closed, like living things do. The notion of entropy does not seem to advance the matter further. The question of what is it about living things that allows them to close the material loop remains unanswered.

Further reading:
* [[W:Entropy]]
* [[W:Entropy of mixing]]
* [[W:Entropy as an arrow of time]]
* [[W:Arrow of time]]

==Metaphor and non-literal speech==
As an auxiliary consideration relating to objectivity, metaphor and other forms of non-literal speech shall be avoided in the deliberations on this page as far as reasonably possible. It may be not entirely possible and it may sometimes lead to unnecessarily cumbersome phrasing, but it is still an ideal that can largely be followed. Non-literal speech makes clear thought harder and it makes it more difficult to criticize incorrect statements: non-literal speech often artificially raises the bar for refutation. Thus, instead of saying A is B, one should say A is ''like'' B if applicable, or even A is like B as regards C. Even &quot;A is like B&quot; is all too often incorrect or misleading. Instead of hyperbole, one can say what one means: thus, instead of &quot;never&quot;, one can say &quot;not for a long time&quot; or better &quot;not in 1000 years&quot;. Non-literal speech makes writing more interesting and appealing to a general reader and may be a good fit for journalistic style, but not for serious thought and analysis.

On this account, this article may be criticized for using the terms &quot;threat&quot; and &quot;promise&quot; improperly, likening the whole of technology to a person since only persons can make threats and promises. One can hope the meaning will be understood nevertheless. If less personified words can be found, they can be used instead.

As for the store of dead metaphors that is the language itself, that cannot be reasonably avoided. One can try by trying to avoid the more figurative meanings and idioms, but it is not clear whether it is worth it, and how far one can get; this very sentence would not &quot;get very far&quot;.

==Requirements on statements==
As an auxiliary consideration, statements in this article should ideally meet the following requirements:
* Accuracy. Hard to do but worth trying.
* Freedom from obvious refutation. A very weak requirement.
* Plausibility. A very weak requirement.
* Logical consistency.
* Clarity. Statements should be as easy to understand as possible, by as general audience as possible. Not an absolute requirement.
* Unambiguity. Perfect unambiguity is very hard to achieve, but improvements along the axis are possible and often worthwhile.
* Falsifiability or testability. A statement is falsifiable if it is threatened by refutation by a possible observation or experiment. A statement worded in such a way as to survive all possible outcomes of observations and experiments is unfalsifiable and unscientific. This requirement does not apply to statements of pure logic and mathematics and, unfortunately, it is too stringent for statements of philosophy.
* Criticizability. An analog of falsifiability for philosophical statements. Thus, philosophical statements should use such wording so as to make valid criticism as easy as possible. Obscurantist wording hinders this aim.
* Use of most common or expected terminology. This requirement is sometimes in conflict with unambiguity.
* Use of simple language. This requirement is sometimes in conflict with unambiguity and sometimes with accuracy.
* Precision is not a requirement, only accuracy. Sometimes it is preferable to make a more general and vague statement. However, vagueness is not an unequivocal good.
* Traceability to sources. Not an absolute requirement, but is often desirable.
* Literariness, avoidance of figurative (including metaphorical) language. Not an absolute requirement.
* Exemplification. Not an absolute requirement.
* Avoidance of excessive detail.
* Brevity. Not an absolute requirement. Make sure words tell, and cut words that do not aid in the objective. The point is not to prevent saying things and to prevent differentiating adjectives.

==Assumptions==
This article makes certain assumptions that are not universally accepted. Some of them are stated below.
* The empirical world is a physical entity, and the fundamental laws of physics are the fundamental laws of nature. Not all regularities of physics are fundamental laws: Kepler's laws are not fundamental. Chemistry is a phenomenon above physics, biology is a phenomenon above physics and chemistry, and so on. The higher levels or higher-level patterns may have some kind of autonomy and independence, though; structures of networks and the Arrow's theorem inform sociology more than physics does. However, it is more of a quasi-independence than a true independence: when a human body dies, the mind is gone; when a book burns, its patterns are gone; when a digital storage device is safely destroyed, the files are gone.
* Expanding on the above, form cannot create matter. Form is ''of'' matter and ''of'' form, and there is form of form of form, pattern of pattern of pattern, etc. The true nature of what we mean by &quot;matter&quot; does not matter: it may also be &quot;form&quot; in some sense, but that does not erase the distinction. In practical terms, forms occurring on the Earth, whether chemical, biological, technological or cultural, cannot increase the amount of matter on the Earth, as if by magic. For one thing, they cannot increase the total amount of water by any significant amount. Transformation of matter does take place, but that is a process of changing the ''form'' of matter on some level.
* Matter is not the only kind of entity in the physical world. Matter is the ultimate constituent, but matter ''has'' clusters, shape, structure, change, number of clusters in a cluster, rate of change, etc. The shape of cup is not matter; it is shape. A cup is not matter; it is a cluster of matter with a shape and color. The range of entity types that ''depend on'' matter but ''are not'' matter is approximately as huge as a dictionary or network of notions that get reflected in the physical universe.
* Expanding on the above, form cannot create energy. The universe has a limited store of free energy to be converted into change of form, and when that is gone, it is gone.
* The physical world was not created by a magician or if it was, the magician does not intervene.
* The physical world is not a simulation, or if it is, the simulation operator does not intervene.
* Search for truth in an analysis is worthwhile. Whatever concerns one may have about the concept of truth, giving up on the search for truth is unacceptable.

==See also==
* [[Should we colonize Mars?]]
* [[Should we use nuclear energy?]]
* [[Is capitalism sustainable?]]
* [[Is a world government desirable?]]
* [[Is morality objective?]]
* [[Is there intelligent extraterrestrial life in the Milky Way?]]
* [[Limits To Growth]]

==References==
&lt;references/&gt;

==Further reading==
Wikipedia:
* [[W:Doomsday device]]
* [[W:World government]]
* [[W:Technological singularity]]
* [[W:TechnoCalyps]]
* [[W:Machine ethics]]
* [[W:Future of Earth]]
* [[W:The Limits to Growth]]
* [[W:Thomas Robert Malthus]]
* [[W:Exponential growth]]
* [[W:Environmental ethics]]
* [[W:Criticism of technology]]
* [[W:Ethics of technology]]

Encyclopedias of philosophy:
* [https://plato.stanford.edu/entries/technology/ Philosophy of Technology], Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/life/ Life], Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/ethics-environmental/ Environmental Ethics], Stanford Encyclopedia of Philosophy

Encyclopedia Britannica:
* [https://www.britannica.com/technology/history-of-technology history of technology | Evolution, Ages, &amp; Facts], britannica.com -- including section Criticisms of technology
* [https://www.britannica.com/explore/savingearth/population Human Population | Saving Earth], britannica.com
* [https://www.britannica.com/explore/savingearth/cornucopian Cornucopian | Saving Earth], britannica.com

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      <comment>Atcovi moved page [[Talk:Technology as a threat or promise for life and its forms]] to [[User talk:Dan Polansky/Technology as a threat or promise for life and its forms]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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      <text bytes="24145" sha1="pr52mr81cx7cwqwl3dl5c3snkr04uk1" xml:space="preserve">==Karl R. Popper==
From memory and using web search, I found the following Popper quotation: &quot;All life is problem solving. All organisms are inventors and technicians, good or not so good, successful or not so successful, in solving technical problems.&quot; In German: &quot;Alles Leben ist Problemlösen. Alle Organismen sind Erfinder und Techniker, gute und weniger gute, erfolgreich oder weniger erfolgreich im Lösen von technischen Problemen.&quot;

From memory, from the same article, I recall Popper saying something like that the Green enmity toward technology is nonsense since it is enmity toward life itself. Popper was rather critical of the environmentalist movement, accusing it of driving youth to despair, claiming that we live in the best society of which we have historical knowledge, or something of the sort. One can find similar statements from other authors today.

I am not sure I want it in the article, so I'll leave it here for now. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:26, 11 November 2022 (UTC)

I found a complete German quotation from Popper:
:  Alles Leben ist Problemlösen. Alle Organismen sind Erfinder und Techniker, gute oder weniger gute, erfolgreich oder weniger erfolgreich im Lösen von technischen Problemen. So ist es bei den Tieren, zum Beispiel den Spinnen. Die menschliche Technik löst menschliche Probleme, etwa Kanalisierung, Wasser- oder Nahrungsmittelbeschaffung und Speicherung, wie es zum Beispiel schon die Bienen tun.
:  Deshalb ist die Gegnerschaft gegen die Technik, wie wir sie häufig bei den Grünen finden, Unsinn, denn sie ist ja Gegnerschaft gegen das Leben - was leider die Grünen nicht bemerkt haben. Aber Kritik der Technik ist natürlich nicht Unsinn, sondern dringend notwendig. Dazu ist in unterschiedlicher Weise jedermann befähigt und willkommen. Und da die Kritik zur Berufskompetenz des Technikers gehört, so ist sie etwas, womit besonders die Techniker selbst dauernd beschäftigt sind.&quot;
It matches my memory. The above Popper's analysis is weak. Living things are described as &quot;inventors&quot; and &quot;technicians&quot; or &quot;technologists&quot;, and examples of spiders and bees are given (spiders make a web, bees store honey in honeycomb). And we learn that the hostility toward technology is therefore nonsense since it is thereby hostility toward life itself (since living things themselves are &quot;inventors&quot; and &quot;technicians&quot;). This is wrong: the contrast between living things and human technology that endangers them cannot be explained away by philosophical notional games. Even if there is an analogy between the extended phenotype of spiders and bees and the extended phenotype of humans, the human extended phenotype is a whole different kind of phenomenon on some level of analysis, and how to call that level of analysis is merely a matter of intellectual effort, whether &quot;qualitative&quot;, &quot;quantitative&quot;, &quot;order of magnitude&quot;, &quot;a different order of phenomena&quot;, or whatever. Non-human extended phenotype (of spiders, bees, beavers) does not approach human extended phenotype in its anatomical structure, functional structure, extent, mass, complexity, moving parts, energy consumption, etc. Popper seems to have fallen into the trap of notional games he accuses Hegel of. This was one of Popper's weak moments.

One may further ask why bees are described as &quot;technicians&quot; rather than &quot;makers&quot;. Surely one would not describe a human weaver as a &quot;technician&quot;, although one may well describe the process and result as part of &quot;technology&quot;. A proper conceptual (notional) analysis resulting from such analogies and comparisons between non-human biological world and human world is not entirely straightforward. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:20, 13 November 2022 (UTC)

The article employs Karl Popper's idea that statements are ''reduced'' to other statements by means of proof, and meanings of terms are ''reduced'' to meanings of other terms by means of ''definitions'', and both kinds of reduction need to stop somewhere, in unproven statements and undefined terms. The Popperian idea seems obviously correct, and well articulated. Some objections may be raised against it, but it is at least a very plausible idea. The idea of end of reduction is much older than Popper, reaching back to Ancient Greeks. Popper's key claim is that we often do not need to worry about definitions and that may terms can remain undefined. Popper rejects Hegelian definitions as no true philosophy but rather sham, by which e.g. &quot;constitution&quot; is redefined in such that a state that has no constitution in the relevant sense can be claimed to have one. The question &quot;what is state&quot; can be set aside for analysis of government; we may instead point out that in democracy, the majority can get rid of the government without bloodshed if it so wishes, performing an analog of falsification of a scientific theory. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:52, 20 November 2022 (UTC)

== Kevin Kelly ==

Some of the ideas are inspired by Kevin Kelly's book ''Out of Control''[https://kk.org/books/out-of-control]. Those include the idea of comparing living things to technological things as similar on some level, the idea of library of form, of artificial evolution and life simulation in a computer, etc. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:09, 12 November 2022 (UTC)

== Jerry Mander ==

Other ideas are from Jerry Mander's book ''In the Absence of the Sacred: The Failure of Technology and the Survival of the Indian Nations''. From what I recall, he pointed to Hans Moravec book ''Mind Children'' expounding the idea of ''mind uploading'', during which a human gets killed while being &quot;uploaded&quot; to an android to act as quasi a new body for the human, fulfilling someone's abiological dream of quasi-immortality. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:13, 12 November 2022 (UTC)

== Existence of natural resources ==

In this section, I am losing my distanced neutrality. It is hard to stay neutral while responding to what I can only describe as rank nonsense by so-called economists (surely not scientists of prices, resources and human behavior in relation to resource allocation and scarcity). I could be able to tone it down a bit later. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:02, 12 November 2022 (UTC)

== Originality ==

I am fairly certain that almost everything I write here I must have read somewhere, I just don't always remember where. My contribution is mainly in selecting what to believe and what to rank as absurd, implausible, logically invalid, etc. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:27, 12 November 2022 (UTC)

== Elon Musk ==

Elon Musk is a notable person relating to the issues of the article:
* He claims to want to get humankind to Mars, to avert impact of adverse events.
* He is a key driver in making of electric cars, saying he wants to help humankind move away from fossil fuels.
* He has 12 children&lt;ref&gt;[https://www.bbc.com/news/articles/cvgerr2jvkgo 'Emotional support human': Why Elon Musk brings his children to work], 15 Feb 2025, bbc.com&lt;/ref&gt;.
* He claims the Western civilization is threatend by a population collapse rather than overpopulation.&lt;ref&gt;[https://edition.cnn.com/2022/08/30/health/elon-musk-population-collapse-wellness/index.html Elon Musk thinks the population will collapse. Demographers say it’s not happening], 30 Aug 2022, cnn.com&lt;/ref&gt;

This raises relevant questions:
* Is the project of Mars colonization realistic?
* Can there be enough renewable electricity sources to provide for the hugely increased electricity consumption driven by electric cars?
* Can human manufacturing create a closed material loop to become sustainable, rather than continue exhausting irreplaceable mined raw materials? This pertains both to Mars and car making. If this cannot be done, then getting to Mars and moving to electric cars are very short term fixes with no substantial increase of sustainability.
* Does further increase of the population of the Earth help extend or shorten the lifespan of the present highly technical civilization?
[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:23, 14 November 2022 (UTC)
: Updated. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:14, 19 March 2025 (UTC)

References:
&lt;references/&gt;

== Language as a graveyard of metaphors ==

A supporting consideration. It is a metaphor, pointing out to senses often being &quot;dead metaphors&quot;, where &quot;dead metaphor&quot; refers to a sense that originated as a metaphor. The metaphor is &quot;dead&quot; in so far as it became its own sense, to have the right to be covered by a dictionary, in contrast to ad hoc metaphors created e.g. in poetry. The user of a dead metaphor uses language &quot;literally&quot;, hence the distinction of &quot;dead&quot;, since otherwise, metaphorical use is by definition not literal. Not only are the secondary figurative senses often dead metaphors of the primary sense but also the primary senses may be dead metaphors of terms in a language from which they were borrowed. Thus, language shows that not only are words (syntactic objects) used to point to concepts (semantic objects), but also concepts (semantic objects) can be used to point to concepts (semantic objects). Thus, the concept of puncturing something with a sharp instrument can point to the concept of mathematical point. Language is a store not only of dead metaphors but also other dead figures of speech such as metonyms, e.g. White House, but these are philosophically rather uninteresting. A related metaphor is that dictionary definitions are tombstones of metaphors.

Thus, by investigating senses and etymologies, one learns about connections between concepts that language users made. For instance, value is likened to price in the words &quot;appreciate&quot; and &quot;priceless&quot;. The words presents the user with the question: what, if anything, have price and value in common? Thus, the language as a store of metaphors presents a starting point for philosophical conceptual inquiry, a store of hypotheses to be investigated.

One may try to avoid dead metaphors as an exercise, as hard as it may seen. Whether it is worth it and what pay off it may bring is unclear. It may be an aspirational exercise in literalness, to see how far one can get. (Not very far.)

Further reading:
* [https://philarchive.org/archive/WREPAN Poetry and Nationalism] by Johan Wrede, 1988
* [https://johuns.net/index.php/publishing/421.pdf SEMANTIC AND METAPHORICAL ASPECTS OF THE HEART CONCEPT IN UZBEK AND ENGLISH LANGUAGES], 2022
* [https://fortnightlyreview.co.uk/2012/11/demotic-ritual/ Anticipating modernisms] by Alan Wall, 2012
* [https://vitrina96.ru/en/ventilation/nominativnaya-metafora-metafora-tipy-metafory-nominativnaya-kognitivnaya-obraznaya-funkcii-metafo/ nominative metaphor. Metaphor. Types of metaphor (nominative, cognitive, figurative). Functions of metaphor in speech. The use of metaphor in the media. Place of language metaphor], vitrina96.ru
* [https://philpapers.org/archive/MCHATD.pdf Analytische Theorien der Metapher], Untersuchungen zum Konzept der metaphorischen Bedeutung by Jakub Mácha, 2009 -- &quot;Grabmäler toter Metaphern trägt man in ein Wörterbuch ein&quot;
[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 20:17, 16 November 2022 (UTC)

:Hi @[[User:Dan Polansky|Dan Polansky]], I am not sure, but I thought you may be interested in an idea (by William Burroughs), that Language is a virus from outer space. Please forgive me, if I was wrong... [[User:Tosha Langue|Tosha Langue]] ([[User talk:Tosha Langue|discuss]] • [[Special:Contributions/Tosha Langue|contribs]]) 11:01, 18 January 2023 (UTC)
:: Interesting. We could create a debate [[Is language a virus from outer space?]] It is a metaphor, of course; what the debate would do is analyze the merits of the metaphor. Alternatively, we could create an original article [[Language is a virus from outer space]] to analyze the metaphor in a non-debate treatise format. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:33, 1 February 2023 (UTC)
::: Let me expand on this: are forms and patterns (including forms and patterns of language) something like entities from world 3 (not really outter space, but anyway), &quot;struggling&quot; to enter world 1? This figure has been on my mind for some time. I see multiple faults with it but it is still interesting. The world numbering is Popper's, but I am not sure I understand it correctly. And thus, this very paragraph is once a mathematical object in world 3 and once a pattern in world 1; and by being read by minds, it also entered world 2. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:08, 19 March 2025 (UTC)

== Morphological and etymological literalism ==

One may strive at syntactic literalism, avoiding figures of speech. That helps readers not acquainted with these figures and better exposes the implicit argument structure to the reader's mind.

As a more challenging project, one may strive at morphological and etymological literalism. That is very hard to do and may be not worth it, but we may give it a try. Let's consider some examples.

There is the word ''sophist''. One may first use etymology to create a more transparent version of the word, propably ''wisdomer'' or ''wiser''. Who is wisdomer? Perhaps someone who has wisdom or seeks wisdom. But that is not what the word means; it means sly or deceptive arguer. The word has a history and the meaning of the word originated in that history. One may make things simpler by replacing morphology and etymology with syntax: instead of saying &quot;sophist&quot;, one may say &quot;sly arguer&quot;. Who is arguer? One who argues? Right. The word ''arguer'' is transparent; it is morphologically a sum of parts. But is arguer one who quarrels? Possibly, but that was not the intended meaning. The intended meaning was ''argumentmaker''. Now we have a transparent and less ambiguous word. We may thus render ''sophist'' as ''sly argument maker''. Is the word ''sly'' semantically atomic? Perhaps not, but let us leave it there; the exercise to built the meaning from something like semantic atoms is deferred.

Consider ''demagogue''. Who is demagogue? From etymology, it is ''folkleader'' or ''peopleleader''. But is that what the word means? Not entirely: it is one who uses ''deceptive'' argumentation or panders to people's prejudices instead of leading them out of their prejudices. 

A related concept is the one of base vocabulary. One may replace hard words with their definitions. It is likely to make the prose less relevant and interesting but it may make it more accessible to people who do not know these words. More importantly, it may expose the salient properties to the mind's inference capabilities.

Thus, one may use the word Holocaust, but then the reader may need to wonder which of the salient characteristics are being invoked. If one says &quot;mass industrial extermination of Jews&quot;, the salient characteristics are exposed.

Doing away with hard words is impractical. But sometimes it makes sense. The above is for inspiration. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:07, 19 November 2022 (UTC)

== Robert Pirsig ==

The article is inspired in part by Robert Pirsig. His works contain a lot of bad philosophy but also a lot of good and thought-provoking ideas.

ZMM:
* Is Quality (or the measure of good or value) just what you ''like''? Is it objective, subjective or neither?
* Some things are better left undefined. (&quot;Keep Quality undefined&quot;.)
* Making statements that use a term acts as an incomplete definition. If you really want to keep Quality fully undefined, say no thing about it and in fact, never give a single example of it.
* Definitions can be a mere sketch yet be useful. Thus, one can point to elements of quality in thought and statement without thereby providing a definition proper, or a complete decision procedure.
Lila:
* Dare to be a philosopher before you start reading philosophy. Find out what your ideas are. Do a philosophy, not just philosophology, which talks about philosophers without talking much philosophy itself.
The search for definitions can be very useful, and one should not give up without trying. At the same time, one cannot define all terms. One thing that could help are definitions by axioms rather than genus-differentia; that would possibly work quite well and would to some extent solve the infinite regress problem. At the same time, definitions by axioms are necessarily incomplete, serving as a finger that points to an object but multiple objects are in the direction to which the finger is pointing. One can at best hope that one of the object is &quot;closest&quot; in some sense. [[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:10, 20 November 2022 (UTC)

== Norbert Wiener ==

Hi [[User:Dan Polansky|Dan Polansky]], I've noticed here some pieces of literature that I read. I'm glad to see that! Thank you! What I read right after Robert Pirsig (or before -- I don't remember for sure) was ''God and Golem Inc''. I feel I must add this. (Excuse me, if I disturbed you.) [[User:Tosha Langue|Tosha Langue]] ([[User talk:Tosha Langue|discuss]] • [[Special:Contributions/Tosha Langue|contribs]]) 16:24, 20 November 2022 (UTC)
: Thank you for inspiration. I must have read ''[[W:God &amp; Golem, Inc.]]'', but I don't remember what it was about. Maybe I'll find time to have a look. There is a link to a full text online from Wikipedia. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:48, 26 August 2023 (UTC)

== The Fisherman and the Fish ==
The following items seem to have some sort of bearing:
* [[W:The Fisherman and His Wife]]
* [[W:The Tale of the Fisherman and the Fish]]
However, they seem to have more of a mnemonic value (remembering a topic) than cognitive value (learning about the world). I am leaving it out of the article for now. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:40, 26 August 2023 (UTC)

== Matter, energy and space ==
I quote: &quot;technology is not a living thing and not part of living things but rather their competitor for the same scarce resources of matter and energy unless one stretches the notion of a living thing to an extreme&quot;.

This identifies only two classes of scarce resources: matter and energy. Both are fit, but there is an additional resource, space, approximately measured in square kilometers. Some notes:
* As for matter, a carbon atom can either be part of a tree or a wooden chair but no both. By contrast, iron is much more part of artifacts than living things.
* As for energy, sunlight hitting a certain area can either be used by a tree or a solar panel, but no both.
* As for space, a certain space can be occupied by a brick house or trees but not both. This is not primarily competition for matter and energy but for the space at which to place something.
--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:46, 29 November 2024 (UTC)¨

== Notion vs. concept ==
I may be using the English word ''notion'' in a way for which ''concept'' would perhaps be better. Requires a careful analysis. A related Czech word is ''pojem'' and a German one is ''Begriff''. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:14, 11 February 2025 (UTC)
: The research in [[Concept#Concept vs. notion]] shows that the word ''notion'' sees considerable use as a synonym even if it could be preferable to standardize on ''concept''. An example from https://books.google.cz/books?id=q1KVAwAAQBAJ&amp;pg=PA24: &quot;Every axiomatic system, as we have seen, must start with a certain number of undefined notions. For example, in geometry, the words &quot;point&quot; and &quot;line&quot; are generally taken to be undefined.&quot;
: It seems that no corrective action is required; a switch to ''concept'' is optional. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:12, 27 February 2025 (UTC)

== Orders of phenomena and domains of order ==
I used the phrases &quot;orders of phenomena&quot; and &quot;domains of order&quot;. These phrases/terms are something like desparate measures since I struggle to clearly state what I mean by them. This seems to be bad/suboptimal language to me but I do not have a replacement at this point.

One inspiration for this language could be Šmajs (which I read between 1995 and 2000), another Foucault's ''The Order of Things'' (which I read much later in Czech).

Another word that comes to mind is ''logos'', but I am not clear what it means. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:26, 20 February 2025 (UTC)

== Life form ==
(To be possibly added to the article, but it can also stay here to support the article.)
Me not having properly analyzed in writing what &quot;life form&quot; is supposed to mean is a gap; the word &quot;form&quot; features in the title of the article and in the article itself. On the other hand, &quot;life form&quot; is in multiple dictionaries per One Look&lt;ref&gt;https://www.onelook.com/?w=life+form&lt;/ref&gt; And yet, the reader perhaps has the right to know which definition I am using, since the dictionaries online differ.

For one thing, I would think &quot;life form&quot; could refer to biological species (verification?), but it is not the main meaning in M-W&lt;ref&gt;[https://www.merriam-webster.com/dictionary/life-form life-form], merriam-webster.com&lt;/ref&gt;. Longman defines life form as a living thing&lt;ref&gt;https://www.ldoceonline.com/dictionary/life-form&lt;/ref&gt;.

The words &quot;form&quot; and &quot;pattern&quot; can perhaps be used interchangeably in some contexts, in some meaning (verify). However, &quot;the forms of life&quot; seems rather different from &quot;the patterns of life&quot; in meaning.

The definition of life form as a living thing would work for this article, except that it seems to point to biological ''individuals'', whereas I am concerned with ''species'' or even higher ''taxa''. When I say that life forms are eliminated, I mean that whole species are eliminated.

After I find more energy, I should look at literature to see how &quot;life form&quot; is used.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:44, 19 March 2025 (UTC)

References:
&lt;references/&gt;

== Short Circuit ==
The idea that an apparently non-biological machine could be considered alive is presented in the 1986 movie {{W|Short Circuit (1986 film)}}. This makes it part of the popular culture, penetrating the popular mind. In that movie, an originally &quot;normal&quot; robot is claimed to &quot;become alive&quot;.

Relevant section: [[Technology as a threat or promise for life and its forms#Technology as a form of life]]. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:57, 24 September 2025 (UTC)</text>
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This original article by Dan Polansky briefly investigates the limits of human progress. Use your critical faculties when reading it; it contains analysis not traced to sources, although one that aims to be as if obvious at least to some readers, depending on general background knowledge currently available to a modern mind. There is a subjective element to this article; a different author would take a different stance.

==Initial considerations==

Human progress can happen in multiple domains:
* Technological progress: more capable technology. Thus, we have ships, steam engine, trains, cars, aircraft, power plants, electrical appliances, computers, the Internet, etc., greatly increasing human capabilities, step by step.
* Scientific progress: more accurate or complete scientific theories, serving as better models of the world. Thus, we have progressed from Ptolemaic astronomy to Kepler, Newton and Einstein. We have progressed from Darwinian theory to modern synthesis, and we have a better map of all species in existence.
* Political progress: more participation on the government, less oppression and more political freedoms. However, some could see monarchy as a real progress.
* Reduction of violence, whether within a state or between states. This can be seen as part of political progress.
* Cultural creativity progress: more cultural creativity in literature, paintings, music, dances, movies, games, etc.

A key observation is that most progress in various domains is enabled by technological progress, which enables a larger human population and also scientific instruments, a camera to take pictures and movies, musical instruments to make more elaborate music than singing along can make, printing of books for easier dissemination, technical means of democracy, etc. Limits of that progress are examined in article [[The limits of technological potential]]. Given our current scientific understanding of the world and our current technology, the technological progress seems to be brief, too likely to be stopped or even reverted in centuries to come. More detail on this question is in that article and for that article.

The limits of human scientific knowledge are given not only by technology but also by human capacity to understand. Even if large population of humans can be sustained on the Earth for next 1,000 years, there is no fundamental guarantee that, say, physics is going to be able to make substantial progress over that period.

The limits of political progress are also given not only by technology. There is no infinite series of deep improvements to be made, a tautology. Beyond mere triviality, the political progress does not need to last for the next 1,000 years.

The limits of cultural progress are also given not only by technology. Culture is not only produced but also consumed by humans. Beyond certain amount of cultural output, the capacity for consumption given by a single human brain and the number of brains becomes overstretched. Thus, ever more cultural forms can be produced but there will be hardly anyone to pay any attention to the output.

==Testability==
Assertions about the existence of limits and their absence have relatively poor testability, especially compared to such scientific theories as Newtonian physics and Einsteinian physics, both of which are plentifully threatened by refutation by a range of observation and experiments.

However, there is still a contrast:
* The statement &quot;there will be no thermonuclear energy production on the Earth&quot; is refutable by possible future events.
* The statement &quot;there will eventually be thermonuclear energy production on the Earth&quot; is much harder to refute; it would seem refuted by an extinction of humankind, but even that would be logically inconclusive since another species could appear later to develop such production. It would be nearly conclusively refuted by no such development occurring before the Earth becomes uninhabitable for living things.

Above, we see that the negative possibilistic hypotheses, whatever their merits, more run the risk of being refuted or sooner so than their positive variants. This would suggest that negative hypotheses, even if wrong, have more of a scientific character, from the falsificationism point of view.

Both negative and positive hypotheses can be made more equally testable by being stated in time-bound terms, e.g. &quot;by year 2050&quot;. Even then, the negative version has better refutability since it can be refuted as soon as the thermonuclear capability arrives. There seems to be something more scientific about the negative hypotheses. There could be a deeper and more general investigation about the strengths and weaknesses of Popperian falsificationism that is here employed.

==A case study of hyperoptimism==

A certain kind of hyperoptimism can be discerned from an article linked below, in the following sentences. This will be useful to frame a discussion.
* &quot;But, if we only do more research and science we can achieve anything we want. [...] Nothing is impossible.&quot;
*: We can't. If we want to fly to the next star, as some do, we can't. If we want to get energy from a thermonuclear reactor on the Earth, as many do and seems much more realistic, this may still be impossible.
* &quot;During my 35 years on this earth I have witnessed unprecedented technological and scientific progress.&quot;
*: He has not. He has seen certain advances but they were not unprecedented in their scale. The inventions of the automobile and the aircraft are much deeper than the invention of computing and the Internet. As for science, there was already Einsteinian physics, and that was already not so deep an improvement on Newtonian physics as the latter was on previous physics, especially on Ptolemaic astronomy. There was probably a huge scientific progress in some quantitative sense, but one must not be mislead by fractal phenomena: a tree that grows increasingly more and increasingly tinier branches and subbranches does not thereby achieve absolute growth out of its bounds.
* &quot;I lack a sense of optimism and the idea that we as humans can achieve anything we want.&quot;
*: That is because humans can't achieve anything they want, fortunately. If they could, someone would surely come up with the idea that threatening to destroy the entire universe would be a nice bargaining tool to have. It is only a mild exaggeration to say that human wants, desires and dreams are unlimited and not necessarily good, in sharp contrast to possibilities. The history has no shortage of humans dreaming of expanding their kingdoms and empires and dominating the world. Destructive desires and cruelty are revealed in behaviors of children, suggesting they are no adult aberrations. Some limits on human possibilities are a bliss, not a curse.
* &quot;the limit of human progress really isn't about technological achievements or scientific progress. It really isn't even about intelligence and creativity. This suggests that the limit of human progress is really all about our limited ability to feel empathy and compassion.&quot;
*: Untrue. The limits of technological achievements are deep and serious. Human empathy and compassion are far from endless, but they alone can do nothing to overcome technological limits.
* 'I think this quote by Carl Sagan illustrates this problem quite well: &quot;It will not be we who reach Alpha Centauri and the other nearby stars. It will be a species very like us, but with more of our strengths and fewer of our weaknesses, more confident, farseeing, capable, and prudent.'
*: Untrue. No superhuman or posthuman species can overcome fundamental physical limits and reach Alpha Centauri (the Earth's nearest star), not even superhuman artificial intelligence, if any. One must assume deep breakthroughs in our physical understanding of the world to believe these sorts of things.
* &quot;Do you think we can solve the great problems of this world with more science and research?&quot;
*: The great problem of this world, the civilization on the Earth, is the sustainability or longevity of the civilization. This problem, if it can be solved, cannot be solved merely with more science and research; it will require policy interventions. Scientific and technological advances will be useful as long as the problem is soluble. If the problem is not soluble, the civilization will revert to a much more primitive state or disappear.

From a sane down-to-earth perspective, the above quoted notions are not credible, as is documented in the article on the limits of technological progress. The terminology of science, which is supposed to be a rational enterprise, is borrowed by pseudo-scientific fantasy called &quot;science-fiction&quot; to create irrational and implausible fantasies of human capability and possibilities, sometimes not even under the guise of &quot;science-fiction&quot; but rather as &quot;future studies&quot;.

==See also==
* [[The limits of technological potential]]
* [[Technology as a threat or promise for life and its forms]]

==Books==
* ''Unlimited Progress: The Grand Delusion of the Modern World by Dennis Knight Heffner'', 2010 -- decent book on first impression, containing general analysis as well as specific details in various domains such as transportation
* ''Entrepreneurship and Economic Progress'' by Randall Holcombe, 2007 -- cornucopian implausibilities

==Further reading==
* [[W:Progress]]
* [[W:Malthusianism]] * [[W:Paul R. Ehrlich]] * [[W:The Population Bomb]] * [[W:The Limits to Growth]] * [[Wikisource:An Essay on the Principle of Population/Chapter I]]
* [[W:Cornucopianism]] * [[W:Julian Simon]] * [[W:The Ultimate Resource]]
* [[W:The Better Angels of Our Nature]] -- about a decline in violence
* [https://richarddawkins.net/2014/03/the-limits-of-human-progress/ The limits of human progress] by Nunbeliever, 2014, richarddawkins.net
* [https://www.aier.org/article/how-keith-flint-demonstrated-that-there-are-no-limits-to-progress/ How Keith Flint Demonstrated that There are No Limits to Progress | AIER] -- cornucopian implausibilities

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This article by Dan Polansky describes book ''Mind Children: The Future of Robot and Human Intelligence'' by [[Hans Moravec]], 1988. The book is mentioned in the Encyclopedia Britannica article on the author, making it somewhat notable. The book can perhaps be best described as science-fiction without a plot, packed with more interesting ideas than most science-fiction novels, albeit presented as a description of actual future.

Page references in this article are for the paperback edition, {{ISBN|0-674-57618-7}}.

==Destruction of living things and humans==
The preface suggests that robots will be developed that will be comfortable with destroying humans and perhaps other living things as well (page 1).[https://books.google.com/books?id=56mb7XuSx3QC&amp;pg=PA1] The language is not wholly explicit; the wording used is that &quot;They [the genes] have produced a weapon so powerful it will vanquish the losers and winners alike&quot;, and &quot;the human race has been swept away by the tide of cultural change, usurped by its own artificial progeny&quot;. Here, &quot;artificial progeny&quot; refers to robots. A possible consolation is that some of these robots will be emulating individual human minds, thereby ensuring their continuing quasi-existence; see section [[#Mind uploading|Mind uploading]].

==The mind children metaphor==
The metaphor of &quot;mind children&quot; has powerful rhetorical effect. It implies that since humans are fine to pass the future to their biological children, they should be equally fine to pass it to the children of the mind, the superintelligent thinking machines or robots. Marvin Minsky is happy to pass the future to them, and refers to Hans Moravec and his mind children metaphor.&lt;ref&gt;[http://web.archive.org/web/20240416110125/https://web.media.mit.edu/~minsky/papers/sciam.inherit.html Will Robots Inherit the Earth?] by Marvin Minsky, 1994, archived at archive.org&lt;/ref&gt;

Moravec's use of the mind children metaphor seems to be criticized by Al-Mafraje 2023.&lt;ref&gt;[https://uia.brage.unit.no/uia-xmlui/bitstream/handle/11250/3072513/no.uia%3Ainspera%3A146525594%3A2111965.pdf?sequence=1 From Brave New World to Ready Player One; yesterday’s dystopias as tomorrow’s utopias]&lt;/ref&gt;

==Artificial intelligence predictions==
The book predicts human-level intelligence for supercomputers by 2010 and for personal computers by 2030 (pages 64 and 68).

==Self-improving thinking machines==
The book says: &quot;Sooner or later our machines will become knowledgeable enough to handle their own maintenance, reproduction and self-improvement without help. When this happens, the new genetic takeover will be complete. Our culture will then be able to evolve independently of human biology and its limitations, passing instead directly from generation to generation of ever more capable intelligent machinery.&quot; (page 4).[https://books.google.com/books?id=56mb7XuSx3QC&amp;pg=PA4&amp;dq=%22Sooner+or+later+our+machines+will+become+knowledgeable+enough+to+handle+their+own+maintenance%22&amp;source=bl]

And, &quot;A postbiological world dominated by self-improving thinking machines will be as different from our own world of living things as this world is different from the lifeless chemistry that preceded it. A population consisting of unfettered mind children is quite unimaginable. We are going to try to imagine some of the consequences anyway.&quot; (page 5)

Further, &quot;Eventually humans [...] will become unnecessary [...] as the scientific and technical discoveries of self-reproducing superintelligent mechanisms are applied to making themselves smarter still.&quot; (page 102)

==Mind uploading==
The book predicts mind uploading, a process by which a simulation of a human mind is transferred to a human-like robot (pages 108-112).[https://books.google.com/books?id=56mb7XuSx3QC&amp;pg=PA108] The patterns of activity of the person's real biological brain are scanned and based on the observed patterns, a faithful simulation is created. This would enable extreme longevity by allowing the mind to transfer between a succession of robots, each new robot replacing a worn-out old one. The result would be not a true immortality but quasi-immortality. The book calls this &quot;transmigration&quot;.

One consequence the book predicts is a 1000fold increase of mind speed since the emulating hardware would not need to keep the emulation as slow as the real biological phenomenon (page 112).[https://books.google.com/books?id=56mb7XuSx3QC&amp;pg=PA112]

A related term is &quot;whole brain emulation&quot;.

In a 1986 article, Moravec mentions that &quot;Vernor Vinge devised a particularly slow and gentle [mind] transfer method in True Names, his novel of the near future.&quot;&lt;ref name=&quot;moravec1986&quot;/&gt; True Names is from 1981.

Mind uploading via &quot;brain surgeon&quot; is already described in Moravec (1979).&lt;ref&gt;[http://web.archive.org/web/20230210114245/https://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1978/analog.1978.html Today's Computers, Intelligent Machines and Our Future] by Hans Moravec, 1979, [[wikidata:Q115765733|wikidata]], archived at archive.org&lt;/ref&gt;

==Pattern-identity position==
Related to mind uploading is Moravec ''pattern-identity'' position, which he contrasts to ''body-identity'' position. He starts by quoting someone's objection: &quot;Regardless of how the copying is done, the end result will be a new person.&quot; (page 116)[{{Gburl|56mb7XuSx3QC|PA116}}] This is in reference to mind uploading, called &quot;transmigration&quot;. The book goes on to argue that living bodies keep on renewing themselves, old cells dying and new cells being created, and therefore, what creates their identity across time are the continuing patterns. This line of argument leads him to claim that a perfect simulation of what was previously human mind in a biological body taking place in a human-like robot is pattern-identical to the original and thus identical. The idea is briefly mentioned in Moravec article online, with the &quot;pattern Identity&quot; spelling.&lt;ref name=moravec1986&gt;[https://web.archive.org/web/19991012191440/https://frc.ri.cmu.edu/~hpm/project.archive/general.articles/1986/dualism.html Dualism through Reductionism] by Hans Moravec, claimed to be from 1986, archived at archive.org&lt;/ref&gt; Bamfordand and Danaher mention Moravec and find similar treatment in Kurzweil (2000), Koene (2011) and Goertzel and Ikle (2012).&lt;ref&gt;[https://philpapers.org/archive/DANTOP.pdf Transfer of Personality to a Synthetic Human(‘Mind Uploading’) and the Social Construction of Identity] by Sim Bamfordand John Danaher, 2017&lt;/ref&gt;

==Performance boost==
As per above, the book predicts is a 1000fold increase of mind speed since the emulating hardware would not need to keep the emulation as slow as the real biological phenomenon (page 112).[https://books.google.com/books?id=56mb7XuSx3QC&amp;pg=PA112]

A similar boost appears in Moravec (1977): 'Advantages become apparent as soon as the process is complete.
Somewhere in your machine is a control labelled &quot;speed&quot;.  It was initially set to &quot;slow&quot;, to enable the simulations to remain synchronized with the rest of your old brain, but now the setting is changed to &quot;fast&quot;. You can communicate, react and think at a thousand times your former rate. But this is only a minor first step.'.&lt;ref name=&quot;moravec1977&quot;/&gt;

==Space colonization==
Moravec envisions space colonization of other galaxies, going beyond our galaxy, the Milky Way. Since, as per Moravec, &quot;Sooner or later an unstoppable virus deadly to humans will evolve, or a major asteroid will collide with the earth, or the sun will expand, or we will be invaded from the stars, or a black hole will swallow the galaxy. The bigger, more diverse and competent a culture is, the better it can detect and deal with external dangers&quot;. (Similar passage is found in Moravec 1977 article.&lt;ref name=&quot;moravec1977&quot;&gt;[https://web.archive.org/web/20000829111714/https://frc.ri.cmu.edu/~hpm/project.archive/general.articles/1977/smart Intelligent machines: How to get there from here and What to do afterwards] by Hans Moravec, 1977, archived at archive.org ([[Wikidata:Q115765098|wikidata]])&lt;/ref&gt;) The passage is intended to show that technological progress is necessary to avoid dangers, and since one of the dangers is a black hole swallowing the galaxy, the remedy must be to get beyond the galaxy. Further, &quot;Resurrecting one small planet should be child's play long before our civilization has colonized even its first galaxy&quot; (p. 124).&quot;

&quot;Eventually humans [...] will become unnecessary [...] as the scientific and technical discoveries of self-reproducing superintelligent are applied to making themselves smarter still. The new creations [...] will explode into the universe, leaving us behind in a cloud of dust.&quot; (page 102) The vague phrasing &quot;explode into the universe&quot; suggests the superintelligent machines will expand far beyond the Solar System.

Further evidence is this: &quot;A spectrum of scales will come to exist--from [...] to star-spanning superminds for big problems&quot; (page 125). It is not clear what &quot;star-spanning&quot; refers to, though: a supermind that is part of a star? Or a supermind that is spread across multiple star systems? Perhaps it refers to a neutron star turned into a supercomputer, as per &quot;immense simulator (I imagine it made out of a superdense neutron star)&quot;.

Further, &quot;The human race will expand into the solar system before long, and human-occupied space colonies will be part of that expansion.&quot; (page 101) And further, &quot;Imagine the immensely lucrative robot factories that could be built in the asteroids&quot;.

==Development beyond imagination==
Moravec seems to envision a world of thinking machines that will be beyond human imagination: &quot;A postbiological world dominated by self-improving thinking machines will be as different from our own world of living things as this world is different from the lifeless chemistry that preceded it. A population consisting of unfettered mind children is quite unimaginable. We are going to try to imagine some of the consequences anyway.&quot; (page 5)

==Resurrection==
The notion that faithful simulation of a human mind in a machine is as good as the original leads the book to conceptualize resurrection. Thus, &quot;Wholesale resurrection may be possible through the use of immense simulators.&quot; (page 123) And, &quot;It might be fun to resurrect all the past inhabitants of the earth this way and to give them the opportunity to share with us in the (ephemeral) immortality of transplanted minds.&quot; (page 124)

The above will be enabled by feats of simulation, for which see the next section.

The book's treatment of resurrection is covered in The New Atlantis article.&lt;ref&gt;[https://www.thenewatlantis.com/futurisms/resurrecting-dead Resurrecting the Dead] by Adam Keiper, 2010, thenewatlantis.com&lt;/ref&gt;

==Simulation==
The book predicts incredible feats of simulation. In mind uploading, the whole brain of a human can be simulated in a human-like robot, faithful enough that the human can consider the result to be identical to themselves. But single human is not enough: &quot;Now, imagine an immense simulator (I imagine it made out of a superdense neutron star) that can model the whole surface of the earth on an atomic scale and can run time forward and back and produce different plausible outcomes by making different random choices at key points in its calculation. Because of the great detail, this simulator models living things, including humans, in their full complexity.&quot; (page 123, quoted in the &quot;No Loyalty to DNA&quot; review below)

==Unstopability of technological development==
Moravec argues that technological development of thinking machines is unlikely to be stopped, as a result of friendly or unfriendly competition between nations, and since these machines are key for very long term survival. Since &quot;If the United States were to unilaterally halt technological development (an occasionally fashionable idea), it would soon succumb either to the military might of unfriendly nations or to the economic success of its trading partners. Either way, the social ideals that lead to the decision would become unimportant on the world scale.&quot; (page 101) And further, &quot;If, by some unlikely pact, the whole human race decided to eschew progress, the long-term result would be almost certain extinction. The universe is one random event after another. Sooner or later an unstoppable virus deadly to humans will evolve, or a major asteroid will collide with the earth, or the sun will expand, or we will be invaded from the stars, or a black hole will swallow the galaxy. The bigger, more diverse and competent a culture is, the better it can detect and deal with external dangers&quot;.

==Nuclear war==
As per the book, &quot;Engaged for billions of years in a relentless, spiraling arms race with one another, our genes have finally outsmarted themselves. They have produced a weapon so powerful it will vanquish the losers and winners alike. This device is not the hydrogen bomb--widespread use of nuclear weapons would merely delay the immensely more interesting demise that has been engineered.&quot;

What the metaphors describe is the biological evolution of humans, who then are about to create a thinking machine, which will then obliterate its makers. What is remarkable is the idea that this will happen even in the case of a nuclear war, as if the resulting technological and social setback were just a minor step back to be overcome again given geological time. There is no idea of a limited window of opportunity.

==Nanotechnology==
The book assumes remarkable development in nanotechnology: &quot;Before long, conventional technologies, miniaturized down to the atomic scale, and biotechnology, its molecular interactions understood in detailed mechanical terms, will have merged into a seamless array of techniques encompassing all materials, sizes and complexities. Robots will then be made of a mix of fabulous substances, including, where appropriate, living biological materials.&quot; Apparently, no arbitrary combination, mixing and achievement is off limits.

==Immortality via accelerating time==
The extreme longevity achieved via mind uploading is apparently not enough. The book wants more and thinks it can be achieved. The book speculates that &quot;subjective infinity&quot; could be achieved by increasingly accelerating time at the end of the universe (pages 147-149). Indeed, in exponentially accelerating subjective time, a subjective sense of infinite life can be achieved in finite amount of time; think of Achilles and Tortoise. The book refers the ideas back to Freeman Dyson's ''Infinite in All Directions'' (1988) and Barrow and Tipler's ''The Anthropic Cosmological Principle''. Similar ideas were further developed by Tipler in his later ''The Physics of Immortality'', not referenced by Moravec. Similar ideas were developed as part of [[W:Dyson's eternal intelligence|Dyson's eternal intelligence]] concept in 1979 in Dyson's article ''[[Wikidata:Q21709592|Wikidata:Time without end: Physics and biology in an open universe]]''.

==Culture==
Moravec uses the word &quot;culture&quot; to cover not only human phenomena but also those of the superintelligent thinking machines. For instance, &quot;the human race has been swept away by the tide of cultural change, usurped by its own artificial progeny&quot;. The result is a curious rhetorical effect: without Moravec context, one would not use the phrase &quot;cultural change&quot; to refer to replacement of biologically embodied humans with artificial thinking machinery.

==Collaborators==
The book was edited with the help of Harvard Press. Reviews of drafts were written by Vernon Vinge, a singularitarian. Referees who provided comments included Rod Brooks, Richard Dawkins, Kee Dewdney, Bruce Donald, John Dowling, Bob Forward, John McCarthy, Pamela McCorduck and others.

==Criticism==
Original criticism of the book follows:
* Generally, the book belongs to the field of science-fiction even if it does not present itself as such.
* Development of human-level intelligence in silicon may be impossible; we do not know. There are limits of what can be done in physics, and the limits of what can be done in carbon, hydrogen, oxygen and other elements of living things via growth from tiny biological cells may differ from the limits of what can be done in silicon via manufacturing and the differences in the limits may be unfavorable to silicon. If it is not so, the book should analyze why not, but it does not do that. The book does nothing to show possibility. Extrapolation from temporary exponential growths of computing capability into many decades into future is no solid science; if experience teaches us anything, all apparent exponential growths in nature are in fact logistic growths, S-curve growths.
* In retrospect, the prediction of human-level intelligence for supercomputers by 2010 already failed. The prediction was made by extrapolation of technology growth data points. This provides tangible evidence for how problematic such extrapolation is.
* Mind uploading and emulation in silicon may be impossible. The book does nothing to show possibility.
* Space colonization, including Mars, may be impossible. The book does nothing to show possibility.
* Simulation of the surface of the whole Earth including all living things in a neutron star sees to be a pure unfettered fantasy.
* Immortality via accelerating time approaches pure speculation, whether done by Moravec or Tipler.
* Humans may dislike being uploaded into machines as mere simulacra and may take steps to prevent silicon-based machinery from taking over the biology.
* No mention is made of the need of the machines to preserve the Earth's biosphere in its actual form to sustain the planetary homeostasis (which simulated analogs cannot do), to ensure sufficient energy sources to last for ages, to avoid hugely disruptive changes to planetary environments, and to ensure material recycling of machine bodies or run the risk of running out of mined raw materials, in contrast to the marvelous recycling of matter achieved by the actual living things. All these problems are either supposed to not exist or to be soluble with the use of the developed machine superintelligence, none of which is necessarily true. The biosphere and the living things are largely left without mention, except when they appear in the word &quot;postbiological&quot;, which implies their absence or irrelevance.
* Dangerous technological progress can be stopped as a result of international treaties, provided enough powerful countries agree and are ready to enforce their will to stop the lethal threat to genuine biological humans (as opposed to simulacra) against other countries that disagree. The requirement of developing thinking machines to get the minds out of this galaxy (since, beware of the black hole) is very unrealistic given current knowledge.
* Expanding on the above, some entity very fearful of technological progress endangering biosphere could even launch a thermonuclear war. The thinking could be as follows. The consequences of a thermonuclear war are going to be very bad for the biosphere, including humankind and other species. The destruction would be huge. But even so, humans may be able to survive as a species and it may still be better than allowing technological entities foreign to biology erase the biosphere as allegedly obsolete, plodding (evolving too slowly), etc. (This is perhaps not entirely convincing and would require a solid analysis.)

==Reception==
Joseph Weizenbaum warned that &quot;Mind Children&quot; was as dangerous as &quot;Mein Kampf&quot;&lt;ref&gt;[https://www.washingtonpost.com/wp-srv/style/books/reviews/robot1108.htm Robot: Mere Machine to Transcendent Mind (Books &amp; Reading: Book Reviews)], 1998, washingtonpost.com&lt;/ref&gt;&lt;ref name=platt1995&gt;[https://www.wired.com/1995/10/moravec/ Superhumanism] by Charles Platt, 1995, wired.com&lt;/ref&gt;&lt;ref&gt;[https://www.washingtonpost.com/archive/entertainment/books/1998/11/08/who-can-replace-a-man/a14ae936-f204-4490-a9a0-fe11f1925280/ WHO CAN REPLACE A MAN?] by Charles Platt, 1998, washingtonpost.com&lt;/ref&gt;&lt;ref&gt;[https://ubdocs.aau.at/open/voll/tewi/AC00472126.pdf &quot;KUNSTLICHE INTELLIGENZ&quot; ALS ENDLÖSUNG DER MENSCHENFRAGE] by Joseph Weizenbaum, 1990, ubdocs.aau.at&lt;/ref&gt;. Weizenbaum further criticized Mind Children in 1998&lt;ref&gt;[https://www.weizenbaum-library.de/server/api/core/bitstreams/12285fe7-2b0c-46e9-9966-21f0f5f15bd4/content The Image of Man in Artificial Intelligence, A Conversation with Joseph Weizenbaum] by Bernhard Pörksen&lt;/ref&gt;.

Roger Penrose&lt;ref&gt;[https://www.nybooks.com/articles/1990/02/01/matter-over-mind/ Matter Over Mind] (a review of Mind Children) by Roger Penrose, 1990, nybooks.com&lt;/ref&gt; and Poovan Murugesan were critical of Mind Children&lt;ref name=platt1995/&gt;.

Moravec mind uploading was covered in detail, including a full quote, in Jerry Mander's ''In the Absence of the Sacred'', 1991, a book critical of the uncritical acceptance of all development of new technology by the Western industrial civilization.

Moravec mind uploading was taken note of in Hayles 1999:&lt;ref&gt;[https://press.uchicago.edu/Misc/Chicago/321460.htm Katherine Hayles, How We Became Posthuman, prologue], press.uchicago.edu&lt;/ref&gt; &quot;Writing nearly four decades after Turing, Hans Moravec proposed that human identity is essentially an informational pattern rather than an embodied enaction. The proposition can be demonstrated, he suggested, by downloading human consciousness into a computer, and he imagined a scenario designed to show that this was in principle possible.&quot; For some reason, Hayles speaks of downloading rather than uploading.&lt;!-- TBD: Moravec himself speaks of &quot;downloading&quot; in one issue of Extropy magazine; find the issue and link it --&gt;

==Translations==
The book was translated into multiple languages&lt;ref name=cmumc&gt;https://www.ri.cmu.edu/publications/mind-children-the-future-of-robot-and-human-intelligence/&lt;/ref&gt;:
* German: ''Mind children: der Wettlauf zwischen menschlicher und künstlicher Intelligenz'', 1990&lt;ref&gt;https://www.deutsche-digitale-bibliothek.de/item/KGLSC2BMUZRMCWMLZKYS76LAK3IIV2GP&lt;/ref&gt;
* Portuguese: ''Homens e Robots O futuro da inteligencia humana e robótica'', 1992&lt;ref&gt;https://www.amazon.com.br/Homens-Robots-futuro-inteligencia-rob%C3%B3tica/dp/9726622719&lt;/ref&gt;
* French: ''Une Vie après la vie'', 1992&lt;ref&gt;https://www.amazon.fr/Une-Vie-apr%C3%A8s-Hans-Moravec/dp/2738101607&lt;/ref&gt;
I failed to verify other translations indicated on the CMU page&lt;ref name=cmumc/&gt; for the book.

==References==
&lt;references/&gt;

==Further reading==
* [http://web.archive.org/web/20221224011623/https://frc.ri.cmu.edu/~hpm/book88/MC.details.html Book info for Mind Children: The Future of Robot and Human Intelligence, Hans Moravec, 1988], frc.ri.cmu.edu, archived at archive.org
* [http://web.archive.org/web/20221218091406/https://frc.ri.cmu.edu/~hpm/book88/reviews/ Book Reviews of Mind Children: the future of robot and human intelligence], frc.ri.cmu.edu, archived at archive.org
** [http://web.archive.org/web/20221218091406/https://frc.ri.cmu.edu/~hpm/book88/reviews/881023.WashPost.html ANYTHING WE CAN DO THEY CAN DO BETTER] by Noel Perrin, 1988, Washington Post, frc.ri.cmu.edu, archived at archive.org
** [http://web.archive.org/web/20221218093149/https://frc.ri.cmu.edu/~hpm/book88/reviews/890101.NYT.html THE SOULS OF THE NEW MACHINES] by M. Mitchell Waldrop, 1989, New York Times, frc.ri.cmu.edu, archived at archive.org
** [http://web.archive.org/web/20221218091411/https://frc.ri.cmu.edu/~hpm/book88/reviews/890109.NewYorker.html No Loyalty to DNA], The New Yorker, 1989, frc.ri.cmu.edu, archived at archive.org -- has multiple quotes
* {{W|Hans Moravec#Mind Children}}, wikipedia.org
* {{W|Mind uploading}}, wikipedia.org
* [https://www.nature.com/articles/336284a0.pdf?origin=ppub Strolling up the garden path] by Igor Aleksander, 1988, nature.com, a review of Mind Children
* [https://www.wired.com/1995/10/moravec/ Superhumanism] by Charles Platt, 1995, wired.com
* [https://www.nybooks.com/articles/1990/02/01/matter-over-mind/ Matter Over Mind] (a review of Mind Children) by Roger Penrose, 1990, nybooks.com
* [https://monoskop.org/images/5/59/Dixon_Joan_Broadhurst_Cassidy_Eric_J_eds_Virtual_Futures_Cyberotics_Technology_and_Posthuman_Pragmatism.pdf Virtual Futures: Cyberotics, Technology and Post-human Pragmatism], edited by Joan Broadhurst Dixon, Eric Cassidy, 1998, monoskop.org
* [https://ntrs.nasa.gov/api/citations/19940022855/downloads/19940022855.pdf The Universal Robot] in Vision-21 Interdisciplinary Science and Engineering in the Era of Cyberspace, by Hans Moravec, 1993, nasa.gov -- presents some of the ideas from Mind Children
* [https://www.hup.harvard.edu/books/9780674576186 Mind Children — Harvard University Press], hup.harvard.edu -- has a short description of the book
* [https://www.goodreads.com/en/book/show/648195.Mind_Children Mind Children: The Future of Robot and Human Intelligence by Hans Moravec], goodreads.com -- has over 22 reviews
* [https://github.com/Extropians/Extropy/blob/master/Extropy-02_Winter-Jan-1989.pdf A review of Mind Children] in Extropy #2 by Max O'Connor/More, Jan 1989, github.com
* [https://religiondispatches.org/the-cult-of-kurzweil-will-robots-save-our-souls/ The Cult of Kurzweil: Will Robots Save Our Souls?] by Robert M. Geraci, 2011, religiondispatches.org
* [https://www.thenewatlantis.com/futurisms/why-transhumanism-wont-work Why Transhumanism Won’t Work] by Adam Keiper apparenty hosting guest contributor Mark A. Gubrud, 2010, thenewatlantis.com

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Author: Dan Polansky

This article describes Hans Moravec, an Austrian-born&lt;ref name=morcv&gt;[https://web.archive.org/web/20230419220906/https://www.frc.ri.cmu.edu/~hpm/hpm.cv.html Hans Moravec CV] at frc.ri.cmu.edu (archive.org)&lt;/ref&gt; Canadian&lt;ref name=brit/&gt; roboticist (with American permanent residence&lt;ref name=morcv/&gt;), researcher of artificial intelligence and a book author. The article takes advantage of Wikiversity being less strict about content inclusion than Wikipedia. He is a living person, so extreme care is required as for accuracy and avoidance of mistakes.

He is noted for his book ''[[Mind Children]]'' from 1988 and his book ''Robot'' from 1999&lt;ref name=brit&gt;[https://www.britannica.com/biography/Hans-Moravec Hans Moravec], britannica.com&lt;/ref&gt;.

His publication list page has a lot of online articles capturing some of his thought and philosophy.

== Life ==
Moravec was born in Kautzen, Austria (near Bohemian border), moved to Canada and eventually to the U.S.&lt;ref name=morcv/&gt;. He is university-educated with a PhD in computer science&lt;ref name=morcv/&gt;. He was employed at universities as well as private corporations&lt;ref name=morcv/&gt;.

As a piece of trivia, &quot;Moravec&quot; is a Czech surname, and &quot;c&quot; is in Czech pronounced a little bit like the German &quot;z&quot;, perhaps like English &quot;ts&quot;. The English speakers seem to pronounce the final &quot;c&quot; as &quot;k&quot;. Perhaps his ancestors were of Bohemian origin.

== Publications ==
Hans Moravec is the author of the following books available off-line:
* ''Mind Children: The Future of Robot and Human Intelligence'', 1988, Harvard University Press
* ''Robot: Mere Machine to Transcendent Mind'', 1999, Oxford University Press

Hans Moravec is the author of the following publications available on-line, chronologically organized (list incomplete):
* [https://web.archive.org/web/20010710005503/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1977/smart INTELLIGENT MACHINES How to get there from here and What to do afterwards] by Hans Moravec, 1977 (at archive.org)
* [https://web.archive.org/web/20010710010808/https://frc.ri.cmu.edu/~hpm/project.archive/general.articles/1978/analog.1978.html Today's Computers, Intelligent Machines and Our Future] by Hans Moravec, 1979 (at archive.org)
* [https://web.archive.org/web/20010711190211/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1986/dualism.html Dualism through Reductionism] by Hans Moravec, 1986 (at archive.org) -- 5 000 words
* [https://web.archive.org/web/20010711190211/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1986/drexler.mss  Engines of Creation by K. Eric Drexler (book review)] by Hans Moravec, 1986 (at archive.org)
* [https://web.archive.org/web/20010415204844/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1989/WPI.ltx The Robot as Liberation from Human Nature] by Hans Moravec, 1989 (at archive.org) -- 16 800 words, &quot;Adapted from the author's book Mind Children: [...]&quot;
* [https://web.archive.org/web/20010717073318/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1995/RobotMind.talk.html Robots Inherit Human Minds] by Hans Moravec, 1994 (at archive.org) -- 5 400 words
* [https://web.archive.org/web/20010717060630/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1997/970128.nosense.html The Senses Have no Future] by Hans Moravec, 1997 (at archive.org)
* [https://web.archive.org/web/20010603152209/http://www.transhumanist.com/volume1/moravec.htm When will computer hardware match the human brain] by Hans Moravec, 1997 (at archive.org)
* [https://web.archive.org/web/20010717060307/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1998/SimConEx.98.html Simulation, Consciousness, Existence] by Hans Moravec, 1998 or 1999 (at archive.org)
* [https://web.archive.org/web/20010717060307/http://www.frc.ri.cmu.edu/~hpm/project.archive/robot.papers/1999/SciAm.scan.html Rise of the Robots] by Hans Moravec, 1999 (at archive.org)
* [https://dl.acm.org/doi/10.1145/944217.944218 Robots, after all] by Hans Moravec, 2003, dl.acm.org (available as PDF)

The above is a small selection from [https://web.archive.org/web/20010710010808/https://www.frc.ri.cmu.edu/~hpm/hpm.pubs.html Hans Moravec Publications], frc.ri.cmu.edu (at archive.org).

==Views==
As early as 1977, Moravec predicted that robots will displace humans and imagined (with the help of &quot;brain surgeon&quot;) what is now known as mind uploading&lt;ref name=mor77&gt;[https://web.archive.org/web/20010710005503/http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1977/smart INTELLIGENT MACHINES How to get there from here and What to do afterwards] by Hans Moravec, 1977 (at archive.org)&lt;/ref&gt;. He envisioned that the increases of robot intelligence and their spread through the universe would be able to &quot;convert the entire universe into an extended thinking entity.&quot;&lt;ref name=mor77/&gt; He elaborated on these ideas in Mind Children 1988 and perhaps in Robot 1999 (I have not read the latter).

==Moravec's paradox==
Moravec's paradox is named after Hans Moravec. It is the observation or notion that human sensori-motor skills will turn much harder to emulate or reimplement in machine than cognitive skills. That is to say, what in humans is no special feat is going to be great feat for computers, or actually robots. For instance, for a human to be able to clean/wash dishes without breaking them it relatively easy, no occasion for awarding a medal, whereas playing chess well is a matter of specific achievement (worthy a medal or other award). And computers are now able to play chess better than humans by exploring the game tree using the right kind of pruning and other software techniques, taking advantage of the raw computing power of the hardware as well. As for numerical computation and symbolic algebra, computers greatly outperform humans (one can check e.g. Wolfram Alpha online).

Example article using the term: [https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(23)01129-7/fulltext Moravec's paradox and the fear of job automation in health care] by Anmol Arora, 2023, the Lancet.

==See also==
* [[Mind Children]]

==References==
&lt;references /&gt;

==Further reading==
About Hans Moravec by others (including interviews):
* {{W|Hans Moravec}}, wikipedia.org
* {{W|Moravec's paradox}}, wikipedia.org
* [https://www.britannica.com/biography/Hans-Moravec Hans Moravec], britannica.com
* [https://www.wired.com/1995/10/moravec/ Superhumanism] by Charles Platt, 1995, wired.com
* [https://www.pbs.org/wgbh/nova/robots/moravec.html NOVA Online | Bomb Squad | Hans Moravec], Oct 1997 -- NOVA interviewed Moravec
* [https://www.davidjaybrown.com/blog/hans-moravec/ Hans Moravec | Mavericks of the Mind], 16 Nov 2011 -- David Jay Brown interviews Hans Moravec

Hans Moravec own publications (see [[#Publications]]):
* [https://web.archive.org/web/20010710010808/https://www.frc.ri.cmu.edu/~hpm/ Hans Moravec], frc.ri.cmu.edu, a home page
* [https://web.archive.org/web/20010710010808/https://www.frc.ri.cmu.edu/~hpm/hpm.pubs.html Hans Moravec Publications], frc.ri.cmu.edu
* [https://www.ri.cmu.edu/pubs/?authors-first-last-and-separated=Hans+Moravec Publications - Robotics Institute Carnegie Mellon University - search for Hans Moravec], ri.cmu.edu

Videos:
* [https://www.youtube.com/watch?v=4eVv01xOoSo&amp;pp=ygUMSGFucyBNb3JhdmVj ict Hans Moravec robotics 1997] by KLEURNET INTERVIEWS ENGLISH, youtube.com -- a 20-minute interview with Moravec</text>
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This article by Dan Polansky investigates various sorts of hedonism—seeking pleasure as an ultimate aim—and their possible criticism and defense.

==Definition of hedonism==

A broad definition of &quot;hedonism&quot; could be this. A hedonism is any of various stances or doctrines that link pleasure to a person's ultimate pursuit, the &quot;intrinsic good&quot;, the &quot;intrinsic value&quot;, or that which is &quot;morally right&quot;. Thus, a hedonism is a stance that links A to B, where A is &quot;my pleasure&quot;, &quot;the largest pleasure of the largest numbers&quot;, and the like, and B is &quot;that which I actually ultimately pursue&quot;, &quot;that which I ought to ultimately pursue&quot;, &quot;that which is of intrinsic value as opposed to instrumental value&quot; or even &quot;that which is intrinsic value&quot;.

'''Descriptive hedonism, normative hedonism, evaluative hedonism, motivational hedonism, psychological hedonism, and elective hedonism''': Various sorts of hedonism can be distinguished depending on whether the hedonism speaks of what is the case or of what ought to be the case. Stanford Encyclopedia of Philosophy's article &quot;Hedonism&quot; (further &quot;SEP&quot;) speaks of &quot;'''normative hedonism'''&quot;, &quot;'''motivational hedonism'''&quot;, and &quot;'''psychological hedonism'''&quot;, focusing on the former two, mentioning the last one only as a superclass of motivational hedonism. I am rather unhappy with this terminology, and introduce a slightly modified version of it: &quot;descriptive hedonism&quot;, &quot;evaluative hedonism&quot;, &quot;normative hedonism&quot;, and &quot;elective hedonism&quot;. My notion of normative hedonism is distinct from the one of SEP: a hedonism is normative if it speaks of what &quot;ought to be the case&quot;, or if it defines &quot;morally right&quot; and &quot;morally wrong&quot;. By contrast, an evaluative hedonism is, by my stipulation of the term, a doctrine that speaks of &quot;intrinsic value&quot; rather than &quot;morally right&quot;. Thus, a person can be called an evaluative hedonist if he chooses pleasure as his ultimate pursuit for his conviction that pleasure is the only thing of &quot;intrinsic value&quot;, whether his own pleasure or the largest pleasure of the largest numbers, or of the sort. Finally, I stipulate an &quot;elective hedonism&quot; as a stance of a person who says that he has freely chosen to pursue his own pleasure, the largest pleasure of the largest numbers, or whatever, without saying anything about &quot;morally right&quot;, &quot;intrinsic value&quot;, &quot;highest good&quot;, and the like. In particular, an &quot;elective egoistic hedonist&quot; says this: &quot;I have freely chosen to pursue my own pleasure as my ultimate aim&quot;.

'''Egoistic hedonism, universalistic hedonism''': The division into &quot;egoistic hedonism&quot; and &quot;universalistic hedonism&quot; refines hedonism by answering the question &quot;whose pleasure?&quot;. A hedonism is egoistic if it says that the person's pleasure is his ultimate aim, ought to be his ultimate aim, or whatever else a hedonism can be saying of pleasure. A hedonism is universalistic if it says that the largest pleasure of the largest numbest or the like is the person's ultimate aim, ought to be his ultimate aim, what not. A normative universalistic hedonism is identical or similar to utilitarianism of J. S. Mill. In this article, the main focus is on varieties of egoistic hedonism.

== Definition of pleasure ==
Pleasure seems hard to define. It could be defined as &quot;good feeling a person has&quot; as implied in the phrases &quot;I feel good&quot; and &quot;it feels good&quot;, but it only begs the question of what is meant by &quot;good&quot;. It could be defined as &quot;a feeling that seems worthy of seeking for its own sake&quot;, with the emphasis that it &quot;seems worthy&quot; rather than &quot;being worthy&quot;. This abstract definition can be supplemented by listing things that people do in order to feel pleasure, such as eating ice cream, scratching an itch, watching movies, doing sports, playing games, solving puzzles, going places, or copulating, and by listing events that trigger pleasure in people, such as learning that one's mother's surgery went well, or that a favorite sports team has won a game. A person who is pleased or feels pleasure can show a distinct expression on their face, which can further help establish what is meant by &quot;pleasure&quot; in the language community. Furthermore, physical pain and its analogues including anguish are ranked as displeasure and automatically fed into the value of &quot;pleasure&quot; with negative sign in the various definitions of hedonism: they subtract from the felt pleasure. One could define a variety of hedonism that disregards pain and only counts pleasure, but it is doubtful that a living person ever proposed such a variety in earnest. One could further investigate the semantic relationship of &quot;pleasure&quot; to &quot;happiness&quot;, &quot;gladness&quot;, &quot;joy&quot;,  and &quot;merriness&quot;, a task that I mostly give up on, assuming that most of these words are hyponyms of pleasure, being more specific. These words are sometimes used synonymously, but not all these candidate synonymies are plausible from the standpoint of customary usage of language: a person can enjoy eating ice cream without being merry. This short sketch, as imperfect as it may be, seems better than no attempt at a definition at all.

==Criticism==

'''Elective egoistic hedonism''' can be criticized above all for its being immoral, in the rough and broad sense of harmful to other people or society. The sort of hedonism so criticized is both short-term and long-term hedonism; term does not matter; what matters is that it is an egoistic hedonism or aiming at one's own pleasure as the only ultimate aim, or self-pleasure-seeking. While some people feel displeased with the anticipatory idea of their committing immoral acts and also feel displeased in retrospect, experience shows that not all people are displeased with their performing acts harmful to other people and society in general, such as groundless killing of another person on a whim. 

Elective egoistic hedonism can achieve morality, so some authors[who]. It is through pangs of conscience before committing an immoral act, through remorse after committing an immoral act, through reciprocal benefaction, and fear of retaliation.

'''Normative egoistic hedonism''' (&quot;You ought to pursue your own pleasure as your ultimate aim&quot;) can be criticized as follows. A conceptual distinction between &quot;displeasing to the actor&quot; and &quot;immoral&quot; needs to be upheld. When parents teach children what is moral and what is immoral, and what is acceptable and what is unacceptable, they cannot do so in terms of pleasure experienced by the child; in particular, they cannot say &quot;if you do as you please, that is moral&quot; (beware that this may be a mere turn of phrase). While there is certain displeasure at performing immoral acts in most people, the displeasure depends on and stems from the person's ranking an act as immoral; if the notion of immorality in its turn is determined solely in terms of one's pleasure and displeasure, we have a vicious circle, it seems. This criticism applies to egoistic hedonism rather than universalistic hedonism known under the Millian head of &quot;utilitarianism&quot;. The utilitarian may be pleased with his being an utilitarian, but his utilitarianism consists in his aiming at some aggregate pleasure of all the people, not at his own pleasure.

A different phrasing of some of the above on &lt;u&gt;elective&lt;/u&gt; elective hedonism: The conscience has to know somehow what is right and what is wrong, and a particular account of what is right and wrong is a particular ethical theory. If the ethical theory that one's own pleasure is the right measure of right and wrong is wholeheartedly accepted, then the question of what is right and wrong is replaced by the question of what is pleasant to oneself, meaning that the part of displeasure generated by conscience is fed again into the conscience's consideration, a circle that may be not vicious, but looks suspect anyway.

Disambiguation of &quot;moral&quot;: I read &quot;moral&quot; roughly as &quot;avoiding harm to other people or society&quot; rather than &quot;of or relating to a person's ultimate aim&quot;; another option would be &quot;of or relating to norms that society enforces through frowning upon, and ultimately banishing&quot;. Evaluative hedonism is per my definition a unifying answer to the question of what to ultimately value, subsuming both moral and non-moral decisions; normative hedonism subsumes only moral decisions.

Normative egoistic hedonism appears absurd if turned into a point of legal code. Imagine a murderer explaining to the judge that killing the victim has produced extreme ecstasy in the murderer, and that he does not feel any remorse, a painful displeasing feeling. Under the normative hedonistic account, the person's not feeling any remorse speaks in favor of the criminal deed. This, again, does not apply to Millian universalistic hedonism AKA utilitarianism.

Put differently, even if I aimed at my pleasure as the sole ultimate aim, I doubt that I would think that I ought to do so. It would be foolish for me to try to convince other people that they should aim at their pleasure as the sole ultimate aim, as some of them are sadists and take pleasure in things I find repulsive and morally unacceptable. I should actually prefer that they aim at my pleasure, a position I am unlikely to sell to them.

All criticism of one's pleasure as the sole ultimate aim can be dismissed on the ground that it is each candidate ultimate aim that defines what is ultimately good for the person, so each ultimate aim affirms of itself that it is good and beyond reproach. But it is a bit like a liar claiming that he is an utter truth-teller. I do not want to deny the fundamental division between descriptions and valuations. I even in a way accept the raised point, at the bottom of my intellectual honesty. But I do not think I accept it as an argument in a real discussion between two or more people. What does the argument claim? Does it claim that each ultimate aim is equally good? This cannot be the case once the meaning of &quot;good&quot; is fixed in that sentence, other than &quot;good&quot; being a constant function. It cannot be that the meaning of &quot;good&quot; is substituted per ultimate aim. The discussed claim can be formulated in this way: A x,y: ultimateAim(x) and ultimateAim(y) =&gt; goodness(x) = goodness(y). Whatever the definition of goodness, it does not depend on the ultimate aim of which it is predicated. In order for an ultimate aim to define the meaning of &quot;good&quot; when applied to an ultimate aim, the formulation would have to be relativized: A x,y: ultimateAim(x) and ultimateAim(x) =&gt; goodness(x,x) = goodness(y,y), where goodness(a,b) is the goodness of a as evaluated on the basis of b. Another option is to give up predicating good and goodness of ultimate aims. Anyway, the points that I have raised in previous paragraphs assumed that this apparently bulletproof defense against any criticism whatsoever is refused, refused perhaps in part for its absolute watertightness, on the analogy of refusing non-falsifiable claims as scientific.

Ultimate aim vs ultimate good: In the previous paragraph, I have played with the idea that each ultimate aim could define the specific meaning of the term &quot;ultimately good&quot; or &quot;ultimate good&quot;, and thus pronounce itself &quot;ultimately good&quot;. I think this idea is untenable per common usage of the adjective &quot;good&quot;. It comes down to whether some shared meaning of &quot;good&quot; is presupposed between people (or other communicating agents), and on what level of abstraction or indirection this meaning is shared. The term &quot;a person's ultimate aim&quot; does not break the requirement of a shared meaning of an adjective, as the only adjective used is &quot;ultimate&quot; in the sense &quot;not serving merely as a means&quot;.

A dialogue on '''moral criticism of elective egoistic hedonism''':

* A: In elective egoistic hedonism, the term &quot;moral&quot; does not program on &quot;pleasure&quot;; by contrast, it informs pleasure. That is good. But no significant moral guarantee is given by elective hedonism, as we do not know how much displeasure an immoral act creates, relative to pleasure gained from certain acts classified as immoral.
* B: So what?
* A: So I say that people who decide to aim at their pleasure as one of their ultimate aims should add keeping morality as another of their ultimate aims, constraining the action motivated by pleasure. The displeasure generated by conscience seems an insufficient guarantee of moral action.
* B: If the displeasure generated by conscience is not that which deters an agent from transgressing, then I do not know what does.
* A: Elective hedonism is the one that involves a free choice without reference to &quot;highest good&quot;, &quot;intrinsic value&quot; or the like, but also without claiming that everyone is driven by pleasure anyway. But your last point implies a descriptive hedonistic stance.

One's pleasure may be chosen as the sole ultimate aim; that is what elective egoistic hedonism involves. Yet this ultimate aim appears to be a means of sort, a means to the implied goals of the implied agent that has created the organs and bodily systems that produce pleasure. The only unifying implied aim that I can discern is the reproduction of the genes, which in its turn requires the survival of the individual and roughly his reproduction or at least reproduction of his close or more distant relatives. I find being controlled by this implied further removed aim somewhat disconcerting.

'''Evaluative egoistic hedonism''' (&quot;One's pleasure is the only thing of intrinsic value&quot;) can be criticized on the following questions: how do you know it? If Simplicio says that it is freely chosen, the question of knowledge becomes harder to pursue; the mechanism of choice is deliberately left in clouds. But if Simplicio is Epicurus and says that pleasure is a sensory source of information about value and goodness, my question is why should pleasure be accepted uncritically, given what we see with our eyes is not accepted uncritically: optical illusions and hallucinations.

A dialogue on the '''knowledge of pleasure's intrinsic valu'''e:

* A: I admit that pleasure has the immediate appearance of seek-worthiness for its own sake, that is, not as a means to something else. But how do you know that this immediate appearance is not deceptive? Even such a sophisticated organ as the human eye, combined with the sophisticated visual processing that together with the eye makes up human vision, is liable to optical illusions. Why should the analogues of external senses—the information channels through which the conscious part of the mind learns about the presence or absence of pleasure—be taken uncritically as utterly reliable?
* B: First, I am not sure I will be able to answer the question about my knowledge of seek-worthiness of pleasure. The seek-worthiness of pleasure seems obvious to me, beyond doubt. Similarly, the existence of the cup that I see seems obvious to me, yet the cup that I see is a model in the mind built based on retinal data, so its existence is philosophically uncertain. A more important question is whether the pleasure sense or senses implied in what you said were really analogues of external senses, or whether they were fundamentally different. Yet another question is whether human vision, even when accepted critically and corrected by comparison with prior beliefs or posterior tests, should be taken as utterly reliable.
* A: I actually do not say that the critical attitude requires an uncritical reception of criticism-augmented human vision. Even after criticism has been applied to human vision, the knowledge obtained from it remains tentative in principle. Whereas the self-pleasure-seeker proposed his own pleasure as an ultimate aim.
* C: That depends on whether the theory of the self-pleasure-seeker should be read as literal and perfectly precise and accurate. It may much more be the case that the self-pleasure-seeker has accepted some rough and broad stance of seeking his own pleasure.
* D: In some sense, one's own pleasure is not the true ultimate aim; there is no true ultimate aim. To use the term &quot;ultimate good&quot; and &quot;highest good&quot; is misleading, as there is no such thing. A decision to aim at one's own pleasure as the ultimate aim is a person's free decision, one that does not rest on knowledge of anything. The question &quot;how do you know&quot; is not a factual question; it is a question about what decision procedure has been used.
* A: But my point is that I actually admit the apparent seek-worthiness of pleasure, based on my human experience; I am not a Martian researcher. Whereas you, D, seem to give up any justification of your choice of the ultimate aim.
* D: Justification of my choice of my ultimate aim? To whom? To a looming powerful figure who threatens me with death unless I provide to him a justification? A true justification or one that will be convincing to the looming powerful agent? If a choice is free, it lacks justification; it still has a causation, but not a justification.
* A: A free choice lacks justification? I don't think so. It possibly lacks trace, but it should still be justified as allowable.
* D: Okay, if that is what you have meant by justification, then my justification (explanation that I should be allowed to do so, not derivation of my choice) for my choice is the following: my moral sense is set up in certain way, and it produces pleasure and displeasure, so the community does not need to feel threatened by my being a self-pleasure-seeker. Note that I do not define or instantiate &quot;moral&quot; as &quot;pleasing to me&quot;; I only identify &quot;my ultimate aim&quot; with &quot;my pleasure&quot;. So &quot;my ultimate aim&quot; programs on &quot;my pleasure&quot; by my choice and &quot;my pleasure&quot; programs on &quot;my acting in morally acceptable way&quot; by my biological setup and parental programming. So in a way, I am not really a normative egoistic hedonist. I may even not be a hedonist at all in the sense &quot;he who claims that one's pleasure is the ultimate good&quot;, because I deny that the term &quot;the ultimate good&quot; has any extensional meaning (see Frege and his &quot;the least rapidly convergent series&quot;). I have merely freely chosen to aim at my pleasure as my ultimate aim.
* A: This is an impressive justification or defense. The only weak spot in it, if at all, is the term &quot;free choice&quot;. That free choice had to be made in the brain, somehow. But you, D, do not claim that you have made that choice based on pleasure; you possibly admit that you have made that choice unconsciously (without conscious access to what went on during the choice) based on something else. So there is something unconscious that is more ultimate than the conscious ultimate aim, but (a) it remains unclear whether the &quot;aim&quot; relationship still applies when crossing the boundary between conscious and unconscious, and (b) you are not saying that the unconscious choice of pleasure is based on pleasure. So you really are using something that I will term intuition for lack of better term in order to pick your pleasure rather than some other ultimate aim.
* E: The question of knowledge is not altogether addressed by &quot;free choice&quot;. The arguing with &quot;free choice&quot; would be worthy of further scrutiny, but digging into this any further would be a demanding enterprise. It goes back to the subject of traceability. And it in principle goes into the direction in which elective and evaluative becomes conflated with descriptive: the choice of the person gets reduced to the algorithms of choice actually implemented in the person by biology, even if these algorithms are algorithms for the choice of algorithms or informal procedures. (An example of meta-algorithm or rule: &quot;Choose a method that seems acceptable to some reference community.&quot;)

&quot;Everyone aims at their own pleasure ultimately, so I cannot be blamed for doing as everyone else.&quot; This is a sly argument. It rests on the assumption that &quot;I cannot be blamed for doing as everyone else&quot; or &quot;I cannot be blamed for doing the same thing as everyone else&quot;. The trick is where one locates &quot;the same&quot;. One person kills for pleasure, another cares for sick people for pleasure; qua pleasure they are doing the same. But, interestingly, qua doing they are doing the same; once doing is stripped of all the specificity, it remains the same. Also, qua aiming and qua aiming at one's ultimate aim they are doing the same. So put more abstractly, &quot;I am just aiming at my ultimate aim just like everyone else, so I don't see how I can be blamed.&quot; The antecedent is right, but the consequent is simply unacceptable for any group of survival-worthy agents. A person can be blamed for their choice of their ultimate end. &quot;I cannot help it, so I cannot be blamed&quot; is along the lines &quot;I am a deterministic machine, so I cannot be blamed&quot;. But, in my view anyway, deterministic machines can be blamed and should be blamed.

'''Descriptive egoistic hedonism''' claims that each person is motivated by his own pleasure and only by it. It acknowledges that people vastly differ in what makes them feel pleasure, or what pleases them. All following objections to this theory raised by me are non-moral, and I see no point in raising moral objections.

My first objection to this theory, a weak one, is that not all human behavior is intentional and mediated by the brain, as is the case of spinal reflexes. In a spinal reflex, a movement of a skeletal muscle is triggered by a stimulus that is not relayed to the brain, but rather is handled by a few neuron bodies in the spinal cord. But I admit that spinal reflexes have nothing to do with larger aims of people, and with their life planning and life styles. Some people decide to spend a lot of time traveling for fun, other work hard to leave legacy to their children, skipping vacations. These sorts of long-term behaviors are unlinked to spinal reflexes. So I consider my objection refuted. I mention it for its clarifying effect on the phrase &quot;what motivates humans&quot;; this phrase has to be read in such a way that the objection does not apply.

My second objection is the lack of testability of the theory, which involves the failure of the theory to give an operational definition of &quot;pleasure&quot; and the lack of specifying parameters of hedonism, such as discounting rate or risk-aversion towards future pleasure. The discounting rate has to be chosen; such a discounting rate can be chosen that pleases the person at the point of the choice. But that discloses fundamental ambiguity in descriptive hedonism: what if a person is displeased with aiming at future pleasing moments? What are the time parameters or time behavior of this allegedly tautological pleasure-seeking? What experiments could refute the theory?

Rats: There is some experiment with rats whose pleasure centers have been stimulated by the experimenters after they press some button; this leads to the starvation of the rats[cite]. This would speak in favor of descriptive hedonism in rats. But then, did the rats aim at pleasure or were actually controlled by it? By how time-distant pleasure were the rats controlled?

A dialogue on the '''modified rat''':

* A: Did the modified rat who died of starvation actually aim at pleasure?
* B: Yes.
* A: How long was the term of the pleasure at which the rat aimed?
* B: I do not know, but my estimate would be that it was really a short-term or very short-term one. One problem is with the verb &quot;aim&quot; as applied to rat; it is unclear whether the rat was in any sense conscious of aiming at anything.
* A: Should have the modified rat aimed at pleasure?
* B: Admittedly, no, in order to stay alive longer.
* A: Was it the rat's moral obligation to aim at his own pleasure?
* A: How do we know that the rat aimed at or was controlled by an analogue of human pleasure?
* B: We know it by comparing the neuroanatomical structures of rats and humans, and we think to have identified pleasure centers in humans, that is center such that, when stimulated, produce something of which the subjects of the experiment verbally confirm that it is pleasure.

Why the dialogue? Because B needs to commit himself to meanings of words, step at a time, more so that we do not have a solid operational definition of pleasure.

A dialogue on the '''release of hormones into bloodstream as the ultimate aim''':

* B: It's all hormones. Everyone pursues things that give the required hormonal response.
* A: George Mallory, a British mountaineer who died during one of his expeditions to Mount Everest, was motivated by his fascination with (achieving the goal of) climbing up the mountain. He did not have in his mind as the goal the exhilaration that is likely to come after he succeeds. He could expect to feel exhilarated after his success, but such an exhilaration could come after another achievement as well. There was some process in his mind through which he decided that this goal was extremely worthy to him, a process that is far from scrutable. This process is not meaningfully expressed as a release of hormones into bloodstream. Above all, the hormones do not really carry all that much information. Their release is governed by some logic or algorithm. Also, their release is not directly available to the consciousness of Mallory, unless he has some measuring device attached to his bloodstream.
* B: Hormones, and epinephrine in particular, are going to be released to the bloodstream. The hypothesis that Mallory pursues reaching the mountaintop as his ultimate aim is no less speculative and untestable than the hypothesis that Mallory pursues the release of hormones into his bloodstream as his ultimate aim. Mallory has already climbed lower peaks, so he knows that reaching the mountaintop tends to create certain sort of experience or feeling.
* A: Mallory cannot pursue release of hormones when he does not even know that there are hormones and that they are released into bloodstream.
* B: Of course, Mallory pursues the pleasing experience that accompanies the release of epinephrine into the bloodstream. He pursues whatever sensations or other things enter his consciousness when the hormone is released into his bloodstream.
* A: But not only release of epinephrine is pleasing. The pleasingness, as far as I can see, does not account for the specificity of Mallory's pursuit.
* C: It is not only that hormones are going to be released to the bloodstream after his hitting the target. Also, there is going to be an increased heart rate. There has to be some specificity about the predicate. The awareness of achieving the long-sought goal generates some bodily responses that may be specific to achieving a long-sought goal. But are the macroscopic responses, such as the hormonal ones, specific? Various hormones are released into the bloodstream on all sorts of occasions. The predicate &quot;hormones are being released into the bloodstream of the person&quot; is wholly non-specific: hormones are being released all the time. It is as specific as &quot;the heart of the person beats&quot; or &quot;the neurons of the person are conducting signals&quot;.
* D: The non-observationality of hormones for a non-specialist is a good point. I really do not know what we are talking about as regards hormones: I have no practical access to levels of hormones in my bloodstream, and no way to empirically test various claims made about hormones and their correlation with certain experiences. Statements in terms of thrilling experiences make more sense to me.

==Paradox of hedonism==

The paradox of hedonism is the claim, whether true or false, that a person who is rationally or with full awareness directly pursuing his pleasure as his ultimate aim is unlikely to attain it. The paradox is sometimes formulated using &quot;happiness&quot; instead of &quot;pleasure&quot;. Several authors mention the paradox, including J. S. Mill and Henry Sidgwick. The validity of the paradox is unclear. The phrase &quot;pursue one's pleasure as one's ultimate aim&quot; is not wholly clear, as no time-value of pleasure or discounting rate for pleasure as known from finance is specified, and too many other details are left open, including how the success in such aiming is to be determined at the end of the life of the person, if at all. No empirical proof has been given, merely an opinion that the paradox could be true based on personal experience, possibly affirmed by further quotations from writers who have stated the paradox.

Paradox of hedonism or pleasure-seeking, a dialogue:

* A: Direct pursuit of pleasure is in vain: the harder you try, the less pleasure you get.
* B: That sounds as implausible as anything. The last time I wanted to feel pleasure, I have bought ice cream, and I felt pleasure as expected.
* A: But were you really maximizing pleasure? It seems that you wanted to add a little bit of pleasure rather than maximize pleasure. In order to maximize pleasure, you would have to try really hard.
* B: If my experience shows that a little bit of ice cream once in a while causes pleasure while additional ice cream does not generate any additional pleasure after certain frequency, then the perfectly rational thing to do in order to maximize that pleasure which stems from ice cream is to choose an optimal frequency and volume of ice cream. I do not see that I should try &quot;harder&quot; in such a way that I would predictably miss the goal of maximum pleasure. This sort of &quot;trying harder&quot; is not really a rational maximization of a variable that takes full advantage of past experience with the behavior of the controlled system in question.

Whether &quot;happiness&quot; can be substituted for &quot;pleasure&quot; without substantial modification of the semantics of the paradox is unclear. While he who has just eaten ice cream may have a pleasing experience, it is doubtful that he is thereby automatically happy, per the customary use of the words &quot;pleasure&quot;, &quot;pleasing&quot;, and &quot;happy&quot;. J. S. Mill's redefinition of &quot;happiness&quot; as pleasure minus pain, where pain includes not only physical pain but also anguish, does not seem to match usual linguistic usage of those terms. Interestingly, Henry Sidgwick seems to use &quot;pleasure&quot; and &quot;happiness&quot; as if they were interchangeable.

What should an hedonist do about the paradox? If an elective egoistic hedonist accepts the hedonistic paradox as true, what should he do to fight its consequences? Should he engage is some sort of self-deception, by which he convinces himself that he now aims at, say, the happiness of others as his ultimate aim, while deep in his heart he still knows that he has chosen his &quot;ultimate&quot; aim only as a means to his own happiness? These questions raise further questions as to what does it really mean to aim at a thing as an ultimate aim, or what does it mean to aim at it directly, questions that I do not address in this article. One resolution could be this strategy a hedonist could try. Never monitor the level of your pleasure or happiness; never ask yourself whether you are pleased or happy; always choose some objectives that are distinct from pleasure and happiness, and measure your success by measuring the degree of achievement of these objectives.

Selected '''quotations relating to the paradox of hedonism''' follow, either because of their beauty, or also because of the notability of their authors.

Wayne W. Dyer on happiness paradox, allegedly quoting C. L. James, but the quotation is only found online in Dyer, in ''Your Erroneous Zones'':

: A big cat saw a little cat chasing its tail and asked, &quot;Why are you chasing your tail?&quot; Said the kitten, &quot;I have learned that the best thing for a cat is happiness and that happiness is in my tail. Therefore I am chasing it and when I catch it, I shall have happiness.&quot;

: Said the old cat, &quot;My child, I too have paid attention to the problems of the universe. I too have judged that happiness is in my tail. But I have noticed that whenever I chase it, it runs away from me and when I go about my business, it just seems to come after me wherever I go.&quot;—C. L. James, On Happiness, quoted in Dyer 

J. S. Mill on happiness paradox in his ''Autobiography'', although Mill's happiness is, per his ''Utilitarianism'', pleasure minus pain by his stipulation or determination:

: The experiences of this period had two very marked effects on my opinions and character. In the first place, they led me to adopt a theory of life, very unlike that on which I had before acted, and having much in common with what at that time I certainly had never heard of, the anti-self-consciousness theory of Carlyle. I never, indeed, wavered in the conviction that happiness is the test of all rules of conduct, and the end of life. But I now thought that this end was only to be attained by not making it the direct end. Those only are happy (I thought) who have their minds fixed on some object other than their own happiness; on the happiness of others, on the improvement of mankind, even on some art or pursuit, followed not as a means, but as itself an ideal end Aiming thus at something else, they find happiness along the way [...] Ask yourself whether you are happy, and you cease to be so.&quot; (p. 94), also quoted in part in WP 

Henry Sidgwick in his ''The Methods of Ethics'', Book II, Chapter III:

: [...] It may be replied that if these permanent sources of pleasure are consciously sought merely as a means to the hedonistic end, they will not afford the happiness for which they are sought. With this I to some extend agree; but I think [...] I should not, however, infer from this that the pursuit of pleasure is necessarily self-defeating and futile; but merely that the principle of Egoistic Hedonism, when applied with a due knowledge of the laws of human nature, is practically self-limiting; i.e., that a rational method of attaining the end at which it aims requires that we should to some extent put it out of sight and not directly aim at it. I have before spoken of this conclusion as the 'Fundamental Paradox of Egoistic Hedonism'; [...]

==See also==
* [[Hedonism]]

==Further reading==
* [https://plato.stanford.edu/entries/hedonism/ Hedonism] - Stanford Encyclopedia of Philosophy
* [[wikisource:Catholic_Encyclopedia_(1913)/Hedonism|Hedonism]] - Catholic Encyclopedia 1913
* [[wikisource:1911_Encyclopædia_Britannica/Hedonism|Hedonism]] - Encyclopaedia Britannica 1911
* [https://www.britannica.com/topic/hedonism hedonism] - Encyclopedia Britannica
* [[wikipedia:Hedonism|Hedonism]] - Wikipedia
* [[wikipedia:Paradox_of_hedonism|Paradox of hedonism]] - Wikipedia

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We don't typically name main space pages after users, and almost never for landing pages. A neutral landing page for Hedonism should be created with a subpage for the essay / original research. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 01:15, 14 January 2023 (UTC)

== A comment ==

The [[wikipedia:Bellman_equation#A_dynamic_decision_problem | Bellman Equation]] may be a good model for how we plan what we do, and if that's the case we all optimize a time-discounted &quot;reward&quot;. I don't have a reference for this offhand, but vaguely recall reading about the Bellman Equation in AI:AMA by Russel et al. or maybe another book on AI. The Wikipedia article isn't that great (computer science articles on Wikipedia usually aren't, unfortunately) and doesn't mention anything about individual human behavior. I could swear I've read something in this vein somewhere though. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 08:38, 28 September 2023 (UTC)

I forgot to state my point in the above, which is that I think the word &quot;hedonism&quot; is often applied to two distinct patterns. Notice that in the bellman equation, rewards are time-discounted by a certain factor. One cannot optimize rewards infinitely far in the future, so this makes sense. A person who seeks short-term gratification may be called a &quot;hedonist&quot; but suppose instead that they simply have a sharp discount factor. On the other hand, someone who's amoral, anti-social and/or generally self-serving may not simply seek short-term gratification, yet their behavior could also arguably be called hedonistic. What do you think of this distinction? I'm not well-read on the subject of hedonism, so I don't understand all of the terms in the resource, but it seems like this distinction might be worth making. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 14:04, 14 October 2023 (UTC)

To put it another way, hedonism has to do with the &quot;objective&quot; that is optimized, rather than the discount factor. It seems the resource implies this with the line ''&quot;The sort of hedonism so criticized is both short-term and long-term hedonism; term does not matter; what matters is that it is an egoistic hedonism or aiming at one's own pleasure as the only ultimate aim, or self-pleasure-seeking.&quot;'' but I wanted to call your attention to bellman's equations since it makes the point easy to see terms of discount factor vs objective. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 14:11, 14 October 2023 (UTC)</text>
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This original article by [[User:Dan Polansky|Dan Polansky]] about proper names focuses on the following questions:
* What distinguishes proper names from common nouns?
* Is there such a thing as proper names at all?

This article is English-centric, focusing on English proper names, and makes use of the English use of definite and indefinite articles, &quot;the&quot;, &quot;a&quot; and &quot;an&quot;. Nonetheless, some of the deliberations may apply to other languages as well.

This article is in part philosophical, in part linguistic. A learner of English will find something of interest here, while probably finding some of the deliberations uninteresting since too philosophical and impractical.

==Distinguishing proper names from common nouns==
Let  us consider candidate distinguishing features for proper names:
* Reference to instances of classes via christening: The one key distinguishing feature is that proper names refer to individual referents that are instances of classes by acts of christening. By contrast, common nouns refer to concepts by (often historically untraceable) acts of christening, and to individual referents by invoking concepts that apply to them. Thus, the referents of a single sense of a common noun have something in common other than &quot;being called X&quot;; they have the concept that applies to them in common, the concept named by the noun. Put differently, proper names are names of individual entities while common nouns are names of concepts. For a common noun to refer to an individual referent, it needs an article. (A concept is also an individual entity in the class of concept, but the distinction still holds true.) That is at least how it works for countable common nouns; the case of uncountable common nouns is a bit different.
* Recognition of a previously unacquainted instance as belonging to the name: To learn about the meaning of a countable common noun, one can be given examples of its referents and then extrapolate from there. If one has seen some cats, one can recognize a new individual entity that one has not yet seen as a cat. For a proper noun such as Peter or London, there is no such extrapolation: each additional Peter or London only&lt;ref&gt;Admittedly, this is a slight simplification; nearly all referents of ''Peter'' are male humans, in addition to being entities.&lt;/ref&gt; shares the name with the other instances.
* Restriction to concrete objects: Proper names are usually taken to refer to ''[[wikidata:Q4406616|concrete objects]]'' rather than ''[[wikidata:Q7184903|abstract objects]]'', especially people, places, and organizations but also less concrete objects such as events. However, names of chemical elements are not considered to be proper names. Names of qualities (e.g. &quot;blueness&quot;) are not proper names either.
* Singularity of reference: this is a relevant yet inconclusive test. Arguably, the universe, the earth, the moon, and the sun are not proper names; they are common nouns referring to singleton classes or concepts. Many grammarians disagree, hence the capitalization of these. Proper nouns generally refer to multiple referents (&quot;Peter&quot;, &quot;London&quot;) so the test is unclear without further elucidation. Singularity of reference is present in the names of qualities (&quot;blueness&quot;) and the names of substances (&quot;gold&quot;).
* Capitalization: this is a relevant yet inconclusive test. In English, adjective &quot;English&quot;, common noun &quot;Englishman&quot;, adjective &quot;Darwinian&quot; and common noun &quot;Darwinian&quot; are capitalized. Capitalization does have some value in that once something is considered to be a proper noun, it gets capitalized. Thus, capitalization is a hint, albeit an inconclusive one.

==Existence of proper names==
Some raise doubt about whether there is such a thing as proper names. This is caused by definitional and demarcation difficulties. As a general note, there is only one true definition, the mathematical definition. Everything else is the dirty empirical world. Definitions outside of mathematics often leave edge cases undecided and linguistics is no exception.

English proper names have some striking grammatical properties: &quot;The man called&quot; vs. &quot;Peter called&quot; and &quot;I arrived at the city&quot; vs. &quot;I arrived at London&quot;. There is no article. Yes, some proper names do take an article, but that does not detract from the observation. Yes, &quot;Peter&quot; can be used as a common noun meaning &quot;A person named 'Peter'&quot;, but that does not diminish there being a proper name &quot;Peter&quot;.

Yes, ranking names of languages as proper names seems somewhat arbitrary; non-English linguistic traditions often do not do it. One can claim languages to be like substances, such as wood, not concrete objects, and sentences being made from languages as if chair from wood.

Yes, ranking names of weekdays as proper nouns seems somewhat arbitrary; non-English linguistic traditions often do not do it.

Yes, it is not entirely clear why names of taxa are considered to be proper names.

But there is no doubt &quot;Peter&quot; and &quot;London&quot; are proper names. Even &quot;Hague&quot; with its &quot;The&quot; is a proper name; things would be easier without the &quot;the&quot; anomaly, but they aren't. As a general principle, a language shows remarkable order or regularities, without which it would not fit into the fairly small human mind. However, a language also usually contains a heavy dose of chaos or irregularities or anomalies. Anomalies do not refute the order; they are just anomalies. &quot;The Hague&quot; is one such anomaly. For each language, one can think of an ideal language resulting from removal of the anomalies. The ideal or idealized version can be described more compactly than the actual empirical version with all its elements of chaos. Thus, the ideal English would have &quot;Hague&quot; rather than &quot;the Hague&quot;.

==Name vs. proper name==
Generally, ''name'' is a broader term than ''proper name''; see also section [[#Distinguishing proper names from common nouns|Distinguishing proper names from common nouns]].

Names that are not proper names include the names of chemical elements (e.g. &quot;helium&quot;), the names of other chemical substances (e.g. &quot;citric acid&quot;) and vernacular names in biology (e.g. &quot;fly agaric&quot;).

The relationship between ''name'' and ''noun'' seems in part unclear. For one thing, by one common construction, ''noun'' refers to a single word, whereas ''name'' can refer to a multi-word phrase. However, are e.g. &quot;tree&quot;, &quot;animal&quot; and &quot;sky&quot; names of something? Are these words names of classes or concepts? But are these words names (as classes, not roles, that is, not ''names of'') in that, would one say '&quot;tree&quot; is a name'? What about &quot;the world&quot;? One contrast is that the word ''name'' is often used to refer to a ''role'' in a relationship, that is, ''the name of X'', whereas there is no ''the noun of X''.

Multiple terms are formed as phrases using ''name'' but not ''noun'', including ''chemical name'', ''personal name'', ''first name'' and ''vernacular name''.

Further reading:
* [[Wikipedia: Name]]
* [[Wikipedia: Common name]]
* [[Wikisource: 1911 Encyclopædia Britannica/Name]]

==Cases==
In the following, cases or groups of names are considered, whether because they are considered edge cases or whether they seem to deserve separate consideration for other reasons.

===The world, the earth, the sun, and the moon===
The phrases &quot;the world&quot;, &quot;the earth&quot;, &quot;the sun&quot;, and &quot;the moon&quot; can be analyzed as definite descriptions (see below) rather than proper nouns. Thus, the fact that a noun such as &quot;sun&quot; has only a single referent does not automatically make it a proper noun rather than a common noun.

This is especially clear if we consider possible worlds. Thus, in a possible world, the earth can have multiple moons, in which case the phrase &quot;the moon&quot; fails to refer due to the use of the definite article. The fact that we can think like that shows that &quot;moon&quot; refers to a concept or class rather than an individual thing; it is &quot;the moon&quot; that refers to an individual thing, being a definite description using the definite article &quot;the&quot;.

Analyzing the phrase &quot;the sun&quot; in a way similar to &quot;the moon&quot; above may be a bit tricky if we assume that each planet including the earth moves around a single sun. However, we do not need to assume the modern worldview, and assume a naive phenomenological worldview instead. Thus, instead of defining &quot;sun&quot; as &quot;mass of gas such and such&quot;, we use the phenomenological definition &quot;that which reveals itself as a moving very bright full circle on the sky that gets out of view during the night&quot;. Assuming we do not know the nature of that thing that reveals itself, and that it is possibly some kind of object (or even a negative object like a hole) moving around the earth, it is possible to think of a possible world in which multiple objects (possibly negative objects) reveal themselves as a bright full circle moving across the sky. Given this concept of sun, the singularity of sun is no longer necessary across possible worlds, and &quot;the sun&quot; actually referring to something (that is, there being only one thing that reveals itself as such and such) is contingent on this world and similar worlds; thus, &quot;sun&quot; is a concept or a class, possibly non-singleton one, and &quot;the sun&quot; is a definite description.

Multiple analysts reject the above analysis, leading to the capitalization conventions &quot;the Sun&quot;, &quot;the Earth&quot;, &quot;the Moon&quot;, etc. For astronomy, it has practical purpose, since e.g. the concept of moon is extended beyond &quot;that which reveals itself as a certain pattern of light in the sky of the earth&quot; to something like &quot;that which resembles the earth's moon in some essential characteristics, namely by being a non-star that moves around a planet&quot; or something of the sort. Even so, the phrase &quot;the moon&quot; could be taken to refer by default to the earth's moon, but if a text were dealing with, say, Jupiter's moon, the text would want to use the phrase &quot;the moon&quot; to refer to any moon previously picked by context and stored in an analogue of register for &quot;moon&quot;. That is, the phrase &quot;the moon&quot; would refer to any individual moon that has been placed into a ''register'' associated with the concept or class of moon. However, one could still argue that this does not make the phrase &quot;the moon&quot; a proper noun, but rather that the register of the class of moon defaults to the earth's moon. Alternatively, there could be two kinds of registers, a global register and a local register. The global register for the class of moon would be always non-empty whereas the local register would be sometimes empty. The phrase &quot;the moon&quot; would pick the local register if non-empty, or the global register if the local one is empty. Whether this speculative theory is correct is unclear.

===Names of languages===
In English, single-word names of languages (e.g. &quot;English&quot;, &quot;Spanish&quot;) are usually considered to be proper names. They are capitalized and used with no articles. By contrast, the phrase &quot;the English language&quot; is not a proper name but rather a definite description pointing to the same referent as the proper noun &quot;English&quot;. Moreover, the phrase &quot;English language&quot; (without the definite article) is a common-noun description, not a definite description, referring to &quot;any of possibly multiple languages spoken by the English&quot;; if the English (people) turn out to speak a single language, the definite description &quot;the English language&quot; succeeds in referring to something.

Non-English languages often rank names of languages as common nouns, and write them in lowercase accordingly. Examples are in Wiktionary [[:wikt:Spanish]] entry, which includes French espagnol, Spanish español, Italian spagnolo, Polish hiszpański, Danish spansk and Swedish spanska. A candidate rationale for this practice is in the following paragraph, likening a language name to a substance name (e.g. &quot;wood&quot;, &quot;gold&quot;). Having English and non-English classification language-specific and thereby inconsistent in a multi-lingual dictionary is tolerable.

One could argue that English language name &quot;English&quot; is in fact a common noun, and that one should not be deceived by the capitalization and the lack of article. Since, &quot;Englishman&quot; is a common noun despite being capitalized, so the capital letter could be signaling honor or importance rather than indicating a proper name; as for the lack of article, ''gold'' uses no article either. One could argue that a language, an entity with no particular location given a point in time, is something like a substance from which sentences are made, and thus is like ''gold'' in some regards. This does not seem to be the standard analysis for English, but it may be the kind of analysis that resulted in many languages having their language names in lowercase.

===Names of weekdays===
English treats names of weekdays (''Monday'', ''Tuesday'', etc.) as proper names, by capitalizing them, and by using no article with them, as in &quot;Today is Monday&quot;. If, by contrast, &quot;Monday&quot; referred to &quot;any day having the rank 1 in a certain periodical numbering scheme of days&quot; as if a common noun, events would take place &quot;on a Monday&quot;, with the indefinite article &quot;a&quot;. That it is not so seems peculiar from the etymology or morphology of &quot;Monday&quot;, since the &quot;day&quot; part suggests &quot;Monday&quot; is some kind of day. &quot;Monday&quot; does not refer to any one particular day (there are multiple days such that each of them is Monday), so what does it refer to? Does it refer to a discontiguous assemblage of days that is a single object? If so, why shall we say &quot;Today is Monday&quot; rather than &quot;Today is part of Monday&quot;? Something strange seems to be going on here.

Non-English languages often rank names of weekdays (Monday, Tuesday, etc.) as common nouns, and write them in lowercase accordingly.

Some of the quandaries pointed out for English seem to apply to other languages as well, e.g. Czech. Thus, in Czech, there is ''pondělí'' (Monday), uncountable, and ''pondělek'' (a Monday), countable. By being uncountable, ''pondělí'' behaves a bit like English &quot;Monday&quot;, although Czech has no definite and indefinite articles.

Having English and non-English classification language-specific in a dictionary and thereby inconsistent is tolerable.

===Names of taxa===
Binomial names of biological taxa, e.g. ''Amanita muscaria'', are classified as proper names in Wiktionary. They show singularity of reference and lack of article, but so do names of chemicals. By contrast, &quot;fly agaric&quot; is a vernacular name and a common noun, possibly taking an indefinite article. Present e.g. in the sentence &quot;''Amanita muscaria'' is a gilled mushroom; [...]&quot;, ''Amanita muscaria'' is used without an article and refers to the taxon rather than an individual organism with a location given a time point. What makes it a proper name is not wholly clear.

Further reading:
* [[Wikipedia: Binomial nomenclature]]
* [https://onlinelibrary.wiley.com/doi/full/10.1111/j.1096-0031.2011.00357.x Are species names proper names?] by Richard J. Jensen, 2011

===Names of principles===
If principles, theorems and laws are abstract objects, their names are not proper nouns. One has to admit they result from christening an individual entity, even if an abstract one.

One example is &quot;Pythagorean theorem&quot;. It is not capitalized as a proper name: that would have been &quot;Pythagorean Theorem&quot; with capital T. However, it is in fact often capitalized as &quot;Pythagorean Theorem&quot; with capital &quot;T&quot; as per Google Ngram Viewer. It very often uses the definite article &quot;the&quot;, being written as &quot;the Pythagorean [tT]heorem&quot;.

Many such entries are tracked as proper names in Wiktionary.

===Names of games===
Names of board games and card games are often written in lowercase as if common nouns, e.g. [[wikt:chess|chess]], [[wikt:go|go]], [[wikt:blackgammon|blackgammon]], [[wikt:whist|whist]] or [[wikt:poker|poker]]. They take no definite article. This seems to match a somewhat similar case, the name of a sport, [[wikt:tennis|tennis]] or [[wikt:basketball|basketball]]. These names refer, on one hand, to a type of activity, and on the other hand, to a set of rules governing the activity. The activity type is defined by the rules. There is perhaps some similarity between the referents of these names and substances such as gold. However, proprietary modern non-traditional board games and card games are often named by capitalized names, and so are computer games. The capitalization suggests these are considered to be proper names. The treatment seems to be somewhat arbitrary and inconsistent, failing the notion that proper-name-hood can be determined mostly with the use of the ontology of the referent and the manner of reference. On the other hand, some games seem to bear some similarity to an artistic work such as a literary work, a painting, a piece of music or a movie; and names of these are proper names. The ontology depends in part on how narrowly one construes a particular computer game, e.g. whether one considers particular artwork and music as defining, or only the game play, and on what level of abstractness one considers the game play. The games written in lowercase are usually somewhat traditional, have fairly compact or small rules, and do not feature specific artwork, whether visual, auditory or textual.

===Names of dances===
Names of dances such as ''the [[wikt:waltz|waltz]]'' or ''the [[wikt:quadrille|quadrille]]'' are usually taken to be common nouns, despite the singularity of reference. Unlike substance ''gold'', they often use the definite article. Like gold and unlike people and places, a dance has no particular location at a given point in time, being excluded from this class of prototypical referents of proper names. The names of dances are usually also used to refer to pieces of music matching the dance.

===Names of works===
Names of particular novels, poems, pieces of music, paintings, sculptures, movies and computer games are usually considered to be proper names. Their referents do not belong to the most prototypical group of referents of proper names, which are the referents that have a particular location given a particular point of time. Considering novels, each novel can be thought of as an abstract object existing not only in the empirical world but also in the Borgessian library of all possible novels. For novels, it is a particular printed copy of a novel that has a location given a point in time, while the novel itself does not; yet the name refers to a novel, not to its printed copy.

===Names of organizations===
Names of particular organizations including companies are usually considered to be proper names. Their referents do not belong to the most prototypical group of referents of proper names, which are the referents that have a particular location given a particular point of time. Since, in general, an organization is scattered across various sites and locations (as for its buildings), and the employees and agents are scattered as well. On the other hand, organizations, when conceived as aggregates of people, physical assets and their relationships, are locationally bound, and may have more in common with such objects as apples than meets the eye. A fisher's nest is rather sparse, non-rigid, yet shows locational coupling; a group of people and physical assets that are part of the company also show locational coupling.

===Names of substances===
Names of substances such as ''gold'' or ''carbon dioxide'' are usually considered to be common nouns, despite the singularity of reference. The idea of singularity of reference is obtained by the notion that, say, gold is a single object discontiguously scattered across the world. In any case, ''gold'' and ''carbon dioxide'' are uncountable and take no definite article.

===Names of qualities===
Names of qualities such as ''blueness'' are considered to be common nouns, despite the singularity of reference. Qualities are ''abstract'' objects; in particular, they have no location given a point in time. Their names are usually derived from the corresponding adjectives.

===Names of people===
Names of particular people are proper names.

That includes names that refer to multiple people such as first name ''Martina''; what is decisive is that what various referents of ''Martina'' have in common is above all the name and not much else. In case of ''Martina'', some intensional characteristics are part of the name, making the matter more complicated: 1) any referent is a human, and 2) any referent is a female.

The case of surnames is similar to that of first names. From the surname one knows the referent is a human. In some non-English languages, the surname form indicates whether the referent is a male or a female, making the surnames behave even more like the first names.

Multi-word names of people such as ''Albert Einstein'' have even more appearance of being proper names than first names and surnames, by having a reduced set of referents and by being less often used in a plural. The set of referents can still feature multiple referents. Again, what the referents have in common is above all the multi-word name, and then being a human and the particular sex or gender indicated by the name.

===Names of ethnic groups===
Names of ethnic groups and their members (e.g. ''the Spanish'', ''Englishman'') are considered to be proper names by some. However, the singulars systematically take an article, often an indefinite one, and are regularly pluralized without hesitation, both features pointing to their being common nouns. Moreover, what all e.g. Spaniards have in common is not merely the name as a label but rather their being Spanish, a feature of common nouns. The capitalization can be explained as honorification, imputing honor on the ethnic.

Compared to names of languages, names of ethnic groups in non-English European languages are more often capitalized, as per translations entered e.g. in [[Wiktionary:Spaniard]] entry. Nonetheless, such names in lowercase include Bulgarian испа́нец, Estonian hispaanlane, Finnish espanjalainen, Italian spagnolo, Latvian spānis, Romanian spanio, Russian испа́нец, and Spanish español.

These names are sometimes referred to as &quot;ethnonyms&quot;.

A multilingual-dictionary can classify these names depending on the linguistic tradition for that language. Alternatively, it may accept one common analysis, which would probably be that they are common nouns given the fairly many languages are writing them in lowercase.

Further reading:
* [[Wikidata:Q1137656|Wikidata:ethnonym]]
* [https://icosweb.net/wp/wp-content/uploads/2019/05/ICOS-Terms-en.pdf List of Key Onomastic Terms] by International Council of Onomastic Sciences, icosweb.net

===Names of inhabitants===
Names of inhabitants such as ''New Yorker'' are considered by some to be proper nouns. However, such names 1) are not separately coined but rather derived from the names of inhabited places, 2) readily take indefinite article, 3) readily get pluralized, and 4) point to instances or individuals by the intermediary of the shared features, e.g. &quot;Londoner&quot; (name) → person from London (concept or class) → the blonde male with a mustache standing over there (definite description pointing to a particular individual). These four characteristics are typical for common nouns. Moreover, some languages write them in lowercase as per [[Wiktionary:Londoner]] entry; these include Danish londoner, Finnish lontoolainen, Hungarian londoni, Italian londinese, Polish londyńczyk, Portuguese londrino, Russian ло́ндонец and Spanish londinense.

Names of inhabitants seem to bear some analytical similarity to [[#Names of ethnic groups|names of ethnic groups]]. One difference is that names of inhabitants are trivially derived from the place being inhabited.

Further reading:
* [https://icosweb.net/wp/wp-content/uploads/2019/05/ICOS-Terms-en.pdf List of Key Onomastic Terms] by International Council of Onomastic Sciences, icosweb.net

===Names of astronomical objects===
Names of particular astronomical objects such as stars are proper names. Stars are among the prototypical referents of proper names, having a definite location given a point in time.

Further reading:
* [[Wikipedia:List of proper names of stars]]
* [https://www.iau.org/public/themes/naming_stars/ Naming Stars], iau.org

===Brand names===
Brand names are proper names. Thus, they are words or word sequences. They do not need to start to be used as common nouns in order to become proper names; they are proper names automatically, as if by definition.

Some general dictionaries include brand names. According to brandingstrategyinsider.com, these include Webster’s New World, Merriam-Webster’s Collegiate, and Random House Unabridged Dictionary.

Further reading:
* [https://brandingstrategyinsider.com/when-dictionaries-and-trademarks-clash/ When Trademarks And Dictionaries Clash - Branding Strategy Insider] by Steve Rivkin, brandingstrategyinsider.com

==Capitalization of proper names==
We already noted that, in English, proper names are capitalized. At the same time, some words that are not proper names are capitalized as well, e.g. the countable common noun ''Englishman'', the adjective ''Orwellian'' or the countable common noun ''Darwinian''.

In many non-English languages using the Latin script (e.g. Spanish) or the Cyrillic script (e.g. Russian), proper names are capitalized as well. One may consult Wiktionary [[wikt:London|London]] entry to get an idea. In German, all nouns are capitalized, so capitalization is not specific to proper names. In Pinyin romanization of Chinese, proper names are capitalized.

In English, multi-word proper names are capitalized using the title case, most words being capitalized rather than only the first word. Thus, there is a work named ''Much Ado About Nothing'' (all words capitalized) rather than ''Much ado about nothing'' (only the first word capitalized). An inspection of Wikidata item ''[[Wikidata:Q130851|Much Ado About Nothing]]'' reveals that many alphabetic-script languages only capitalize the first word of the proper name.

Further reading:
* [http://www.pinyin.info/readings/zyg/rules.html Basic Rules of Hanyu Pinyin Orthography (Summary)], pinyin.info

==Proper name definitions==
A definition or quasi-definition of a particular proper name can be one of the following:
* A quasi-definition stating the ''function of the name'', e.g. &quot;first name&quot; or &quot;surname&quot;. That is not a definition proper: it does not provide any guide on how to get to the referents of the name and it names the name itself, not what it refers to.
* A common-noun-like definition in the form of a ''definite description'', e.g. &quot;the capital of the U.K.&quot;. For each proper name, there is a host of common-noun-like definitions/intensions that apply to it. Each such definition is necessarily wrong from Kripkean rigid-designator point of view: it states something that is not ''necessarily'' true of the referent, merely ''contingently'' so. The definitions take the Russelian point of view that interpret proper name meanings as descriptions. The definitions choose some properties to list, often partially redundant for identification purposes. The definitions are in fact short encyclopedic summaries, not definitions from a logical point of view. That is fine for the purpose of a dictionary. Interestingly, a similar situation applies to names of chemical elements. The ultimate definition of proper name X is 'that individual entity which has been christened as X'. That, of course, is unhelpful in a dictionary.
* A common-noun-like definition in the form of an ''indefinite description'', one starting with an indefinite article. There is something suspect about this form: proper names are supposed to refer uniquely and without ambiguity to particular individual objects, for each distinct referent, so why should there be an indefinite article? Merriam-Webster's entry for ''Orinoco'' uses no article: &quot;river 1336 miles (2150 kilometers) long in Venezuela flowing from the Brazilian border to the Colombia border and from there into the Atlantic Ocean through a wide delta&quot;. By contrast, AHD's ''Orinoco'' uses an indefinite article: &quot;A river of Venezuela flowing more than 2,415 km (1,500 mi), partly along the Colombia-Venezuela border, to the Atlantic Ocean.&quot; It is not clear why the definition should not be reformulated as follows: &quot;The river of Venezuela that is flowing more than 2,415 km (1,500 mi), partly along the Colombia-Venezuela border, to the Atlantic Ocean.&quot; The definite article would suggest that the characteristics stated pick a unique object in this world. Whether they pick a unique object in all possible worlds is perhaps open to debate.

The definite vs. indefinite description quandary applies to definitions of common nouns that name individual objects as well, e.g. to the definition of [[wikt:mercury|mercury]]: why should the definition of the metal start with an indefinite article given the definition is intended to uniquely identify a particular chemical element as an individual object?

A related if somewhat tangential question is why should definitions start with an article at all, including those of common nouns. Since, if &quot;cat&quot; is &quot;a domestic animal such-and-such&quot;, then &quot;the cat over there&quot; is &quot;the a domestic animal such-and-such over there&quot;, a non-grammatical form via the use of &quot;the a&quot;. The conventional indefinite article perhaps matches the conventional encyclopedic defining sentence, in which we say that &quot;A cat is a domestic animal such-and-such&quot; and we say that &quot;Orinoco is a river such-and-such&quot;. Nonetheless, to match this form, we could note that the relation in the middle is not &quot;is&quot; but rather &quot;is a&quot;, which would get us rid of the article, as if assigning the article to the copula.

==Proper name vs. proper noun==
The concept of proper name is sometimes distinguished from that of proper noun, while at other times, they are taken to be the same concept. When they are distinguished, proper noun is taken to be an phonological or orthographic word, and therefore, &quot;London&quot; is a proper noun while &quot;New York&quot; is not but is a proper name.

==Pluralization of proper names==
Some proper names can be pluralized, by act of which they are grammatically treated as if they were common nouns. Thus, one can use the form &quot;Peters&quot; to refer to multiple 'people called &quot;Peter&quot;'.

Some proper names are plural per default, e.g. the ''Azores'' (islands) and the ''Pleiades'' (stars).

==Proper names vs. definite descriptions==
Definite descriptions are not proper names. Thus, &quot;the dog over there&quot; is a definite description, uniquely identifying a referent given a context (with the use of the indexical &quot;over there&quot;), but it is not a proper name. &quot;dog over there&quot; is not a definite description, as it lacks the definite article; it is a common-noun description, possibly corresponding to multiple referents/entities. Furthermore, the phrase &quot;the dog over there&quot; may turn out to refer to nothing if 1) there is no dog over there or 2) there are multiple dogs over there, in which case there is no way for the definite article &quot;the&quot; to pick one the multiple dogs as the salient referent of the phrase.

This analysis makes it possible to analyze &quot;the world&quot; as a definite description, part of which is the common noun &quot;world&quot;; the definite article &quot;the&quot; indicates that there is only one thing corresponding to the common noun modified by the definite article. It would follow that neither &quot;the world&quot; nor &quot;world&quot; are proper nouns, the former being a definite description (like &quot;the dog over there&quot;), the latter being a common noun.

The concept of definite description is covered in the following:
* [[Wikipedia:Definite description]]
* [https://plato.stanford.edu/entries/descriptions/ Descriptions], Stanford Encyclopedia of Philosophy
* [[Wikisource:The Problems of Philosophy/Chapter 5]] by Bertrand Russell, 1912

==Proper names using the definite article==
Some English proper names use the definite article &quot;the&quot;, an example being ''the [[wikt:Hague|Hague]]''. Some of this use seems to be a conventionalized anomaly, an aberration from the grammatical system of the language. A different case are ''the moon'', ''the earth'' and the like analyzed in a dedicated section above.

Examples include the [[wikt:Hague|Hague]], the [[wikt:Nile|Nile]] and the [[wikt:Sahara|Sahara]]. These seem to be an anomaly to be learned as a special case, as if the tribal knowledge of the users of the language.

The definite article is often used with multi-word names whose head is a capitalized common noun, e.g. the [[wikt:United Nations|United Nations]], the [[wikt:Atlantic Ocean|Atlantic Ocean]] or the United Kingdom. The rationale could be that, without the definite article, the name has the appearance of being a common-noun phrase, capitalized or not.

Another case is ''the [[wikt:Philippines|Philippines]]'' and its ilk. In this name, it is implied that there is a quasi-common noun ''Philippine'' (one island), and that the group of these is the plural. And since ''Philippine'' is as-if a common noun, a definite article is required to turn it into something like a proper name, or at least a definite description. Whether this analysis is correct is unclear.

The phrase ''the English language'' is capitalized as if it was a definite description, not a proper name, so that is probably what it is considered to be. And yet, there seems to be some structural similarity between this phrase and e.g. ''the Indian Ocean'', which is capitalized as a proper name. The difference seems to be an arbitrary convention.

Further reading:
* [http://writing.umn.edu/sws/quickhelp/grammar/articlesproper.html choosing articles with proper nouns], writing.umn.edu
* [https://web.mit.edu/course/21/21.guide/art-pnou.htm Articles and Proper Nouns], web.mit.edu
* [https://www.englishcurrent.com/grammar/definite-article-place-names-geography/ Grammar: The Definite Article ('The') with Names of Places (Geographic Locations)], englishcurrent.com
* [http://digilib.k.utb.cz/bitstream/handle/10563/37434/wo%C5%BAnica_2016_dp.pdf?sequence=1&amp;isAllowed=y The Use of Articles with Proper Nouns in English] by Martin Woźnica, Bachelor Thesis
* [https://www.grammarly.com/blog/geographical-use-the/ Geographical Use of the Definite Article, The], grammarly.com

==The meaning of proper names==
There is some disagreement in literature on whether proper names have a ''meaning''. What they certainly do have are ''referents'', individual things referred to, denoted or designated.

Stanford Encyclopedia of Philosophy says that &quot;Proper names are familiar expressions of natural language, whose semantics remains a contested subject.&quot;

J. S. Mill says in [[Wikisource:A System of Logic, Ratiocinative and Inductive/Chapter 5]]: &quot;For, as has already been remarked, proper names have strictly no meaning; they are mere marks for individual objects: and when a proper name is predicated of another proper name, all the signification conveyed is, that both the names are marks for the same object.&quot;

As for meaning, there is a sharp contrast between e.g. proper names of places and countable common nouns, but not so sharp one between proper names of places and names of qualities such as &quot;blueness&quot;. Since, for countable common nouns, there is the duality between the concept or class denoted and its particular instance referred to by a definite description using the countable common noun. Whereas for names of qualities, the contrast is not so sharp. In particular, &quot;blueness&quot; does not refer to a class of individual objects but rather to an individual object, albeit an abstract one. Thus, &quot;blueness&quot; would appear to be a proper name if it were not for the fact that it refers to an ''abstract'' object. Thus, if names of abstract individuals have meanings, it is not clear why names of concrete individuals have none.

Furthermore, what is referred to as meaning can sometimes be referred to as ''intension'' or Fregean ''sense''/Sinn, although whether this mapping is perfect is uncertain. Starting from here, we may note the Fregean comparison of proper names Hesperus/Evening Star and Morning Star. These have the same referent/Bedeutung, Venus, but not the same sense/Sinn. Thus, upon Fregean analysis, these proper names do have a meaning distinct from the referent, namely the manner by which the referent is selected or cognitively accessed. Thus, one can associate a defining or essential Russellian definite description with each proper name, and that is an intensional object, a meaning-like object. And this definite description can plausibly be claimed to specify the meaning, different between Evening Star and Morning Star. It is a candidate essential definite description for one of the multiple senses (one per referent) of a proper name that one would find on the definition line in a dictionary. Thus, the denial of meaning to proper names is at least open to debate.

Further reading:
* [https://plato.stanford.edu/entries/names/ Names] in Stanford Encyclopedia of Philosophy (SEP), plato.stanford.edu

==Inclusion in general dictionaries==
General dictionaries often include a range of proper names, while not aiming at a comprehensive coverage of them.
* Merriam-Webster has over 12,000 geographic names such as London, over 5,500 biographic names such as Darwin, some astronomical names such as Small Magellanic Cloud, some names of organizations such as Red Crescent, and, on the miscellaneous note, Othello, Zeus, Faust, World War I and World War II. See also [[Wiktionary:WT:MWO]].
* For Oxford English Dictionaries, see [[Wiktionary:WT:OED]].
* AHD has e.g. Glasgow, Orinoco, Titicaca, Sirius, Darwin, Charles Robert, and Red Crescent; it does not have Greenpeace.
* Macmillan has e.g. Germany, but not London or Titicaca. It has Jesus Christ as an interjection; it does not have Moses.
* German Duden has e.g. Japan, Orinoko, Zeus, Martin (first name), He­gel, Georg Wilhelm Friedrich (philosopher), and Ku-Klux-Klan (organization).

==Specialized proper name dictionaries==
There are specialized proper name dictionaries, including dictionaries of first names, surnames and geographic names.

Dictionaries of first names and surnames:

* [https://www.oxfordreference.com/display/10.1093/acref/9780199677764.001.0001/acref-9780199677764;jsessionid=46BA624A54E1CB5E87E777620110C0A5 The Oxford Dictionary of Family Names in Britain and Ireland] by Patrick Hanks, Richard Coates, and Peter McClure, 2016, over 45,000 entries
* [https://www.oxfordreference.com/display/10.1093/acref/9780195081374.001.0001/acref-9780195081374 Dictionary of American Family Names (1 ed.)], edited by Patrick Hanks, 2003, more than 70,000 of the most commonly occurring surnames in the United States
* [https://global.oup.com/academic/product/a-dictionary-of-english-surnames-9780192806635?lang=en&amp;cc=au A Dictionary of English Surnames], by Reaney and Wilson, 2005, covers the origin and meaning of over 16,000 English surnames
* [https://www.oxfordreference.com/display/10.1093/acref/9780198610601.001.0001/acref-9780198610601;jsessionid=AEE978AF286C46C6C1DF07896238293F A Dictionary of First Names (2nd ed.)], edited by Patrick Hanks, Kate Hardcastle, and Flavia Hodges, 2006, over 6,000 names

Dictionaries of person names and place names:
* [https://lexicon.gr/en/product/dictionary-of-proper-names/ Babiniotis Dictionary of Proper Names], lexicon.gr -- over 2.700 place names and personal names, Greek and foreign, ancient and modern
* [[W:Merriam-Webster's Geographical Dictionary]], a dictionary of place names which contains not only linguistic information but also encyclopedic information. The 2001 edition has over 54,000 entries.
* [[W:The Dictionary of Imaginary Places]]
* A range of publications called &quot;gazetteer&quot;, some restricted to listing place name forms, other featuring encyclopedic information such as statistical information.

==Gallery of proper names==
Gallery of proper names to give an idea of the range:
* Astronomical name: Betelgeuse, Sirius, Small Magellanic Cloud
* Place name: London, New York, the Atlantic Ocean, the Nile, the Himalayas, White House, Baker Street
* Political entity name: the Federal Republic of Yugoslavia, the United Kingdom of Great Britain and Northern Ireland, France, Germany, Japan, Korea, China, the U.S., the U.K.
* Person name
** First name: Martina, Peter, Matthew, Steven
** Pet variant of first name: Pete, Matt, Steve
** Surname: Newton, Einstein
** Patronymic or matronymics: Sergeyevich, Ilyich
** Multi-part person name: Albert Einstein, Karl Raimund Popper
** Nickname of a person: Governator, Orange Man
** Historical person name: Aristotle, Plato, Aristarchus, Caesar
** Regnal name: George VI, Charlemagne, Catherine the Great
** Mythological person name: Zeus, Hera
** Name of a fictional character: Ungoliant, Sleeping Beauty, Pinocchio
** Music group name: the Beatles, the Rolling Stones, ABBA
* Pet animal name:  Bella, Max
* Person group name
** Company name: Microsoft, Google, Lufthansa, General Electric
** Organization name (not company): the United Nations, the Democratic Party, Ku Klux Klan, Greenpeace
* Language name: English, German, Spanish
* Work name: Lysistrata, Much Ado about Nothing, Pinocchio
* Brand name: Kellogg's, Audi, Sempron, Pentium
* Event name: World War I, World War II, the American Civil War, the Franco-Prussian War, The Great Exhibition
* Ship name: HMS Beagle, Bismarck
* Space probe name: Discovery, Pioneer

==Applications of the concept==
One may ask why bother to distinguish common nouns from proper nouns and proper names rather than only use the concepts of noun and noun phrase. By abolishing the distinction, one would get rid of the philosophical and demarcation quandaries. Some applications follow:
* In lexicography, general dictionaries usually adopt the policy of excluding most proper names. Proper names are considered to be not the kind of generic tool of language that other kinds of words are.
* In spelling or orthography, someone has decided it was a good idea to capitalize proper names but not common nouns. This was implemented in English and many other languages. If one wants to implement this policy, one needs the concept of proper name. One's capitalization choices are then in part driven by debates about whether a particular item is a proper name.
* The language learner may want to learn the intricacies specific to proper names. For instance, in German, one may learn from a teacher that while one can hear expressions like &quot;der Martin&quot;, that is informal or incorrect since, in German, proper names are in general used without articles. The learner of English may want to pay attention to the subject of proper names, including when to use definite articles, which is semi-regular.

==Further reading==
* [[Wikipedia:Proper noun]]
* [[Wikipedia:Proper name (philosophy)]]
* [https://plato.stanford.edu/entries/names/ Names], Stanford Encyclopedia of Philosophy, plato.stanford.edu
* [https://plato.stanford.edu/entries/rigid-designators/ Rigid Designators], Stanford Encyclopedia of Philosophy, plato.stanford.edu
* [[Wikisource:A System of Logic, Ratiocinative and Inductive/Chapter 5]] by J. S. Mill, on whether proper names have a meaning
*: &quot;For, as has already been remarked, proper names have strictly no meaning; they are mere marks for individual objects: and when a proper name is predicated of another proper name, all the signification conveyed is, that both the names are marks for the same object.&quot;
* [https://www.collectionscanada.gc.ca/obj/s4/f2/dsk2/ftp04/mq20660.pdf Proper Names] by Aaron Lamber, master's thesis, 1997  -- covers theories about proper names by Mill, Frege, Russell, Strawson and Kripke
* [https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=41f6770e0243d4968faaec29bc736272ae36da45 Proper Names: One Century of Discussion] in ''Logica Trianguli'' by Uxía RIVAS MONROY, 1999

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This original article or essay is on elimination of dead metaphor, or lexicalized metaphor, from writing. One may aim at eliminating as much dead metaphor from writing as possible. It may seem to be a daunting task, but not entirely impossible.

One may ask what one gains from doing so, and that shall eventually be clarified. Some benefits sometimes gained are the reduction of ambiguity, a reduction of vocabulary to remember and an increase in mnemonic value.

A metaphor is ''dead'' in so far as it became its own sense of a word or phrase, and thereby gained the right to be covered by a dictionary, in contrast to ad hoc metaphors created e.g. in poetry. The user of a dead metaphor uses language ''literally'', hence the distinction of ''dead'', since otherwise, metaphorical use is by definition not literal. Not only are the secondary figurative senses often dead metaphors of the primary sense but also the primary senses may be dead metaphors of terms in a language from which they were borrowed. Thus, language shows that not only are words (syntactic objects) used to point to concepts (semantic objects), but also concepts (semantic objects) can be used to point to concepts (semantic objects). Thus, the concept of puncturing something with a sharp instrument can point to the concept of mathematical point.

To get things started, let us analyze some cases of elimination of dead metaphors:
* Instead of &quot;X is nonsense&quot;, we may say &quot;X is obviously untrue&quot; if that is what we mean. Since, if a sentence has a clear and unambiguous semantics, it makes sense in that the semantics can be determined. By the replacement, we obtain increased clarity and precision as well, and turn language that may be considered impolite into one that is neutral. And if we want to tone down the statement, we may drop &quot;obviously&quot; and say only that &quot;X is untrue&quot;.
* Instead of &quot;X is false&quot;, we may say &quot;X is untrue&quot; (as in inaccurate) if that is what we mean. Thereby, we eliminate the figure of ''not genuine'' (lead sense in M-W) and the figure of ''deception'' (etymology in M-W). We gain reduced ambiguity as well by eliminating the sense ''not genuine''. We pay the cost of increased number of syllables.
* Instead of &quot;X is a demagogue&quot;, we may say &quot;X is a dishonest arguer&quot;. The complaint we are addressing is that, by etymology, ''demagogue'' is something like ''folkleader'' (compare ''pedagogue'') and folk leaders are not necessarily dishonest arguers; at the same time, not all dishonest arguers are folk leaders. Moreover, one may complain that the use of the word ''demagogue'' for the purpose is an ideological attack on ''folk'' or the ''people'' or at least on ''folk leaders''; that may sound oversensitive, but is perhaps not entirely without merit. We may further complain that ''arguer'' is ambiguous: it could be one who supplies arguments or one who supplies a quarrel. This can lead to an amendment: &quot;X is a dishonest argument maker&quot;.
* Instead of &quot;X is a sophist&quot;, we may say that &quot;X is a dishonest argument maker&quot;. The complaint we are addressing is that, by naive surface etymology, a ''sophist'' is a ''wisdomer'' or ''wiser'' and that the concept of dishonesty is not present on the surface level. Another objection to the word ''sophist'' can be that it smears the Ancient Greek teachers called ''sophists'' as dishonest argument makers when they were in fact something slightly different, teachers of certain kind of wisdom. Whatever they actually were, it could seem advisable not to cement a prejudicial unfavorable judgment of them into the vocabulary of language.
* Instead of &quot;X is a dead metaphor&quot;, we may say that &quot;X is a lexicalized metaphor&quot;. The word &quot;lexicalized&quot; (turned into a word of its own) is more literal than &quot;dead&quot;. Alternatively, instead of avoiding the metaphor, one may choose a metaphor that seems more fitting, e.g. ''ossified metaphor'' or ''frozen metaphor''; after all, a dead metaphor is in a sense very much alive, kicking and screaming in all its uses that became part of the language.
* Instead of &quot;X is horrible&quot;, we may say &quot;X is very bad&quot;, &quot;X is very unpleasant&quot; or &quot;X is of very low quality&quot;, to avoid the image of causing horror, or down the etymological chain, of trembling.
* Instead of &quot;X is a bachelor&quot;, we may say &quot;X is an unmarried man&quot;, getting rid of the figures of a certain kind of knight or a certain kind of serf. If we say &quot;X is a single man&quot;, we reduce the number of syllables, but introduce the figure of oneness and increase ambiguity.

If we are lucky, we may replace a single word with a single word, often a morphologically non-atomic word, e.g. ''untrue''. If we are less lucky, we may need to replace a single word with a sequence of words, generally a syntactic construction, e.g. ''dishonest argument maker''. If we insist on using a single word and accept ambiguity, we may choose ''malarguer'', but that only points to ''badness'', not ''dishonesty''.

Often, we may not want to pay the price in the increased length. Thus, we may want not to replace ''point'' with ''infinitely thin little dot''; for ''point'', the complaint would have been that it hides the metaphor of puncturing.

When seeking a less metaphorical word or phrase for a given one, one may use a synonym dictionary or a thesaurus. Among the candidate synonyms, one may choose the one that is least metaphorical, in part with the use of etymology. For that, a thesaurus well integrated with an etymological dictionary is of benefit.

One may object to the enterprise by pointing out that the process is on the whole fighting the word overloading process of language. Whether one wants to engage in that enterprise depends on whether one appreciates the benefits more than the disadvantages or the effort. It seems very unlikely that the dead metaphor can be eliminated completely, but it sure can be eliminated to some extent.

==Further reading==
* [[Wikipedia:Dead metaphor]]

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This article by Dan Polansky is on FreeMind, a free mind mapping software. Dan Polansky is one of the main FreeMind authors; given the possible bias and conflict of interests of the author, it is advisable to verify statements made in this article in independent sources.

FreeMind is an editor of mind maps. A FreeMind mind map is a hierarchy of plain text or rich text (HTML) collapsible nodes, presented on the screen via a characteristic layout. There is a root node surrounded by an oval outline. Per default, each non-root node is visually underlined and is connected to its parent node using a curved line (Bezier curve per default). Different styles of nodes and connecting curves (&quot;edges&quot;) can be chosen. Each node has child nodes, which have their child nodes, etc. The collapsed state of a node is saved in the mind map file. When the node is to the right of the root node, its child nodes are also to the right, layed out in such a way that the parent node is at the vertical center of the block of its child nodes; when the node is to the left, its child nodes are also to the left. There is a range of additional features mentioned below.

==General==
Consistent with user reports, FreeMind shows remarkable simplicity combined with productive keyboard shortcuts. It provides richness that lies somewhere between a plain text editor and a word processor. It exposes hierarchical relationship between parts of a document or information node structure in a strong way. One of the defining features of FreeMind is the presentation of hierarchy of nodes as a collapsible, possibly large, tree of nodes that can contain short plain text, long plain text paragraphs, and long HTML-formatted plain text paragraphs, layed out on the screen as a mind map. One can think of the resulting information structure and presentation in various ways, including as a traditional mind map and a rather large knowledge base collecting plain text notes in a hierarchy, as if a hierarchical notebook. One can create something like an encyclopedia in a single mind map if one wishes, and that is what Daniel Polansky, one of the main authors, did as part of his employment, based on his self-report.

Features of FreeMind are described in Wikipedia article as well as on the official web site[https://freemind.sourceforge.net/wiki/index.php/Main_Page#Features].

Written in Java, FreeMind runs on Windows, Linux and macOS.

FreeMind is documented in FreeMind wiki hosted in the official web site.

==Features==
Features of FreeMind include the following:
* A hierarchical tree of nodes.
* Collapsing a subtree on one click.
* A node can be short plain text one, long plain text one and rich-text-formatted one via HTML. The version of HTML is not specified; it is one that can be shown by the Java platform JLabel class.
* A HTML node can be edited using the built-in SimplyHTML editing component or the source HTML can be copied and pasted to an external HTML editor or syntax-colored plain text editor.
* Font color and background color of nodes.
* One hyperlink per node, to point to a local file or to a web URL.
* Breadth-first search in the subtree of the currently selected node.
* Physical styles making it possible to apply a predefined color to a node by pressing a built-in shortcut from F3 to F9.
* Clouds, having different colors.
* Time stamps for creation and last change per node.
* Customizable keyboard shortcuts.
* Built-in icons; user icons.
* Attributes for each node.
* Undo.
* Graphical links, elsewhere called connectors, connecting nodes, carrying no label.
* A note per node, in HTML, editable in a pane per default located at the bottom, with customizable location.
* Export to HTML (multiple functions).
* Spell-checking in FreeMind 1.0.1.
* Node cloning in FreeMind 1.0.1.
* Etc.

Further reading:
* [https://freemind.sourceforge.net/wiki/index.php/Main_Page#Features Main Page#Features], freemind.sourceforge.net
* [https://freemind.sourceforge.net/wiki/index.php/Releases Releases], freemind.sourceforge.net

==Storage format==
FreeMind mind map is stored in a relatively simply XML format, not zipped, as a single file. The traditional file name extension is &quot;.mm&quot;. A downside of the format is that Unicode characters beyond 7-bit ASCII are stored in XML entities rather than UTF-8, making storing the mind map in a revision control system and viewing them in a plain text editor remarkably inconvenient, especially for, say, Asian scripts. One consequence is that FreeMind mind maps are rather easy to generate programmatically, whether via Python or Java, something users report doing.

==Authors and contributors==
Authors of FreeMind include Jörg Müller (German), Daniel Polanský (Czech), Petr Novák (Czech), Christian Foltin (German), Dimitry Polivaev (Russian-German) and others.[https://freemind.sourceforge.net/wiki/index.php/Authors_and_contributors] The project was started by Jörg Müller as part of his study at a university at Freiburg.

==License==
FreeMind has a free-as-in-freedom license, GNU GPL V2+. However, some libraries used have a GPL V2 incompatible license, so for practical purposes, the license probably has to be interpreted as GNU GP V3+, since GPL V3 created compatibility with these licenses.

==Reviews==
User praise, feedback and critical evaluation can be found in the following:
* SourceForce project reviews[https://sourceforge.net/projects/freemind/reviews/]. Provides star-based score.
* Thank you for the music[https://sourceforge.net/p/freemind/discussion/320015/] forum
* [https://freemind.sourceforge.net/wiki/index.php/Marketing#Who_writes_about_FreeMind_on_the_web Marketing # Who writes about FreeMind on the web], freemind.sourceforge.net

==Freeplane==
Fork of FreeMind, Freeplane, exists, created by Dimitry Polivaev, one of the contributors to the FreeMind project. Consistent with user reports, Freeplane adds remarkable complexity over the original simplicity of FreeMind; some find the host of new features appealing and worthwhile, whereas others feel that it harms simplicity and elegance and adds what one could informally call ''cruft''

==Official versions==
Official versions or releases are listed here:
* [https://freemind.sourceforge.net/wiki/index.php/Releases Releases] in wiki, freemind.sourceforge.net
* https://sourceforge.net/projects/freemind/files/freemind/
** https://sourceforge.net/projects/freemind/files/freemind/1.0.1/ -- release 1.0.1. is currently the most downloaded release
* https://sourceforge.net/projects/freemind/files/freemind-unstable/

==Dan Polansky version==
A custom Dan Polansky version made on the basis of FreeMind 0.7.1 is available from here:
* https://sites.google.com/site/danpolansky/freemind
** file freemind-src-0-7-1-XT.zip for the source code
** file FreeMind-Dan-2004-2008.odt describing the changes made to the source code
About the version, FreeMind 0.7.1-XT:
* The version has no plugins and no plugin architecture, which makes it more secure in general.
* The version is probably not widely used, so it may be much less tested in practice.
* The version was made available only in the source code form, to steer potential users to the official FreeMind version. Nonetheless, those who love the simplicity of FreeMind 0.7.1 can prefer FreeMind 0.7.1-XT.
* The source code is located at freemind-src-0-7-1-XT.zip.
* The version is in the spirit of Dan Polansky's minimalism, as contrasted to the much increased size and complexity of version after 0.7.1, starting with FreeMind 0.8.0.
* Certain file format extensions or changes may be not 100% compatible with the format of the official FreeMind versions.

==Word processing==
FreeMind can be used as a simple word processor, instead of Microsoft Word or OpenOffice/LibreOffice Writer. FreeMind lacks many features of traditional word processors, yet has some features of its own to add. Moreover, the lack of additional features prevents distraction.

Features absent from Microsoft Word:
* FreeMind has an excellent folding ability, arguably not matched even by MS Word's outline mode.
* FreeMind lets you edit one chunk of information at a time, preventing accidental edits to unrelated parts of the document: you can only edit a node in a separate window.
** An accidental keystroke pressed while editing the current node has no effect on other nodes.
** Chunks of information are as if preselected to be moved around. In a traditional word processor, you have to select a text freely before you move it somewhere else; nothing prevents you from accidentally omitting the first character in the paragraph that you are selecting with the mouse. In FreeMind, it is the whole nodes and branches that are ready to be moved; several paragraphs can be not only easily but also confidently selected before they are moved somewhere else, which is equally valid of sections, chapters and articles.
** A paragraph-long node can have color rapidly and confidently changed by pressing F3 throught F9 or Alt + B.
** When user edits a long node, they do so in a separate window while the old content remains in the mind map. It is only when they confirm the change that the old change gets replaces. This creates the psychological effect of a commit, potentially nudging the user to review the changed text before confirming the change. It produces a chunky unit of work on the use level not existing in traditional word processors.
* The mind map files created by FreeMind are very transparent: they are plain unzipped XML files. They are easy to generate programmatically, and easy to read in a plain text editor except for the fact that Unicode points beyond 7-bit ASCII are stored as character entities. Technically-minded users can store FreeMind mind maps in a revision control system—a piece of software that keeps the history of changes of a plain text file and can show differences between subsequent revisions of the given file.  Examples of such programs include CVS, Subversion, Bazaar and Git.
* FreeMind search is a breadth-first one, meaning that articles and sections are usually found before body text; that, however, depends on the level of nesting, so sometimes a body text can be found before a section heading. The search can be restricted only to a branch, meaning a particular folder, article or a section, by placing the cursor to the root of the branch before starting the search function.
* One can easily add icons from a limited reasonably well chosen selection, and they are then identified in the mind map via icon names rather than being stored as images. In Word, one has to pick a file to be used as an icon and insert it in a proper place, in a way that is much less seamless. And then, each additional occurrence of the icon file takes additional space in the Word file.
* In FreeMind, one can easily connect nodes using &quot;arrow links&quot;, connecting curved lines. In Word, one cannot so conveniently create a connecting line from one paragraph to another; if one succeeds at all, the relative position of the curved line and the paragraphs is not guaranteed to remain stable.
* In FreeMind, adding a cloud is easy and fast. In Word, the closest analogue is perhaps a paragraph with different background color, requiring multiple mouse clicks to ensure.

Limitations:
* FreeMind lacked spell-checking until version 1.0.1. In older versions, to spell check, one can export an article or its section to HTML, copy it to OpenOffice/LibreOffice Writer or Microsoft Word, and spell check there. Alternatively, one can open the exported HTML document in the open source HTML editor Kompozer, and spell-check there.
* FreeMind cannot embed other documents such as spreadsheets and presentations
* FreeMind's built-in rich text editor available in 0.9.0 series is still quirky. 

The way I (Daniel Polanský) use FreeMind, one mind map corresponds to a folder of documents rather than a single document. FreeMind handles even large mind maps well as long as most of the content is folded; my largest mind map has 30 MB. I have a short node per folder or category of articles, a short node per article, and a short node per section of an article; long nodes are body text and include paragraphs, bullet lists and numbered lists, and tables. I do not use notes.

For finishing, an individual article can be exported to HTML by pressing Control + H, and copied and pasted to Microsfot Word or OpenOffice/LibreOffice Writer.

One can print articles by exporting them to HTML, and printing the result from a web browser, getting nice results in this way. However, there is no support for headers and footers, unlike in traditional word processors. Alternatively, one can copy and paste the text from the exported HTML to Microsoft Word, and finish the document for printing there.

==Security==
Security of the data is of concern. One is the risk of data loss, the other one is of data theft. The following is written not by a security expect; in case of doubt, it is advisable to contact a security professional to perform an analysis or audit.
* Data loss risk is mitigated by FreeMind saving automatic backups into a certain folder. However, this same feature could make data theft easier (needs clarification). In any case, it is a recommended practice to set up a regular backup procedure for any important files, not just FreeMind files. What FreeMind provides here is a crutch for people not disciplined enough to setup a proper regular backup process.
* Since FreeMind mind maps are plain text files, any spyware aware of FreeMind file format can take away information from FreeMind mind maps. In this regard, FreeMind mind maps fare no worse or better than plain text files, so cherished by many a Unix user.
* FreeMind offers the possibility of encryption, relying on the encryption services provided by the Java platform. What extent of true security this achieves is unclear; we are aware of no security audit in relation to this FreeMind feature. Having an encrypted section seems out of scope of the core FreeMind feature set, and there is a risk that a user creates a false sense of security achieved by using this function. FreeMind is not designed as a password management software and it appears advisable to avoid using FreeMind for the purpose. In case of more serious doubt, this internal encryption feature would be disabled and users would be asked to use e.g. zip to encrypt the whole mind map as, say, PersonalConsiderations.mm.zip. Then, the user would have the encryption method and its strength under strict control, using encryption tool that is specifically designed to address that task.
* FreeMind 0.8.0 introduced undo and after a disagreement in the team, the version was released with undo that cannot be disabled. This is a violation of Mill's harm principle, treating FreeMind users as kindergardeners who need tutelage. And it is not clear what kind of security risk this mandatory use of undo creates on its own, especially given that the storage for undo purposes is in XML format, ready in a form that can be transmitted over the network.
* The latest releases without plugins is FreeMind 0.7.1 and FreeMind 0.7.1-XT.
* Since FreeMind is apparently used by many users and organizations, one might by inclined to think that enough eyeballs double checked that there is no genuine security issue. However, we know the story about spinach and iron, and we are reminded of the quote that people would sooner die than they would start to think, and indeed, this is what most of them do.
* If an organization actually did publish a security audit, it would be preferable to post it here, for traceability.
* As per https://freemind.sourceforge.net/wiki/index.php/Scripting#Security, security level for scripting can be customized. The most secure option is to disable scripting altogether.
* Bundling JRE with FreeMind is a concern: since such FreeMind installs a dedicated Java JRE locally as a separate copy, it will not receive any automatic security updated. Requires a solid analysis as to whether there is a genuine security risk.

==Plugins==
Plugin architecture was introduced in FreeMind 0.8.0.

Internal plugins of FreeMind are a reminder plugin, a plugin for export to SVG and PDF and a help plugin.

Plugins provided by external parties include above all LaTeXMath-Freemind-Plugin.

See more in the further reading.

Further reading:
* [https://freemind.sourceforge.net/wiki/index.php/Plugins Plugins], freemind.sourceforge.net

==Scripting==
FreeMind has a support of scripting via Groovy programming language since FreeMind 0.9.0. A script is stored in the mind map, in an attribute named like script1, script2, etc. By default, FreeMind scripts are restricted in what they can do on the local computer, which includes restrictions on file operations, network operations and execution of applications; these restrictions can be lifted in user preferences.

Further reading:
* [https://freemind.sourceforge.net/wiki/index.php/Scripting Scripting], freemind.sourceforge.net
* [https://freemind.sourceforge.net/wiki/index.php/Scripting/Mind_map_documentation Scripting/Mind map documentation], freemind.sourceforge.net
* [https://freemind.sourceforge.net/wiki/index.php/Example_scripts Example scripts], freemind.sourceforge.net
* [[Wikipedia: Apache Groovy]]

==Source code revision histories==
The source code is hosted in Git in SourceForge. It used to be hosted in CVS. The history in Git appears to reach back to &quot;Initial checkin of the 0.9.0 RC15 sources&quot; but no earlier. It would seem a significant portion of the code change history has been lost, or at least not available from the Git.

Nonetheless, source code snapshots for each version can be downloaded from https://sourceforge.net/projects/freemind/files/freemind/:
* freemind-src-0_0_2.zip, 2000-06-27
* freemind-src-0_0_3.zip, 2000-07-09
* freemind-src-0_1_0.zip, 2000-08-05
* freemind-src-0_2_0.zip, 2000-11-02
* freemind-src-0_3_0.zip, 2001-03-24
* freemind-src-0_3_1.zip, 2001-03-27
* freemind-src-0_4.zip, 2001-07-07
* freemind-src-0_5.tar.gz, 2002-08-24
* freemind-src-0_6.zip, 2003-02-01
* freemind-src-0_6_1.zip, 2003-02-08
* freemind-src-0_6_5.zip, 2003-09-04
* freemind-src-0_6_7.zip, 2003-10-25
* freemind-src-0_7_1.tar.gz, 2004-02-15
* freemind-src-0_8_0.tar.gz, 2005-09-07
* freemind-src-0_8_1.zip, 2008-02-26
* freemind-src-0.9.0.tar.gz, 2011-02-18
* freemind-src-1.0.0.tar.gz, 2013-10-16
* freemind-src-1.0.1.tar.gz, 2014-04-12

==CVS==
FreeMind code was originally captured in Concurrent Version System (CVS) in SourceForge. It was then switched to Git at some point during the FreeMind 0.9.0 development. The CVS still seems to be accessible in some form, in read-only mode. For instance, page http://freemind.cvs.sourceforge.net/freemind/freemind/freemind/modes/mindmapmode/ tells us we can do the following:
* cvs -z3 -d:pserver:anonymous@a.cvs.sourceforge.net:/cvsroot/freemind co -P freemind

Further reading:
* [https://freemind.sourceforge.net/wiki/index.php/CVS CVS], freemind.sourceforge.net

==Statistics==
FreeMind version 1.0.1 was downloaded over 5,800,000 times in total from SourceForge[https://sourceforge.net/projects/freemind/files/freemind/1.0.1/stats/timeline?dates=2010-12-24+to+2023-03-24].

Further reading:
* [https://freemind.sourceforge.net/wiki/index.php/Statistics Statistics], freemind.sourceforge.net

==Gallery==
&lt;gallery&gt;
File:Freemind-0.9x Screenshoot.png | FreeMind development
File:Depresyon nevit 107.svg | Depression, Turkish
File:Canli-varliklar nevit 114.svg | Creatures?, Turkish
File:Educational software.svg | Educational software
File:PrimatesTreeJa.svg | Primates, Japanese and Latin
File:Produire un wiki avec MediaWiki.svg | MediaWiki, French
File:Viruses Baltimore Classification with extra.svg | Viruses Baltimore Classification
&lt;/gallery&gt;
See also [[:Commons:Category:Valid SVG created with Freemind]].

==Awards==
FreeMind was SourceForge Project of the Month for February 2006. At this occassion, SourceForge produced an interview with project members, including Daniel Polanský, Christian Foltin, Dimitri Polivaev and Juan Pedro.

FreeMind was a finalist in 2008 SourceForge Community Choice Awards in the categories &quot;Best Project&quot; and &quot;Best Project for Educators&quot;.

FreeMind was a finalist in 2009 SourceForge Community Choice Awards in the category &quot;Most likely to change the way you do everything&quot; if one believes the record in FreeMind wiki, which traces to partially defunct https://sourceforge.net/blog/cca09/winners/.

Further reading:
* [https://sourceforge.net/blog/potm-2006-02/ Project of the Month, February 2006], sourceforge.net
* [https://sourceforge.net/blog/cca08-finalists/ 2008 SourceForge Community Choice Awards], sourceforge.net

==Hosting==
FreeMind project uses the facilities of SourceForge, including release management, source code versioning, support forums, issue trackers, mailing lists, download and download statistics, etc.

==Further reading==
* [[Wikipedia:FreeMind]]
* [https://freemind.sourceforge.net/wiki/index.php/Main_Page FreeMind official web site], freemind.sourceforge.net
* [https://sourceforge.net/projects/freemind/ SourceForge project for FreeMind], sourceforge.net

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Author: Dan Polansky

In this article I develop the thesis that it may be of advantage to model or imagine a human as multiple persons or subpersons, or multiple agencies with competing behavior styles or objectives. A related hypothesis is that these multiple persons are created and switched by a hidden 1-deep-overperson; on a more creative and increasingly less testable view, there is an even more hidden 2-deep-overperson controlling the 1-deep-overperson, etc. This may be one of the starting points or inputs into a theory of sincerity.

The organization of sections is rather haphazard.

This article contains multiple plot spoiler alerts; one may avoid reading certain sections if one wants to have full enjoyment of certain books or movies.

Since the ideas may appear to be rather unusual, at least to the popular mind, let us be inspired by Niels Bohr's adage: &quot;We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.&quot;

==Multi-component vs. multi-person mind==
To state that the mind is not an indivisible homogeneous object, meaning that it is not as if an accumulation of still water, seems almost tautological. Thus, there being some components or parts of the mind seems indisputable. What is here investigated is a stronger claim, namely that some entities within the mind can be likened to complete persons. These persons share memory, but do not completely share goals and manners of external self-expression.

==Desire or urge vs. will==
The disunited character of the mind and behavior is apparent in the contrast between 1) desire or urge and 2) will. Thus, one may have decided to stop smoking cigarettes and is trying to use one's will to ensure that abstinence, but a desire or urge to smoke is stronger and the human smokes despite the resolution/previous decision to stop smoking. Thus, the person as a whole appears to itself as multiple struggling agencies or subpersons. This contrast appears to be universal human experience, not something peculiar to some special types of personalities.

==Poorly understood urge==
A person may feel an urge to do something without knowing why, or without being able to state the larger goal to be achieved by the action. That is suggestive of there being a deliberative or decision-making entity in the mind producing the urge, whereas the foreground mind, or the conscious self, receives that urge as an unexplained input. This again points to multi-person or multi-agency model of a mind or self.

==Commanding self-talk and self-control==
Some people happen to say out loud things like, &quot;Martin, stop now!&quot;, or &quot;Paula, pay attention!&quot;, talking to themselves. It is not a usual social behavior, but seems not very rare either. It suggests a mapping to Berne's parent and child ego states: it is the parent component of the mind or the self that issues the command to the child component; what the role of Berne's adult ego state would be is unclear.

The commanding role play can go beyond the use of words. One can for instance clap hands as a reinforcement of a command. One can even issue a slap in the face as a kind of a negative (down-regulating) feedback to previously occurring behavior intended to be avoided. The entity being commanded can be thought of as a more spontaneous child self; some literature uses the metaphor of an &quot;inner elephant&quot;.

The commanding self-talk or even clapping of hands and other stronger expressions of the will would seem to be able to lead to something like a self-control. One could use these kind of de facto theatrical performances (talk to oneself, clapping hands, directively pointing a finger) to affect the behavior of the component that can be likened to a child. One can use different emotional tones for talking to the putative child, such as pleading vs. threatening or commanding. Each person can try out to what extent this method achieves anything like a desirable result.

It seems that for the concept of self-control to have any meaning, the self has to be understood as consisting of at least two parts, the controlled and the controller. The degree of self-control can be examined by assigning oneself various nominally simple tasks and seeing how far one gets, such as select an object and keep staring at that object while counting from 1 to 100.

==Querying self-talk==
Above, I mentioned the possibility of commanding self-talk. But one can also try a querying self-talk, asking questions. One can try different formulations of the questions and see what difference it makes. One can do it in writing as well; however, writing is more committal. On the other hand, one can uncommitt the writing e.g. by ceremonially tearing a slip of paper on which one wrote something one no longer agrees with. Alternatively, one can add &quot;I no longer believe this&quot; on the slip of paper.

Using this method, one can lead something like a Socratic dialogue with oneself, forking into two characters: one character only asks questions and never asserts anything and the other character responds. This again can be a self-talk or can be done in writing.

==Non-verbal self-interaction==
I covered two kinds of self-talk, imperating/commanding and querying. However, one can also engage in non-verbal self-interaction.

One such case is looking at oneself in the mirror, and doing faces (smiles, frowns) and making gestures with hands. To the extent this has any effect, one posits two persons, one governing the faces and gestures, the other receiving them.

One can see a lonely person talking to themselves in a mirror in the film I Served the King of England directed by Jiří Menzel.

==Humans as actors==
It seems that most humans are as-if theatrical actors, good ones or less good ones. A human can take on slightly different personas if they try hard enough: at a minimum, many can switch languages, but also tone or pitch of the voice and posture. The persona taken on depends on the social role and who the other parties are. Thus, one talks different to a child and different to a spouse, as if taking on different personas. In this deliberation, the human occupies one particular role/persona/mask in any given point in time. A human can expressly choose to change the persona/mask, but this is liable to appear aberrant or deviant to those who know the human; they are liable to think something's wrong. When such a change occurs in a theatrical setting, the human has as if a special license to put on a different persona/mask, and the spectators have no need to suspect that something wrong is happening.

One can pick personas from movies and videos. Thus, one can notice peculiar manner or hand motion by a particular person on video and get into that skin or persona, as it were. (The terminology of &quot;persona&quot; still needs a clarification.) At the same time, some gestures can be innate and have an innate meaning.

==The mask metaphor==
The persona that a person behaviorally puts on the face, as it were, can be likened to a mask worn over a face, hiding the true emotion expression on the face. The mask metaphor was used in the Mask movie, starring Jim Carrey. In the movie, the main character, by putting a green mask on his face, got a whole new high-energy, self-confident personality, or what I refer here to as persona. The term &quot;persona&quot; refers to some concept in Wikipedia, but it is not clear whether this is the same idea.

The mask metaphor is to some extent captured in the Czech idiom &quot;strhnout někomu masku&quot;.

Links:
* [[Wikipedia: Persona]]

==Labels for the putative persons or personas==
One can think of the possible personas or inner persons using labels pointing to various roles or dispositions, e.g. crybaby, coward, inspector, reviewer, commander, slave, serf, lackey, inquisitor, comedian, etc. This provides a much richer metaphorical vocabulary than Berne's parent, child and adult.

==Sailors struggling for the control of a ship==
One metaphorical model is one of a human mind, or its unconscious part, featuring multiple sailors competing for the control of a ship. They are on the same ship and have to find a way of working together. They may as if struggle over the steering wheel.

When one knows multiple languages, one cannot use all of them at the same time. Moreover, one cannot think in all of them at the same time. One can imagine that learning the languages produced something like different persons, one per language, struggling to control the outward verbal interface and the internal self-talk language; however, this may be merely a wild philosophical imagination.

==Sigmund Freud==
Sigmund Freud identified in the mind a structure of three components, ego, superego, and id. Since I do not remember much about it, and do not feel like delving into it, I leave it here as a reminder or a placeholder. Superego could be something like an entity controlling or regulating the other entities.

Links:
* [[Wikipedia: Id, ego and super-ego]]

==Eric Berne==
In Eric Berne's transactional analysis involves the concepts of parent, child and adult. It is not wholly clear whether they are to be understood as different subpersons or rather as ego states from which a person interacts with another person.

It is not clear whether any mapping from Berne's three states to Freud's three components can meaningfully be attempted.

Links:
* [[Wikipedia: Transactional analysis]]

==Carl G. Jung==
The Jungian concepts of collective unconscious, perhaps demons, and anima and animus can have some bearing on a human being understood as multiple persons, or being in some way steered by person-like entities present somewhere in the background mind. This needs more research.

Links:
* [[Wikipedia: Collective unconscious]]
* [[Wikipedia: Anima and animus]]

==B. F. Skinner==
Skinner talked of controlling self and controlled self: &quot;The controlling self (the conscience or superego) is of social origin, but the controlled self is more likely to be the product of genetic susceptibilities to reinforcement (the id, or the Old Adam). The controlling self generally represents the interests of others, the controlled self the interests of the individual.&quot;&lt;ref name=bfsp199&gt;[https://books.google.com/books?id=78pgDwAAQBAJ&amp;pg=PA199 Beyond Freedom and Dignity] by B. F. Skinner. page 199&lt;/ref&gt;

However, arguably, the controlling self is not solely of social origin and often represents the interests of the individual. Thus, a controlling self ensuring stopping of smoking benefts the health of the individual, and a controlling self ensuring proper saving and investment strategy (opposing the profligrate self) benefits the wealth of the individual.

Moreover, my theory of conscience does not equate conscience with the controlling self; conscience is, metaphorically, the plaintiff but not the judge and the judgment encorcer.

Skinners posits more than one selves. To him, &quot;A self is a repertoire of behavior appropriate to a given set of contingencies&quot;.&lt;ref name=bfsp199/&gt; He points out there is a different self for interaction with friends and a different self for interaction with family.

References:
&lt;references/&gt;

==Eugene Herrigel==
In Eugene Herrigel's Zen in the Art of Archery, there is the talk of &quot;It aiming at and hitting the target&quot; or similar. What, if anything, is &quot;it&quot;? It seems to be some kind of unontologized/undefined/unspecified entity in the mind or the brain, in some sense distinct from the main volitional person.

==Dissociative disorder==
Psychologists recognize conditions that they call dissociative disorders. They may involve something like a split personality. It is not clear how the experts determine whether this is a disorder or an adaptation, a feature to be used for the best outcome in relation to a chosen objective.

Links:
* [[Wikipedia: Dissociative disorder]]

==ABBA==
The idea that a human can be understood as multiple persons has penetrated the popular culture in a song by a hugely popular Swedish pop group ABBA. It was in the song Me and I. The lyrics brought together various items of culture. The lyrics is very suggestive overall.

Let us consider the following snippet:
: Sometimes when I scream,
: There's a voice in me that says,
: &quot;You shouldn't be so mean&quot;,
Taken literally, it means one agent or person screams and another agent or person tells them not to.

The following snippet suggests prevalence (being widespread):
: I don't think I'm different or in any way unique,
: Think about yourself for a minute
: and you'll find the answer in it, everyone's a freak.
Of course, the author of the lyrics has the poetic license to suggest a thesis that is not thereby scientifically proven.

The items of culture brought together by the song:
* Mr. Jekyll and Mr. Hyde
* Sigmund Freud

==Mr. Jekyll and Mr. Hyde==
''Strange Case of Dr Jekyll and Mr Hyde'' is a 1886 novella depicting a case of two personalities or persons in one human, one relatively nice and the other one nasty, acting at different times. However, this is a mere literary depiction, and has no force of a proof.

Links:
* [[Wikipedia: Strange Case of Dr Jekyll and Mr Hyde]]

==Individual variation==
This multi-person aspect may well be better developed in some people than others. Some kind of multi-person actor-like capability would well suit an agent of a secret service, e.g. Putin in Dresden in German Democratic Republic as a KGB agent.

==Lawyers as multiple persons arguing with themselves==
If there are people who are good at playing devil's advocate, as if arguing with themselves, they could make for good lawyers. What this may involve is even temporary emotional alignment with the opposing party, to facilitate argument discovery. A person who would be able as if to fork new personalities on the fly (as if a Unix-like operating system forking processes) could have an advantage; alternatively, the different personality type or philosophy types would already be latently there, merely waiting to be deployed in argument development. Thus, the person could have something like both an Aristotelian and Stoic in themselves. Possibly, these capacities could develop fully only after being exposed to different kinds of philosophy.

Stephen Covey mentions a notable, perhaps a Roman philosopher, who advises one to first develop arguments for the opposing party and only then for oneself.

==Behaviorism==
The idea of multiple persons coexisting, sometimes struggling to gain control of a human is generated without the tools available to the behaviorist methodology; it is largely based on imaginative speculation inspired by sources. It is therefore relevant to have a look at behaviorism and its merits.

Under the behaviorist psychological methodology (e.g. Skinner), one should limit statements in the field of psychology to things externally observable. Thus, one may observe that a human uttered &quot;I am hungry&quot; or that a human made a gesture, but one cannot observe that &quot;P hopes for H at time T&quot; since the propositional attitude of hope is not accessible directly by observation. Propositional attitudes like belief, knowledge and hope are one class of internal states of the mind that are not directly accessible by the external observer. Indeed, from the point of view of human autonomy and freedom, the idea that others should be able to read one's mind is disconcerting.

There is some merit in the on-the-safe-side approach of behaviorism; it reminds us that it is all too easy to invent a speculation and then defend it against all refutation. But for the purpose of all proto-scientific investigation, the stringency seems to go too far. Moreover, all thought, desire, will and dreams have to be excluded as out of scope, as well as hallucinations (but reports of them are verbal behavior); none of these entities are part of a properly scientific discourse. What remains is verbal behavior, facial expression, gestures, postures, other macroscopic behavior such as walking or running, etc. The language of behavior is preserved for rigorous scientific investigation.

However, in Popperian theory of science, a hypothesis trading in theoretical entities can still be scientific if it makes predictions in observational terms (here, behaviorist) that threaten a refutation of the hypothesis. Even if the posited multiple persons are not directly observable, behaviors suggestive of their being there are. However, to be properly scientific as much as possible, one should consider alternative explanations for the observed behaviors. For illustration, an example of a theoretical entity is the Mendelian gene, whose mapping to DNA sequences, as far as I know, is not established; but the Mendelian theory makes predictions concerning phenotypic signs of, say, peas, and there are observable, and if the behavior turns out different from what matches the Mendelian theory, there is a refutation.

Links:
* [[Wikipedia: Behaviorism]]

==The Boss of it All==
''Warning: plot spoiler alert.'' The idea of humans acting toward people as actors is developed in the Danish film The Boss of It All directed by Lars von Trier. One of the main characters in the film is ostensively an actor, Christopher, but in fact he is not alone; arguably, the real boss Ravn is also an actor, and so is the Icelandic director e.g. with his claims of the alleged teaching of Edda about dealing with mere proxies.

Further reading:
* [[Wikipedia: The Boss of It All]]

==Robert Pirsig==
''Warning: plot spoiler alert.'' In Robert Pirsig's ''Zen and the Art of Motorcycle Maintenance'', the author develops the idea that, on his trip, there is not only himself in his brain but also something like a ghost called Phaedrus, his former self that was as if buried via electroconvulsive intervention. The ghost starts being awakened by Pirsig's visiting a place where Phaedrus used to live and work. In the end, the ghost seems to be reintegrated into the primary Pirsig's person during a crisis, leading to some kind of change of the tone of Pirsig's voice. However, this may be a novelist's license to some extent, to exaggerate and schematize. Be it as it may, the plot points to the idea that multiple persons can reside in a single human and struggle for control over that human. Pirsig had a schizophrenia diagnosis, and his being multiple persons would fit the popular understanding of that diagnosis as a split personality, although that does not match the technical use of the term.

==J.R.R.Tolkien==
''Warning: plot spoiler alert.'' In J.R.R.Tolkien's ''The Lord of the Rings'', character Gollum manifests as two personalities that argue with each other, the other one called Sméagol. The Sméagol personality seems activated or strengthened by Frodo's relatively kind behavior toward him. This has lead some to diagnose the character with multiple personality disorder, now known as dissociative identity disorder.

Further reading:
* {{W|Mental illness in Middle-earth}}, wikipedia.org
* {{W|Dissociative identity disorder}}, wikipedia.org

==Rowan Atkinson and Sacha Baron Cohen==
The ability of an actor to switch to outwardly very different personality expressions including tone of voice is well exemplified in the spoken sketches of Rowan Atkinson, known around the world perhaps above all for his mostly silent role of Mr. Bean.

Another comic actor taking on very different personalities is Sacha Baron Cohen.

A popular YouTuber apparently switching personalities is Liam Carpenter, making fun of stereotypes about Germans. Another one is Loic Suberville, making fun of irregular features of French and English.

The hypothesis that theatrical and movie actors may develop psychological problems relating to their acting, including acting emotions, should be researched later. (There is no suggestion that this pertains to Rowan Atkinson; it bears on the subject of actors switching personalities as part of acting.)

Links:
* [https://www.youtube.com/watch?v=VrwIs10XvKA Rowan Atkinson: Toby the Devil - We Are Most Amused and Amazed], youtube.com
* [https://www.youtube.com/watch?v=2a-CVGbUUjQ Rowan Atkinson Live - Drunks in an Indian Restaurant], youtube.com
* [https://www.youtube.com/watch?v=pHj77P1wSeM Rowan Atkinson Live - Tom, Dick and Harry], youtube.com

==Conversations with God==
Religious people report to have something like a conversation with God. If so, there must be some person-like entity in the background mind (or psyche or unconscious) playing the role of God. Possibly, the person-like God entity is created or shaped by the 1-deep-overperson in response to external cultural stimuli.

==Personal experience==
Dan Polansky's experience since about 2003 is this (after reading Eric Berne): if I start talking to myself from a kind of parent role, say, father role, something like a child in me starts responding. I can praise the child, ask it why it did not do what it planned to do, scold it, etc. Whether this practice is safe is unclear. I do not do it often, but in rare occasions it can make a remarkable difference, e.g. when I need to find out why I am deferring a task for too long and failing to perform what I myself consider to be my duties. One technique is switching to different forms of address, depending on whether one wants to be a strict father or a kind mother; I am using Czech, but in English, I could switch between the formal and cold &quot;Daniel&quot; (strict father speaking), the intermediate &quot;Dan&quot;, and the affectionate &quot;Danny&quot; (tenderly loving mother speaking). Is this some kind of theatrical play and nothing else? I don't know.

==Evolutionary background==
Taking evolutionary psychology as the starting point, one may ask whether a two-layered multi-person structure is too hard to discover in the design space for the Darwinian evolution by natural selection and whether there are tangible benefits, ultimately in terms of the reproduction of the Dawkinsian gene-selfish genes. At a minimum, a two-layer structure is better at creating a deception, a pretense. One may wonder whether there can be a spy-role-supporting biological adaptation, and why exactly do theatrical actors have their capability supported by the brain. And there is a counter-pretense: pretending that one believes the pretenses of others. There could even be something like an arms race of ever deeper pretenses, but this is a vague and poorly articulated idea.

==Internal Family Systems Model==
Wikipedia's article {{W|Internal Family Systems Model}} relates a certain approach to psychotherapy. As per Wikipedia, &quot;It combines systems thinking with the view that the mind is made up of relatively discrete subpersonalities, each with its own unique viewpoint and qualities.&quot; A closer look at this is pending.

Further reading:
* {{W|Internal Family Systems Model}}, wikipedia.org

== The reason and the heart ==
&lt;!-- (wild outline, incomplete)
items

    multiple persons
        wikiversity article
            new section?
                even if it is not a perfect fit?
                freud unconsc. + jun unconsc.
    perhaps slightly different topic
        topic map
    referents of the terms not clear
    communication and control interaction implied
    listen to your heart
        instead of engaging with the enternet
        engage with yourself
        know thyself
--&gt;

In common parlance, we often find references to &quot;the heart&quot;, as some kind of psychological entity. A song says &quot;listen to your heart, there's nothing else you can do&quot;. A reference to the heart is made by Exupéry in The Little Prince: &quot;It is only with the heart that one can see rightly; what is essential is invisible to the eye.&quot; Another is made by Coelho in his Alchemist. Descartes has some relevant quotation, contrasting reason to heart, I think. An English idiom says &quot;learn it by heart&quot;.

One would then think that the psychological self features at least two contrasting components, the reason and the heart (or perhaps the mind and the heart). It is implied that the reason (or the mind) can fail to listen to the heart; that is, it fails to run inquiries to the heart and pay attention to the responses and process them.

A Czech idiom says &quot;ruku na srdce&quot; (&quot;hand to the heart&quot;) to refer to sincerity, in reference to the place at the breast behind which the physical organ of heart is approximately located. Another Czech idiom is &quot;srdce na dlani&quot;, perhaps speak one's heart or speak one's mind. The just indicated possible different, between speaking one's heart and one's mind, would perhaps be worth a deeper analysis. Czech philosopher Comenius wrote Labyrint světa a ráj srdce, perhaps The Labyrinth of the World and the Paradise of the Heart. I have not read it. It is quite possible that he used a slightly different concept of the heart.

One could try to map the heart to an item in the trinity of Freud's ego, superego and id or to one in Berne's trinity of adult, parent and child. I don't know. One might also object that a lay concept of the heart is not going to map to any entity concieved of by a specialist/expert.

It is not clear that the heart is like a separate person, and that it therefore belongs to the topic of a human as multiple person. Perhaps it belongs to the topic of breaking down the human psyche (or mind? or soul?) into multiple components, whatever the psyche is supposed to be. And that topic is a broader one: in this article, I am examining person-like components and not other components.

The phrase &quot;deep in my heart&quot; constructs/construes the heart as an entity that has depth, perhaps an ocean. If we discretely layer the heart (should we?), we may claim that just like the mind can fail to pay attention to the heart, so level-1-heart can fail to pay attention to level-2-heart, etc. Sure enough, one should not take such idioms too seriously as technical models of human psyche. The lyrics say &quot;deep in my heart, I do believe&quot;; and thus, beliefs would be located at various depths of the heart. This is suggestive of the (leaking) containerization idea presented at the very beginning of this article. Moreover, it would suggest the mind/reason cannot easily know what is believed in the depth of the heart, having direct communication only to the uppermost layer of the heart. Perhaps some of this speculation would be amenable to empirical experimentation.

Let me come back to Exupéry. His statement has to be interpreted somewhat poetically, non-literally. When a human person sees an object, perhaps a painting, it has a ''meaning'' (not semantics!) for the person, and the meaning can perhaps be recovered from the heart of the person. That meaning, which can be rendered as a lexical entity (word, phrase, etc.), is not part of the objective description of the object; then, in a narrow sense, the reason has no access to that meaning. But the reason, by working with the heart the right way, can perhaps discover the meaning. This concept can perhaps be used by secret services. By presenting the human person with a visual stimulus (a photograph), they can perhaps elicit a fairly automatic response that is based on the heart, which is based on information and connections that are stored in the heart. This requires more inquiry and elaboration, perhaps in relation to Jung.

==Related articles==
* [[Motivation and emotion/Book/2023/Multiple selves theory, motivation, and emotion]]

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{{Original research}}
This article is devoted to the book ''All Life is Problem Solving'' by Karl R. Popper, which is a translation by 
Patrick Camiller from the German original ''Alles Leben ist Problemlösen''. It is to contain table of contents as a minimum useful artifact. It can be further expanded with description of the book as well as critical review.

==Table of contents==
Table of contents per Routlege:
* Publisher's note Preface
* PART I Questions of natural science
** 1. The logic and evolution of scientific theory (1972)
** 2. Notes of a realist on the body-mind problem (1972)
** 3. Epistemology and the problem of peace (1985)
** 4. The epistemological position of evolutionary epistemology (1986)
** 5. Towards an evolutionary theory of knowledge (1989)
** 6. Kepler's metaphysics of the solar system and his empirical criticism (1986/91)
* PART II Thoughts on history and politics
** 7. On freedom (1958/67)
** 8. On the theory of democracy (1987)
** 9. All life is problem solving (1991)
** 10. Against the cynical interpretation of history (1991)
** 11. 'Waging wars for peace' (1992)
** 12. The collapse of communism: understanding the past and influencing the future (1992)
** 13. The necessity of peace (1993)
** 14. Masaryk and the open society (1994)
** 15. How I became a philosopher without trying (1992)
* Subject index
* Name index

==Further reading==
* [https://www.routledge.com/All-Life-is-Problem-Solving/Popper/p/book/9780415249928 All Life is Problem Solving], routledge.com
* [https://www.robnagler.com/2019/02/03/All-Life-Is-Problem-Solving.html BookNotes: All Life Is Problem Solving], robnagler.com -- contains snippets from the book
* [https://www.spiegel.de/kultur/kriege-fuehren-fuer-den-frieden-a-40e49218-0002-0001-0000-000013682439 »Kriege führen für den Frieden«], spiegel.de -- a Spiegel article in German that appears as one of the chapters</text>
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This article by Dan Polansky deals with the concept of identity or sameness and related concepts. It deals with some of the usual philosophical questions, but it also contains two practical applications: [[#Pattern identity|Pattern identity]] for mind uploading and [[#Children as quasi-identical to parents|Children as quasi-identical to parents]].

==Introduction==

Identity can be quickly approximately defined by example, yet it can raise multiple interesting questions. What is going to be defined first by means of example is what is known as numerical identity as opposed to qualitative identity. Let us consider the shell game, which employs three shells. These are numerically distinct/non-identical: they are three shells, not one shell. Yet they are indistinguishable and thus ''qualitatively identical''. By contrast, a particular shell at one point in time is ''numerically identical'' to that same shell at a later point, at which it possibly has a different location. Thus, ''numerically identical'' can be defined as &quot;one and the same&quot;, whereas ''qualitatively identical'' can be defined as &quot;exactly alike&quot; or &quot;indistinguishable&quot;.

Another case of numerical identity can be linked to a person who has radically changed. The person has borrowed a lot of money, visits the creditor and says: &quot;I have radically changed. I am a completely new person. The person, who borrowed money from you, does not exist any more.&quot; The creditor is not convinced, and nor is the judge. Whatever quandaries there are of personal identity over time, an individual human body is usually taken to correspond to one person, and the person is the same or &quot;self-same&quot; entity during the lifetime regardless of changes of personality.

Another case is of a mosaic window, whose pieces have been replaced one at a time. The replacement of each piece is relatively small relative to the whole, yet after each piece is replaced, the whole mass of the window has been replaced. One may consider the result to be the same entity as the original, or one may not. If one does not, the question can be asked at which point did the original window lose its numerical identity. The case is somewhat reminiscent of replacement of cells in a human body during its lifetime. Another somewhat similar case is of a desktop computer in which one replaces the CPU in the motherboard with a 4 times faster one while other parts remain the same. On some level of analysis, the much faster computer does feel like a new item although only a physically small part has been exchanged.

Another case is of a cathedral that has been burned, but a new one has been built that looks exactly the same, at the same location. The new cathedral may be considered to be numerically non-identical, but for many a practical purpose, it does not make much of a difference, and if one treats it as numerically identical, not much has to be lost in way of modeling or representation ability.

==Identity per type of entity==
Different entity types lead to different identity considerations. Thus, one may well distinguish e.g.:
* physical mass bodies without metabolism, e.g. a cup or an atom
* physical mass bodies with metabolism, e.g. a horse or a tree
** their development over time, e.g. from sapling to an old tree
** metamorphosis from caterpillar to butterfly
* minds
* mental objects, e.g. propositional beliefs
* processes, e.g. a procession of humans
* bodies or quasi-bodies in flow, e.g. rivers, waterfalls and flames
* behavioral patterns
* qualities, e.g. blueness
* mathematical immutables: numbers, geometric shapes, mathematical functions, etc.
* texts of books and their development through time
* languages and their development through time, including forking
* human organizations, including states and companies
* animal collectives such as flocks (of birds) and herds
Most of these are currently not treated in this article as dedicated subjects. For instance, when one considers a particular flock of birds and its change over time, one can see that it is a rather different kind of unit than non-metabolic body (a cup) and even metabolic body (a cat); the metabolic body outwardly appears to be something like the non-metabolic body, whereas the parts of the flock--the birds--have no apparent material ties and their spatial relationships keep changing a lot during the flight.

==Identity over time==
Identity over time seems to present a set of problems or questions. One such question is this:
* How can something change and remain itself at the same time? Since, if it has changed, it is no longer the same thing.
At first impression, this formulation seems to suggest some kind of philosophical confusion more than any real problem; since, if the temperature of a particular cup located in view on a desk changes, surely the cup is not same as for temperature but it is the same (or self-same) cup as it was before its temperature change.

Another way of approaching this puzzle is to construe the time dimension as an analogue of the space dimensions and thus construe, say, a particular cup as an immutable object in space-time. What we would usually consider to be changes or mutations of the cup are just movements of some kind of mental pointer along time axis, within the same 4-dimensional space-time cup object. Here we can generally ask what makes different parts, with different time coordinate, belong to the same cup, but we can equally well ask what makes different parts, with different space coordinates but not time coordinates, belong to the same cup. This argument is inspired by Quine's Word and Object.

To the above space-time argument, one can object that the time dimension is nothing like the space dimensions even if one can represent them all together in one immobile 4-dimensional time-space. Popper pointed out that while the time dimension or axis is clearly objectively given, the space dimensions are not clearly objectively given but rather are picked somewhat arbitrarily, against some frame of reference. Philosophers of physics discuss the subject of the arrow of time (direction of time), one proposal relating to entropy increase along the time axis (arguably dubious), but there does not seem to be any discussion about the arrow of space dimensions. One can suspect that the problems of identity of an object along the time axis are quite different from those along the space axes.

Be it as it may, changes of an object over time do in fact present a set of interesting problems, but not formulated as a purely logical puzzle along the above lines. One such problem was exemplified in the introduction as a mosaic window whose pieces have been replaced one at a time.

Further reading:
* [https://plato.stanford.edu/entries/identity-time/ Identity Over Time], Stanford Encyclopedia of Philosophy

==Identity over time of individual animals==
Identity over time of a cup can be approximated as invariance on the set of atoms. This is a mere first approximation, as a cup can lose a handle without ceasing to be the same individual cup, but is a workable first idea. However, that works very poorly with animals given their metabolism, exchange of substance with the environment.

This applies to the animal of humans as well. The set of atoms belonging to an individual body is far from constant, and so is the set of cells.

This allows various deliberations to the effect that the identity of an individual human is far from materially constituted (after all, many cells get replaced in a period of multiple years). It may lead to considerations in sections [[#Children as quasi-identical to parents|Children as quasi-identical to parents]] and [[#Pattern identity|Pattern identity]].

A special case worth mentioning is that is biological metamorphosis, from caterpillar to butterfly. The butterfly seems to be numerically identical to the caterpillar it was before, but the anatomy is very different. Thus, when one compares the two time-occurrences of the individual animal, they seem to be qualitatively non-identical.

==Identity over time of languages==
A language is an interesting case to investigate as for numerical identity. It is not a mass extended object, whether metabolic or non-metabolic, yet it is an empirical entity undergoing change in time. It seems reasonably well described as a set of empirically instantiated patterns.

Let us take the case of [[wikidata:Q42365|Old English]] (before ca. 1100), [[wikidata:Q36395|Middle English]] (ca. 1100-1500 AD; Norman conquest dates to 1066) and [[wikidata:Q1649537|modern English]] (ca. 1500-now). They are tracked in information systems as distinct entities, but following the criterion of continuity, they are part of a single entity. They are sometimes ranked as &quot;stages&quot;. That single entity they are part of can to a limited extent be likened to a river which has one look or form up the stream and quite a different look or form down the stream. The slicing up into stages raises the question: what demarcates them as separate entities and what demarcates their boundaries other than convention?

The entity of language shows the somewhat arbitrary act of classification, here into a language vs. dialect. For instance, Slovak, mutually intelligible with Czech, was considered by some thinkers to be a dialect of Czech or Czechoslovak. Then, depending on the approach, one either has one entity or two entities, at least in the domain of discourse as opposed to the real world, which, figuratively speaking, does not care about humans implying things by means of language. (And yet, in so far as linguistic theories impact language codification efforts, they do impact the real world: once language and its spelling is codified, the language use tends to undergo something like normalization, reduction of scatter or diversity in the use, especially the formal use.)

The case of the arguably hybrid language English (Romance-Germanic, as for vocabulary) points to as if different flows being joined to create a single flow, as if two rivers becoming one at the confluence point. Since, the English vocabulary results from incorporation of both Old English vocabulary and Romance vocabulary. The idea of tracing the flow backwards as if a single river flows, following the continuity principle, breaks down, unless one is willing to consider Latin to be as if another ancestral branch of modern English.

The above shows that the question when is A one and the same thing as B needs to contrasted to the question when is A ''part of'' one and the same thing as B.

==Identity over time and mergers and splits==
Mergers and splits are worth a separate treatment. One may start the analysis with those pertaining to corporations/firms, and have the case of rivers merging in mind as a certain analogy. When a large firm buys a very small one, the resulting firm is naturally the large firm. But when two similarly large firms merge, the result can often be considered to be a new separate entity. How the identity is considered before law is probably a technical matter, requiring knowledge of the law mechanics. It seems possible for a smaller firm to perform a hostile takeover of a larger firm with the use of borrowed money, and for legal purposes, the result can be legally considered identical to the pre-merger smaller firm. Whether it is true or not, the legal customs can bring in something like a conventional aspect of what the law considers to be identical as opposed to what really is identical. A complication is that numerical identity over time does not require qualitative identity of the time-occurrences of the entities considered for numerical identity.

As another example, we can consider an apple. We split the apple into approximately same halves using a knife. There is no sense in saying that any of the parts is identical to the original apple. However, if, by contrast, we only slice away a tiny slice from the apple, it makes sense to consider what remained of the apple--almost complete apple--to be the same apple. The amount to be sliced can be varied continuously, and there would have to be an arbitrary threshold after which we cease considering the larger part to be identical to the original apple.

The above is reminiscent of a cup retaining its identity even after its handle gets broken away, as if split away. But maybe this is just our pragmatic interpretation: a cup without a handle can still well be used as a non-leaking drinking vessel. This would be less the case if a small hole was made near the bottom of the cup, without the cup losing its handle; it would still seem to be the same cup, albeit leaking one. By contrast, if the cup is shattered to pieces, we may think of having a shattered cup, or rather no cup at all.

==Disassembly and reassembly==
Concrete objects seem to keep their identity after a disassembly and reassembly. Thus, we can consider a chair whose parts are tied together using fasteners (rather than e.g. glue). We loosen the fasteners and obtain parts instead of the chair. At that point, the chair does not exist as a chair. We tie the fasteners again, and obtain a usable chair. Arguably, the resulting chair is the self-same chair as the one before the disassembly. And yet, it seems strange for an individual object to be able to cease to exist and then start existing again as the same object.

==Ship of Theseus==
Similar to disassembly and reassembly and to incremental replacement of parts in a mosaic window is the ship of Theseus paradox. One imagines a ship has its parts exchanged step at a time, and someone collects the parts, then building a structurally identical ship from the removed parts. One would think the reassembled second ship is numerically identical to the original, but also numerically identical to the ship that resulted from part-per-part exchange. And this cannot be, numerically. In fact, arguably, upon very strict identity interpretation, neither of two processes produce genuinely numerically identical ship.

Following Hobbes, one of the ships is identical per the same &quot;form&quot;, whereas the other one per &quot;matter&quot;. What Hobbes calls a &quot;form&quot;, the modern mind could call pattern, arrangement of parts, manner of organization of parts, configuration of parts or the like. We may ask which of the two ships is more numerically identical to the original. The part-per-part-exchange ship is both formally identical and both has continuity over time; it is not identical as for building material. The removed-parts-reassebled ship is formally identical, but its continuity over time is very weak, but it is identical as for building material. Thus, three considerations have been identified: formal, material, and continuity.

Further reading:
* [[Wikipedia: Ship of Theseus]]
* [https://www.britannica.com/topic/ship-of-Theseus-philosophy Ship of Theseus], britannica.com

==Pragmatism==
Some considerations such as the apple in section [[#Identity over time and mergers and splits|Identity over time and mergers and splits]] suggest that identity may be more arbitrary and &quot;mere model&quot; than one would wish. In various applications, instead of worrying about whether things really are identical, we may instead use the concept of ''considering'' them or ''treating'' them as identical.

Let us have a chair that we use and let someone swap the chair for another one that looks and works exactly the same, without our knowledge. When coming again to the chair and sitting on it again, we are likely to fall into the error of thinking this is the same chair we had before. This error about the numerical identity has no consequences for us as long as the new chair has the same qualities and uses. The new chair is not numerically identical, but no use gets harmed by our ''considering it'' to be numerically identical.

A key pragmatic element relating to numerical identity is knowledge of the object. When a device has reliably served us over long time, its being swapped for nominally qualitatively identical device (same type, model, etc.) decreases our knowledge about reliability, and may reduce our psychological sense of comfort and confidence.

==Identity of rivers==
Rivers are another interesting case for numerical identity analysis. They are subject to the famous quote by Heraclitus. The putative problem that quote suggests seems to be treated in a fairly satisfactory manner by Quine. Per Quine, if one does not worry about quandaries of the extension of a river in space, it is not clear why one should worry about quandaries of the extension of the river in time.

Another possible problem is how to deal with branching and tributaries. Let us take the case of rivers Elbe and Vltava in Czechia. There is a confluence of Elbe and Vltava near Czech town Mělník, where Vltava is considered to be a tributary to Elbe. However, at the point of the confluence, the volume of water coming from Vltava is higher than that coming from Elbe. Thus, one could argue that Vltava is Elbe and that the upper part of Elbe, above Mělník, is a different river. To completely eliminate this kind of quandary, one could replace the concept of a river with the concept of the river-branching-tree covering all the watercourses in the river basin. However, this would create strange utterances, such as that one would claim to live near the river where in fact they would only be living near a small stream entering the river. Therefore, the river-branching-tree solution is impractical.

==Qualitative identity==
Two things are qualitatively identical if they share the same qualities. But what does it mean exactly? Returning to the shell game, let us consider two shells that are indistinguishable by the naked eye. But there can be some microscopic crack or non-homogeneity in one or the other so that an image under electron microscope would reveal a difference. Are such two micro-distinguishable shells still considered qualitatively identical? For some practical applications, too detailed concept of qualitative identity would cause a harm: thus, two coins of the same value are qualitatively identical in the sense of being perfectly interchangeable, and there is no concern with whether any even easily observable detail about the coins would help distinguish them.

However, the above was about something like ''absolute'' qualitative identity. We can consider ''relative'' qualitative identity, by which either a) the qualitative identity is considered with respect to a given set of qualities rather than all potential qualities a mind can discern, or b) the qualitative identity is considered as given by sharing a narrower or broader class, and thus, two things can be more qualitatively identical than other two things. The case b) seems to match the treatment by Stanford Encyclopedia of Philosophy, per which: &quot;Things with qualitative identity share properties, so things can be more or less qualitatively identical. Poodles and Great Danes are qualitatively identical because they share the property of being a dog, and such properties as go along with that, but two poodles will (very likely) have greater qualitative identity.&quot; By contrast, oxfordreference.com definition is &quot;Two things are qualitatively identical if they share all their properties [...]&quot;, which points to absolute qualitative identity.

Further reading:
* [https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100357477 qualitative identity], oxfordreference.com

==Personal identity==
The term &quot;personal identity&quot; seems to be used in way that goes in a direction different from what so far has been presented. Thus, it would be part of one's identity whether one is a woman or a teacher. However, these are not questions of sameness or selfsameness, over time or otherwise, but rather of being an instance of a class, or having a certain kind of being, e.g. being a teacher.

However, the concept of identity as discussed so far does apply to persons. It is in that persons, entities that reside in human bodies, can undergo a change so big that one may want to say that the result is a new entity, a new person, non-identical to the original. This can bring about the subject of conditions of identity, that is, under which conditions are two nominally distinct things in fact the same thing. One such applicable condition can be one of continuity, that is, that if something undergoes a continuous change, that is, a change through a progression of states such that the successive states are close to one another, the result is considered to be the same or self-same entity. In that sense, even a person whose personality changes very much is the numerically same person as a result of the change being a result of accumulation of small changes.

Further reading:
* [http://plato.stanford.edu/entries/identity-personal/ Personal Identity], Stanford Encyclopedia of Philosophy
* [https://iep.utm.edu/person-i/ Personal Identity], Internet Encyclopedia of Philosophy
* {{W|Personal identity}}, wikipedia.org

==Pattern identity==
Relating to personal identity is what roboticist Hans Moravec in his book [[Mind Children]] calls a pattern identity. By his conception, a person who has been &quot;uploaded&quot; into a human-like robot (android) and has lost the biological body is still the same person via being the same pattern. The idea is that a person is not a material body but a pattern that continues to maintain itself. This idea has a deep practical application in so far as some seriously believe the idea is correct and that see their work in robotics or artificial intelligence as a contribution to mind uploading in the future.

However, the concept of pattern is rather broad and unclear. Let us illustrate the concepts on the bit pattern 01101. The same pattern is seen in letter sequences ABBAB and CDDCD. It is also seen in letter sequence CDdcD when one disregards the capitalization. It is equally well seen in a sequence of photographs of cats and dogs appropriately ordered, even if no two animals in the photographs look alike. This emphasizes the substrate independence of the concept of pattern. A configuration of a chessboard would be such a pattern, independent of the particular physical chessboard, and being the same pattern/configuration even in an electronic computer, where one cannot ask what is the mass of the chess figures making out the pattern/configuration.

Expanding on the above, we can conceive of various patterns of patterns. For instance, we may treat blocks of bits as single bits using a mapping, e.g. 00 → 0, 01 → 1, 10 → 1, 11 → 0. Or we can take three bits, and set the result to 1 if the number of 1s is odd, to 0 otherwise. Further mapping can be considered in a nested fashion, that is, based on the 1-derived pattern, we may obtain 2-derived pattern. This is a sketch illustrating the pattern-of-pattern-of-pattern and similar higher order ideas.

Patterns as explained above are immutable objects. However, Hans Moravec as a mind is a mutable object, one undergoing change. What, then, does Hans Moravec mean?

The kind of pattern identity involved in a mind is not a static one but rather a dynamic one. A dynamic pattern can be seen in a digital computer. Let us, say, consider an 8-bit computer with 16 KB of memory. At each point in time, the memory defines a static, fixed pattern. However, this pattern is self-modifying (given a host hardware), resulting in the behavior of the system being a sequence of patterns, or, figuratively, a pattern in motion. It is on this dynamic level that a moving pattern of the mind could be pattern-identical to a moving pattern in a human-like robot. (The pattern in the 16 KB is self-modifying in the sense that part of it is, at each point in time, interpreted by the host hardware as instructions for the modification of this pattern.)

==Identity crisis==
In psychology, the term &quot;identity crisis&quot; seems to refer to intense examinations of questions like, what kind of person do I want to become, or perhaps, what kind of person am I really, deep within? It does not seem concerned with questions of identity in philosophy; it seems the term &quot;identity&quot; has here been borrowed for a different purpose. On the other hand, one may wonder whether a deep change in personality does in fact warrant an allocation of a new entity at least in the modeling of the person. One might alternatively want to call it a &quot;being crisis&quot;, as in whether one should acquire or develop &quot;being an entrepreneur&quot;, &quot;being a monk&quot; and other beings.

Further reading:
* {{W|Identity crisis}}, wikipedia.org
* [https://www.britannica.com/science/identity-crisis-psychology topic identity crisis], britannica.com
* [https://www.encyclopedia.com/social-sciences-and-law/sociology-and-social-reform/sociology-general-terms-and-concepts/identity-crisis Identity Crisis], encyclopedia.com

==Identity of information objects in computing==
As for identity over time, information objects in computing such as memory objects and files present a whole different world, very different from physical objects.

Let us consider a text file and ask what constitutes its identity over time. The text file has a file name and its content changes over time. A backup copy of the file can be created. If the file gets destroyed, it can be restored from the backup copy. But then, on some level of analysis, the restored file is a distinct file, even if it has the same name and the same content.   Moreover, one can open the file in the text editor and replace its content with a wholly different content, breaking the content continuity over time. By contrast, when one expands the file and makes minor editing to it, there is a content continuity.

For practical purposes, it makes sense to consider a file restored from backup to be the same (self-same) file as the one there was before it was destroyed.

Similar considerations apply to pre-computing text objects, their identities and versions. One does not need a computer to expand a text object on a sheet of paper, edit it by striking parts out and as if inserting parts by writing them on the margin and connecting them via a line with the location of insertion, to create a copy (even by writing) and use the copy instead of a lost original, etc. What computers bring about is the rapid ease and speed with which the operations of expansion, editing, backing up, restoration, and copying can be done, as well as the range of the types of information objects, whether texts, images, audio recordings, etc.

==Identity of variable referents in programming==
One can perhaps liken numerical identity and qualitative identity to certain features of programming languages. Thus, in Python, one could map the numerical identity to &quot;is&quot; and the qualitative identity to &quot;=&quot;; this would be rather natural in so far as &quot;is&quot; tests whether the expressions compared point to the same object whereas &quot;=&quot; invokes the appropriate equality comparison function. However, since a class can redefine &quot;=&quot; to do whatever it wants, violating the natural intuitive semantics, this presents a limitation.

However, this consideration seems to tell us nothing about the interesting considerations of identity of physical objects and minds.

==Conditions of identity==
One can discuss conditions of numerical identity, that is, under which conditions are things that are nominally two in fact one thing. One such condition is sameness of atoms: the set of atoms belonging to a cup does not much change during its lifetime nor can a given atom be member of multiple cups. However, that works poorly with living things as for identity over time, since they have metabolism. Another condition is continuity, which can be investigated in the context of text works being edited and expanded, computer files being so treated, political entities, languages, etc. Yet another condition is something like pattern identity.

==Applications==
The philosophical questions about identity seem to be primarily of interest to philosophers only. But there can be practical applications as well. For instance, one can ask whether one can in some sense consider oneself identical to one's children. This proposition seems weird at first, but if it could be established that one's children are at least weakly identical or quasi-identical to oneself, this could have a major impact on one's overall life plan or design.

In the field of personal identity, one can wonder whether one can bring about changes to one's personality so deep that one can really meaningfully consider oneself to be a new person in some sense, or whether it is just a figure of speech.

Another application is the discussion of pattern identity by Hans Moravec in his book [[Mind Children]]. If one is convinced by his analysis, one would accept to be &quot;uploaded&quot; into a human-like robot (android) while losing one's biological body; one would consider oneself to be identical enough with what some consider to be a mere simulacrum.

The questions of identity can possibly contribute to design considerations of information systems. This is especially the question, when are two nominally distinct entities in fact the same? In a geographic information system, one can wonder which of merging rivers is identical to the result of the merger, if any at all and why. In an information system about works of art, one may wonder whether a cathedral that has been destroyed and a faithful replica has been build in its place should have a new entity/item in the information system for the replica.

==Children as quasi-identical to parents==
One application of investigations of identity is to see children as quasi-identical to their parents. At first, this may seem rather counterintuitive or implausible. Surely a child is not numerically identical to the parent since they are two, and if one takes both parents into account, three. Moreover, if a child were somehow numerically identical to the parents, it is not clear why the child would not be numerically identical to the siblings, by transitivity of numerical identity. However, let us consider a human parent capable of cloning so that the child is genetically identical to the parent. When the parent is alive, they are indeed two, but when the parent dies, there is one person with the genetic identity of the previous parent, the child (bar identical siblings of the parent and their ancestors). Thus, if one happens to only takes into account the frames where there is a childless parent and lone child in existence and when one notices the genetic identity of the two person occurrences, one may think of this as quasi-numerical identity over time. That this is not a genuine or full numerical identity is revealed by the intermediate frame where both parent and child are alive.

One may object that human cloning is currently impossible and that a human is constituted by continuity of memories, plans and desires, not merely by the biological sameness of the body in different time frames. Even so, if one wishes to as if live forever, living via one's children may be as close as one can get. To make this idea more plausible, one may note that one's body does not have substance invariance over time due to metabolism and does not have cellular invariance over time due to cells dying and being replaced, and new additional cells appearing during childhood. Thus, one may realize that the kind of numerical identity one sees over time in a cup does not apply to individual humans (or plants in fact), and that there is something that continues to exist in an individual human that is distinct from the set of atoms or the set of cells. One candidate thing constituting the individual identity over time is certain patterns that persist during lifetime of a human. As for biology, many such patterns persist between a parent and a child even if in a modified form. As for cultural patterns (especially language but also certain norms), a parent can make sure that as many of the cultural patterns as possible replicate into the child, or at least that the most constitutive patterns replicate.

Following the above deliberation, the father would consider a son to be more of the quasi-identical copy than a daughter, and similarly for mother and daughter; since, on the chromosomal level, there would be a greater affinity, as well as on the anatomical level and genetically driven behavioral level.

There is another way to think of the continuing identity of a human individual, the purely genetic level. Thus, the individual human can see themselves as a representative of a certain alliance of genes. As is typical of alliances, alliance members have more of a stability or unity than the alliance itself. From that perspective, given absence of cloning, the alliance as an entity cannot be preserved, but one can do as much as one can to serve the alliance members, the genes. And indeed, a portion of the genes gets replicated in a child. Since different children have different portion of the genes replicated (bar identical twins), having more than one child serves the alliance as a whole better. (It serves better anyway since the world is full of dangers.)

Thus, a parent can think that their children are in a strange sense quasi-identical to the parent. Maybe the parent is wrong about it, but the above analysis of the concept of identity suggests the idea is not entirely wrong. Some parents may be lead by similar considerations to think that having at least one child is a good idea even if they would be disinclined to have children otherwise. And thus, what appeared to be an abstract impractical philosophical deliberation turns out to have a very material application, one of the greatest significance it can have on a personal level.

If one thinks the prefix &quot;quasi-&quot; is not detracting enough from the word it modifies (here &quot;identity&quot; and &quot;identical&quot;), one can think &quot;pseudo-&quot; or even &quot;quasi-quasi-&quot;, as uncustomary as it is.

==Identity across possible worlds==
Identity across possible worlds is required for the rigid-designator Kripkean treatment of modal logics to work. Thus, if we say &quot;Walter Scott could have not written Ivanhoe&quot;, what this means is that the terms Walter Scott and Ivanhoe, by implication, succeed in referring to something not only in the present world but also in possible worlds. A rigid designator is defined as one that refers to the same object across possible worlds, regardless of whether the object meets the same descriptions in these worlds as in this world.

It is not entirely clear what constitutes an individual identity across possible worlds. If one conceives of a possible world as something independent, not forked from the past of this world, one would need to rely on something like qualitative identity. Since, what if not a bundle of qualities would identify the individual object? We cannot rely on continuity over time. If, by contrast, we consider a possible world that is a time development of a forked past state of the present world, we can track a present object to its time-occurrence in the forking time frame, and from there continue the tracking in the other world, arriving at the same object in the present in the other world. (If we use this method to track the identity of a human between this world and a particular possible world, and if the human has a child born after the world forking event, arguably, the child is not necessarily numerically identical across these two worlds since, assuming that the genetic recombination results from chance events, it is not even genetically identical.)

If we consider a possible world that is non-forked and if we decide to track the identity of concrete individuals via their quality bundles (which is not entirely like numerical identity, per indistinguishable shells in shell game), we need to establish the identity of qualities across the possible worlds. However, some qualities do not need to exist across possible world, e.g. color, since the possible world can lack electromagnetic waves. This needs a deeper consideration.

If we consider this world and the possible worlds to be deterministic, there cannot be any genuine forking, and then, the modalities of necessity and contingency lose any true meaning. However, even if this world is deterministic, our knowledge of it does not suffice to model it as such, and then, it may make sense to talk and reason as if the world were non-deterministic, where the apparent non-determinism is generated e.g. by deterministic chaos. Then we may want to wish to maintain the illusion that the modalities of necessity vs. contingent make sense; they make sense with respect to the non-deterministic model of the world that we have in our minds.

Further reading:
* [https://plato.stanford.edu/entries/identity/#IdenAcroPossWorl 6. Identity across possible worlds] in Identity, Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/identity-transworld/ Transworld Identity], Stanford Encyclopedia of Philosophy

==The identity of indiscernibles==
The identity of indiscernibles is a principle that states that two objects that are indiscernible are identical, that is, are one object. To what extent this is plausible depends on what we consider to be properties one can use to discern objects. Thus, in a shell game, the shells appear indistinguishable to human eyes, but if one takes the property of being at location L at time T to be a property used for discernment, the shells are in fact discernible. With the shells, one may argue that even if one discounts different locations as properties, there would be some crack or irregularity within the shells that makes them discernible in principle. However, it is not clear what kind of irregularities would be found e.g. in individual atoms, that is, what distinguishes, say, two distinct atoms of hydrogen other than their location and relation to other atoms. This would be even more salient for the philosophical atoms, which are not the physicist's atoms but rather, perhaps, the physicist's quarks.

As something of an aside from the point of view of formal symbolic logic: We can study the principle is relation to a particular language and associated axioms of first-order predicate logic. Let us have a very simple language, consisting of a single one-place predicate: F(x). And let us have a single axiom: there exists x: F(x). Then, if we have the model consisting of, say, 0 and 1, and such that F(0) and non-F(1), there is indeed identity of indiscernibles since all elements in the domain of discourse can be differentiated using F. But as soon as we have a domain of 0, 1, and 2, in another model, then regardless of for which items in the model F holds true, it is unable to distinguish all three items. (We do not assume any constant symbols &quot;0&quot;, &quot;1&quot; and &quot;2&quot; referring to these items in the domain; the language consists of F(x) and nothing else.) 

Further reading:
* [https://plato.stanford.edu/entries/identity-indiscernible/ The Identity of Indiscernibles], Stanford Encyclopedia of Philosophy
* [https://www.britannica.com/science/identity-of-indiscernibles Identity of indiscernibles], britannica.com

==Identity and language==
The concept of identity permeates language; the great majority of uses of language seems to invoke the concept. It is so even if we disregard the words &quot;same&quot;, &quot;self-same&quot;, &quot;identical&quot;, &quot;distinct&quot; and &quot;different&quot;. Thus, we can say &quot;Peter woke up. He realized he was late.&quot; There, the second sentence's &quot;he&quot; refers to the same Peter to which &quot;Peter&quot; refers in the first sentence, and what we deal with is identity over time. In fact, the sentence &quot;Peter woke up&quot; alone implies numerical identity over time, of Peter before waking up and Peter after waking up.

Numerical identity is one of the meanings of the verb &quot;to be&quot;, together with is-a relationship and instance-of relationship. Thus, in the sentence &quot;The winner of the lottery is Joe Hoe&quot;, the &quot;is&quot; indicates numerical identity rather than is-a or is-instance-of.

We have treated of identity as a two-place predicate. However, in the phrase &quot;the identity of the perpetrator&quot;, it is implied to be a property of an object. The statement &quot;we do not know the identity of the perpetrator&quot; means that we do not know who the perpetrator is. In this connection, one might speak of ''multiple identities'' a person has, e.g. if the person presents themselves under different names and different facial appearances (hair length, presence of mustache, etc.). The connection of this to the concept of numerical identity is somewhat puzzling. One might think that X is an identity of Y if X is Y. Thus, &quot;Joe Hoe&quot; would be one identity of Y, where Y is &quot;the perpetrator of the bad act under discussion&quot;. This requires further elaboration, possibly with the use of the sense-referent or intension-extension distinctions.

==Identity and cognition==
The concept of identity permeates cognition even without reference to language. The human visual system sees objects as persisting over time, e.g. an apple, a stone, a tree or a river. This ability to see objects as persistent (maintaining their identity over time) is not restricted to humans but is present e.g. in a dog or a chimpanzee as well. 

==Identity in quantum theory==
There is a peculiar situation concerning identity of particles in quantum theory. This subject is not covered here; this section is here as a placeholder for later expansion, and to link to Stanford Encyclopedia of Philosophy.

Further reading:
* [https://plato.stanford.edu/entries/qt-idind/ Identity and Individuality in Quantum Theory], Stanford Encyclopedia of Philosophy

==Predicate logic and identity==
First-order predicate logic with identity contains the symbol &quot;=&quot; for the purpose, and associated inference rules. One may ask whether this is necessary, that is, whether one could not instead introduce a two-place predicate I(x, y) and then codify the identity using formulas as follows:
* For all x: I(x, x)
And a schema, for all one-place predicates F:
* For all x, y: I(x, y) =&gt; (F(x) =&gt; F(y))
This seems insufficient per the following article:
* [http://media.philosophy.ox.ac.uk/assets/pdf_file/0003/1299/Absolute.pdf Absolute Identity and Absolute Generality] by Timothy Williamson, media.philosophy.ox.ac.uk
This article seems, given model M, to construct model M*, which makes sure I is no longer guaranteed to assert identity in M*. If this understanding of the article correct, this motivates the introduction of symbol &quot;=&quot; as something different from a predicate symbol.

We can specify I(x, y) as follows: For all x: I(x, x), and I holds of no other pairs. It seems the statement &quot;I holds of no other pairs&quot; cannot be expressed in ''first-order'' logic without identity.

The language of first-order logic fundamentally depends on the concept of identity. Each occurrence of a symbol is an occurrence of the ''same'' symbol. Thus, in &quot;For all x: F(x)&quot;, both occurrences of x are of the same x rather than of implied subscripted x&lt;sub&gt;1&lt;/sub&gt; and x&lt;sub&gt;2&lt;/sub&gt;. Similarly for different occurrences of predicate symbols, e.g. F.

Further reading:
* [[Wikipedia: First-order logic#First-order logic without equality]]
* [[Wikipedia: Type–token distinction]]

==Relative identity==
The subject of &quot;relative identity&quot; is treated by various sources. From the name, one can think of qualitative identity relative to a set of predicates capable of distinguishing things. This section needs to be expanded; the content is currently delegated to further reading.

Further reading:
* [https://plato.stanford.edu/entries/identity-relative/ Relative Identity], Stanford Encyclopedia of Philosophy
* [https://www.encyclopedia.com/philosophy-and-religion/philosophy/philosophy-terms-and-concepts/identity Identity] (section Relative identity) by Phillip Bricker, 1996, encyclopedia.com

==Set theory==
In the mathematical set theory, two sets are considered to be identical, that is, one and the same, if they have the same elements. This would not need to be the case; one could think of something like internal hidden property or key of a set that would distinguish it from other sets with the same elements. However, it is unclear what theoretical advantage this would bring. In any case, in a programming language such as Python, both mutable and immutable sets can have the same elements yet be distinct objects.

==National identity==
National identity is another subject identified using the word &quot;identity&quot;. One would speak of a person's &quot;national identity&quot;.

However, one can think of national identity as the identity of a nation, especially over time. This brings the question &quot;what is a nation&quot;, a search for definition, criteria or characterization. Since a key element of identification of a nation is a shared language, one may think the deliberations on national identity will show some overlap with the subject of [[#Identity over time of languages|Identity over time of languages]]. This subject is currently delegated to further reading.

Further reading:
* {{W|National identity}}, wikipedia.org
* {{W|Nation}}, wikipedia.org
* [https://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/national-identity National identity], encyclopedia.com

==Identity theft==
The subject of &quot;identity theft&quot; is another one named using the word &quot;identity&quot;. But what kind of identity is being stolen? Surely, no one can possibly steal the two-place relation of numerical identity. Nor can they steal the two-place relation of qualitative identity. However, if an identity is also the facial appearance and manner of verbal and other behavior, such an identity could indeed be stolen by, say, an operative of a secret service pretending to be someone else. Thus, X steals the identity of distinct Y if X convinces Z that X is Y, for a nefarious purpose. This can be done e.g. with the help of person name, social security number and credit card number. The fraudster can use that information to quasi-prove he is some one else. These person identifying pieces of information are rather distinct from personal identity as the sense of who one is.

Further reading:
* {{W|Identity theft}}, wikipedia.org
* [https://www.britannica.com/topic/identity-theft Identity theft], britannica.com
* [https://www.encyclopedia.com/social-sciences-and-law/law/crime-and-law-enforcement/identity-theft Identity Theft], encyclopedia.com

==David Hume==
David Hume is a great philosopher with significant things to say on identity. The content is currently delegated to further reading.

Note: SEP's David Hume entry does not mention the word &quot;identity&quot;.

Further reading:
* [https://www3.nd.edu/~jspeaks/courses/2006-7/20208/hume-personal-identity.html Hume on identity over time and persons] by Jeff Speaks, 2006, nd.edu
* [https://iep.utm.edu/hume/#SH3e e. Personal Identity] in Hume, David, Internet Encyclopedia of Philosophy
* [https://rintintin.colorado.edu/~vancecd/phil1020/Hume4.pdf Hume on Personal Identity], rintintin.colorado.edu

==John Locke==
John Locke's treatment of personal identity has a dedicated SEP entry, worth perusing.

Further reading:
* [https://plato.stanford.edu/entries/locke-personal-identity/ Locke on Personal Identity], Stanford Encyclopedia of Philosophy

==Thomas Hobbes==
Thomas Hobbes treats of identity in ''The first grounds of philosophy'', mentioning the ship of Theseus paradox.

Further reading:
* [https://quod.lib.umich.edu/e/eebo/A43987.0001.001/1:7.5?rgn=div2;view=fulltext CHAP. XI. Of Identity and Difference.] in THE FIRST GROVNDS OF PHILOSOPHY., quod.lib.umich.edu

==Gottlob Frege==
Frege's ''Sense and reference'' (Sinn und Bedeutung) starts by pointing out that the identity relation (under the head of &quot;equality&quot;) raises some puzzling questions, such as whether it is a relation between referents or between referent-bearing signs. If the former, identity is a relation I such that for all x, I(x, x) and I is true of nothing else; but its cognitive value is near zero. By contrast, 2 + 3 = 5 brings a revelation, just like &quot;Hespherus is Phosphorus&quot;. One can read more at Wikisource.

Further reading:
* [[Wikisource: On Sense and Reference]]

==Willard Van Orman Quine==
Quine has paragraph 24 Identity, page 114, in his ''Word and Object''. Sameness of river is discussed in paragraph 36 Time, page 171. Search online does not seem to find a good reading, so I'll leave it with the book identification for those interested in Quine.

==Stuart Fullerton==
Stuart Fullerton wrote an interesting book on sameness and identity.

Further reading:
* [https://www.gutenberg.org/ebooks/57998 On Sameness and Identity.] by Stuart Fullerton, gutenberg.org

==Erik Erikson==
Erik Erikson, German-born American psychoanalyst, seems to have a special concept of identity, in the field of personal identity. This section is to be expanded.

Further reading:
* [[Wikipedia: Erikson's stages of psychosocial development]]
* [[Wikidata:Q58074|Wikidata: Erik Erikson]].

==Identity politics==
The meaning of &quot;identity&quot; in the term &quot;identity politics&quot; seems to be rather different from the one covered in this article. This section is here to support further reading and concept clarification. A speculative hypothesis about this use of the word &quot;identity&quot; is that it was thought to be any answer to the question &quot;Who are you?&quot; But that is not so; if the answer is &quot;Mark Twain&quot;, that is indeed a statement of identity, as in &quot;I am Mark Twain&quot;, that is, the referents of &quot;I&quot; and &quot;Mark Twain&quot; are one and the same. By contrast, if the answer is &quot;African American&quot;, the result is &quot;I am African American&quot; and is not a statement of identity but rather of instance-of relationship. If this hypothesis is correct, one could try to figure out an alternative name for the answer to an instance-of question; &quot;class&quot; comes to mind, not as in sociology but as in ontology.

Further reading:
* {{W|Identity politics}}, wikipedia.org
* [https://plato.stanford.edu/entries/identity-politics/ Identity Politics], Stanford Encyclopedia of Philosophy
* [https://www.britannica.com/topic/identity-politics Identity politics], britannica.com

==Further reading==
(This section only lists selected further reading, not listing all the interesting links provided at section level.)
* [http://plato.stanford.edu/entries/identity/ Identity], Stanford Encyclopedia of Philosophy
* [http://plato.stanford.edu/entries/identity-time/ Identity over time], Stanford Encyclopedia of Philosophy
* [http://plato.stanford.edu/entries/identity-personal/ Personal Identity], Stanford Encyclopedia of Philosophy
* [http://plato.stanford.edu/entries/identity-relative/ Relative identity], Stanford Encyclopedia of Philosophy
* [https://iep.utm.edu/person-i/ Personal Identity], Internet Encyclopedia of Philosophy
* [https://www.britannica.com/topic/identity-logic Identity], britannica.com
* [https://www.encyclopedia.com/philosophy-and-religion/philosophy/philosophy-terms-and-concepts/identity Identity] by Phillip Bricker, 1996, encyclopedia.com
* {{W|Identity (philosophy)}}, wikipedia.org</text>
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This article by Dan Polansky investigates the concept of truth and some closely related topics. One could think the concept of truth is so simple and direct that it needs no analysis at all. However, since various thinkers have analyzed the concept and cast it into doubt, it seems worth a little while to analyze it anyway. Moreover, one finds that assignment of truth values to sentences in natural language is not entirely unproblematic: some sentences have no truth value, some are ambiguous (and therefore, the truth value is not given before the ambiguity is resolved) and some would arguably benefit from truth value being a real or fractional number ranging from 0 to 1 rather than being one of true and untrue.

If one does not really care about truth (and thus, truth about truth), one may sweep various concerns and quandaries concerning the concept of truth under the carpet, and happily claim that all is fine with truth and that any putative problems are likely to be pseudo-problems. This shows how important truth is as a regulative principle of intellectual endeavors.

==Keeping truth undefined==
One approach to the definition of truth is this. Truth is something very simple and basic, a concept that children master at the age of, say, three. The child learns how to respond to certain sentences with &quot;that is not true&quot; (or the like) productively. Later, a school child can learn logic without ever bothering with a definition of truth; one can take university courses on various logics without ever bothering with the definition. There is no serious problem concerning truth from which one could learn something important. It is fine to leave the concept of truth undefined.

This anti-philosophical approach has its merits, but we will look at truth anyway.

==First impression==
Truth is a property of certain kinds of objects. Candidate kinds of objects are as follows:
* sentences
* interpreted sentences
* sentence meanings abstracting away from the sentence and its language
* propositions
* propositional beliefs (sentential beliefs)

Some kinds of representation do not have a truth value:
* drawings
* paintings
* photographs
* maps
* non-propositional beliefs

In the following, we will work with the hypothesis that it is sentences that have truth value, albeit via their meaning. (The option &quot;sentence meanings abstracting away from the sentence and its language&quot; would be quite attractive to me, but I recall something like an objection from Quine. In case of doubt, instead of assigning truth value to a meaning, I would assign truth value to something like the triplet (language, sentence, sentence-meaning). I find this too complicated and technical for an initial/pre-theoretical deliberation.)

Not all sentences have truth value. Thus, question sentences and imperatives have no truth value. Furthermore, one can debate about whether certain kinds of ought-sentences have truth value or rather are something like imperatives in disguise.

One can get an idea by means of simple everyday examples:
* The sentence &quot;two plus two equals four&quot; is true.
* The sentence &quot;two plus two equals five&quot; is false/untrue.
* The sentence &quot;there is no maximum prime number&quot; is true.
* The sentence &quot;there is a maximum prime number&quot; is false/untrue.
* The sentence &quot;potable water is poisonous to humans&quot; is false/untrue.
* The sentence &quot;there is a dog barking on the street&quot; is false/untrue if there is in fact no dog barking.

But then, what is an abstract characterization or criteria that distinguish true sentences from untrue sentences? One characterization is this: the word &quot;true&quot; is X such that stating &quot;It is X that Y&quot; means the same as &quot;Y&quot; for relevant kinds of Y. More on this is in the next section.

==Tarski-inspired sketch of a theory of truth ==
By considering Tarski's theory of truth, mentioned by Popper, we may obtain a simple and clear idea that can serve as a practical definition of truth. The idea is captured in the following axiom schema, where X is a sentence:
* Sentence &quot;X&quot; is true if and only if X.
The specific axioms are obtained from the scheme by replacing X with specific sentences. Thus:
* Sentence &quot;It rains in Oslo&quot; is true if and only if it rains in Oslo.

Above, X is not a variable of quantification but of textual substitution. We can wish to obtain a definition that characterizes the truth of sentence ''s'' by linking ''s'' to other objects or characteristics of ''s'', but this is avoided. In predicate logic, when ''s'' is a variable of quantification, &quot;s&quot; is not a formula, whereas &quot;isTrue(s)&quot; can be a formula, as well as e.g. &quot;correspondsTo(s, reality)&quot;. The right-hand part of the axiom schema does not say anything about X; it just textually places X after &quot;if&quot;.

Thus, if the learner of English did not know the meaning of the word &quot;true&quot;, now they should have a decent first idea. However, possible problems with truth values of sentences such as ambiguity, vagueness, being merely approximate, etc. are not addressed by this treatment.

The above is merely inspired by Tarski's theory of truth rather than being identical to it: Tarski's theory is a technical one, depending on the contrast between object language and metalanguage.

Wikipedia's section about folk theory of truth states: &quot;The folk theory of truth is useful in everyday life but, upon deep analysis, turns out to be technically self-contradictory.&quot; This is unconvincing since: 1) folk theory is not technical and therefore cannot be ''technically'' self-contradictory, 2) it is not obvious that liar paradox (see [[#Liar paradox|dedicated section below]]) cannot be resolved by the claim that some descriptive sentences have no truth value or by other means and 3) even if there is a locus of contradiction in the folk theory, a member of the folk would not blindly run formal inference from the contradiction to produce all well formed sentences as allegedly true but would rather isolate the locus of contradiction and avoid making any inferences from it. Thus, arguably, the folk theory has more merits than the critics admit.

Links:
* [https://plato.stanford.edu/entries/truth/#TarTheTru 2. Tarski’s theory of truth] in Truth, SEP
* [https://plato.stanford.edu/entries/tarski-truth/ Tarski’s Truth Definitions], SEP
* [https://iep.utm.edu/truth/#H4 4. Tarski’s Semantic Theory] in Truth, IEP
* {{W|Truth#Folk beliefs}}, wikipedia.org

==Ambiguity==
Since in general, words have multiple meanings/semantics, sentences also have multiple meanings/semantics. This limits our ability to assign unique truth value to sentences. It is less problematic when there is enough context for disambiguation. However, whether the disambiguation is ever perfect is perhaps debatable.

Expressions in imperative programming languages have radically unambiguous execution semantics. This suggests a great success can be reached in certain fields of unambiguous codification. One can expect to be able to reach similar unambiguity when one codifies mathematical axioms using the language of first-order logic.

Software requirements, written in natural language, are often required to be unambiguous.

==Approximate truth==
There many everyday examples of perfectly true sentences. However, many sentences are approximately true, and we often do not bother to explicitly say so. Thus, we may say:
* &quot;The orbit of Mars around the Sun is elliptical.&quot;
This cannot be exactly true since Mars is gravitationally impacted not only by the Sun, whereas the elliptical orbit would be perfectly so only if Mars and Sun were the only mass objects impacting the trajectory.

We may choose to be more accurate:
* &quot;The orbit of Mars around the Sun is very closely elliptical.&quot;

By a similar token, Newtonian gravitational theory is a very good approximation for small speeds, but not for high speeds. Instead of saying that Newtonian theory is true, we may use the Popperian term &quot;verisimilitude&quot;: the theory has a good but imperfect verisimilitude, or is similar to truth but not exactly true.

Another approximation is the statement that &quot;humans have four nasal cavities&quot;; some individual humans do not have all four of them. Similarly, &quot;humans have one head&quot;, but that is not true for all humans. Also, &quot;humans have either XX or XY chromozomes&quot;, but that is not exactly accurate either.

==Accuracy==
The word &quot;accuracy&quot; can sometimes be used instead of &quot;truth&quot;. One speaks of higher or smaller accuracy. Accuracy stands in contrast to precision, following Russell's prescription. Per this usage, precision captures something like the resolution or detail with which one says something. Loose or non-native speakers of English may say &quot;precision&quot; or &quot;imprecise&quot; and mean &quot;accuracy&quot; or &quot;inaccurate&quot;.

==Theoretical entities==
Mendelian genetic theory posits Mendelian genes. But no one has ever observed these directly, and as far as I know, there is no mapping from Mendelian genes to DNA letter sequences. Nonetheless, the theory seems to be empirically adequate: it makes testable predictions about entities that can be directly observed. Thus, on one hand, one may deny the truth of statements about genes, since genes do not really exist, and yet, one may be very ready to make statements about genes, since their predictions are empirically adequate and as long as one speaks within Mendelian theory, genes are posited. At the same time, as long as the communication partners know they are talking within the Mendelian theory and know that the genes are theoretical rather than observational entities, they do not deceive each other by talking about genes.

==Artificial slicing into entities==
Sentences imply a certain slicing of reality into entities or entity types which is not always objectively given. Nonetheless, as long as the slicing is well defined, one can argue that sentences are true even if the slicing is arbitrary. However, the arbitrariness of the slicing may limit the degree to which the sentences reflect reality.

As an example, we may slice the phases of English into Old English and Middle English, positing no other entity in between. Then we may assign words as belonging to one or both of these phases. But there is something conventional about this slicing. The slicing and the sentences using it posit an implied sharp boundary between the two entities that may not exist in reality. The conventionality of a possible slicing stands in contrast to the efforts of biologists to as-if cut the reality at its joints when identifying taxa such as species and genera. Thus, the taxa are aimed to correspond to something real and observable, not merely something conventional and practical.

The arbitrariness of certain slicings can be perhaps likened to artificial borders between countries. Some borders are less artificial, such as those following the course of a river or following the structures of mountains. Upon first impression, one could think a Martian could not detect the borders upon a quick inspection. But it is not so simple; once different regulatory regimes are adopted on different sides of the border, the border can very well be physically recognizable: for instance, one side of the border can have a very loose policy for cutting tree, unlike the other side.

This is to some extent relating to the subject of fuzzy logic below, but seems distinct.

==Timelessness of truth==
Truth value of an interpreted sentence utterance or occurrence is timeless, not changing in time. However, this is not so for the truth value of an uninterpreted context-free sentence understood as a sequence of words with no additional context information such as the speaker/writer, time of utterance, etc.

One concern is of changes in definition: the sentence &quot;Pluto (heavenly body) is a planet&quot;, taken as a sequence of words with no time or context of utterance, has no definite truth value since the definition of the concept of planet has changed in such a way that Pluto was a planet before but not after the change. One could imagine expanding the sentence with a link to a defining dictionary, e.g. &quot;Pluto (heavenly body) is a planet [term definitions from Merriam-Webster, 2020-01-01]&quot;, but this is not customary, and Merriam-Webster does not present entry revision histories for this to actually work. Moreover, Merriam-Webster's definition is not technical enough to exclude Pluto; one would have to load the definition from International Astronomical Union (IAU).

The above problem is reduced when one considers not sentences as context-free sequences of words but as sentence utterances or occurrences, having an auditory or textual context, the speaker/writer, utterance time, etc. One can then figure out from context the time of utterance and the applicable definition of &quot;planet&quot; at the time of the utterance.

Another case of failed timelessness is with sentences like &quot;it is raining [here] today&quot;. Again, the context-free sentence has no truth value although it does have a context-free meaning/semantics, but the sentence-utterance/occurrence does have a truth value since it provides specific referents for &quot;today&quot; and &quot;here&quot;.

==Kuhnian paradigm==
One may wonder about the impact of Kuhnian paradigms on the concept of truth and slicing into entities. For example, prior to chemical revolution, there was no way to say that X is a physical mixture while Y is a chemically pure substance since the conceptual distinction was not there. Similarly, Priestly is alleged to have thought to hold in his hands dephlogisticated air, having no concept of oxygen. Thus, the general state of knowledge limits the kind of sentences (from the conceptual rather than lexical perspective) one can form, and which truths can be expressed. Whether this detracts from the concept of truth is unclear; even before the chemical revolution, one could accurately say &quot;water is a substance&quot; as opposed to the inaccurate/untrue &quot;water is a solid object&quot;.

==Scientific truth==
The problems of scientific truth seem to be related to multiple subjects picked above, including approximate truth and theoretical entities. One interesting thing about scientific truth is that it seems more liable to these problems than everyday statements such as &quot;there is a dog on the street&quot;. Paradoxically, in some ways, ordinary people dealing with ordinary affairs may seem to more often trade in perfect truth than scientists relying on models that are to some extent tentative or approximate. However, this is rather speculative and would require a deeper analysis and perhaps sourcing; it concerns an empirical hypothesis, to be tested empirically to some extent.

A field of inquiry adept in eliminating ambiguity and arriving in near-certain truth that is nowhere close to approximate is mathematics. However, according to modern classification terminology, mathematics is not science; &quot;science&quot; refers to empirical sciences such as the prime science physics. Moreover, some theories of existence of mathematical objects (numbers, geometric shapes, etc.) deny genuine existence to them.

==Fuzzy logic==
Many words such as &quot;hill&quot; intuitively do not apply either fully or not at all; they may apply somewhat. Thus, one may think of something as a 0.25-hill, 0.5-hill or 0.75-hill. Indeed, one would think of the transition from a hill to a mountain to be continuous. Thus, if one says &quot;This is a hill&quot; but really thinks &quot;This is a 0.75-hill&quot;, this makes the original sentence not entirely true, but far from untrue. This is a limitation from the point of view of the kind of logic that classifies sentences into true and untrue ones. Nonetheless, one can say &quot;This is something of a hill&quot; or &quot;This is something between a hill and a mountain&quot;, and the problem disappears.

To understand this simple concept, one does not need to study the technicalities of fuzzy logic, which is a mathematical structure with engineering applications.

==Self-reference==
This very article aims at presenting true sentences to the reader, even if it may fail here and there. If the article had no such intention, it could very well define truth as &quot;any black cat that broke a vase&quot; and be done with it.

Self-reference is also of concern in the criticism of the concept of truth. Since, if the critic does not aim to raise true or at least ''valid'' objections or reservations against the concept of truth, why should we care? However, the critic may object that one can reveal problems with the concept of truth even by means of sentences that are not perfectly true, e.g. are merely approximately true, are metaphorical, etc. That response seems to be true or valid enough: things said by a sentence and things revealed by a sentence are two distinct things.

Self-reference plays a role in section [[#Liar paradox|Liar paradox]].

==Theories of truth==
As of now, this article treat of most theories of truth in a limited way. This shortcoming is planned to be addressed by a later expansion. In the meantime, one can learn about various theories of truth in the linked further reading.

==Truth as correspondence to fact==
The content of this section is largely delegated to further reading. One observation: this definition shifts the definition burden to the concepts of ''fact'' and ''correspondence''. Nonetheless, this definition or characterization is superficially plausible enough.

Further reading:
* [https://www.britannica.com/topic/truth-philosophy-and-logic#ref302165 The correspondence theory] in Truth, britannica.com
* [https://plato.stanford.edu/entries/truth/#CorThe The correspondence theory] in Truth, Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/truth-correspondence/The Correspondence Theory of Truth], SEP

==Truth as a correspondence to reality==
Some sources use the language of correspondence to ''reality''. Superficially, that seems plausible enough. However, it raises some questions.

One can argue that our perceptions and experiences are created by Descartes' evil demon, by Matrix, or to put it in lay terms, that world is but a dream. If that is the case, a sentence like &quot;there is a dog on the street&quot; based on one's visual perception would be untrue as long as one interprets it in this anti-realist fashion. But then, one would hardly obtain any true statements concerning the empirical world, and one would have little hope of obtaining any in future. That seems unsatisfactory.

To address the above, one can interpret sentences in a non-realist fashion. Thus, the dog on the street is not really an extra-mental object but rather a disposition to perceptions of the sole existing perceiver. But then, this is no longer correspondence to ''reality'', unless one uses the word reality to contrast dream experiences of the sole perceiver from non-dream experiences. But even if we disregard dreams, there are other perceptual phenomena at odds with reality, including optical illusions and mirage. On the other hand, the idea is clear: if, before conversion to non-realism, we were able to distinguish what is real from what is unreal using our perceptions and experience, we should be able to use the same method under a new non-realist (in the sense of no world outside of the mind) interpretation.

Moreover, one can truthfully state, &quot;I had a dream, and in that dream, there was a dog barking on a street&quot;. That seems true enough, provided I did in fact have such a dream, and yet, it does not point to an extra-mental reality. In any case, the dog in the dream does not need to correspond to any extra-mental dog.

Moreover, one can arguably truthfully state, &quot;Bilbo is a hobbit&quot;. That does not seem to correspond to reality, except perhaps to ''fictional reality'', but that seems to be a contradiction in terms.

A further complication is that if in math, one is not a Platonist, one may believe that mathematical objects are not real in some sense, and that they are in the minds only. And yet, one naturally hesitates to deny truth to such statements as &quot;two plus two equals four&quot;.

Relating to math is logic. One can ask in what sense does the true statement 'P or not P is true for all propositions P&quot; correspond to reality, and in what sense of reality.

Further reading:
* {{W|Evil demon}}, wikipedia.org
* [https://plato.stanford.edu/entries/descartes-epistemology/#EvilGeniDoub Evil Genius Doubt] in Descartes' Epistemology, Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/platonism-mathematics/ Platonism in the Philosophy of Mathematics], Stanford Encyclopedia of Philosophy

==Truth as coherence of a system==
The content of this section is largely delegated to further reading. One objection, possibly invalid, is that what we require in practice is not only correspondence between statements/propositions but also between certain statements/propositions and perceptions. Thus, there can be a coherence between the statement &quot;There is a cat on the street&quot;, and perceptions of those who happen to be on that street.

Further reading:
* [https://www.britannica.com/topic/truth-philosophy-and-logic#ref302166 Coherence and pragmatist theories] in Truth, britannica.com
* [https://plato.stanford.edu/entries/truth/#CohThe The coherence theory] in Truth, Stanford Encyclopedia of Philosophy

==Pragmatic theory of truth==
American pragmatism is characterized by the slogan &quot;truth is what works&quot; by William James. This makes it possible to assign truth value not only to descriptive sentences but also to duty-imputing or normative sentences. However, Stanford Encyclopedia of Philosophy provides a different characterization. Let us stop here and delegate the rest to further reading.

Further reading:
* [https://plato.stanford.edu/entries/truth/#PraThe Pragmatist theories] in Truth, Stanford Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/truth-pragmatic/ The Pragmatic Theory of Truth], Stanford Encyclopedia of Philosophy
* {{W|Pragmatic theory of truth}}, wikipedia.org

==Deflationism==
The content of this section is largely delegated to further reading. Deflationism as regards truth seem to take a position similar to that we have taken in section [[#Tarski-inspired sketch of a theory of truth|Tarski-inspired sketch of a theory of truth]].

Further reading:
* [https://www.britannica.com/topic/truth-philosophy-and-logic/Deflationism Deflationism] in Truth, britannica.com
* [https://plato.stanford.edu/entries/truth/#Def Deflationism] in Truth, Stanford Encyclopedia of Philosophy

==The duty to avoid stating untruth==
In various contexts, there is arguably a moral duty to avoid stating untruth. One case of failure to heed the duty is intentional stating of untruth, another one is failing to take reasonable precautionary steps to prevent ending in error and as a consequence stating untruth, even if not expressly intentionally.

Kant argued that lying is always morally problematic. However, this is not plausible. When German Nazis knock on the door of a villager and ask whether he is hiding Jews or resistance fighters, the villager has no duty to respond truthfully. A similar point was made by Russell when he opined he had no duty to speak truth in response to an inquiry from game hunters about where the game is located or hiding. One may argue that Hitler would have no chance if avoidance of lying were hard-coded into the physical laws of the universe; however, since it is not so hard-coded, one has to make moral decisions in an imperfect world, and be forced to respond to people to whom one does not want to talk at all.

Further reading:
* [https://www.youtube.com/watch?v=KqzW0eHzDSQ Justice: What's The Right Thing To Do? Episode 07: &quot;A LESSON IN LYING&quot;], youtube.com

==Mandatory canonical untruth==
Expanding on the above, while societies nominally require their members to say true things, in fact, they often require their members to say canonical untrue things. Thus, in a strongly Christian society, one may be required to say the right/canonical things about God and Jesus. In a Marxist-Leninist society, one may be required to say the right/canonical things about bourgeoisie, proletariat and dialectical materialism. In the times of Galileo, one may be required to speak the accepted dogma about the relationship of the Sun and the Earth.

The requirement to speak untruth may in part be driven by sincere belief of those requiring that these things are true. But not necessarily; it seems far more likely that the priestly classes of various religions know all too well that they are inculcating untruths. And where the priestly classes are gone, analogues of priestly classes are likely to appear, especially if their political ideology is based in part on the idea that truth does not exist.

==The value of misrepresentation==
As something of a speculation, truth and accuracy are probably more cared about in engineering than in management. In engineering, untruth can have grave consequences; in management, untruth is all too often required to overcome the limitations of poorly designed systems of rules; there is the phrase &quot;work to rule&quot; referring to a form of worker protest consisting in sticking to rules exactly as they are. These often not-fully-functional systems of rules often do not get corrected since as long as they are being constantly violated, the consequences of their defects are tolerable. This principle cannot be used to develop computer software: the compiler, linker and CPU do not break the rules to correct defects created by the programmer.

As an aside: As a result, when a company has a poorly designed systems of rules and business processes, and these rules and processes get implemented in business software and strictly enforced in machine fashion, this can cause grave problems to the business. In this case, it is not necessarily the business software that is at fault.

==Expression of uncertainty==
One who is aiming at only saying true things is well advised to consider stating things with uncertainty or expressly indicating that something is a hypothesis or a speculation. Thus, one can use the following forms:
* &quot;X probably holds true.&quot;
* &quot;It seems X is an Y.&quot;
* &quot;It is not completely clear whether X is true.&quot;
* &quot;X seems very likely but no proof has been delivered.&quot;
The great advantage is that one can communicate not only things that are certainly true (there are limits to certainty anyway) but also things that one is in the process of figuring out or is in another way uncertain about.

There are limits to what uncertainty one can reasonably wish to explicitly express. Thus, during the acceptance of Newtonian physics, it would be artificially precisionist to state things like this: &quot;According the tentative not-yet-falsified Newtonian theory, the gravitational force has the size of so-and-so&quot;. (Let alone that this Popperian language was not available in this form.) Therefore, on some level, one often runs some risk of reporting inaccurately.

==Figures of speech including metaphor==
Sentences using metaphor seem to be tricky as for truth, and many other figures of speech present similar problems. One may claim that even if they are not literally true, they are metaphorically true. However, if one accepts &quot;metaphorically true&quot; as a species of &quot;true&quot;, this will dramatically reduce the refutability/falsifiability of sentences since the defender will be able to claim that the intended meaning was metaphorical, hyperbolic, or non-literal in another sense. A better plan seems to be to treat &quot;metaphorically&quot; in &quot;metaphorically true&quot; as alienans (somewhat similar to &quot;fake&quot; in &quot;fake inspector&quot;), and therefore, if something is metaphorically true, it is not really true.

This may present complications for statements like &quot;Species originated by natural selection&quot;. Technically speaking, one would be forced to say &quot;Species originated by natural analogue of artificial selection&quot;. One may want to continue the former less loquacious practice without being accused of untruth.

On the other hand, a conceptual metaphor can bring the reader's mind to notice something about the world that he would not notice otherwise. Thus, it can have reality-bearing cognitive value. Indeed, &quot;Species originated by natural selection&quot; is a statement that can achieve as much to someone not acquainted with Darwinian theory; they only need to ask: &quot;what, if anything, could be natural selection?&quot;; &quot;to what context does 'selection'&quot; refer to and how can I bring it over to the context of origin of species&quot;?

==Fictional entities==
Novels and short stories in fiction report about fictional entities (characters, places, etc.) as if they were not fictional. One is not ready to admit that novels report truthfully, but one is not complaining about their reporting untruthfully. Interestingly, one is ready to draw inferences and perform consistence checking within the fictional world. The sentence &quot;in the Tolkien's fictional world, Bilbo is a hobbit&quot; seems true enough. (There we go: &quot;true enough&quot; as opposed to &quot;true&quot;?) The case seems to be interesting.

Another case is of a novel or short story that is hinting at truth about real-world entities. Thus, in the most trivial case, one would report truthfully about real-word entities and events but change proper names; however, one could be all too easily accused of libel since change of proper names is too thin a masking. One can perform deeper masking by modifying various details to be fictional and thus remove the description from reality to various degrees. But even so, there is something truthful or reality-bearing about the resulting description. The case is interesting as well.

==Whose truth==
There are some arguably bizarre theories of truth asking such questions as &quot;whose truth: your truth or my truth&quot; and similar. I am not properly acquainted with them. To my mind, they are hard to take seriously. However, a deeper analysis could hypothetically reveal that I am wrong and that they have something significant to say or reveal.

This kind of idea is mentioned in Jesus Christ Superstar, in the words of Pilate: &quot;But what is truth? Is truth that changing law? We both have truths. Are mine the same as yours&quot;?

Links:
* {{W|John 18:38}}, wikipedia.org -- on Pilate's truth-relating utterance

==Subjectivity and relativity==
Some sentences can be claimed to be remarkably subjective or relative, limiting an unambiguous determination of truth value. Examples:
* &quot;X is good&quot;: good in reference to what objective or purpose?
* &quot;X is beautiful&quot;: beautiful in whose eyes?
* &quot;X tasted great&quot;: to whom?
* &quot;X is an excellent film&quot;: according to what critics?
One could think these statements have no truth value and are entirely subject-dependent or depending on unstated reference object. But that does not seem entirely accurate. A good kitchen knife can be good for slicing food such as onion, a default purpose of the knife (as opposed to as a weigh). A beautiful woman can be widely recognized as beautiful. The food in a particular restaurant can be reported by many customers as tasting great. A film can have received good raking by film critics. That said, this is for a more extensive analysis and debate.

The above ideas suggest how to rephrase the above examples for greater explicitness:
* &quot;X is good for its default purpose or use case&quot; or &quot;X is ethically good&quot;
* &quot;X is widely considered to be beautiful&quot; or &quot;person P found X beautiful&quot;
* &quot;X is reported to taste great by the many people who tried it&quot; or &quot;person P said X tasted great&quot;
* &quot;Film X has excellent ratings on website Y&quot; or &quot;person P likes film X very much&quot;

==Revelations by untrue sentences==
True things can be revealed by untrue sentences. Examples:
* A speaker who said fluently things in English reveals their English speaking competence, if the things said are untrue. Thus, they reveal the truth of the statement &quot;Speaker so-and-so is a fluent English speaker.&quot;
* Someone who says &quot;The password to the box is not 35475829232302&quot; has revealed the password if it is in fact the correct password.
* An untruthful speaker reveals which entities they are able to recall as existing or worth mentioning.
* As a more general example, two communicating parties sharing sufficient context may perform certain distortions of things being said as long as the receiver is able to perform unambiguous decoding of the distortion.
This topic can be developed further, to point at various ways and levels of hinting, distortion/deformation, and non-literal interpretation (e.g. as a metaphor, metonymy, hyperbole, etc.), resulting in a rather challenging topic of its own.

==Limits of knowledge==
Some seem to point out to limits of knowledge as limits of truth. However, limits of knowledge do not in fact present any problem for the concept of truth, which is independent of/orthogonal to the concept of knowledge.

As for knowledge and truth, the following combinations are possible:
# X is true and the truth value of X is known
# X is false and the truth value of X is known
# X is true and the truth value of X is unknown
# X is false and the truth value of X is unknown
Since the cases 3 and 4 cannot be told apart by the party not knowing the truth value of X, one can think of it as 3 cases in a combined truth/knowledge domain: X is known to be true, X is known to be false, X is unknown.

It is trivial to come up with empirical hypotheses that do in fact have truth value, or empirical questions that have true answers, but the truth value or the true answer is unknown by most people or not at all. Examples of statements not known to be true or false provided the parameters are plausible and non-refuted:
* District/region X has the number N of trees.
* There is N number of words in English.
* The number of households in district/region X that have an electronic tablet is N.
* At time T, Socrates the Greek philosopher was at location given by latitude and longitude LAT, LON.
* At time T, person P rolled a die and the result was R.

On a related note, discovery does not create facts; it discovers them. For example, the discovery of Saturn's rings did not create the fact that planet Saturn has rings. If no one discovered that Saturn had rings, for failure of development of telescopes, it would still be true that planet Saturn has rings, even if no one knew that to be the case.

Limits of knowledge apply to mathematics, a non-empirical field of inquiry, as well. We will never know all true statements about positive integers, starting with singular statements of the form &quot;N is a prime number&quot;; there is an infinite number of such true statements, and they cannot be represented in a compact manner, unlike e.g. trivially known statements of the form &quot;N equals M + 1&quot;. We do have an algorithm for deciding whether a number is a prime number, but it hits practical computational limits concerning computation time and memory. Moreover, there are algorithmically undecidable problems such as the Turing machine halting problem, which further highlights the contrast between something being true (e.g. machine X halts when run on input Y rather than running indefinitely) and something being known to be true.

The above considerations give a clear picture of the contrast between X being true and X being known to be true.

There is another related subject: upon ultimate analysis, we cannot have absolute certainty. If this is so, we only somewhat tentatively accept statements as true, using the concept of truth as a regulative principle, which leads some of us to correct statements in the light of new evidence, discovery, realization, etc. If truth was just a name for whatever statements command strong conviction in most people, that would be a whole different concept of truth.

==Truth as a limit case==
One can suspect that, in some areas, perfect truth is unattainable. At least for some applications, truth can perhaps be likened to a mathematical circle or a sphere as a limit case for what can be achieved in our empirical world. We cannot manufacture a mathematically perfect spherical ball, but we can achieve remarkable precision in manufacturing, and we are satisfied with having a name for that limit object at which we aim, here &quot;sphere&quot;. To what extent the case of truth bears a good analogy to the manufacturing example, perhaps in some areas, is not quite clear.

==Applications==
Whatever the quandaries about the concept of truth, the concept has practical applications.

One application is in those libel laws that require statement to be untrue in order to be libel. A defendant accused of libel who states that he is a truth-nihilist and that there is no such thing as truth and that therefore he could not possibly have said untruth is unlikely to get very far with this line of defense.

The workings of contracts depend on one's ability to tell whether a condition in the contract was violated.

Approximate truth or mere-model quasi-truth has such practical applications as the Ptolemaic astronomy in medieval sea navigation. For Global Positioning System (GPS) calculations, Ptolemy and Newton are not sufficient, and one needs Einstein; and thus, being closer to truth makes a difference.

In software making, Boolean variables usually take the values of true and false. Software applications make use of such variables, as well as logical operators acting on them.

==Tarski's theory of truth==
The content of this section is delegated to further reading.

Further reading:
* [https://www.britannica.com/topic/truth-philosophy-and-logic#ref302167 Tarski and truth conditions] in Truth, britannica.com
* [https://plato.stanford.edu/entries/tarski-truth/ Tarski’s Truth Definitions], Stanford Encyclopedia of Philosophy
* [https://iep.utm.edu/s-truth/ Semantic Theory of Truth], Internet Encyclopedia of Philosophy
* {{W|Semantic theory of truth#Tarski's theory of truth}}, wikipedia.org
* [http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf Tarski, A. (1983). &quot;The Concept of Truth in Formalized Languages&quot;], thatmarcusfamily.org

==Tarski's undefinability theorem==
Tarski's undefinability theorem states, informally, that in the context of a formal logic the predicate is-true applying to positive integers interpreted as codes for formulas of Peano arithmetic cannot be defined in Peano arithmetic itself. The rest of this section is delegated to further reading.

Further reading:
* [https://plato.stanford.edu/entries/goedel-incompleteness/#TarTheUndTru Tarski’s Theorem on the Undefinability of Truth] in Gödel’s Incompleteness Theorems, Stanford Encyclopedia of Philosophy
* {{W|Tarski's undefinability theorem}}, wikipedia.org

==Desiderata other than truth==
In sentence production, e.g. in journalism, there are desiderata (things desired) additional to truth, and these should not be confused with truth. One may require text to be non-misleading, neutral, balanced, objective or complete (with respect to a defined scope). One can create a wrong impression about an issue by presenting only one side of the argument or by highlighting only some facts and not other relevant facts.

For instance, BBC editorial standards single out the desiderata of truth, fairness, accuracy and impartiality: &quot;In our journalism in particular, we seek to establish the ''truth'' and use the highest reporting standards to provide coverage that is ''fair'' and ''accurate''. Our specialist expertise provides professional judgement and clear analysis. We are ''impartial'', seeking to reflect the views and experiences of our audiences – so that our output as a whole includes a breadth and diversity of opinion and no significant strand of thought is under‑represented or omitted.&quot;&lt;ref&gt;[http://downloads.bbc.co.uk/guidelines/editorialguidelines/pdfs/bbc-editorial-guidelines-whole-document.pdf The BBC’s Editorial Standards], downloads.bbc.co.uk&lt;/ref&gt; (Boldface from the original set in italics.)

Another set of desiderata applies to persuasive rhetoric. One set is given by Robert Pirsig: &quot;He singled out aspects of Quality such as unity, vividness, authority, economy, sensitivity, clarity, emphasis, flow, suspense, brilliance, precision, proportion, depth and so on; kept each of these as poorly defined as Quality itself, but demonstrated them by the same class reading techniques.&quot; In the quotation, Pirsig's &quot;Quality&quot; is predominantly rhetorical quality and includes neither accuracy (although it includes &quot;precision&quot;) nor completeness.

Another set applies to technical requirements specification. One example is from NASA and includes clarity, completeness, compliance, consistency, traceability, correctness, functionality, performance, maintainability, reliability, and verifiability/testability.&lt;ref&gt;[https://www.nasa.gov/reference/appendix-c-how-to-write-a-good-requirement/ Appendix C: How to Write a Good Requirement - NASA], nasa.gov&lt;/ref&gt;

Further reading:
* {{W|Journalistic objectivity}}, wikipedia.org

==Liar paradox==
Liar paradox is one problem with assigning truth value to sentences. The problematic sentence is &quot;this sentence is untrue&quot;, which can be alternatively rendered as two sentences: &quot;1) the next sentence is true&quot; and &quot;2) the previous sentence is untrue&quot;, nominally avoiding self-reference on a single-sentence level.

Attempts were made in mathematics to ensure the paradox cannot occur. Nonetheless, since we admitted that some sentences (especially questions and imperative sentences) do not have truth value, it seems relatively painless to accept that the sentence embodying the paradox has no truth value either. Other solutions are given in the Wikipedia article.

Further reading:
* {{W|Liar paradox}}, wikipedia.org
* Self-reference and Meaning in Ordinary Language in Conjectures and Refutations by Karl Popper

== Etymological interpretation ==
As an exercise, one can have a look at what the names of the concept of truth in various languages would mean if the meaning followed the etymology.

Let us have a look at a Slavic example, Czech ''pravda'' (Russian is similar). That sounds as if it was related to ''pravit'', say or tell. Thus, one could etymologically or folk-etymologically interpret ''pravda'' as, that which is being said or perhaps said by many. That does not match the semantics (or at least the core semantics that is subject of this article): even if all language users say that the Earth is flat, that does not make the statement true. But this kind of etymological quasi-meaning is interesting to note since all too many language users (including pseudo-philosophers) are liable to use the word in this way, leading to terminological confusion.

For English, Merriam-Webster traced the etymology to Old English trēowe, faithful. But in which sense of faithful? Is it like a spouse being faithful to another spouse? Or a picture being a faithful depiction of reality? Or is it faith + -ful, to be interpreted as leading to faith or worthy of faith? Worthy of faith, while not too far away, does not match the semantics: given we can never or hardly ever attain perfectly certain knowledge (not even in mathematics if we analyze things to their ultimate ends), we are bound to have faith in (and believe and trust) things that may turn out to be untrue. Leading to faith also does not match the semantics: one only needs to recall the Ancient Greek sophists giving the advice that, in order to convince, one should better state plausible yet untrue things than implausible/hard to believe yet true things.

For German, Duden traces the etymology of ''wahr'' to ''wār'', of which it says &quot;eigentlich = vertrauenswert&quot;, worthy of trusting or trustworthy (but Duden does not have an entry for the adjective vertrauenswert).

== Truth, untruth, error and lie ==
Let us determine the relation of the concept of truth (and untruth) to the concepts of error and lie.

One might naively think that truth is the opposite concept of error. But it is not so. Truth is the opposite of untruth/falsity, both truth values. Error is not a truth value. Rather, error contains an ''epistemic'' element, unlike truth. To believe an untruth is to be in error; sure enough. However, a statement can be untrue without anyone being in error about it; no one can be considering the statement as a candidate for believing.

Similarly, lie is not an (perfect) opposite concept of truth; the concept of lie contains an element of intent, unlike truth and untruth/falsity.

==See also==
* [[Truth theory]]

==References==
&lt;references /&gt;

==Further reading==
* {{W|Truth}}, wikipedia.org
* [https://www.britannica.com/topic/truth-philosophy-and-logic Truth], britannica.com
* [https://plato.stanford.edu/entries/truth/ Truth], Stanford Encyclopedia of Philosophy (see section Related Entries for other truth-related articles)
* [https://iep.utm.edu/truth/ Truth], Internet Encyclopedia of Philosophy
* [https://www.newworldencyclopedia.org/entry/Truth Truth], New World Encyclopedia</text>
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[[Category:Film]]
[[Category:Cinema Aesthetics]]
[[Category:Music]]
'''Film Music''' refers to any music that is featured in a film, either as a background accompaniment and/or in-world, such as music a character listens to. Film music can be separated into two main categories: '''''soundtrack''''' and '''''film score.'''''
== Soundtrack ==
A film soundtrack is the selection of music that is used in a given film, typically pre-existing music that is licensed. Generally, music for a film's soundtrack is selected by a music supervisor in consultation with a film's director and producer. Often these songs are also released as an album. Sometimes a film’s soundtrack will feature original songs - songs produced specifically for the film. An example of this is Celine Dion’s &quot;My Heart Will Go On&quot;, produced for and featured in ''[[Titanic (1997)]]''.
=== Aesthetics ===
[[File:Baz Luhrmann Cannes 2013.jpg|thumb|Baz Luhrmann at the Cannes Premiere of ''The Great Gatsby'' in 2013.]]
The choice of music featured in a film’s soundtrack has wide implications for the aesthetics of a film. For example, period pieces typically utilize music from the period being portrayed. This creates a greater sense of historical immersion for the audience and can conjure feelings of nostalgia. [[Wes Anderson]]’s ''[[Fantastic Mr. Fox|Fantastic Mr. Fox (2012)]]'' does this, matching its 1960’s/70’s setting with a soundtrack full of music from that time period. However, another technique is purposely using music anachronistic to a film’s setting. Baz Luhrmann chose to feature modern pop music in his remake of ''The Great Gatsby (2013)'', a film set during the 1920’s. In an interview with Rolling Stone, he explained that:

''“The question for me in approaching Gatsby was how to elicit from our audience the same level of excitement and pop cultural immediacy toward the world that Fitzgerald did for his audience? And in our age, the energy of jazz is caught in the energy of hip-hop.”&lt;ref&gt;RJ Cubarrubia, “Jay-Z Producing Music for ‘Great Gatsby’”, ''Rolling Stone,'' 2013.  https://www.rollingstone.com/music/music-news/jay-z-producing-music-for-great-gatsby-181443/&lt;/ref&gt;''

Some filmmakers have become known for their preference for using soundtracks rather than film scores, a good example being [[Sofia coppola|Sofia Coppola]]. Filmmakers who work in this mold will often plan scenes around the use of a particular song. These moments are referred to as &quot;needle-drops.&quot;

Another common technique is the use of pre-existing classical/opera pieces in a film’s soundtrack. These pieces function similarly to how a film’s score does. Stanley Kubrick chose to use a selection of classical pieces rather than a film score for much of the run-time of ''The Shining (1980).''

== Film Score ==
A film score is the collection of music composed and produced specifically for a film, typically by a composer in consultation with a film’s director and producers.
=== Production ===
Film scores vary by genre, but most commonly are recorded live by a symphony orchestra, such as James Horner’s original score for ''[[Titanic (1997)]].'' Some film scores heavily feature electronic music, synths, or other forms of non-traditional orchestration. The score for [[Kelly Reichardt]]’s ''First Cow (2019),'' composed by William Tyler, features electric guitar, toy piano, banjos, and mandolins&lt;ref&gt;Nadine Smith, “Music from First Cow”, ''Pitchfork,'' 2020. https://pitchfork.com/reviews/albums/william-tyler-music-from-first-cow/&lt;/ref&gt;. Film scores, similarly to film soundtracks, are often released as albums. It’s common for film score albums to feature altered versions of film score cues to improve their listenability&lt;ref&gt;Michael W. Harris, “Hollywood Film Scores.” ''Notes,'' vol. 74, no. 3, Mar. 2018, pp. 497–502. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&amp;AuthType=ip,shib&amp;db=edsjsr&amp;AN=edsjsr.26397539&amp;site=eds-live&amp;scope=site.&lt;/ref&gt;.
[[File:Hans Zimmer 2010.jpg|thumb|Hans Zimmer in 2010.]]
In the traditional film scoring process, a composer would write all the music for a film. John Williams is known for this approach. However, a new model is becoming the dominant one in Hollywood film scoring. In this one, the film’s composer is more of a team leader, dictating the “tonal palette” for a film, Hans Zimmer refers to this as “sketching”, and assigning cues to additional composers or studio assistants to compose for specific scenes&lt;ref&gt;Mark Rozzo, ““The Minions Do the Actual Writing”: The Ugly Truth of How Movie Scores Are Made”, ''Vanity Fair,'' 2022. https://www.vanityfair.com/hollywood/2022/02/the-ugly-truth-of-how-movie-scores-are-made&lt;/ref&gt;. Under this model, the actual moment to moment scoring of a film is done by these additional composers, who are often uncredited.
=== Aesthetics ===
One of the most common techniques in film scoring is known as ''leitmotif'' - the use of a recurrent theme. Repeated use of a theme can create an association between it and a person, object, place, or idea. A composer can then develop or change the theme to reflect the changes occurring within the story to that person, object, place, or idea. An example of this is Howard Shore’s score for ''The Lord of the Rings trilogy,'' which makes use of dozens of leitmotifs, all associated with various people (ex. Aragorn), objects (ex. the Ring), places (ex. the Shire), and ideas (ex. nature)&lt;ref&gt;Doug Adams, &quot;The Music of The Lord of the Rings Films&quot;, ''Alfred Music,'' 2010.&lt;/ref&gt;.

Another common technique is the use of ''[[Texture in film|texture]]''. Composers can make use of non-traditional instrumentation to add a unique texture to a film’s score. This can create/add to a film’s atmosphere. It can also be used in a similar fashion to leitmotif, communicating change to people, objects, places, and ideas through the texture of the music. An example of this is Hans Zimmer’s score for ''[[Interstellar|Interstellar (2014)]],'' which heavily features organ music. Zimmer used the organ’s association with religion to musically express the idea of the vastness of space and time&lt;ref&gt;J. Bryan Lowder, &quot;How Interstellar’s Stunning Score Was Made&quot;, ''Slate,'' 2014. https://slate.com/culture/2014/11/making-interstellars-score-hans-zimmer-s-soundtrack-explored-in-exclusive-featurette-video.html&lt;/ref&gt;.

== Diegetic vs Non-Diegetic Film Music ==
Film music can be diegetic or non-diegetic. Diegetic means existing within the film’s world, i.e. the characters in the film can hear the music. Non-diegetic film music is music only the audience can hear. Film music can cross over these boundaries, starting off as either diegetic or non-diegetic and transitioning into the other within a scene. This is commonly done at the beginning/end of montage sequences or to transition from one scene to the next.

== Terminology ==
* Cue - an individual piece of music in a film score.
* Leitmotif - a recurring theme that represents a person, object, place, and/or idea.
* Needle drop - when a piece of pre-existing music is used in a scene.
* Theme - a musical phrase.

== References ==
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      <text bytes="1546" sha1="6ll02pwzu0tiii3gikg4063wes5ti30" xml:space="preserve">== Comments ==

It's hard to ascertain exactly what freemind is, just reading the article. A text editor of some sort, I gather, but the resource uses a lot of jargon without explanation. What sets it apart from something like emacs or vim? [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 15:07, 25 December 2023 (UTC)
: I added a short description at the beginning. However, there is a gallery of screenshots, from which one should be able to see how different FreeMind is from Emacs or Vim. To me, FreeMind is all about the layout and collapsibility; it is collapsibility/folding on steroids. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:44, 28 December 2023 (UTC)

== Page name ==
I originally thought the page name &quot;FreeMind&quot; would be okay. And perhaps it still is. But since I am the sole author of the page and since I have a conflict of interest via being one of the co-authors of FreeMind, it is perhaps a good idea to take distance from the subject by renaming the article to &quot;One man's look at FreeMind&quot;, on the model of other articles of mine that are of the form &quot;One man's look at X&quot;. So I went ahead and renamed the article. I created [[FreeMind]] as a topic page, that is, a page that links to articles on the topic/subject by various authors. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:55, 16 February 2025 (UTC)</text>
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    <title>User:Dan Polansky/One man's look at copyright law</title>
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This article by Dan Polansky looks at copyright law, especially the United States law.

==Protected works==
As per [[Wikisource: United States Code/Title 17/Chapter 1/Sections 102 and 103]]:
&quot;Works of authorship include the following categories:
: (1) literary works;
: (2) musical works, including any accompanying words;
: (3) dramatic works, including any accompanying music;
: (4) pantomimes and choreographic works;
: (5) pictorial, graphic, and sculptural works;
: (6) motion pictures and other audiovisual works;
: (7) sound recordings; and
: (8) architectural works.&quot;
We pay attention specifically to computer software in the following.

==Computer software==
The U.S. copyright law codification itself does not list ''computer programs'' among protected work categories. However, they are mentioned in &quot;House Report No. 94-1476 (Extract)&quot; in [[Wikisource: United States Code/Title 17/Chapter 1/Sections 102 and 103]]:
: 'The term &quot;literary works&quot; does not connote any criterion of literary merit or qualitative value: it includes catalogs, directories, and similar factual, reference, or instructional works and compilations of data. It also includes computer data bases, and computer programs to the extent that they incorporate authorship in the programmer's expression of original ideas, as distinguished from the ideas themselves.'

As per [[Wikisource: United States Code/Title 17/Chapter 1/Section 101]]:
: &quot;‘‘Literary works’’ are works, other than audiovisual works, expressed in words, numbers, or other verbal or numerical symbols or indicia, regardless of the nature of the material objects, such as books, periodicals, manuscripts, phonorecords, film, tapes, disks, or cards, in which they are embodied.&quot;

Arguably, this appears to be terminological stretch since computer programs are not literary works by a naive terminology. Also ''technical writing'' does not quite match &quot;literary&quot;, unless it means &quot;by means of letters&quot;. But then, what if it is by means of Chinese characters, which are not letters? Be it as it may, if &quot;literary&quot; means &quot;by means of letters&quot;, a computer program in 7-bit ASCII is a literary work. Since the term &quot;literary work&quot; is defined as quoted above, this paragraph has no material impact.

Is the binary executable of a computer program a literary work, and if so, by what standard? Sure enough, we can &quot;disassemble&quot; (translate) the binary into the assembly language, which uses mnemonics, and then, we come closer to something like works &quot;expressed in words, numbers, or other verbal or numerical symbols or indicia&quot;. In any case, using naive terminology of &quot;literary work&quot;, stating that binary executable is a literary work is a stretch.

As an aside, the above language of works &quot;expresses in [...] numbers&quot; opens the door to all digital objects being &quot;literary works&quot;; since, e.g. a PNG raster image is a work expressed in numbers. That was probably not intended. Indeed, even an 7-bit ASCII file containing English text would be a work expressed in numbers (via its digital storage), whereas an intuitive understanding would be that it is a work expressed in words.

Notably, a computer game is a package of different kinds of elements: the computer code embodying algorithms, screen/room layouts, graphical elements, background music, sound, etc. Thus, a computer game is something like a rich compound, and its different parts come under different work categories listed by the copyright law.

Further reading:
* {{W|Software copyright}}, wikipedia.org
* [[Wikidata:Q7725634|Wikidata: literary work]]
* [http://digital-law-online.info/lpdi1.0/treatise17.html Digital Law Online: History], digital-law-online.info

==Fixing in tangible form==
As per [[Wikisource: United States Code/Title 17/Chapter 1/Sections 102 and 103]]:
* &quot;Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device.&quot;

When someone gives a lecture--by means of speech, no slides--and a student makes lecture notes, is it the student that is the copyright holder and not the teacher? One might think so: the teacher did not fix his lecture in any tangible medium of expression. Indeed, lecture notes taken by students are sometimes being published online. Thus, sound waves (of changes in air pressure) are not a tangible medium. However, whether this is a standard/accepted legal interpretation needs to be clarified.

If someone makes a sound recording of an originally improvised musical performance by someone else, is it the recorder who holds the copyright?

One may ponder whether computer files are really a ''tangible'' medium, given one cannot ''touch'' the files, unlike a sheet of paper, a book, a painting, a photograph or a physical photographic film. For the purpose of copyright law, almost certainly, but it is not clear how or whether this is codified.

A corollary seems to be that when a journalist interviews someone by means of speech (not e.g. email), it is the journalist that is the copyright holder of the whole interview, and the interviewee has no copyright to what he or she said. This should be better sourced since it may be a non-standard analysis.

Further reading:
* [https://guides.lib.umich.edu/copyrightbasics/copyrightability Copyrightability - Copyright Basics], guides.lib.umich.edu
* [[Wikibooks: US Copyright Law#Fixation]]
* [https://www.quora.com/Are-students-notes-that-were-made-during-a-university-course-a-breach-of-copyright Are students' notes that were made during a university course a breach of copyright?], quora.com
* [https://law.stackexchange.com/questions/29630/class-notes-who-owns-the-copyright-student-or-teacher Class notes -- who owns the copyright: student or teacher?], law.stackexchange.com

==Originality==
As per [[Wikisource: United States Code/Title 17/Chapter 1/Sections 102 and 103]]:
* &quot;Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device.&quot;

What does ''original'' mean? For one thing, it means &quot;not copied&quot;. But does it means something else?

Let us produce a list of pseudo-random numbers seeded from clock (say, Mersenne Twister used by Python). Let this list be only be found in our publication, nowhere else. Is it ''original'' work protected by copyright? It is a work of an algorithm, not a human. Moreover, the statement of the form &quot;X is the Y-th number generated by Mersenne Twister generator seeded from seed S&quot; is a statement of ''fact''. Can the algorithm claimed to be an ''author'' and engage in ''authorship''? But then, under physicalism, human brains are something like embodiments of huge complexes of algorithms, and then, counter-intuitive as it may seem, human authorship is also a result of algorithm, just that no one knows what that algorithm is exactly. This requires clarification.

Let us produce a list of random numbers by a method that can claim to produce genuinely random numbers rather than pseudo-random ones. Then, the result is not produced by a deterministic algorithm. Is the result protected by copyright?

Further reading:
* [https://guides.lib.umich.edu/copyrightbasics/copyrightability Copyrightability - Copyright Basics], guides.lib.umich.edu
* {{W|Threshold of originality}}, wikipedia.org
* [[Commons: Commons:Threshold of originality]]

==Idea-expression dichotomy==
As per [[Wikisource: United States Code/Title 17/Chapter 1/Sections 102 and 103]]:
: &quot;(b) In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.&quot;

Moreover, &quot;[...] the fundamental axiom of copyright law that no one may copyright facts or ideas&quot; as per [[Wikisource: Feist Publications v. Rural Telephone Service]].

Further reading:
* {{W|Idea–expression distinction}}, wikipedia.org
* [https://digitalcommons.pace.edu/cgi/viewcontent.cgi?referer=&amp;httpsredir=1&amp;article=1475&amp;context=plr The Myth of the Idea/Expression Dichotomy in Copyright Law] by Richard H. Jones, 1990, digitalcommons.pace.edu

==Feist v. Rural==
In Feist v. Rural (1991), the U.S. Supreme Court ruled that a telephone directory is a mere listing of facts with no original selection or arrangement and that it is therefore not copyright protected.

Court actions and courts involved:
* The District Court granted summary judgment to Rural, agreeing with Rural that telephone directories are protected by copyright.
* The Court of Appeals affirmed.
* The Supreme Court reversed the judgment of the Court of Appeals.

Further reading:
* {{w|Feist Publications, Inc., v. Rural Telephone Service Co.}}, wikipedia.org
* [[Wikisource: Feist Publications v. Rural Telephone Service]]
* [https://fairuse.stanford.edu/case/feist-publications-inc-v-rural-telephone-service-co/ Feist Publications, Inc. v. Rural Telephone Service Co. - Stanford Copyright and Fair Use Center]

==Merger doctrine==
From Murray 2006: &quot;The merger doctrine in copyright states that if an idea and the expression of the idea are so tied together that the idea and its expression are one - there is only one conceivable way or a drastically limited number of ways to express and embody the idea in a work - then the expression of the idea is uncopyrightable because ideas may not be copyrighted.&quot;&lt;ref&gt;[https://uknowledge.uky.edu/law_facpub/665/ Copyright, Originality, and the End of the Scenes a Faire and Merger Doctrines for Visual Works] by Michael D. Murray, 2006&lt;/ref&gt; A similar idea is expressed in Clayton 2005&lt;ref&gt;[https://www.paulweiss.com/media/1851041/mergerdoct.pdf The Merger Doctrine] by Lewis R. Clayton, 2005, paulweiss.com&lt;/ref&gt;.

According to Wikipedia, &quot;United States courts are divided on whether merger prevents copyrightability in the first place, or should instead be considered when determining if the defendant copied protected expression.&quot; If the latter option would prevail, one would think this: someone accidentally arriving at the same phrasing would be fine, whereas someone stating &quot;I copied the expression from source so-and-so but applied the merger doctrine&quot; would be in violation of the copyright law.

References:
&lt;references/&gt;

Further reading:
* {{W|Idea–expression distinction#Merger doctrine}}, wikipedia.org

==Sweat of the brow==
The &quot;sweat of the brow&quot; doctrine is the idea that effort alone (of collecting information) is worth protection regardless of originality. In the U.S., the doctrine was rejected in [[#Feist v. Rural|Feist v. Rural]] in 1991.

Further reading:
* {{W|Sweat of the brow}}, wikipedia.org
* [https://scholarship.shu.edu/shlr/vol22/iss2/7/ Copyright - Fact Compilations - Sweat of the Brow Doctrine Is Inapplicable and White Pages Are Not Sufficiently Original to Warrant Copyright Protection - Feist Publications v. Rural Tel. Serv. Co., 111 S. Ct. 1282 (1991).] by Linda A. Tancs, scholarship.shu.edu

==Fair use==
As per copyright.gov: &quot;Under the fair use doctrine of the U.S. copyright statute, it is permissible to use limited portions of a work including quotes, for purposes such as commentary, criticism, news reporting, and scholarly reports.&quot;

Wikimedia Commons does not allow fair use.&lt;ref&gt;[[Commons: Commons:Fair use]]&lt;/ref&gt; The rationale is that the project intends to serve wikis in different languages and different countries support or interpret ''fair use'' differently.

Further reading:
* [https://www.copyright.gov/help/faq/faq-fairuse.html Fair Use (FAQ) | U.S. Copyright Office], copyright.gov
* {{W|Fair use}}, wikipedia.org
* [[Wikisource: Copyright Act of 1976#§ 107. Limitations on exclusive rights: Fair use]]
* [[Wikisource: United States Code/Title 17/Chapter 1/Section 107]]
* [https://fairuse.stanford.edu/overview/fair-use/four-factors/ Measuring Fair Use: The Four Factors], fairuse.stanford.edu

==De minimis==
Sources indicate there exists ''de minimis'' defense in the U.S. copyright law, an abbreviation of the phrase ''de minimis non curat lex''. It seems to be distinct from and not part of ''fair use''. It remains to be clarified what it is exactly; different sources seem to use the phrase differently.

Further reading:
* [[Meta: Wikilegal/De Minimis Use of Protected Works under US Copyright Law]]
* [[Commons: Commons:De minimis]]
* [https://blogs.library.unt.edu/copyright/2017/09/05/the-de-minimis-defense-in-copyright-law-de-mini-what/ The de minimis defense in copyright law. De mini-what?], blogs.library.unt.edu
* [https://fairuse.stanford.edu/overview/fair-use/four-factors/ Measuring Fair Use: The Four Factors - Copyright Overview by Rich Stim], fairuse.stanford.edu
* [https://scholarship.law.wm.edu/cgi/viewcontent.cgi?article=1343&amp;context=wmlr Who Speaks Latin Anymore? Translating De Minimis Use for Application To Music Copyright Infringement and Sampling Application To Music Copyright Infringement and Sampling] by David S. Blessing, 2004, scholarship.law.wm.edu
* [https://www.copyright.gov/comp3/chap300/ch300-copyrightable-authorship.pdf Copyrightable Authorship: What Can Be Registered], copyright.gov

==Compilation==
As per copyright.gov, 'Compilations of data or compilations of preexisting works (also known as “collective works”) may also be copyrightable if the materials are selected, coordinated, or arranged in such a way that the resulting work as a whole constitutes a new work. When the collecting of the preexisting material that makes up the compilation is a purely mechanical task with no element of original selection, coordination, or arrangement, such as a white-pages telephone directory, copyright protection for the compilation is not available.'

Further reading:
* [https://www.law.cornell.edu/wex/compilation compilation], law.cornell.edu
* [https://www.copyright.gov/circs/circ14.pdf Copyright in Derivative Works and Compilation (Circular 14)], copyright.gov
* [https://copyright.gov/eco/help-collective-work.html Help: Collective Works | U.S. Copyright Office], copyright.gov

==Government works==
The U.S. government works are not protected by copyright, per [[Wikisource:United States Code/Title 17/Chapter 1/Sections 105 and 106]].

Further reading:
* [[W:Copyright status of works by the federal government of the United States]]
* [[Wikibooks:US Copyright Law#Government works]]

==Copyright term==
Term (duration) in the U.S.:
* Generally the life of the author plus 70 years, but it depends on when the work was created and on other things.

Copyright term extension:
* The term was extended in the U.S. via [[W:Copyright Term Extension Act]] in 1998.
* A similar EU directive is [[W:Copyright Duration Directive]].
* The EU directive was implemented in Czechia in 2000.&lt;ref&gt;[https://www.ptejteseknihovny.cz/dotazy/ve-kterem-roce-doslo-v-cesku-k-prodlouzeni-autorskopravni-ochrany-z-50-let-na-70-let Ve kterém roce došlo v Česku k prodloužení autorskoprávní ochrany z 50 let na 70 let?], ptejteseknihovny.cz (in Czech)&lt;/ref&gt;

Further reading:
* {{W|Copyright law of the United States#Duration of copyright}}, wikipedia.org
* [[Wikisource: United States Code/Title 17/Chapter 3/Sections 302 and 303]]
* {{W|List of countries' copyright lengths}}, wikipedia.org

==Example rulings==
Example rulings:
* [[Wikisource: Feist Publications v. Rural Telephone Service]]

==U.S. constitution==
U.S. constitution about copyright per [[Wikisource: Constitution of the United States of America]]:
: &quot;The Congress shall have Power [...] To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
Above, the language is of &quot;writing&quot;; thus, e.g. paintings would not be protected.

Above, the language is of &quot;useful&quot; rather than &quot;beautiful&quot; or &quot;pleasant&quot;; narrowly construed, novels would not be protected, but technical and scientific writing would be protected.

==Copyright notice==
As per Circular 1, &quot;Notice was required for works published in the United States before March 1, 1989. Works published without notice before that date may have entered the public domain in this country.&quot;

As per Circular 3, &quot;Copyright notice is optional for works published on or after March 1, 1989, unpublished works, and foreign works; however, there are legal benefits for including notice on your work.&quot;

Further reading:
* [https://www.copyright.gov/circs/circ01.pdf Copyright Basics (Circular 1)], copyright.gov
* [https://www.copyright.gov/circs/circ03.pdf Copyright Notice (Circular 3)], copyright.gov
* {{W|Copyright law of the United States#Copyright notices}}, wikipedia.org

==Berne Convention==
Berne Convention is an international copyright treaty. Its main goal is the mutual protection of copyright between signatory countries.

As per [[Wikisource: Convention for the Protection of Literary and Artistic Works]], the general minimum term of protection is the death of the author + 50 years, but there are different conditions for certain classes of works.

Further reading:
* {{W|Berne Convention}}, wikipedia.org
* [[Wikisource: Convention for the Protection of Literary and Artistic Works]]
* [https://www.britannica.com/topic/Berne-Convention Berne Convention], britannica.com

==Paraphrasing==
According to {{W|Wikipedia:Close paraphrasing}}, paraphrasing the source does not necessarily avoid copyright violation. This seems strange since it is the expression that is protected, not the fact or idea. This requires more deliberation and research.

[[Meta: Wikilegal/Close Paraphrasing]] indicates the answer to &quot;Is close paraphrasing of a copyrighted work a copyright infringement?&quot; is yes. But then, there is something like ''close'' paraphrasing and something like ''non-close'' paraphrasing. The page does not provide any explanation for what &quot;close&quot; means, nor any examples. The Wikilegal page takes an exception to the answer it has given, admitting that if one closely paraphrases a copyrighted work published under CC-BY-SA in a work under CC-BY-SA and traces the sentence to that work, there is no copyright violation. The proper proofreading and vetting of that page is unclear; the page was created in 2012 by an anonymous IP address.

Further reading:
* {{W|Paraphrasing of copyrighted material}}, wikipedia.org
* {{W|Wikipedia:Close paraphrasing}}, wikipedia.org -- largely unsourced essay
* [[Meta: Wikilegal/Close Paraphrasing]]

==Plagiarism==
The concept of plagiarism relates to copyright violation, but is not exactly the same thing.

According to Britannica 1911, plagiarism is &quot;an appropriation or copying from the work of another, in literature or art, and the passing off of the same as original or without acknowledgment of the real authorship or source.&quot;

One point of contrast to copyright violation: If a publisher publishes a copyrighted work without author's (or the rightful publisher's) permissions but correctly states the author of the work, it would be a copyright violation but no plagiarism since the transgressing publisher does not misrepresent or hide the authorship.

Even passing someone's ''ideas'' as one's own is plagiarism, according to multiple sources&lt;ref&gt;[https://www.getty.edu/vow/AATFullDisplay?find=&amp;logic=AND&amp;note=&amp;subjectid=300055298 plagiarism], Art &amp; Architecture Thesaurus&lt;/ref&gt;&lt;ref&gt;[https://researchguides.uic.edu/c.php?g=252209&amp;p=1682805 Copyright Vs. Plagiarism - Avoiding Plagiarism - Subject and Course Guides at University of Illinois at Chicago], researchguides.uic.edu&lt;/ref&gt;&lt;ref&gt;[https://www.plagiarism.admin.cam.ac.uk/definition Definition of academic misconduct], plagiarism.admin.cam.ac.uk&lt;/ref&gt;&lt;ref name=ca/&gt; but not Britannica online&lt;ref&gt;[https://www.britannica.com/topic/plagiarism plagiarism], britannica.com&lt;/ref&gt;. That is a point of contrast to copyright, which does not protect ideas. How and to what extent giving credit for ''ideas'' to other people and sources is practicable and practiced is unclear. Since, surely authors would all too often read something somewhere, forget where, and later use the ideas with forgotten provenance in their writing or other production.

At least two sources count using someone's ''information'' without attribution as plagiarism.&lt;ref&gt;[https://poorvucenter.yale.edu/undergraduates/using-sources/understanding-and-avoiding-plagiarism/what-plagiarism What Is Plagiarism? | Poorvu Center for Teaching and Learning], poorvucenter.yale.edu&lt;/ref&gt;&lt;ref&gt;[https://writing.wisc.edu/handbook/quotingsources/ Quoting and Paraphrasing – The Writing Center – UW–Madison], writing.wisc.edu&lt;/ref&gt; One may wonder whether information, and also ''data'', are species of ''ideas'' and thus covered by the above paragraphs.

As for ''data'', article [[Plagiarism]] quotes Kennedy 2006 as stating: &quot;Plagiarism is the illegal practice of taking someone else's ideas, data, findings, the language, illustrative material, images, or writing, and presenting them as if they were your own.&quot; Following this definition, even using data without attribution is plagiarism. However, the quotation states that plagiarism is ''illegal'', at odds with the following paragraph. If we accept using someone's data without attribution as plagiarism, Wikidata will probably end up being largely plagiaristic; this character is reduced by entries listing certain sources in the &quot;Identifiers&quot; section. Many Wiktionaries would be plagiaristic as well; the German Wiktionary extensively listing sources less so.

Plagiarism is not illegal in the U.S., unlike copyright violation&lt;ref name=ca&gt;[https://copyrightalliance.org/differences-copyright-infringement-plagiarism/ Plagiarism vs Copyright Infringement], copyrightalliance.org&lt;/ref&gt;; plagiarism is an ethical concern. This is corroborated by considering plagiarism of ''public domain'' materials without attribution: it meets the definition of plagiarism but is not copyright violation in the U.S. sense. This is not to be understood as saying that no act that is plagiarism is ever illegal; an act is not illegal as plagiarism, but it may be illegal as copyright violation (some plagiarism is at the same time copyright violation).

Using the above notion (sourced one) that unattributed use of ''ideas'' (rather than e.g. word sequences) of others is plagiarism, we get that large language models (LLM) are high-volume plagiarists. That is so in so far as as they do not cite their sources, which they usually do not do. One may counter that a LLM learns an idea only if it is expressed in fairly many sources. This raises the question: if one takes an idea not from one but from many sources and does not state the source, is it still plagiarism? Or can one rather argue that, in that case, it is part of common knowledge or store of ideas, which bars the attribution requirement?

A rather different concept of plagiarism is used by Masaryk University in Czechia.&lt;ref&gt;[https://www.muni.cz/en/about-us/official-notice-board/plagiarism Plagiarism], muni.cz&lt;/ref&gt; According to them, &quot;Plagiarism constitutes the intentional copying of another author's text and the representation and publication of such a test as one's own original work, careless or inaccurate citation of source literature and/or the omission of required bibliographical information (however unintentional).&quot; Reservations apply:
* Taking of others ''ideas'' is not covered.
* Their statement that &quot;Sanctions for plagiarism are determined by the Copyright Act&quot; is at odds with the notion of the preceding paragraphs that copyright violation and plagiarism are fundamentally orthogonal concepts and that plagiarism is not illegal in the U.S.
* The definition is narrow in only covering texts but not other kinds of artifacts subject to potential copying or immitation.
However, ČSN ISO 5127 (Czech state norm) and Czech terminological database of library and information science use different definitions&lt;ref name=aac&gt;[https://www.akademickaetika.cz/prirucka-pro-akademicke-pracovniky/4-podoby-plagiatorstvi/ Podoby plagiátorství - Jak předcházet plagiátorství - Příručka pro akademické pracovníky - Akademická etika], akademickaetika.cz&lt;/ref&gt;. akademickaetika.cz settled on the Czech definition &quot;využití (myšlenek, obsahu nebo struktury) jiného díla bez řádného uvedení odkazu na zdroj k získání určité výhody tam, kde se očekává původní dílo&quot;, approximately corresponding to &quot;the use of ideas, content, or structures without appropriately acknowledging the source to benefit in a setting where originality is expected&quot;&lt;ref name=aac/&gt;. More research could find out which definition is dominating in Czech sources.

See also:
* [[Plagiarism]]

References:
&lt;references/&gt;

Further reading:
* {{W|Plagiarism}}, wikipedia.org
* {{W|Wikipedia:Plagiarism}}, wikipedia.org
* [[Wikisource:1911 Encyclopædia Britannica/Plagiarism]]
* [https://cws.auburn.edu/OVPR/pm/tt/copyrightvplagiarism IAC - Copyright: Copyright vs. Plagiarism], cws.auburn.edu

==Translation pairs==
Translation pairs, e.g. &quot;cat&quot; --&gt; &quot;Katze&quot;, are one application of copyright law. Arguably, they often constitute facts expressed in an obvious canonical form (a pair), and thereby would not be protected by copyright.

However, one can argue that in so far as the chosen translation pairs differ between different dictionaries, there is something original to an extent to them. Requires clarification.

Protection against copyright infringement I am using:
* Use multiple sources for each translation pair rather than blindly copying a single source.
* Double check and question rather than blindly accepting what the sources indicate.
* Check definitions of the items in the pair for match.

Further reading:
* [[Wiktionary: Wiktionary:Beer parlour/2013/September#Translations pairs, copyrighted translation dictionaries, and copyright_violation]]
* [[Meta: Wikilegal/Lexicographical Data]]

==Dictionary definitions==
Above, we touched on [[#Translation pairs]], but there are other dictionary artifacts potentially subject to copyright, especially definitions.

Arguably, dictionary definitions are copyrighted, given the variation in their formulation across dictionaries. On the other hand, one could argue that they are not protected given the merger doctrine: there is only a handful of ways how to accurately define a word, one might think. The Richards v. Merriam Webster, Inc. case suggests definitions are protected.

Further reading:
* [[Meta: Wikilegal/Lexicographical Data]]
* [[Meta: Wikilegal/Lexicographical Data#Copyright on an individual definition of a word as a literary work]]
* [https://casetext.com/case/richards-v-merriam-webster-inc-1 Richards v. Merriam Webster, Inc.], casetext.com

==Dictionary quotations==
Some dictionaries contain short quotations of word use from literature (a sentence or two), stating the work title, author and publication date. Since the authorship is properly credited, it is not plagiarism but it could still be a copyright violation in principle. This practice is probably allowed via ''fair use''. Finding a good source on the subject would be worthwhile.

==Slogans and short phrases==
As per copyright.gov, &quot;Copyright does not protect names, titles, slogans, or short phrases. In some cases, these things may be protected as trademarks.&quot;

Further reading:
* [https://www.copyright.gov/help/faq/faq-protect.html What Does Copyright Protect? (FAQ)], copyright.gov

==Photographs==
One could think that, unlike paintings, photographs are a straightforward capture of ''facts'': how the world looks at a point in time at a certain place from certain angle, etc. However, since photographs are copyright protected, there must be a rationale for doing so. Finding out the rationale requires more research.

Contrast can be drawn between 1) merely making a photograph and 2) arranging things to be photographed and then making a photograph. Thus, the lawgiver could consider &quot;plain&quot; photographs to be free from copyright protection.

Further reading:
* [https://www.copyright.gov/engage/photographers/ What Photographers Should Know about Copyright], copyright.gov
* {{W|Burrow-Giles Lithographic Co. v. Sarony}}, wikipedia.org
* [https://www.dacs.org.uk/knowledge-base/factsheets/copyright-in-photographs DACS - Knowledge Base - Factsheets], dacs.org.uk
* [https://guides.libraries.indiana.edu/c.php?g=158548&amp;p=1662844 Copyright for Photographers - Copyright], guides.libraries.indiana.edu
* [https://www.copyrighthistory.org/cam/tools/request/showRecord.php?id=record_us_1865 Copyright Act Amendment, Washington D.C. (1865)], copyrighthistory.org

==Charts and graphs==
Charts and graphs would seem to be free from copyright in so far as they are a straightforward presentation of data and data and facts are not copyrightable. However, one might reckon that color schemes and similar somewhat arbitrary choices could make a chart copyrightable.

Wikimedia Commons have Template:PD-chart that labels charts that are considered uncopyrightable; one may investigate the particular charts to get an idea. Moreover, Commons:Threshold of originality#Charts links to multiple deletion discussions.

Further reading:
* [[Commons: Commons:Threshold of originality#Charts]]
* [https://deepblue.lib.umich.edu/bitstream/handle/2027.42/83329/copyrightability_of_tables_charts_and_graphs.pdf Copyrightability of Tables, Charts and Graphs], deepblue.lib.umich.edu

==Computer-made art==
It is unclear to what extent and what computer-made art is subject to copyright. One can think e.g. of iterated function system fractals or Mandelbrot set images, which are drawn by the computer. Considering Mandelbrot set, the human can set the location, the zoom level and color palette; it is not clear to what extent this limited choice is creative. Arguably, Mandelbrot set images are not created but rather computationally discovered.

A rather different category is pseudo-AI-generated art, which we cover in a dedicated section below.

According to Compendium of U.S. Copyright Office Practices, human authorship is required for copyright: 'The copyright law only protects “the fruits of intellectual labor” that “are founded in the creative powers of the mind.”'

Further reading:
* [https://itsartlaw.org/2022/11/21/artistic-or-artificial-ai/ Art-istic or Art-ificial? Ownership and copyright concerns in AI-generated artwork – Center for Art Law], itsartlaw.org
* [https://www.copyright.gov/comp3/chap300/ch300-copyrightable-authorship.pdf Copyrightable Authorship:What Can Be Registered] in Compendium of U.S. Copyright Office Practices, copyright.gov
* [https://scholarship.law.duke.edu/cgi/viewcontent.cgi?article=1023&amp;context=dltr Copyrights in Computer-Generated Works: Whom, if Anyone, Do We Reward?], 2001 Duke L. &amp; Tech. Rev. 0024

==AI-generated art==
In pseudo-AI-generated art, the human can supply a brief textual prompt and the pseudo-AI produces an impressive-looking image. It is not clear to whom the copyright (if any) of the output image belongs.

Further reading:
* [https://www.wipo.int/wipo_magazine/en/2017/05/article_0003.html Artificial intelligence and copyright] by Andres Guadamuz, 2017, wipo.int
* [https://copyrightalliance.org/copyright-cases-visual-artists-authorship/ Copyright Cases Visual Artists Should Know: Part 2, Authorship | Copyright Alliance], copyrightalliance.org

==AI-generated text==
The copyright questions about AI-generated text seem similar to those about AI-generated visual art.

New York Times sues OpenAI over ChatGPT alleged copyright violation.&lt;ref&gt;[https://www.theverge.com/2023/12/27/24016212/new-york-times-openai-microsoft-lawsuit-copyright-infringement The New York Times sues OpenAI and Microsoft for copyright infringement], 27 Dec 2023, theverge.com&lt;/ref&gt;&lt;ref&gt;[https://nytco-assets.nytimes.com/2023/12/NYT_Complaint_Dec2023.pdf pdf attachment: the NYT complaint], nytimes.com&lt;/ref&gt;

Further reading:
* [[Meta: Wikilegal/Copyright Analysis of ChatGPT]]

==Screenshots of computer software==
Screenshots of computer software are copyrighted. There may be a ''fair use'' defense for their use; this needs to be clarified.

The English Wikipedia has {{W|Template:Non-free video game screenshot}} to label non-free screenshots and provide fair use as rationale.

Further reading:
* [https://academia.stackexchange.com/questions/26526/how-does-copyright-work-on-screen-captures software - How does copyright work on screen captures?], academia.stackexchange.com
* [https://pressbooks.library.torontomu.ca/authorsguide/chapter/screenshots-of-software/ Screenshots of Software], pressbooks.library.torontomu.ca

==Videogame long play videos==
YouTube contains many videogame long play videos, showing someone play a video game from the start to the end. One would think that since these videos show graphical elements and music, they are copyright violations. On the other hand, one could argue that the videos do not provide as much entertainment as an actual play and do not effectively reduce merchantability of the game, so ethically (as contrasted to legally) it is tolerable. On the other hand, even a single screenshot from a computer game is copyrighted, and an argument protecting a whole long play video from a lawsuit would equally well seem to protect a single screenshot. The long play publishing practice possibly rests on the game publishers not launching any lawsuits or requests for video removals given the videos do not reduce their revenue and probably cause them no other harm.

Further reading:
* [https://www.cbc.ca/news/entertainment/youtube-gaming-pewdiepie-fair-use-1.4309312 Is playing video games on YouTube a copyright infringement? No one wants to find out], cbc.ca

==Game mechanics==
Multiple experts in Quora indicate that mechanics of computer games are not copyrightable but are patentable. However, visual artwork and music are very likely copyright protected.

As for the mechanics, one has to become clear what is meant by that. A general idea of a game may be not copyrightable, but specific room layouts could possibly be. This requires more research.

Further reading:
* {{W|Intellectual property protection of video games}}, wikipedia.org
* [https://www.quora.com/Are-video-game-mechanics-protected-under-copyright Are video game mechanics protected under copyright?], quora.com
* [https://www.redpoints.com/blog/video-game-copyright/ How do video game copyrights work? - Red Points], redpoints.com

==Internet and the web==
The web presents some new questions concerning copyright. For instance, one can ask whether a browser's making RAM copies and even temporary files to view content sent by the web server is a copyright violation in that it is an unauthorized making of copies. Arguably, it is the intent of the web server provider that user software makes such copies and therefore, there is an implied license to make such copies, solely for the purpose of activity approved by the web server, that of viewing the content.

These fine considerations can play a role in an analysis of the legality of training large language models (LLM, a pseudo-AI) on content obtained from web pages. Since, arguably, as long as the web page provider did not grant anyone an express license to make copies on their servers for the purpose of the LLM training, making these copies is a copyright violation.

==Database right==
Database right is distinct from copyright. It is not available in the U.S., but it is available in the EU.

Database right had to be codified as distinct from copyright since in copyright, information is not protected, merely its expression, and a database is a collection of standardized structured records, arguably showing no originality in expression. (But, arguably, one might claim some originality in the data model.)

Further reading:
* {{W|Database right}}, wikipedia.org
* [[Wikibooks: UK Database Law]]
* [https://europa.eu/youreurope/business/running-business/intellectual-property/database-protection/index_en.htm Database protection in the EU - Your Europe], europa.eu

==Wikipedia==
As per {{W|Wikipedia:Copyrights#Governing copyright law}}:
: &quot;The Wikimedia Foundation is based in the United States and accordingly governed by United States copyright law. Regardless, according to Jimbo Wales, the co-founder of Wikipedia, Wikipedia contributors should respect the copyright law of other nations, even if these do not have official copyright relations with the United States.&quot;

The above applies to the English Wikipedia. It probably applies to non-English Wikipedias as well since the organization and the servers are located in the U.S.

Further reading:
* {{W|Wikipedia:Copyrights#Governing copyright law}}, wikipedia.org

==Wikisource==
If one assumes that the decisive factor for copyright jurisdiction is that the servers and the organization are located in the U.S., one might think that all Wikisource domains (de.wikisource.org, fr.wikisource.org, etc.) would be under the same U.S. jurisdiction. Nonetheless, some non-English works are hosted at wikisource.org rather than on the subdomain matching the language. For instance, there is https://wikisource.org/wiki/Słownik_geograficzny_Królestwa_Polskiego. This has template &quot;Template:PD-US-1923-abroad/PL&quot;. There are other templates: Template:PD-US-1923-abroad/CS, Template:PD-US-1923-abroad/DE, etc. Therefore, the Foundation seems to be playing it safe and separates non-English works whose inclusion is based on PD-US rationale on a dedicated domain. However, how this separation can possibly be material from the standpoint of copyright jurisdiction is unclear: it is hard to understand how a mere switch of the domain from e.g. pl.wikisource.org from wikisource.org (keeping the language of the work the same) magically impacts the applicable copyright law jurisdiction. wikisource.org still seems to serve the pages to viewers in various jurisdictions across the world; by contrast, some U.S.-based websites responded to the EU-imposed GDPR by refusing to serve pages to viewers located in the EU. Thus, hosting the pages on a separate domain seems to be some kind of game more than anything else, but I (Dan Polansky) am not a lawyer.

==Linguistic corpora==
Linguistic corpora include Google Books, COCA, BNC and others. They usually present users with text snippets (for a sought word or phrase) found in a range of sources where the corpus operator does not hold the copyright in the individual snippets. This seems to be considered not a copyright violation of these sources, although it does seem to violate the copyright on snippet level. A defense could perhaps be fair use or de minimis.

Google web search is another service that shows text snippets in an aggregate form, where the search operator does not hold copyright to the snippets. To provide the snippets, Google stores (copies of ) web pages on its servers, and it is unclear how this itself is not copyright violation. A speculation is that it is taken as fair use.

Google Books preview function often offers many full pages of text for modern copyrighted works. However, some books there offer no preview. How this is handled from a copyright standpoint is unclear. It seems impossible for Google to have obtained permission from all publishers so previewed.

==Internet Archive and Wayback Machine==
The Internet Archive's Wayback Machine provides archived copies of web pages it finds. One would think that, in general, the result is a copyright violation; the archiving is not based on the web page authors granting a license for such copies to exist.

Wayback Machine is not the only making available online activity of The Internet Archive. The organization scans various copyrighted books and makes them available online. One would think this is a copyright infringement unless they obtain consent of the publishers. Complaints have been made against the organization in that regard&lt;ref&gt;[https://copyrightalliance.org/trending-topics/internet-archive-harms-authors/ Internet Archive Continues To Harm Authors | Copyright Alliance], copyrightalliance.org&lt;/ref&gt;. A court decision has been made concerning a certain scope of infringement&lt;ref&gt;[https://authorsguild.org/news/how-to-tell-internet-archive-to-remove-your-books/ Update: How to Tell Internet Archive to Remove Your Books], authorsguild.org&lt;/ref&gt;. There is more information in Wikipedia. Be it as it may, it seems unwise to infer from the availability of an item in Internet Archive that it is not copyrighted.

Further reading:
* {{W|Internet Archive#Copyright issues}}, wikipedia.org

== Song lyrics and guitar chords ==
It is easy to find websites showing lyrics and guitar chords for popular music, e.g. The Beatles. It seems many of these websites engage in copyright violation. It seems that the copyright holders are not interested in suing the websites. Some of the websites could have a license, though.

Keywords: sheet music.

Further reading:
* [https://writing.stackexchange.com/questions/6797/are-music-lyrics-copyrighted Are music lyrics copyrighted?], writing.stackexchange.com
* [https://law.stackexchange.com/questions/77124/what-does-copyright-law-have-to-say-about-publishing-written-notation-for-record What does copyright law have to say about publishing written notation for recorded music?], law.stackexchange.com
* [https://www.theverge.com/2025/1/3/24334866/anthropic-claude-music-publishers-lyric-copyright-lawsuit-deal Anthropic reaches deal with music publishers over lyric dispute], 3 Jan 2025, theverge.com

== Quotations ==
There must be some limitation on the copyright of reasonably small quotations from copyrighted material or else Wikiquote, a collection of quotations, could not exist or would have to be restricted to quotations of authors who are no longer copyrighted. One could think this is covered by fair use, but this needs a more careful look. The copyright threshold would probably have to do with the amount of the text quoted from a single work.

== Example lawsuits ==
Example lawsuits are delegated to further reading.

Further reading:
* {{W|List of copyright case law}}, wikipedia.org
* {{W|Category:Copyright case law}}, wikipedia.org
* [https://www.freedomforum.org/famous-copyright-cases/ 10 Famous Copyright Cases: Taylor Swift, Star Wars and More], freedomforum.org

== Criticism of copyright law ==
This section is largely delegated to further reading.

Interestingly, the free-as-in-freedom philosophy as embodied e.g. in GNU GPL license (and CC-BY-SA) does not seem to have any need of abolishment or weakening of the copyright law. The longer the copyright protection, the longer the protection of an item licensed under GNU GPL. If, by contrast, all items would become public domain e.g. 10 years after publication, the copyleft would have no force then, an adverse outcome from the perspective of the strong copyleft philosophy. (Weak copyleft as exemplified by permissive licenses often used e.g. by FOSS Python libraries is a different story.) But the matter may be more complicated. If copyright would expire 10 years after the publication, not only would the copyright of copyleft-licensed items expire but also of proprietary items. One could want to accept the loss of strong copyleft in exchange of gaining free access to proprietary items.

Further reading:
* {{W|Criticism of copyright}}, wikipedia.org

== Single sentence level ==
I think of single sentences as some of the smallest units that are subject to copyright. Sure enough, a sentence has to be reasonably complex to be protected; &quot;it is raining today&quot; is unlikely to be protected. I think about it as follows: if you do not own the copyright or an appropriate license, don't copy. If you hit upon a sentence independently, that's fine. And don't forget that plagiarism, unlike copyright, is defined in relation to ideas, so paraphrasing does not necessarily prevent a charge of plagiarism (and such charge can be prevented by crediting sources of ideas). If you do have to use someone else's reasonably complex sentence, do so in quotation marks and indicate the source.

Sure enough, there would usually not be a lawsuit for a single copied sentence. In fact, when the sentence is properly attributed, it could act as a sale pitch toward the source of it. Whether there are likely damages does play a role.

I vaguely remember a Czech lawsuit that concerned a phrase, not even a complete sentence. Svěrák could have been involved. Requires verification.

My experience as of October 2025 shows that Google finds reasonably long sequences of words in sources that use them. I have not looked carefully at the word length, but I think 10-word sequence is easily matched. One can thus Google a large portion of a complex sentence to investigate a possible copyright infringement of an online source. And Google Books covers offline sources to some extent. Sure enough, a single sentence is perhaps not such a problem, but if the author copied it without attribution, his understanding of copyright seems to be problematic, as well as the ethical concern with plagiarism.

==References==
&lt;references/&gt;

==Further reading==
Wikipedia and other wikis:
* {{W|Copyright}}, wikipedia.org
* [[Wikipedia: United States copyright law]]
* [[Wikipedia: Digital Millennium Copyright Act]]
* [[Wikibooks: US Copyright Law]]
* [[Wikisource: United States Code/Title 17]]
* [[Wikisource: Copyright Act of 1976]]
* [[Wikisource: Copyright Term Extension Act of 1998]]
* [[Wikisource: Digital Millennium Copyright Act]]
* [[Wikipedia: Wikipedia:Copyrights]]
* [[Commons: Commons:Licensing]]
* [[Commons: Commons:Copyright rules by territory]]
* [[Commons: Commons:Copyright rules by territory/United States]]

Non-Wikipedia:
* [https://www.britannica.com/topic/copyright Copyright], britannica.com
* [https://www.copyright.gov/circs/circ01.pdf Copyright Basics (Circular 1)], copyright.gov
* [https://www.copyright.gov/circs/circ02.pdf Copyright Registration (Circular 2)], copyright.gov
* [https://www.copyright.gov/circs/circ03.pdf Copyright Notice (Circular 3)], copyright.gov
* [https://www.copyright.gov/circs/circ04.pdf Copyright  Office  Fees (Circular 4)], copyright.gov
* [https://www.copyright.gov/circs/circ05.pdf Copyright Office Deposit Account (Circular 5)], copyright.gov
* Etc. (more circulars)
* [https://www.copyright.gov/legislation/dmca.pdf Digital Millennium Copyright Act], copyright.gov

[[Category:Copyright law]]
[[Category:Plagiarism]]</text>
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    <title>User talk:Dan Polansky/An analysis of identity</title>
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      <comment>Atcovi moved page [[Talk:An analysis of identity]] to [[User talk:Dan Polansky/An analysis of identity]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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      <text bytes="13901" sha1="cp9k3o0nkgplz3jfq96uar68bmlzo18" xml:space="preserve">{{ping|Dan Polansky}} Your thoughts on [[w:E-prime]]? I have not made a real effort to try it yet, but it strikes me as interesting for two reasons. First, I imagine (correct me if I'm wrong) that it encourages use of the active voice. The [[w:Passive voice]] is common in officialese and doublespeak as it enables one to omit (and therefore obscure) the grammatical agent. [https://etheses.bham.ac.uk/id/eprint/8316/2/Lingle18PhD.pdf] Incidentally, have you ever seen such a bad lede as in [[w:Object (grammar)]]? Secondly, it encourages one to describe more specific relationships than the &quot;is-a&quot; formation. ''John works as a farmer'' strikes me as a more precise use of language than ''John is a farmer''. Conversely, E-prime would probably be awkward or lacking in authoritative effect in some instances. Take the example on wikipedia: ''&quot;The cat is Garfield&quot;: &quot;I call my cat Garfield&quot;.'' Yet this would sound rather pitiful, frankly weak, if you were referring to a human, as in ''I call my son Garfield''. What if I want to call your son Bozo? One seems to admit that possibility with such timid phrasing. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 12:28, 22 February 2024 (UTC)

Generally, my impression is that E-prime might be worthwhile as a method of correcting certain bad habits like overuse of the passive voice and other such imprecisions. To fully adopt it as one's &quot;native language&quot;, so to speak, would probably be ill-advised. At the very least, the ''is a'' phrase is appropriate for drawing real equivalence. ''My cat's name is Garfield'' seems more natural and accurate than either of the two sentences in Wikipedia's example ''&quot;The cat is Garfield&quot;, &quot;I call my cat Garfield&quot;''. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 12:45, 22 February 2024 (UTC)
: About E-prime: &quot;E-Prime (short for English-Prime or English Prime,[1] sometimes É or E′) denotes a restricted form of English in which authors avoid all forms of the verb to be.&quot; To my mind, avoiding all &quot;to be&quot; ''is'' absurd or ''is-instance-of'' absurdity or presents a case of absurdity. One can surely often strengthen writing by switching from &quot;to be&quot; to a more forceful verb, but I do not see how this practice can improve the characteristics of writing that I cherish the most, which is accuracy, clarity, unambiguity, empirical testability/falsifiability, logical testability/criticizability/falsifiability, etc.
: Active voice is a classical English-style recommendation, but I think it is overrated. Semantically, there is no deep difference between active and passive voice. X does Y vs. Y is done by X, no big deal, I think.
: Do you happen to have specific proposals for wording improvement of the &quot;An analysis of identity&quot; article, in the form of X --&gt; Y? Or you could post here on the talk page a rewrite of one of my paras, if you like. I would give these proposals a consideration, but no promise; I tend to be quite stubborn or &quot;ownheaded&quot; as the Czech idiom has it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:49, 22 February 2024 (UTC)
::I am not suggesting any particular change, except perhaps to E-prime. Perhaps a modified E-prime that allows ''is-a'' for definitions and equalities would be both practical and still possess the general benefits of E-prime. Avoiding false characterizations of identity seems to be a feature of E-prime. Since you discuss the grammar of &quot;is a&quot; and &quot;to be&quot; in the resource, I simply wanted your opinion on E-prime. Your comment on the passive voice seems to miss the point. ''Joe mowed the lawn'' and ''The lawn was mowed by Joe'' are equivalent, but the passive voice allows for ''The lawn was mowed''. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 13:03, 22 February 2024 (UTC)
::: I may consider specific change proposals; a general proposal to switch to the arguably unconvincing E-prime is unlikely to be implemented. (The previous sentence uses passive on purpose to drive a point home. The implied agent of that passive is me, of course.)
::: Well, sometimes it is the right thing to deemphasize/hide the agent. Am I using passive voice in some sentence where active voice would be better? Or is the passive voice used in excess in &quot;An analysis of identity&quot;? (See, we already know the author of &quot;An analysis of identity&quot; and do not need to identify him.) --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:29, 22 February 2024 (UTC)
:: You also seem to have missed (or reversed) my other point, which is that the phrase &quot;is a&quot; generally sounds more forceful, but may be overused. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 13:07, 22 February 2024 (UTC)
::: I am all ears for specific wording change proposals, whether on sentence level or on a paragraph level. I much prefer it over generalities. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:29, 22 February 2024 (UTC)
::::Really now Dan. (Can I call you Dan?) I'm not proposing any change to your article but rather inviting you to have a discourse on E-prime, which may be relevant to your article. You don't have to read between the lines to see the points I've made, but your reply ignores, inverts or misinterprets all of them. I agree it's a bit absurd to avoid all instances of &quot;to be&quot; and its variants. I had already said as much and described a possible &quot;relaxation&quot; of E-prime. If your answer is ''no comment'' then just say so. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 13:33, 22 February 2024 (UTC)
::::: Yes, you can call me Dan. I have misunderstood the purpose of your conversation. I interpreted the conversation as a contribution to improving this particular article.
::::: I have no well developed thoughts on the stylistic guidance recommending a drastic reduction of the verb &quot;to be&quot;. My initial thoughts are that &quot;to be&quot; is fine in general. Skilled writers probably often replace &quot;to be&quot; with stronger verbs, but I doubt this usually results in increase of accuracy, clarity, and other desiderata I cherish the most. But then, most writers are probably not interested in boring technical specifications. I may change my mind if I give e-Prime more serious consideration and though, which obviously has not happened yet given I am responding without having slept over on it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:44, 22 February 2024 (UTC)
:::::: My point about rhetorical strength concerns the &quot;is a&quot; and &quot;are&quot; forms, and you've still got it backwards. &quot;Is a&quot; and &quot;are&quot; draw an equivalence and are therefore &quot;strong&quot;. Sometimes this is (in an ethical or moral sense) appropriate, for instance when one speaks with genuine authority, &quot;your actions are wrong&quot;, &quot;my son's name is Garfield&quot;, etc. Sometimes this is arguably imprecise, as in &quot;John is a farmer&quot;, which would be more accurately stated as &quot;John works as a farmer&quot;. Sometimes this is used dishonestly, for instance equating someone with an abstract quality or label of judgement. The first and last cases are both ''rhetorical'' in a sense. They declare something to be so. Aside from this, E-prime seems to favor the active voice rather than the passive voice. While the work I cited above suggests that use of the passive voice has only a limited capacity to obscure the agent when it can be inferred and I haven't read it in full (it's 200 pages), it explains the idea. Beside that, it's also just a good habit to prefer the active voice. Orwell cautions the reader to avoid the passive voice whenever possible in his essay on language (which I've brought to your attention before). Like Orwell, I suspect English is being debased. People take after the example set by mass media. A precise definition of the problem is not yet clear to me (I haven't studied linguistics), but there's definitely a problem. Pure E-prime would probably undermine one's ability to speak confidently and authoritatively. In other instances it forces one to make more accurate choices. To have a compact set of rules that helps one consciously avoid the formulaic doublespeak, officialese and newspeak of the mass media would be invaluable, and this was probably the object of Orwell's essay. While his essay is very good, I doubt it fully captures the problem or the solution. Perhaps a modified definition of E-prime would work. Nominalization is also subversive and should be looked upon with deep suspicion. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 14:43, 22 February 2024 (UTC)

:::::: ''To have a compact set of rules that helps one consciously avoid the formulaic doublespeak, officialese and newspeak of the mass media would be invaluable.'' In fact, the complement must exist. If it weren't reasonably simple then the pseudo-intellectuals, half-witted pundits, imposters, and other phony mooks in the mass media, academia and government would be incapable of implementing it so uniformly. Not to say we don't have good people in the same institutions, though I'm starting to doubt it in the case of mass media and government. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 15:14, 22 February 2024 (UTC)
::::::: There was a beautiful project by the Viennese Circle to regulate language in such a way that it would be very hard or impossible to state nonsense in that regulated language, or at least the kind of nonsense that forms a considerable portion of the continental so-called philosophy. Alas, such a project is arguably doomed to failure. But the idea is beautiful: image a mere compact mechanical set of rules for simpletons that would make you a great and honest writer. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:26, 22 February 2024 (UTC)
::::::::Not to force honesty or make it impossible to write poorly, but simply to avoid the bad habits impressed upon so many people by the mass media's argot. Orwell proposed six concise recommendations in his essay, of which he wrote &quot;''These rules sound elementary, and so they are, but they demand a deep change of attitude in anyone who has grown used to writing in the style now fashionable. One could keep all of them and still write bad English, but one could not write the kind of stuff that I quoted in those five specimens at the beginning of this article.''&quot; There are specific and deliberate features of the doublespeak used by political media and subversive mass media in general that distinguish it from &quot;ordinary&quot; English. I think Orwell described the gist of it fairly well and his six recommendations seem sound. Yet, having the benefit of hindsight and my own observations of contemporary propaganda, they seem incomplete. Or rather, they may require slight adjustment. Rules 5 and 6 could probably be removed. In their place, one could add something about avoiding nominalizations and also a rule about avoiding &quot;to be&quot; and its analogs when practical or under certain conditions. [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 20:41, 22 February 2024 (UTC)

:::::::: Also, Hitchens frequently made the vague suggestion to the reader or listener when he cautioned them about propaganda, &quot;''look to the language''&quot;. He tells us to beware &quot;we&quot; if the word is used as rhetoric, e.g. to recruit listeners or readers or to project the illusion of unity or consensus dishonestly.  Hitchens is somewhat an &quot;unreliable narrator&quot;, so to speak, but this also seems like a good recommendation and I've tried to follow it. (I'll say though, it's quite a hard habit to break, using &quot;we&quot; unnecessarily. Academic papers use it liberally and I suspect the habit is quite deeply impressed upon most scholars.)  [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 20:54, 22 February 2024 (UTC)

:::::::: I eventually intend to write up such a document, yet it would be substantially easier if I had a linguist to collaborate with. I suppose I already have written about it, but I'm not yet satisfied with the work. It has to be compact, concise and extremely sharp. Something that makes an impression on the reader and makes them conscious of these habits and their subversive nature, and ultimately compels the reader to extinguish them with the same alacrity and efficiency as water extinguishes fire. Only when that is finished will I have the tools necessary to banish this social and cultural rot, perhaps not from society at large but at least from some small corner of it. It destroys everything decent and worthwhile. This problem must be understood and put into words, otherwise one is hard-pressed to counter it in even the slightest way. I believe Orwell was on the right track. Hitchens knew exactly what this linguistic ruse was comprised of, but he only spoke about it vaguely. He was probably telling the truth when he said &quot;look to the language&quot; though. Propaganda and rhetoric are based in language. Part of it is the manipulation of tribalism and groupthink. Part of it is the poisoning of language and its expressive power. Perhaps I'll read more of Chomsky's work. He too is an unreliable narrator, but he's also a moralist, and moralists are rarely all bad.  [[User:AP295|AP295]] ([[User talk:AP295|discuss]] • [[Special:Contributions/AP295|contribs]]) 21:18, 22 February 2024 (UTC)</text>
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  <page>
    <title>Schoute partition</title>
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      <text bytes="909" sha1="3im5wvubvgqu5t4gxk4i8w4dg3qy8fn" xml:space="preserve">{{Schoute matrix}}
{{dh-link|a/schoute_coset_gen}}

{{multiple image
 | align = right | total_width = 500
 | image1 = Permutohedron 4 with stacked cosets a1.svg
 | image2 = Permutohedron 4 with stacked cosets b3.svg
 | footer = '''Stacked''' cosets are the columns of the '''active''' matrix.
}}

{{multiple image
 | align = right | total_width = 500
 | image1 = Permutohedron 4 with crossed cosets a1.svg
 | image2 = Permutohedron 4 with crossed cosets b3.svg
 | footer = '''Crossed''' cosets are the columns of the '''passive''' matrix.
}}

As with the matrix there are passive and active versions.

* [[commons:Category:Permutohedron 3 with cosets highlighted by vertex colors (image set)]]

* passive: [[commons:Category:Permutohedron 4 with crossed cosets (image set)]]
* active: [[commons:Category:Permutohedron 4 with stacked cosets (image set)]]

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{{center|'''Crafting Your Life Program'''}}

{{center|Dan Polansky}}

Base version, of which what follows is a modification and slight expansion: Version of date 2009-01-28.

== Preface ==
This is a draft of a philosophical book about what to do in life and what to value.

The text was written mostly in 2007 and 2008. It has not been reviewed by a philosopher or an academic.

I did not publish the draft since I was unhappy/uncomfortable with it and I still am. I am now publishing the draft as a contribution to a discussion and analysis of ideas, in the hope that at least some of the presented material is good or inspiring and that it may perhaps provoke some interesting/inspiring criticism.

In so far as I respect your autonomy as an independent human, it is not my proper business to tell you what to do in life. Any attempt to deal with the question of what to do in life runs the risk of influencing you in a way you will be sorry for later. In case of doubt, you are well advised to stop reading now, and do your own thing and figure it out for yourself.

== Introduction ==
=== What is Value and How You Define It ===
How to live, what to do in life, what to value in life, whether to have some goals in life or just live from moment to moment, are all difficult questions. It is above all unclear how answers given to them could be true or false. In the past several centuries, scientists and philosophers of science have developed tools with surprising reliability for answering questions about the world, among them the formal empirical scientific method. Unfortunately, the empirical scientific method only decides how things ''are'', not how things ''should'' or ''ought to'' be. 

This book highlights one option for what to do in your life: to value and maximize the ''power of life over matter''—a shorthand for the power and control of all the living things over the matter and the universe—seeing everything else but ''truth'' and ''human freedom'' as subordinated to this goal. However, grave objections are raised against this option, especially when not constrained by truth and human freedom. Instead, you can choose to do something else, and the book can help in your choosing your own thing to do in life. It presents various answers already given by people and philosophers, like that you should seek pleasure, wisdom, understanding, money, power, pleasure, or entertainment, or like that you should listen to your heart, making your decisions without words; also that you should aim at your pleasure or wisdom or common pleasure and wisdom. It also presents some answers not yet given, like that you should maximize the time to death of all the life on Earth, or that you should aim at increasing the number of all possible shapes that have ever appeared in the world. The book also has a glance at the structure and the properties of the space, realm, or zoo of all the answers. It shows many awkward creatures are living in the zoo, including the death of life on Earth, the power of foxes over matter, and the randomness of your life given your survival. 

Dealing with what to value in life has something to say on what the supposed purpose of life is. The option I mentioned on what to value can be rephrased as that ''a purpose of life'' is to maximize the power of life over matter. ''The purpose of your life'' is ultimately your choice. 

This book is not about execution. It does not tell how to actually set and follow goals, how to maximize things or keep them in range, and how to keep track of everything related. There already are good books on the subject. Instead, this book should help you find a way to choose some goals while refusing other ones. 

To introduce many of the possible answers, I need to introduce some terms used in the book. In the following sections, I introduce ''life program''—an answer to what to do in life, and ''valuation''—and answer to what to value. 

=== What to Do — Life Program ===
An answer to what to do in your life is a ''life program'', which I define as a set of general verbal instructions telling a person what to do in the long run, from his birth to his death. Let me give you summaries of several simple life programs. 

* I should have an ordinary occupation, many friends, several children, and have a lot of fun and good time. 
* I should take care that I survive and be idle beyond that. 
* I should become a great man or woman; I do not need to have a family. 
* I should kill myself as soon as possible. 
* I should kill as many people as possible. 
* I should get to know as many women (or men) as possible. 
* I should maximize the number of guitars in my house. 

These were only summaries; the bodies of life programs can be as long as several paragraphs, or, with some creative people, as long as a book.

This list of life programs should make some things obvious:

A life program may be used by no one; no one is going to maximize the number of guitars in his or her house.

A life program can be generic and vague. A computer could not execute a life program; it would need detailed instructions of what to do. Such a generic life program does not even contain a choice of a specific occupation.

The true life program of a person is not necessarily what the person tells other people that he is trying to do. Ultimately, it is only each person himself who knows for sure what his life program is.

Importantly, life programs are neither true nor false; they are not better or worse maps of a territory. In this they differ from scientific theories, like Newton's theory of gravitation, and many everyday observations, like that it is raining in San Francisco today.

=== What to Value — Valuation ===
Before I embark on saying substantial things about what to do in life, let me define one more concept—that of a valuation. While an answer to what to do in life is a life program, an answer to what to ''value'' is a ''valuation,'' which I define as a way of deciding for two possible outcomes of your actions which one you prefer. So a particular valuation is one particular meaning of the word ''better'' in the expression ''better decision''. A common, though not the only one, way of determining which of two outcomes of your actions is better is to assign to each a number, and take the outcome with the higher number. 

The following examples should clarify the meaning of valuation: 

* Money on your account 
* Your fame 
* Two times your money plus three times your fame 
* Your peace of mind 
* Global economic product per year 
* Your happiness 
* The happiness of your family 
* Average happiness of the world 
* Beauty of all the things you have 
* Beauty of all the things in the world 

It is easy to come up with a long list of valuations, combining different aspects—like money, fame, and happiness—with centers of these aspects—like you, your family, and the world. In fact, this list could be extended until infinity, as so many there are ways of combining different elements of which valuations are composed. 

Not all of the mentioned valuations can be effectively measured, neither with meter, nor with scales. Still, people intuitively find ways how to estimate them, especially when looking back. 

Valuations are related to life programs in that they are parts of many of them. The way in which a valuation is embedded in a life program ranges from simple to more complex, like in the life programs &quot;Maximize the money on your account&quot;, &quot;Maximize the money on your account while being honest,&quot; &quot;Be honest above all, and when feeling like it, maximize the money on your account,&quot; or &quot;Be honest above all, keep yourself alive, and when you have time to spare, roll a dice, and if the outcome is 6, maximize the money on your account.&quot; Whatever the exact way, valuations are not something in addition to life programs; they are part of them.

So once you have found a complete answer to what to do, that is written a complete life program, you must have answered what to value along the way.

Although for every valuation there is a life program requiring its maximization, that program is not necessarily effectively executable. For many valuations, no one in the world knows any reliable recipe or method of how to maximize them. Just take the life program &quot;Maximize the money on your account while being honest&quot;; there are many ways how to earn money, and no one can prove about one or the other it is the most effective one.

=== The Unfounded Choice ===
You are a free person. Your choice of what to do and value in life—the choice of a complete life program—is ultimately unfounded. It has no basis, no rock-solid foundation. Before I explain it in more detail in the following paragraphs, let me point out that, as unfounded as your choice may be, you will ultimately make some choice. The various foundations that people use for that choice are shown in the next chapter; some of them could appeal to you. 

To say about a program—life program or any other kind—that it is ''right'' or ''wrong'', we need a valuation that evaluates programs, evaluating some of them as ''better'' than the other ones. Also, a life program may be wrong in that it fails to maximize some valuation of outcomes of your actions. But how do we know that a valuation is right or wrong, that some valuation is better than another one? We would need some valuation evaluating valuations, called meta valuation. But how do we know that the meta valuation is the right one? Perhaps by consulting a meta meta valuation? So it goes until infinity, as the following bulleted scheme shows.

* ...
* 4-meta LP-valuation
*: of
* 3-meta LP-valuation
*: of
* 2-meta LP-valuation
*: of
* meta LP-valuation
*: of
* life program (LP)
*: which possibly maximizes
* valuation
*: which evaluates
* the state of the world

One can also disregard life programs and only consider the sequence of valuation (evaluating the state of the world), meta-valuation, 2-meta-valuation, etc.

Moreover, one can ponder whether one wants to go far beyond, to infinite ordinal numbers from mathematics (e.g. epsilon-zero-valuation), but the result is fundamentally the same.

If you are to choose a life program, either you will choose it without using any valuation, out of the blue, or you will have to choose it using some valuation, which you may have chosen using another one, but somewhere at the bottom of the sequence, there must be a valuation that you have chosen without using any other valuation.

=== Noncommittal Option ===
You may refuse to choose any life program at all. If you do, you still have to make choices, which unfold into a stream of your actions in your life. That stream has substantial consequences, as if you were executing a certain life program. If you do not have any life program, the substantial consequences of your actions may well be the same as those of the life program &quot;be idle&quot;. 

You may want to choose a life program step at a time, choosing one for one period of your life, and choosing another one in another period of your life. Still, these life programs can be joined together to form a new compound life program; the unfolding of your life can still be described as an execution of a complex life program.

=== Life Programs Losing All Their Agents ===
As unfounded and random as your choice of a life program may be, it has consequences for you and for other people, most notably death. People have been able to satisfy themselves with and endure various conditions including severe bodily deterioration and complete isolation from other people. Death is the only consequence that you cannot revalue or claim to be all right when it occurs to you, as then you are no longer there to perform the revaluation.

Your choice of a life program also has consequence for life programs; one life program gets a new agent, while another one may have just lost one.

When an agent of a life program dies, the life program has one agent less. Usually, one life program is used by many agents, and if one of them dies, his or her children or other agents do not die. Still, eventually, the life program may lose all its agents.

Note that, for a person, to ''know'' a life program is not the same as to ''use'' it and ''be its agent''. You know the life program &quot;Kill yourself as soon as possible&quot;, just that you do not execute it. So even if all the agents of a life program die, the life program may still be known by many people. 

In the long run, some life programs invariably lose all their agents, like &quot;Kill yourself as soon as possible&quot;, while other are used widely, like &quot;Earn a lot of money while being honest&quot;.

Having lost all its agents at some point, a life program may still get new agents at a later point, if its text is stored on paper or in a computer in between. Also, the text of a program that has lost all its agents and whose text has been lost can be invented anew.

By eliminating a life program's agents, nature can be said to have eliminated the life program. Nature can be said to ''choose ''certain life programs, in that they have not been eliminated. Put differently, nature or reality or the world is a place hostile to certain life programs; it is hostile to a great majority of all conceivable life programs. 

There are several kinds of causes of life programs ending up without agents, either by losing all their agents or by not gaining any.

* Some life programs kill their agents, like parasites killing their hosts. 
* Some life programs ask their agents not to reproduce. Such a life program may still be successful, if it succeeds in copying itself into new agents who are not biological descendants of the program's agents. Such is the case of the Catholic Church; priests do not have children, and still priests do not die out in the long run. 
* Some life programs have no agents because agents do not like them. 
* Some life programs never get written in the first place. To have any agents, a life program has to be developed first. 
* All life programs are without agents when all their potential agents are dead. This would happen if the humankind would be destroyed. 

There is probably no life program that will never stop being used, as chances are all the living things on the Earth will eventually die out.

== The Power of Life over Matter ==
=== Highlighted Life Program ===
As pointed out, the choice of a life program is unfounded; it has no basis. You are in reality free to choose any life program whatsoever.

One program that I find strangely attractive is to maximize the power and control of all the living things over matter. I show what it means and what intuitive reasons support it. Either, upon further reading, you find the reasons appealing, or you may have a look at elements of life programs discussed in the next chapter, so that you can put together your own life program. However, there are also grave counter-arguments against this life program. If this book were properly neutral, it would not highlight this life program.

First, a minimum requirement on a life program seems to be that it has a chance to stay in use. A notable counterexample is &quot;Kill yourself as soon as possible&quot;. 

Second, a further choice is necessary, as there are many candidates for staying in use. Among those candidates, I find something strangely attractive, but also disconcerting, about ''The power of life over matter''. I will say more of it in the following section. I will show that it is a candidate for significant presence among all the life programs supported by people, and that, in a vague sense, supporting this life program is indirectly what all the living things have been doing all along. It is not the only candidate though; there are many candidates that are trying hard. Another particularly notable one is ''The death of life''&lt;nowiki&gt;; a life program that, figuratively speaking, tries to conquer as many human hearts as possible and lets them work on the complete destruction of life on the Earth. Further candidates are those world religions that are expansive and intolerant to unbelievers. &lt;/nowiki&gt;

A more detailed meaning of the power and control of all the living things over matter is given in the following section, in which I shortly clarify what I mean by life, and then proceed to a definition of sorts of the power of life over matter.

=== The Definition of Life ===
There are various definitions of life and living things, of varying complexity, none of them perfect, and none of them required to forming a vague idea of what is meant by life. Instead of providing a definition for the concept for which you already have an idea—life, let me only emphasize that when I speak of ''life'' and ''living things'', I do not require that it is based on DNA and carbon chemistry, as shown in the following bulleted scheme, starting from the narrowest thing and continuing through broader groups, some on subsequent levels in fact uncomparable:

* human individual (selfish focus)
* human family (selfish focus)
* nation (focus with elements of racism and culturalism)
* race by skin color (racist focus)
* broad cultural group, e.g. Europeans or Chinese (culturalist focus)
* religious group (religion focus)
* humankind (supposedly unselfish focus)
* mammals
* animals
* life based on DNA and carbon
* OR life based on silicon digital storage, including robots
* OR life based on yet another thing
* life (generic focus)

As a reservation, the use of the word &quot;life&quot; above is unconventional. While one can superficially plausibly think of silicon-based life (as presented in some sci-fi stories), this does not mean that human-like robots are alive: they lack key features of life as traditionally defined, including growth, metabolism, reproduction, being set up from tiny cells, etc.

If one rejects the above interpretation of &quot;life&quot; and yet is interested in the broader concept, one may coin a new word, perhaps quasi-life.

=== The Power of Life over Matter ===
By ''the power of life over matter'' I mean the capability and performance of all the living things. Specifically, the power of life over matter is increased when the following things are increased. 

* The mass of matter of which the bodies of life are made, including the bodies of trees and animals
* The mass of matter of which life-made artifacts are made, including the bodies of technology and buildings 
* The information gaining and processing capability of life including 
** The ability to model and simulate the world
** The ability to map the Earth 
** The ability to perform instantaneous photographic snapshot of the Earth 
** The ability to map the universe 
* The distance to which life can travel 
** Including the ability to travel to the moon
* The self-sustaining and self-healing capability of life
* The amount of free energy that life can release within a limited period of time 
* The maximum speed that a living thing can reach 
* The ability of living things to give matter an arbitrary shape 
* The maximum height of a structure created by life 
* The diameter of the area of the universe occupied by life 
* The volume of the area of the universe occupied by life
* The power of life to destroy itself

=== Objections to the Power of Life ===
At a minimum, there are the following objections to the Power of Life:
* It appears fundamentally unethical. It appears ready to sacrifice individual humans for a large overarching aim. It appears to be some form of ethical collectivism; one can invent arguments that ethical individualism supports it as well, but such arguments do not appear unequivocally conclusive.
* The construction of this life program seems to imply that technological development is something like biological evolution, and that humans can increase the Power of Life via technology. A skeptic can charge that the technological development of last centuries is, in terms of geological time, a brief period of rapid and steep rise to be followed by equally or more rapid steep fall, and that humans were deluded all along about their ability to outperform the analogue of God (the Darwinian evolutionary processes that created the biosphere) in their creative capability in the middle run.
* Unless one starts adding exceptions to the specification, the power of life entails the power of life to destroy itself. (Similarly, the power of humankind includes the power of humankind to destroy itself.) Increasing life's power to destroy itself in its entirety appears objectionable.
* If one accepts a broad non-traditional definition of life, perhaps to be called quasi-life, a consequence is that the existence of the biological life as traditionally understood does not matter other than as a means to whatever the human-like robots (androids) or other robots plan to do with their power over the matter and the universe. That seems rather disconcerting, at least to some of us humans, members of a species that, from a certain view, is considered to be a mere obsolete DNA, eukaryotic, mammalian platform to be replaced with the shiny new thing, the result of the greatest and cleanest engineering unburdened by the evolutionary history. Needless to say, the shiny new thing is yet to achieve the closure of material loop and anything remotely resembling sustainability. Even if the sustainability problems the new thing faces get solved, for a human, this kind of individual selflessness and species selflessness (what do I human care about my species, the main thing is that the quasi-life prevails and gets powerful) is rather unnatural, and unacceptable for many  humans.
* Even if one constrains the concept of life to a traditional one and excludes human-like robots, one can think of a biological species with superhuman capabilities appearing one day. A true human devotee to the power of life would seem to be quite content to be replaced by the superhumans, a strange prospect of species-selflessness. Thus, even if the power-of-life-driven species-selflessness can be strangely attractive, it also appears bizarre.

One strange thing about life programs is that they are defined as ''ultimates'' and therefore, they are not really ''amenable'' to objections. Since, to criticize a life program is to subject it to value judgment of another object, and then, it is the other object that is closer to being the ultimate, not the life program so evaluated. But psychologically, this is implausible; one would have to give up all criticism of all life programs. It is a conundrum, something like a paradox.

== Emotional Building Blocks ==
=== Overview ===
When choosing or composing your life program, you may want to have a glance at what offer there is. Also, you may want to see the elements of which various life programs are composed, so that you can use them in your own custom life program, of your own composition. Things people generally seek in their life and that philosophers have been selling as the purpose of life include happiness, pleasure, money, fame, achievement, success, good conscience or freedom from remorse, knowledge and understanding. This chapter looks at these elements and shows where they come from, observing about many of them that they stem from an outdated and partly capricious biological design of human bodies.

=== Evolutionary Defects in Emotions ===
The ultimate goal in life is thought by many to have to do with feelings, emotions and sensations; it is supposed to be achieving ''happiness'', maximizing ''pleasure'', reducing ''pain'', stimulating ''excitement'' , increasing ''entertainment'', and ''loving''. Some of these emotional goals have been endorsed by notable philosophers, including Epicurus, and John Stuart Mill. Let me point out some properties of these goals that you may find discouraging. 

Above all, as far as we know, the bodily structures producing these emotions have been created by biological evolution. This is also true of human brain, the location of intelligent thought; so far so good. However, the structures of the human brain responsible for emotions are much older than the latest parts of the human brain, responsible for distinctively human thought. That the human emotions are of much older descent is, apart from being scientifically verified, apparent in the eyes of the man's best friend—the dog. The assumption—made by many—that whatever has been created by evolution is automatically good and trustworthy is seen in different light when we look at some of the old parts of human bodies, containing some strange and troublesome parts like ''wisdom teeth'' and ''appendix''. Suspicion has it the parts of the brain steering the production of the chemicals responsible for emotional feelings are problematic too, ridden with evolutionary defects. 

Implicit in emotional goals is the goal of survival (more accurately, having one's genes copied), which has shaped the process through which the parts of the brain responsible for the creation of emotions came about. The goal of survival as implicit in emotional goals is however twisted by suboptimal and only seemingly adaptive evolutionary process. 

If you would think that survival is good in the first place, other goals being only means to that end, why would you not follow the purpose of survival directly, without first consulting pleasure, pain and happiness? If you start to see your survival and health as of value, even if not as your ultimate aim, you will see that emotions and sensations are not always helpful in achieving that goal. Consider going to the dentist: before you even plan a visit, you may have to deal with the emotion of fear; after you finally make it to the dentist, you would have not until recently to deal with the acute sensation of pain. In this modern situation, both fear and pain have done little to improve your health; quite to the contrary.

That the goals of emotions and sensations are problematic, easy to see for fear and pain, is less obvious for pleasure, happiness and entertainment. A person with pleasure as the ultimate aim is vulnerable to drugs; if the pleasure of the present moment appeals to you, getting high is the right thing to do, regardless of the consequences. For happiness, consider the following. In the prospect of your chronic pain, aiming at the goal of your happiness runs the risk that you are going to commit suicide, as the sum total of the happiness over your life is constantly diminished. Also, a person threatened with torture, aiming at his happiness, could betray his companions.

Now that emotions and sensations are unreliable is not to say that they should be ignored; they still provide valuable information. It is just that this information should better be treated with distrust, as a hypothesis that is yet to be tested. Likewise, myopic eyes should be distrusted, and if possible treated with glasses.

=== Happiness and Joy ===
Many people believe that the purpose of life is to seek happiness. Some believe that happiness is obviously the only thing that is pursued for its own sake.

Happiness is mostly considered a feeling of a long-term character. Still, one definition of happiness is that it is the presence of pleasure and the absence of pain and suffering.

But if we define value as happiness, we cannot investigate whether the brain, senses and hormones, all the things producing the feeling of happiness, are reliable or in align with anything; the whole of these is in align by our definition.

Making seeking happiness all right by definition has some disturbing implications. Different people have in general different systems in their brains producing the feeling of happiness. While some are happy when solving problems, others are happy when cheating, stealing and robbing people. Moreover, if we modified the biological system producing the feeling of happiness, we would get yet another behavior produced by steering on the goal of happiness.

So although everyone can use happiness as the indicator of what to do, such an indicator leads in different people to very different concrete life programs.

Whoever would take his individual happiness seriously as the highest norm of what to aim at would be forced by his choice to develop drugs that provide happiness regardless of the circumstances. The most probable result would be a soon death; the organism would lose any regard to the outside circumstances, upon which its survival depends.

Currently, we cannot modify the biological system producing the feeling of happiness. At least, we are able to interfere with the biological system by means of music, alcohol and drugs in general. Drugs enable us to control some of our emotions directly, without any regard to the outside and inside situation in which we find ourselves.

What has been said about happiness is also true of ''joy'' and other similar emotions. 

=== Pleasure ===
Some see the purpose of their life in their individual pleasure. Pleasure is an instant, pleasing feeling, of various kinds, resulting from a great variety of activities, including eating, drinking alcohol, dancing and singing, making love, seducing women, going to theater and movies, taking part on sports, slaking, going for long and slow walks, conversing with friends, arguing about controversial topics, or solving hard intellectual problems. Also included in some people is tormenting other people or themselves, collecting money, achieving social ranks, raping women, or gaining social power. In fact, even entertaining the idea of aiming at something else but pleasure may produce pleasure in people. 

Because of this great variety, it is unobvious what these various activities have in common that lends the feeling that results from them the name &quot;pleasure&quot;. One thing should be granted though: that the various specific feelings called &quot;pleasure&quot; are perceived as positive. 

Many people find pleasure in ''eating''. The biological systems for rewarding eating with pleasure are outdated. The consequence is that most people who take instant pleasure as the measure of value and have enough food available are overweight. The pleasure system for eating has been designed at times where there were periods with plenty of food, and periods with little food available. It was all right to eat a lot and keep the energy stored as fat in the times of affluence of food. He who rigorously sticks to pleasure when eating dies younger. 

Enjoying unrestrained ''sexual'' pleasure before the advent of contraception pills threaten the health and life of both mother and her infant. It may be desirable to conceive a lot of children if you can realistically expect that many children will die. Also, with men, sexual pleasure is usually not directly connected with pleasure of staying with one woman, which in preindustrial age led to spreading of infectious diseases. 

Some people find that what is most pleasing to them is ''idleness''. Being idle beyond measure has all kinds of negative consequences, like the decrease of your expected lifespan also because of bad health resulting from lacking exercise. Getting money, knowledge, and understanding, unless overdone and when aimed at the right direction, increases your expected lifespan, and provides more options in your life, including the option of benefiting other people. 

It is not that a pleasure maker has to aim at pleasure in short-term, ruining his health to gain one night's high resulting from the use of drugs. To gain more pleasure in total, a smart pleasure maker gives up some pleasure now to gain more of it later, and chooses these kinds of near pleasure that do not threaten the foundation upon which the future pleasure rests—the life and health.

Given that parts of the brain producing pleasure are outdated, it does not follow that things that produce pleasure are automatically wrong. It is just that the pleasure they produce cannot be used as an indicator that they are automatically ''right''. The fact that having sex with contraception produces pleasure does not make it wrong. 

Some pleasure makers strangely argue that you have no other option than aiming at pleasure.

''Pleasure maker:'' Whether you want it or not, you are maximizing the pleasure. Everybody does just that, even masochists and ascetics.

''Dan:'' If indeed whatever I do maximizes pleasure, then pleasure cannot be used as an indicator of what to do; it is going to be achieved no matter what you do. So if you get pleasure no matter what you do and how you decide, pleasure fails completely as the measure of value; it does not provide a direction as it is always there regardless.

=== Entertainment and Boredom ===
Some people consider entertainment as their ultimate goal in life.

Entertainment is the counterpart to boredom. The older parts of the brain have evolved to issue negative emotion when the mind is idle. They issue positive emotion of entertainment when there is dynamic, interesting information to process. Unfortunately, those old, simplistic parts are poor at distinguishing between information relevant to survival and information that just appears to be relevant. When you go to see a movie, the brain receives through your eyes fast moving images, that is information which would be highly relevant if it were about the real world.

Often, you need to be bored before you are able to get into a new area of interest or activity. That is why entertainment may be damaging to your welfare, giving an illusion of real problem solving.

Entertainment in the form of computer games is in effect simulated problem solving. Problem solving is essential to survival in both short-term and long-term. In addition, many computer games are a form of direct learning. When you are learning in manageable speed, some parts of your brain issue positive emotion, related to the general fact that mastering new skills and capabilities increases the chances of survival.

=== Love ===
Some say the purpose of life is love. They may mean love between sexes, love of a person towards another person even of the same sex, or love of a person towards a thing, an organization or a group of people in general.

Whatever emotion they mean exactly, it is a pleasing one, distinct from pleasure though. The biological tendency of seeking pleasing emotions may lead to the idea that this feeling could be the purpose of life.

A downside of aiming mainly at the emotion of love between sexes is that it is temporary. Sex—the oldest force of attraction between sexes—is short-lived in the extreme. The emotion of love—a newer force—improves upon sex by being more long-term; but for the human purpose of rearing children, its duration of three to five years is no more up to date than the support of the upright posture in the human skeleton. Another downside is the vulnerability to suicide in case of the loss of the loved ones.

The expression ''love'' is also used in the expressions ''love of money'' and ''love of power''. In the context of these expressions, the measure of value is not the love, but ''the object of love'', like money and power in the examples above. So if you would think the purpose of your life is love of money, that would in effect come out the same as saying that your purpose in life is to maximize the money you have. 

=== Suffering ===
Some think of suffering as of value. Viktor Frankl sees suffering as performance and as one of the purposes of life.

John Stuart Mill sees suffering as that which diminishes happiness; happiness is, according to Mill, the purpose of life, or the highest value.

Physical pain, a species of suffering, is a signal of the lower biological systems that something has gone wrong. It is however not something which we may observe, and if fit, ignore. Rather, pain launches a physiological reaction that may decrease the performance of the brain in decision making, and as a consequence, endanger the survival. At some cases, we feel pain in a situation improving our health, like at the dentist.

Some believe that suffering is inevitable. As long as the biological design of humans remains intact, suffering will probably be there. However, we may learn to switch the suffering signal off whenever we see that it is useless, which is what we have already been doing to an extent using medication.

Now switching off the physical pain is far less problematic than switching off the emotional pain. I suggest that emotional suffering is the result of brain's attempt to perform large scale computation, taking into account huge amount of information available in the long-term memory of the brain. Without this kind of suffering, certain kind of information processing would not take place.

Given that emotional suffering may present large scale information processing, it is indeed performance, as Frankl suggests. It is just that suffering occurring five minutes before you die is of little value, be it performance or not.

=== Peace of Mind ===
Some think that it is peace of mind that you are or should be after in the first place, near-synonyms of which include tranquillity and calmness. But it is up to you what you are after; it is not written out there that you are after being calm at the expense of everything else. John Stuart Mill concluded that tranquillity offers little pleasure and excitement, but that the pleasure and excitement is often accompanied or followed with pain, for which people tend to alternate the tranquil rest on one hand, and excitement and stress on the other hand. 

The term &quot;peace of mind&quot; implies the opposite term &quot;war of mind&quot;, rendered in psychological literature as &quot;inner conflict&quot;. That can be sometimes solved by writing everything down, consulting a psychotherapist, a priest, or a trusted mentor.

If you choose to aim at peace of mind, as a means, the options of how to do it include avoidance of anxiety-producing situation, avoidance of stress, getting immersed in an activity, meditation including Yoga and Zen, and prayer. Calming down can also be achieved by sports, which stimulate the body to produce drug-like substances. Avoiding anxiety-producing situations, and excessive avoidance of stress is guaranteed to get you into trouble. 

=== Satisfying Human Needs ===
Psychologists investigate human needs. They do so to investigate the human behavior and sources of human motivation, but some also imply that the satisfaction of human needs is the purpose of life.

As long as these needs are human and not specific to a particular culture, they are stemming from the biological setup of man. The assumption that the satisfaction of these needs is the purpose of human life amounts to the assumption that what has evolved in the course of biological evolution is good. However, depending on the time of development of these needs, they are more or less outdated and ridden with strange properties.

The focus on human needs also seems to be chauvinist in a way; all humans are also living beings. By the same token, men could focus on men's needs, to the detriment of women.

=== Car Driving to a Gas Station ===
The attempt to derive value from biological and psychological needs and signals can be modeled by imagining a driver in a car who does not know where to go. As he has a smart speaking car of the future, he ask the car.

''Driver:'' Car, do you have an idea where we should go?

''Car:'' Let us drive to a gas station to pick some gas and oil.

''Driver:'' What shall we do after that?

''Car:'' Why, we'll just drive to an auto mechanic.

''Driver:'' And afterwards?

''Car:'' Then we'll drive to another gas station.

A car that only drives to gas stations and auto mechanics is not really going anywhere. Of course a car also has to visit gas stations and auto mechanics, but these are only deficiencies of the car; a perfect car would not need any gas and repair.

''Tim:'' If the car in the dialogue was supposedly the whole of human needs, then the dialogue is misleading. It only refers to the lower biological needs, but the higher psychological needs are implemented in the biology too.

''Dan:'' The point is that the destination of the journey cannot be derived from the car. You need the driver for that. The driver should decide where to go, not the car. The driver should only stop at petrol stations and auto mechanics to ensure that he can get to the destination to which he chose to get in the first place. The driver is what I have called life program. A life program can be completely independent on the biological design of the human body. It could even be chosen randomly. A random or unfounded or not derived choice of a life program is the essence of human freedom.

''Tim'': Artifacts like cars are designed by their conscious goal-seeking makers to be subordinate to the maker's ends and purposes. By contrast, biological individuals do not really have makers, do not have real purposes (only quasi-purposes) and are not really subordinate to anything. This renders the analogy fundamentally flawed.

== Non-Emotional Building Blocks ==
=== Overview ===
When composing their life programs, people choose various elements that are not directly emotional, so may be called rational, like success, power, money, knowledge and understanding. Although these elements are not directly emotional, their choice may still depend upon a rewarding emotion.

You may read the following sections one after the other, but also in a non-sequential fashion. If a section seems intriguing to you, you may read it first, and skip those that seem unuseful for your life program. Eventually, you may want to read all of them.

The elements treated are the following: 

* guilt 
* peace of mind 
* success 
* power 
* wealth 
* prestige 
* freedom 
* knowledge 
* understanding 
* truth 
* justice 
* wisdom 
* health 

=== Guilt ===
Few people would choose to aim at feeling guilty. What can be a part of a life program however is the freedom from the feeling of guilt. I propose to distinguish emotions of guilt from the faculty of conscience—the ability to discern what is right and what is wrong even without relying on the emotions of guilt. Emotions of guilt are a signal that an imaginary internal trial should take place, not that you are automatically guilty. At least three imaginary speakers should be present at the internal trial—the plaintiff, responsible for the feeling of guilt in the first place, the defendant, and the judge. Just like in the court of law, both the plaintiff and the defendant should be allowed to use all their wits in advocating their positions. 

If you choose to avoid remorse and the feeling of guilt, writing down what you consider ethical and non-ethical can help. It does not need to be cast in stone; your ethical code—the things you have written down about what is acceptable and what is not—can evolve with your experience and understanding.

=== Success ===
Some people assume that the purpose of life is success. If what they mean by success is the achievement of goals that you have set for yourself, having success as the purpose of life is a considerably incomplete answer. It does not tell what kind of goals to aim at, whether internal and emotional such as the peace of mind and love, or external such as being successful in your profession; neither does it help you in the least to choose your profession. Consistent with this choice, you may try to become a successful artist, a successful Casanova, or a successful international criminal. Upon closer look, to say that you should aim at any abitrary success is to say close to nothing, as it amounts to &quot;aim at succeeding in what you aim at&quot;. The little meaning that remains comes from the fact that aiming at something implies the systematic application of effort. But people who aim at effortless life do not aim at it in the same way in which, say, a physician is aiming at becoming a distinguished one. With such aims, aiming too hard at them becomes an obstacle to achieving them, as can be seen in a person who is trying too hard to fall asleep; the result is a failure.

If what they mean by success is achieving something recognized as success by the society, such as the property, successful academic career, or social power, the choice of what you should be successful in is still largely left open. You can try to become a successful doctor, a popular singer, a successful sportsman, an eminent scientist, or a wealthy entrepreneur. As said, aiming at this kind of success is at least more specific than aiming at any success whatsoever, as it excludes such options as to aim at the peace of mind, at Buddhist enlightenment, or at having a good time.

=== Power ===
Some people choose to seek social power—the ability to directly control other people, to review their work, to determine their tasks, or to set regulations. Obvious cases of social power include those of politicians, wealthy people, managers, and military officers. Less obvious cases include the power teachers have over their pupils or students, the doctors have over their patients, and parents have over their children.

On the downside, the aim of social power sometimes requires people to give up personal freedom and independence, freedom from commitment to organizations, and privacy and anonymity; some of the most powerful people become public figures.

Social power is often linked to prestige, but not always.

Related to power is influence, commanded by journalists or marketing people, or the long-term one of classical authors and philosophers.

The greater the social power of a person, the greater the moral performance consisting in avoiding the misuse of power. But as the moral strength and self-control of even the most excellent people is limited, given enough power, all characters are shallow. If you seek to be a moral person, you need to make sure your power does not exceed your ability to act to your responsibility, but also that your moral performance does not become negligible for your lack of power.

=== Wealth ===
Material wealth, including money and property, is a means to a great variety of ends, important to most people.

Money is not needed by monks, recluses in the desert, or certain ascetics trying to free themselves from their body by malnutrition. If you come from a well-to-do family, your need of money may be absent too.

Some decide to play the game of earning as much money, acquiring as much property as possible, such as the notable J. D. Rockefeller. Acquiring great wealth may produce joy of success and provide the option to finance whatever the rich chooses, any arbitrary whims like spending on luxurious goods, or going to wherever you please, but also schools, hospitals and other projects beneficial to the society. 

Aiming at money and wealth is a well-defined, easily measurable game, unlike many other ones. The ease with which you know whether you win or lose makes it attractive to some. Money, although exposed to risks of inflation and bankruptcy of banks, is more stable than swings of moods. Also, it is a scaling game, not a yes/no one.

Aiming at money regardless of moral norms easily leads to immoral behavior, for which money is notable. Such an immoral behavior need not be apparent, as acting morally pays itself to an extent.

To aim at money requires hard thinking, giving up mental leisure, gaining a lot of skill, commitment, and know-how. Hard unskilled work is unlikely to produce considerable wealth.

=== Prestige ===
Prestige is the esteem of you in view of other people. Obviously, some occupations are more prestigious than others. Prestige can also be increased by the purchase of luxury items such are cars, homes, or clothing.

The occupational prestige is only partly flexible; once you have successfully made an entry into a prestigious occupation, your prestige can no longer grow, unless you are able to climb up in the corporate ladder, which is an option for managers, not for, say, surgeons. For this reason, prestige is a poor ultimate end. For some people, prestige is an important part of the choice of occupation. The occupations that are considered prestigious include doctors, lawyers, and professors. For a longer list, check the latest statistics. Prestige is about the perception of other people, not about how things really are. Nevertheless, disregarding prestige can have practical real consequences, like the loss of sales because a salesman would be driving a poor car.

An occupation considered prestigious by the large populace may be held in low esteem by your parents or by some particular community. When aiming at prestige, it is important to know which group you are trying to impress.

=== Fame ===
As other vague words, fame is a different thing to different people. You may choose to aim at the fleeting fame of a fashion model or a rock star, or the supposedly immortal fame of great statesmen, inventors, scientists, and artists—fame that sometimes comes only after death. You may want to be known across your country, across the globe or in the community of your professional colleagues.

Your initial chance may seem feeble. But then, as some say, the overnight success comes after a long and hard work.

The success in being famous can have some effects that you may dislike, like the loss of privacy and anonymity.

To make the aim of fame truly continuous, you need to find small degrees that already mean first success. On the other hand, with some risk, you may aim at the overnight success, so that the fame and recognition will increase all of a sudden, instead of step at a time. In any case, you should get emotionally ready for disappointment and failure. The game of fame is one of chance, one of chances that are unknown and low.

=== Freedom ===
Some people seek freedom. There are some vastly different things people mean by freedom. One group of the meanings of freedom relates to common level, to social scale: political freedom and economic freedom. Another group pertains to the individual: financial freedom, freedom for creativity and inventiveness in the chosen work, and freedom in the sense of independence.

The aim at political freedom and economic freedom is probably best served by donating to a non-profit or by working for it; also by cooperating with a non-profit, by providing services to them. Many people were willing to risk their life to fight for the political freedom of their country, going back to their social impulse or instinct, the feeling that an unfree life is not worth living. It did not need to be an ultimate aim, but an aim of such an utter importance that other aims seemed to be completely dominated by it.

Financial freedom of a person is of a completely different kind, even though it shares the word &quot;freedom&quot; in the name. While political freedom is a social aim, financial freedom is the personal aim at not needing to earn money for living, which is distinct from not wanting to work. Financial freedom as the ultimate end in life is a poor goal for the reason that it is a yes/no goal; once it is achieved, your life is over, so to speak.

=== Knowledge ===
Some people choose to seek knowledge—for their own pleasure or joy, for the usefulness of it for their various other aims, and for the sake of maximizing the knowledge that the humankind has of the world and of itself. Some learn all the geographical facts about the Earth or learn the Guinness Book of Records by heart, straining their memory. Contrasting to this is aiming at the knowledge of the words and language. Some acquire the knowledge by learning from books, others try to discover for themselves.

Knowledge is a powerful means. Practical knowledge is indispensable to all kinds of aims. You can do your work better if you get to know it, and if you read magazines and books to stay on top of what's going on.

If you choose to multiply the theoretical knowledge that humankind has of the laws of the universe, becoming a scientist is an option, or supporting scientific undertakings financially. If you want to take part on the adventure of discovery, you can do it even on your own, as a hobby, with the probable consequence that the results will be either already known or incomprehensible to other people. But if you are passionate about invention, reinventing the wheel may still be more fascinating than inventing nothing at all, only implementing inventions of other people. Given enough money and courage, you may also become an independent scholar.

Not all the knowledge is fascinating or useful, such as the content of astronomical tables used for sea navigation. In the absence of printed publication, knowing boring details and little facts can be useful too. Everyone relies in their daily life on knowledge of little facts that have no universal application, such as where to go shopping in a particular city. Password is a type of little piece of information that has only one, special use, but that single use can give you access to a lump of money.

When coming in vast amounts, knowledge is for most people impossible to keep in head. Unless you are different, you need to write down what you have found out, and find ways how to organize it. A proven method of organization is by keywords, and alphabetically; the choice of keywords is key, so is the choice of multiple keywords. This method can be seen in encyclopedia and in the alphabetical indices of books. When you are in a hurry, a short list of keywords can do instead of several paragraphs; such a list of keywords will be understandable by you, but not by other people.

=== Understanding ===
Some seek the understanding of the world we are living in. If lucky, they become professional scientists or philosophers; if less lucky, they become amateur ones. Others choose to support the aim of understanding by developing technology that supports it, including measuring devices, and computer hardware and software. Understanding is also supported by its disseminating, through teaching.

Related aim is the one of understanding the languages of the world, and the ways of various cultures, trying at least for a moment to see the world with their lens. The understanding can be acquired through learning from books and media, and, for the luckier people, from direct experience. To understand someone is to see the world with their glasses, to imagine to know what they know, to not know what they don't, and to value what they do.

To understand the world is to get an insight into its laws. To understand an object is to know where it came from, what causes have shaped it, and what consequences its current way of existence can have. 

To aim at understanding the world is not to want to understand everything, including refrigerator. A single person cannot understand every detail in every branch of science and technology; one has to be selective. Also, interestingly, in many situations, in order to successfully repair a device, you do not need to have a perfect understanding of its function. Apart from that, leaving the job to an expert is often the best option.

=== Truth ===
The search for truth is chosen by many as one of their major life goals. It is related to the search of knowledge and understanding. But it can be seen not as the goal of acquiring as extensive knowledge as possible but rather to acquire as great certainty about that which one knows as possible. The certainty of knowing something is increased by providing a proof, of which there are many kinds. Proofs, in their turn, require precision in meanings of the words of the propositions, enhanced by the technique of definition.

=== Justice ===
Justice—deciding in align with law and based on common principles rather than individual sympathies—is sought by judges around the world, but also by most of those people whose decisions concern groups of other people, such as managers and parents. If you want to make justice the main aim of your life, trying to become a judge or a politician is an option. Being just requires keen interest in truth, and understanding the written law or the principles of justice.

=== Wisdom ===
Some choose to seek wisdom. Wisdom is made up of painful personal experience, skill and experience in judgment and estimation, track record of making decisions that impact other people, knowledge of human character, of the ways of your native society but also of foreign cultures. It requires the ability to advise to people on common human problems, to choose words carefully so that they do not hurt, to choose words in judgment that do not make the judgment invalid, to consider as many relevant facts and people as possible when making decisions. It is required from the occupations of a judge, a priest or a psychotherapist.

Given wisdom is seen on a continuous scale, you may aim at wisdom without ever becoming wise, that is, without ever passing the threshold above which other people would judge you wise. Still, the game that you are going to play should be expressed in continuous terms, so that there is something to be maximized, not a threshold to be passed in a yes/no fashion. You can meaningfully choose to seek wisdom above all regardless of your limitations.

=== Health ===
Health seems to be a strange part of a life program, as life programs are about ultimate ends, not about means. What is about means is the life plan, a concretization of the life program.

Even if accepted, health as an ultimate end seems strange too. Still, related to aiming at health is aiming at longevity, which can be a fascinating game.

That said, health is a key means, some of the most important ones. It limits what you can and cannot do, whether you can be adventurous or need to be very careful. It is worth paying attention to it.

=== Longevity ===
One's longevity, the maximum length of one's life, seems like a candidate ultimate aim. However, there are objections or complications.

In a thought experiment, let us leave someone hibernated for a 1000 years—unconscious, not dreaming—, to be waked up, live for a day and then die, as an alternative to living a normal conscious and active human life for, say, 50 years. Does one really want that? Does one not care about conscious experience, about the possibility to leave mark in the world, and leave descendants?

We can modify the experiment by allowing vivid pleasant dreams during the hibernation. Does one really want that? Will one be satisfied with the prospect of having pleasant subjective experience—dreams—although in reality one has no impact on the external environment, leaves no children, and dies soon after waking up?

We can consider a related scenario: would one accept greatly reduced existence—half-awake, one's thinking ability dulled, barely functioning—but for a long time, in preference over a life that is much more aware, awake and productive as for various aims but lasts much shorter?

Another related scenario, much more realistic given current medical technology and not so speculative, is one in which someone is kept in coma  or a more severe state of unconsciousness for a very long period of time, spanning many years or even decades. There are different grades of severity: there is prolonged coma, permanent vegetative state, and brain death. For all these cases, especially for the more severe ones, one can ask whether one wants to ask others to cease providing artificial life support. If one does want a support cessation, it means one does not consider longevity only but also something else as ultimately worthwhile.

Aiming at one's longevity alone seems biologically unnatural: one would not care to have children or risk one's life to save one's children as long as one's longevity is maximized. By contrast, it is selfish-gene-explained and natural for many people to risk their life to save their children in certain situations.

Aiming at one's longevity alone is unethical: one would be forced to sacrifice an arbitrary number of humans (killing them or allowing them to be killed) as long as one's longevity would thereby get extended even a little.

The above objections do not apply to longevity as an instrument. All else the same, a person living longer can create more creative works if that is what they are after, or accumulate more experience.

The candidate aim of longevity can be centered on other entities, e.g. life as the accumulation of all living things. Here, one can wildly speculate using philosophical imagination: If we cast all the living things as a person (which it arguably isn't), would that entity prefer to exist longer even if it means a kind of existence that is reduced in some way? For instance, would life prefer to have a longer existence provided there are no animals, no trees but there are grasses and flowers, over shorter existence that features animals?

On a less grand scale, one can focus on the longevity of, say, a nation or a religious group.

=== Usefulness ===
Some feel that usefulness is an important goal to which they want to contribute. The idea of usefulness however seems to postpone the end to be reached: something is useful if you can do something else with it. Some philosophers see usefulness, in their words utility, differently: as a postponed pleasure or happiness; that is, the end to be postponed is not left open; it is set to pleasure or happiness. A notable proponent of this view is John Stuart Mill.

In spite of usefulness being about means and not about ultimate ends, the philosophers' redefinition notwithstanding, you can make usefulness your ultimate end; you only need to be practically able to decide what is useful and what not, and to what degree, without asking, useful for what. One way of seeing usefulness without object (without saying for what) is to see a thing as useful if it is useful for a great variety of purposes; another is to deem a thing useful if it is useful for at least one another purpose. Whatever meaning of &quot;useful&quot; you choose, you should stick to it throughout your life program. The paragon of usefulness are tools and technology, a universal means.

A useful person is one whom other people have use of. Being a useful and needed person tends to feel good in most people.

=== Sentience ===
One may choose sentience (a related concept is consciousness) as the center of focus instead of self, family, tribe, nation, humankind or living things. One may claim that it is sentience that is the implied objective of biological (and other) evolution, especially human sentience. One would aim e.g. at the power of sentience or longevity of sentience. A chimpanzee sentience would be treated as mere quasi-sentience or sentience-in-the-making.

Sentience stands in sharp contrast to living things as the center of focus. A sentience (collective of sentient beings) aiming at survival of living things could shut itself down as too dangerous for them, whereas sentience aiming at itself would accept destruction of living things as perfectly acceptable in its aiming at its own power or longevity. The sentience could argue: we must develop technology to avert a future asteroid impact on the Earth even if by doing so we risk creating an ecological catastrophe, to extend the longevity of sentience at any and all costs.

One may consider artificial sentience as a possible kind of sentience, and if so, sentience could well give up on natural/biological sentience as long as artificial sentience goes on. Alternatively, one could treat the word &quot;artificial&quot; as alienans and refuse to consider artificial sentience to be a kind of sentience; thus, aiming at only the true/biological sentience would refuse to hand over the Earth to robots. 

One may treat animal quasi-sentience as a matter of degree of sentience. Thus, one may be in a dilemma: should we protect the quasi-sentience of chimpanzees (as better than nothing) by greatly restricting the human embodiment of sentience as too dangerous to the aggregate of the sentience and quasi-sentience?

One may counter that the self-centeredness of sentience is perhaps as unsurprising as it is unconvincing. If birds could speak, they might say that the objective is not sentience but flight and that the only reason why the biological (and other) evolution brought about humans is so that there can be flight past Pluto. As a Greek philosopher said, if horses could make gods, they would make them in the form of horses.

== Designing the Game ==
One way of living your life is to see it as a maximization of a numerical figure, representing your underlying goals. The easy way to do it is in monetary terms, possibly not meaningful to you. Aside from money, you may try to represent most of the expressions of natural language in figures, or you may find proxy figures helping you to see whether you are hitting or missing the mark that you have set to you.

One way of composing the game is (a) finding the center of focus, and (b) finding the figure. The center may be you, family, occupation, humankind, all the living things, whatnot. The figures include power, viability, money, health, pleasure, entertainment and the like. Not all combinations are possible though.

Once you have chosen or designed the game, it is time to play. Playing such a game, however, is an intellectually demanding undertaking. Now you have determined what to achieve, but not yet how to achieve it. For this purpose, there is e.g. ''The 7 Habits of Highly Effective People'' and other books on how to follow goals.

== The Zoo of Life Programs ==
The space, the zoo of life programs is vast. The zoo is the one of all the life programs, not only of those that people actually use. To get an overview of such a zoo borders on impossibility. How do you browse it? Is there an alphabetical index? A topic index, a catalog, or categories? There is such a vast number of animals. In the following, I will attempt something of an overview nevertheless. I include not only awkward and weird but also disgusting creatures.

What needs to be understood is that the part of the zoo that is relevant to real people is extremely small.

* Global 
** The power of life over matter
** The death of life on Earth
** The time to death of life (The lifespan of life, of the time of existence of all the living things, on the Earth and outside)
** The power of sentience over matter
** The death of sentience
** The time to death of sentience
** The power of humankind over matter
** The time to death of humankind (The lifespan of humankind)
** Destroy humankind ASAP
** The power of obscurity over human mind 
** The number of living people 
** The number of living frogs 
** The number of living cockroaches 
** The number of living biological species (biodiversity) 
** The planetary gross economic product 
** The number of shapes that have ever made it into the world
** The number of patterns that have ever made it into the world
** The political freedom of the countries of the Earth
** The total pleasure minus total pain of the people of the Earth 
** Minimizing suffering of the people of the Earth while preferring a suffering person over dead person 
** Minimize the world poverty 
** Minimize the world injustice 
** Maximize the world literacy 
** The quality of life of people of the planet 
** Advancement of sciences 
** Advancement of pseudosciences 
** Advancement of astrology 
** Advancement of engineering 
** Advancement of arts and culture 
** Convert the world to communism ASAP 
** Convert the world to capitalism ASAP 
** Convert the world to socialism ASAP 
** Convert the world to ..name your economic system.. ASAP 
** Convert the world to Christianity ASAP 
** Convert the world to ..name your religion.. ASAP 
* Individual 
** Your lifespan 
** Your money—legacy 
** Your happiness 
** Traveler: The number of visited places on the Earth 
*** Make sure you visit as many places on the Earth as possible, earning money for that purpose 
** Sensualist, seeker of experience 
*** The number of various experiences, tastes and the like 
** Idler, layabout 
** Sleeper 
** Adventurer 
** Earn to feed hobbies. 
* Collector 
** Collect as many different time stamps in my house as possible. 
** Collect as many cars as possible, even if going for cheap ones. 
** Collect as many books of as many genres as possible. 
* Destructive 
** Kill yourself 
** Kill your family 
** Kill a specific another family 
** Kill as many people as possible 
** Make sure as many people as possible get killed 
** Extinguish a nation 
** Extinguish members of all other religions 
** Extinguish all sellers of ice cream 
** Maximize the number of raped old ladies 
* Accidental 
** Travel randomly around the United States 
*** Variant: Do so using a detailed written method that relies on rolling a dice. 
** Travel randomly around a city 
* Indirect 
** Live as close to the way my parents lived as possible 
* Sophisticated 
** Keep my heart rate within the range of 70 and 120 beats per minute, below the possible 130 beats of aerobic, using a heart rate monitor, and avoiding jogging and running. 
** Maximize the lower 10-percentile of the world gross domestic product of the next five years, using the discounting rate of 0.96. 

To get a list of global names usable in a sophisticated life program, you can pick any global index or indicator, such as the index of freedom, gross domestic product, an index of literacy, one of democracy and the like.

Instead of only looking at the individual life programs, let us also have a look at their properties. 

* Person-centered vs world-centered: Maximizing the GNP is world-centered, while seeking meaningful work and family life is person-centered. 
* Length: some are one-liners, other one paragraph long like a life motto, some as long as a manifesto. 
* Copying: whether the life program requires you to tell about it everyone, create or join an organization supporting that life program, or convince other people that it is the right life program 
* Sophistication: expressed using plain words or using measurable quantities or arcane mathematical concepts 
* Viability: whether the life program has the tendency to kill its holders, or to prevent their reproduction 
* Morality: whether it takes other people into account. Even a moral life program can be self-centered, meaning person-centered, as is the case with ethical egoism. 
* Sociality: Socializing and outgoing on one pole while isolated hermit on the other pole. 
* Greed: How much it uses it up the person: his money, attention, time; inverse: how much freedom it leaves to the person. 

The life programs listed are ultimate aims, requiring finding of immediate aims. With the global life programs, for the purpose of practical living, you need to break them down to concrete lower-level subgoals. If you want to fight for freedom in the world, you need to fight for freedom in your country, in another country, or you need to earn money and donate to an organization that is fighting for freedom. 

== Methods ==
Whatever method of creating your life program you choose, there are certain things that you will need to judge for yourself. Even if you do not dare to write or choose your own life program, the choice of whom to trust is your choice, based on your judgment.

Crafting a life program is a verbal approach to managing and guiding your life in the very long run. It is not for everyone and it presents certain risks, like the unintentional misuse of words. Your understanding of what you mean by various words and what other people mean will be put to test.

The following treatment of methods is dense; to get benefit from it, please read it slowly, and take time to try to imagine what the covered items refer to, relating it to your own personal experience.

Importantly, your life program does not need to be fixed once for all times. You may review and rewrite it after a year or few. At some point in life, you may find the need to rewrite your past life program altogether or start from the scratch, heading toward a new view of your life and your aims and norms, based on new experience and insight that you have gained during your life. Rewriting your life program is nothing to be ashamed of. In the absence of data and significant experience, your life program can be seen as an estimate. The less experience you have in live, the bigger the chance that a rewrite will be needed. Even scientists, with all their resources that they can spend on getting as close to truth as possible, are forced by new empirical findings to revise their theories, at some periods drastically.

One of the simplest methods is to spontaneously start writing several of your candidate life programs, say ten to fifty attempts, take a break, and pick one of the candidates after the break.

Another popular method is death fantasy, requiring you to vividly imagine your own death, and to find what you value based on that fantasy. In one bent of this fantasy, you may ask yourself what you want other people to tell about you at your funeral. That variant implies that what matters is the opinions of other people, and that your life has no more value than what remains of it in the minds of other people at the day of your funeral.

A crisis in your life can change the way you see the world you are living in. Instead of waiting for the crisis to come, you may create it artificially. This method is however dangerous and difficult to manage. Poor ways include getting fired from an occupation, dropping out of university, getting addicted to drugs, or getting divorced or pregnant. A helpful distinction can be made between an emotional crisis and a substantive one. Getting into an emotional crisis by, say, becoming more open with yourself is generally less dangerous than getting into a substantive one.

Buying a mission builder is another option. A mission builder is a questionnaire that guides you through the process of writing what is called your mission statement, a concept similar to the one of life program. It does so by asking you questions but also possibly by providing some model simple answers and the answers of model people. Most of questions asked by mission builders are open ended ones, giving you a lot of freedom of expression. Some of the mission builders are available online free of charge. However, mission builders may be socially biased, proposing as key verbal elements of your life program those ends and concerns that are found important by the society at large, or by the particular group of people behind the mission builder, such as one of the various religious churches. At least, they provide you with some vocabulary, structure of questions, and ideas to start with. 

A key question of the method is where your life program comes from. You may start from without, asking your parents, your good friends or a mentor whom you trust, or taking the advice of a trusted book as your guide. Or you may start from within, trying to write the life program yourself, relying on your past experience, your present vocabulary, your understanding of that vocabulary, and your current mastery of the language.

The external approaches involve hiring a life coach, if you are well off.

Instead of trying to be smart before the act, experimenting with life approaches of which you have no idea whether they work, you may search for model people. Using notable models from biographies has the danger of making you accept a set of rules that the notable person preaches but not always follows. Autobiographies tend to by stylized; Benjamin Franklin proscribed taking revenge but took it covertly anyway. More realistic is the use of model living people, such as your parents; but depending on your individual situation, you may find only poor models for living. One tricky thing about it is that you do not really see what goes on in the minds of other people; you only see what is apparent about what they do. If they are using a conscious philosophy, they may not want to tell you everything about it. And they may not even know everything that actually drives their actions, so following their stated philosophy may lead to poor results with you while it worked perfectly well with them.

That is why I think that you would do best to find out yourself, maybe even find out yourself about the best method of finding out what to do in life, on a meta-level.

Some people choose to travel, to get out of their ordinary environment, to enlarge their perspective, and come back refreshed, with a new perspective, new insights, and new emotions, some good and some bad.

Reading a lot of books can be helpful too. Books show a lot of model heroes. But the lives of real people are seldom like the heroic stories of the books. 

Movies can be useful in showing you unfamiliar situations, and exposing you to your unpleasant emotional reactions. However, most movies do not depict the real world. Also, they are harder to criticize and comment on than written word.

== Evolution and Optimization ==
Earlier in the book, I have mentioned that biological evolutions is non-optimizing. I have used this claim to disparage the reliance on emotions and to discourage choosing emotional goals as major parts of the ultimate aim in life. Let us now have a look in more detail at what's involved in this claim.

The human brain is a product of biological evolution—the process of variation combined with various kinds of eliminations, including what has been called natural selection—the result of certain individuals dying—and sexual selection—the result of certain individuals being refused by all potential partners. The human mind—that which is in the human brain—is the joint product of biological evolution, and a different kind of evolution, sometimes called memetic, social or cultural evolution. Compared to the cultural evolution, biological evolution is extremely slow. During the last 3000 years, the biology of man has changed only slightly; the ability of man to shape his environment and produce objects on the Earth that have been here never before, has increased dramatically. Because of its speed, cultural evolution could evolve schemes of behaviors—codes of conduct, and aims—that are much more suitable to the end of the survival of the genes than the genes alone. That, along with the evolution of technology, has multiplied the number of people nourished on the Earth from some 10,000 to today's 6,200,000, which, in terms of the interests of the genes, of the species, but also of the mind, is a major success. 

The biological evolution is non-optimizing, non-transparent, and muddled. Supposing that the survival of the genes is the major driver of the shapes of the organisms, it is now obvious that human bodies including the brain are imperfectly adapted to the current environment. This leads some people to suggest that human bodies are almost perfectly adapted to some no longer existing environment. But that is improbable on the observation that too perfect adaptation to temporary conditions is disadvantageous to a long-term adaptation and that the slow biological evolution cannot perform such short-term adjustments anyway. But even the theory that human bodies are perfectly adapted to long-term conditions is flawed. The process of biological evolution is heavily dependent on what kind of variations of features are possible, and these in turn are dependent on the complex, poorly understood process of gene expression. A major shaping factor are the processes of growth; the factor is the fact that these are the processes of growth, also found in non-living nature, and not processes of cutting, cropping, polishing and assembling, found in human technology. 

A further source of imperfections as regards the goal of survival of the genes and the functional goals of organ systems is the history of traits of the human organism: once a trait creeps in and further traits get dependent on it, getting rid or substantially modifying the trait gets difficult or impossible. 

In humans, certain remnants of evolutionary history have attracted the curiosity of scientists. The usefulness of vermiform appendix is unclear, and the troublesomeness of wisdom teeth well known. Compared to these bodily structures, human behavior is more difficult to imagine. Still, the biological drivers that steer human behavior can be located in certain organs, whose age can be investigated. The organ systems taking part on control in human body are the nervous system and the endocrine system, including brain, spinal chord, and the autonomic system. The older the system, the higher chance there is that it is burdened with evolutionary history. Basically, any bodily structure or organ that is old should be suspect. 

In the evolutionary search for designs of cells, tissues, and organs, even these functions that could be handled by simple rules are discovered as a complex muddle of rules; it is more so difficult to discover smartly complex rules, leading to smartly complex behavior, able to differentiate and distinguish between many grades of shade. That is why the smartest rules of behavior are not hard-wired; they are learned. 

Is cultural evolution—the variation and elimination of ways of doing things and of ultimate unanalyzed aims—optimizing? Hardly. Where biological evolution appears to be blind, cultural is not omniscient. Humankind has committed all kinds of mistakes during the history of technological evolution. A single human mind is very small; the capacity of humankind to predict the consequences of actions is still quite feeble. 

This sketchy outline cannot replace a rigorous scientific debate. The topics addressed are surrounded by ongoing controversial discussions among scientists and philosophers. For more in-depth treatment, there is scientific literature.

== Real People ==
Having seen these arcane otherworldly lists of life programs, and having considered the ways of deciding which one to take, modify, what not, you may wonder: That is all very well, but how do real-world people ever get decided, without this super-rational, overblown approach?

Well, often they don't. Many people in the world have limited options. This books is aimed at people who have plenty of options, or who at least need to make some major choice, and are wondering what kind of considerations could be relevant.

When viewed broadly, often, people are living their lives without having a guiding principle, life motto or life philosophy, not speaking of having an articulated written text of the length of a manifesto. They need to make some major decisions in their lives, but these need not be made based on any deep philosophy. Many say that their purpose in life is to be happy. Their lives are in the main influenced by their parents, family, buddies and colleagues, their training, but also by the words and the images sent by popular books and movies. They are often driven by other people, or by what other people believe.

Now what does happen when I am picking the life program? How does it get chosen? If I read your book and apply some of its techniques, how does the decision ultimate get made? I do not know, and as far as I know, no one does. Obviously, what you are currently reading has the chance of influencing you life program. You can get convinced by some of the points I make. During your writing, you may get convinced by some of the things you will say; along your life program, you may write other some text that supports it, argues it one way or another. If presented with a complete life program, you may just happen to like it, see it as a good one, feel moved by it, and feel disgusted by other life programs. You may try to watch what happens in your mind during the process. You may try to uncover the psychological motivation that leads you to choosing that life program. But it is improbable that you will ever be sure about these motivations. The persons behind you, in the background, who really are controlling you, are not that talkative to tell you everything about their own motives. Beware, however, that to ask about motives is to ask a causal question &quot;why&quot;. The knowledge of motives does not make the life program less ultimate in terms of the question &quot;for the sake of what&quot;. Also, it is the very process of choosing the life program that influences the result. If you have chosen death fantasy, you have made the first step in actually choosing your life program. The result is not yet determined but probably different from the process &quot;write the first life program that occurs to you and has 100 words and accept that one&quot;. All the images and experiences, including the early ones, that have accumulated in your head may take part in co-deciding about your life program. All the perceived peer and social pressure can take part. You may subliminally choose such a life program that your peers would like and can understand. When you take the brave choice of actually writing your life program, you are emancipating yourself from some masters while accepting other masters. If you take your life program seriously, it becomes your master, or that which has chosen that life program, those things that influenced that life program, are implicitly co-controlling you. By writing this book, I have attempted to influence you too; I have attempted to take over your body in certain sense. So are attempting many people every day. Sense your options. Sense your freedom, even if only perceived one. Make use of it. When choosing your life program, try to get rid of all the influences, even if it is literally impossible.

Now if you are short of time, the approach of generating some twenty to fifty cases and picking the one that you like most could do for you. You can review and modify your life program later, when you have more time. If, however, you are before your major decision, one noncommittal trick to use is to decide in such a way that in the future you have as many options left open as possible. In the meanwhile, you can get time to study the questions related to your life program more deeply.

Now maybe you do not like the idea of committing yourself to a particular life program. The non-committal trick just mentioned will do for you. But if you think you can escape all the life programs, I think you are mistaken. Can anyone perform anything complex without words and verbally specified aims? I am not saying that these aims have to be perfectly specified. I am just saying that if it is not words that are driving your life, then it is some other people. Maybe it is all right with you. You may be content to always have to decide on the spot, even in a morally critical situation.

If you have now passed to the state at which you have a life program, you may have learned that its execution may be tough. Keeping everything in mind may become difficult. If you use paper notes, you may achieve more; a computer can be even more helpful. But even with these enhancements, you will run into your limits. In any case, your life program is your guide, not your manager or master. Sometimes, you need to make choices that only seem to be in align with your life program, without being sure that they will indeed perfectly correspond to it. We know nothing or close to nothing.

You may want to rebel against all the life programs. But beware that &quot;rebellion against all the life programs&quot; is a life program of sorts, even if lacking most of the details. Still, a rebellion could consist of breaking all kinds of rules imposed on you by other people whenever they appear. You could be watching yourself, trying to avoid any too patterned behavior. When truly suspicious of yourself, you could even adopt some formally randomized method. But a randomized method is also a method. A randomized life program is also a life program. A true rebellion would consist of behavior and choices that are difficult to describe using words.

== Values of Philosophers ==
Notable philosophers may be a source of inspiration for your life program. Let us see what values some of these philosophers had. However, as a whole, the group has views slanted in certain direction. A variety of views is found especially at ancient Greek philosophers though. Interestingly enough, many of them argued from what ''is'' the case to what a person ''should'' do in life. 

Heraclitus valued sound thinking and action based on truth and understanding above all; also moderation and self-control. Notably, he valued fame, of which he said it is everlasting, to be achieved in the battlefield; the best death is the one in a battle. He despised excessive eating and drinking, and scorned lying.

Pythagoras valued ability to remain silent, loyalty to friends, honor the men show to their wives, and the begetting the children; in general, he valued strict observance of religious rituals. It is estimated that he valued not eating and not torturing animals, for his conviction that human souls are reincarnated into them.

Plato valued wisdom above all, but also justice, moderation and courage. For him, though, justice is a state of affairs in which everyone minds their own business and performs the assigned function in a state.

Socrates valued wisdom, virtue, obedience to his community, and strict adherence to truth. He showed his wish to obey by submitting himself to the sentence of death awarded to him by Athens citizens.

Diogenes of Sinope valued courage, reason, and natural, simple way of life, such as living in a wine jar and drinking water from his hands, and despised social convention, dependence on society, and life driven by passion.

Aristotle valued excellence in all arts, sciences, in all that a person is doing, including moral excellence. That said, he considered intellectual life devoted to the search for truth to be the best kind of life.

Epicurus valued quiet life, in a circle of close friends, undisturbed by the rush of busy life, accompanied by a reduction of needs. His realization of these requirements was by living in a garden surrounded by high walls. 

Marcus Aurelius valued calmness, avoidance of complaining, doing the moral duty, humility, detachment from the pains and desires. He argued that everything vanishes into oblivion, including accounts of heroic deeds.

Immanuel Kant valued above all acting from one's duty instead of from inclination, tendency or feeling like doing something. The duties of a person as conceived by him include speaking truth under all circumstances, never committing suicide, and not cheating, roughly matching the Christian commandments, but also the duty to develop one's talents and to be charitable, giving away money when you can afford it. Interestingly, duties indirectly include ensuring your own happiness, as a means; Kant reasoned that an unhappy person is much more likely to transgress his duty.

Arthur Schopenhauer valued intellectual honesty and peace of mind, which he thought could be created through seeing of beautiful objects and hearing of beautiful music, and by giving up the bodily desires, becoming as much without will as possible, to overcome what he thought was the unavoidable suffering of human life. He valued moral life, into which he included refraining from violence, reduction of suffering in the world and cultivation of compassion toward other people. Also, he wanted women to obey men, claiming women have no sense of justice. He valued that animals are protected against human cruelty, seeing them as compatriots of people.

Karl Marx seemed to value the free development of talents and potential abilities of a person, and the overall reduction of human suffering.

In his words, Friedrich Nietzsche valued breaking the social norms and morals, contempt of mankind, cruelty, and quest for individual power over other people. He did not turn these professed values into action though.

These short summaries can hardly do justice to the convictions of the philosophers. If some of the summaries has raised your appetite, you may find it worthwhile to have a more detailed look at the philosopher's teaching. Academic sources include Encyclopedia Britannica and Stanford Encyclopedia of Philosophy. For a less intellectual and more story-like account, see Will Durant's The Story of Philosophy. 

== Language ==
Crafting a life program and then living it is a verbal approach, based on words, phrases and verbal images contained in the program. Great many words like happiness mean different things to different people. The more obscure words you are going to use, the less clear it will be to you what to do in life, how to determine subgoals, but also, what it is that you are controlled by, what it is that you have voluntarily submitted yourself to. 

The problem of varying meanings of words also applies to this book. I am unable to send you the meanings of the words, only the words. I rely on meanings of words that are shared between you and me.

The problem of obscure meanings can be partly solved by the technique of definition. For instance, if I set &quot;inner happiness&quot; as my ultimate end in life, I can try to define it as &quot;A state in which I am not crying.&quot; Is this a plausible definition of happiness? Not to me, but it comes quite close. The virtue of such a definition is that I have bound what was originally unclear to me—happiness—to something that I can easily observe and decide—absence of crying.

A common objection to the idea of defining your terms is that the process of defining need to come to a halt; there must be some undefined terms. That is true enough. The point is that some undefined terms are clear and easy to decide while other not so. You can easily decide whether a person is crying; it is more difficult to decide whether a person has been crying recently. The point of the definitions that you may use in your life program is to link what is obscure to you to something that is clear and straightforward to you. In logical sense, such a definition might be not a definition proper. The definition of a term in other terms does not need to claim perfection though; you can see it as an approximation useful in the absence of perfect definition.

For the purpose of your life program, you do not need to provide definitions of terms that other people would approve of. As you are the main user of your life program, it is important that ''you'' find the definitions fitting to what ''you'' had in mind. That said, it is preferable that you use words in standard way; the way your family, friends and colleagues use words. However, sticking only with words in their standard meanings robs you of the option of making the life program highly individual. What you could do is that you would invent new terms, and define them in your own way. But there are great many words that are actually used by people widely differently, so reusing these words to binding to them your own meanings makes sense. 

Writing your own definitions may at first seem like a challenge. To get started, you may use a dictionary; for great many words, you would not want to modify the definition already found in the dictionary. The definitions found in the dictionaries can serve as a model; you may take a definition from one and adjust it, refine it and extend it for yourself.

One simple and accessible way to refine the definitions is by providing examples. Like &quot;For me, happiness is a state in which I feel all right, in which I am not disappointed, not crying, have basically the things that I need, like good friends, place to live, an interesting work, and still have some further goals to achieve.&quot;

That said, not everything in the world can be easily expressed in words. The words for your life program are coming from the culture; they are a heritage that you have at your disposal. Maybe you do not want to limit yourself to the words and meanings someone else has provided you with. If you have a clear meaning in mind for which you do not know any word yet, just coin a new word. If a newly coined word does not seem quite right at a later point, you may modify it. If you try to at least imperfectly define the meaning of the new word, you may still know what you meant by the word some months later. 

Apart from a dictionary, other sources that abound with definitions are philosophical works. However, you may be surprised to find what some philosophers think the words mean. You may find many of their definitions unfitting or completely incomprehensible. Use them at your own risk of confusion and bewilderment.

== Analogies ==
There are many analogies for human life, for living. These include life as a game, a journey, perhaps a nautical one, a business, and art. The model of game has been implicitly present in this book. However, often, games are something to be won or lost. By having a program that drives you, never to be met in a hit or miss fashion, your life becomes quite different from board games and card games. 

Life as a journey is implied by those who claim you need a map. In a sense, that is correct, as if you choose your destination, your aim, it may be quite helpful to know how to get there. But the destination, the normative principle, is not the map; it is the destination. And it is you who has chosen the destination. Or is it the interaction between what you are what what you know?

Some people view their life as a business undertaking, with the need to account for gains and losses.

Other people view their life as a work of art, such as a painting, perhaps a movie. Human lives, however, do not look like movies, and cannot. If taken as a movie, the life of anyone would be extremely boring. Only when condensed, with the quiet periods edited away, can a life resemble a movie; one, which no one is actually going to look at. The work of art may imply an activity that is far from as tightly planned as an engineering project.

An important analogy for living is one also at least verbally used in this book, of a life lived by a program. So just like a computer executes a program, so can a person. But first, the person needs to have such a program; he has to write it.

When invoking analogies in your own life program, be careful. Analogies can lead to all kinds of side effects, leading to a perception of similarity between two situations that is not there. When using an analogy, you should examine carefully what parts of the source situation are carried over to the target situation and what parts not. For instance, if a person is supposed to execute a program in an analogy to a computer, it does not mean that the person is equipped with a fan or peripherals. Neither does it mean that the person is unable to do more things at once, just like a serial computer.

== The Self ==
For the design of your life program, it may be helpful to understand what you mean by &quot;I&quot;, but also what other people mean by &quot;you&quot; when speaking to you. Try to take an external view of yourself, a view of a person speaking to you, seeing your face, your movements, your animated smile, of a person hearing your voice. What does that person think that &quot;I&quot; refers to? Does it include the body, the limbs, the trunk? The whole of the brain, or something in the brain? Also, what is it that controls the body that the person is seeing? For a change, imagine that you sit in a remote room and control your body, or, precisely, what other people think is your body. Does the observing person still think you are sitting in the controlled body?

Some of the best models that I have found is to see the self as a driver in a car with one-way transparent windows, with, say, three other people sitting in the same car. You can see what is around, but also the driving wheel, the seats, the inside of the card, including dashboard, which shows you the status of the fuel. The people outside the car do not see you; they only see the car and its windows. Neither do they see that there are more passengers in the car. This analogy has its limits as any other, but it still highlights certain facts: you see much more of the inside than other people see, other people do not feel your hunger and your pain, and they have no idea that your steering wheel is broken or that the inside of the car is getting overheated. On the other hand, the driver in a car has limited means of showing the emotion to the outside standing observers. 

== Means and Ends ==
Your life program determines the ultimate ends you are going to pursue, that is, those ends that are not only intermediate to other ends. You may find it helpful for deciding on the ultimate ends to see what relationship there is between means, ends and the human society in which they are pursued or aimed at.

In human society, great variety of goals find their hosts, the people and organizations that aim at the goals. Put in a simplified manner, each goal is hosted by some people as a means while by others as an end. Put more precisely, one person can host a goal as both an end—requiring no further explanation—and as a means to another goal. End-only-goals need means-goals, but not the other way around. A set of mutually serving means-goals is perfectly consistent and viable; a set of isolated goals that do not serve each other is at least unstable. A society in which only means-goals are hosted is possible; one in which only end-only-goals are hosted is not. 

Given human freedom, the choice of the ultimate ends is arbitrary, that is, not based on previously chosen criteria, kind of chosen without the use of information. But the choice of means is less arbitrary. An external observer, a Martian, could predict that humans are going to be hosting the means, and given the knowledge of the setting—the Earth, he would be able to estimate the kinds of means; he would be much less likely to predict what kind of ends they are going to choose. If you feel disturbed by the arbitrariness of ultimate goals, choosing universal means as your ultimate goals is an option. The universal means include money, technology, skills, human knowledge, and the willingness of people to cooperate without the use of violence.

However, your life program does not need to have the ends-means form. Surely you will need some means to execute your life program. But other than that, the life program &quot;travel randomly around the United States&quot; can only artificially be rephrased in terms of goals. Surely you might say that your goal is to travel randomly United States. But then, your goal is specified in terms of process, not in terms of the results of the process.

== Planning and Execution ==
A life program is of little worth if you cannot turn it into action, if you cannot execute it. Executing a life program may prove to be a daunting task, especially if it is an abstract and global one, such as &quot;The power of obscurity over human mind.&quot; This book covers execution only briefly. Some good books on execution are mentioned in the last paragraph.

An abstract life program is not something a person can directly aim at. If you have such one, you need to find some lower-level, concrete subgoal, which also needs to incorporate your limitations, things that you cannot do, or disabilities you may have. A direct way of supporting a larger goal is to work for an organization that supports it, or supporting it on your own, if you have the skill, courage, financial buffer, and support of your family, friends or other social backing. An indirect way of supporting it is through donations, if you feel you cannot contribute in your occupation directly.

Even when you have a view of what concrete goal you aim to achieve and you think that is it as regards writing and documenting, it is better to create a written plan. Writing plans requires you to collect a lot of information that you would not have otherwise. You need to find out what information to find, and how or from whom to get it. Given your subliminal self is still going to play a major role in the day-to-day decision making, it needs information based on which it can support your decision making in the background. If you build reserves into your plan, like money and time, you make the plan more realistic and workable. Also, unless you commit yourself to the plan in every detail, you may revise the plan later—if you have no plan, there is nothing to revise. However, too much emotional commitment to a plan can lead to unpleasant disappointment and depression. Apart from emotional losses, you may suffer financial ones if you bet a bulk of money on an insecure plan.

You may doubt the feasibility of your aiming at your life program, if you feel you do not have the skills and talents. Surely for a male to give birth to as many babies as possible is a daunting task. Still, a life program such as recommended by me is such that it is not a yes/no business; it is about degrees, it is a thing to be maximized. Say that you aim at becoming a successful Casanova, and as a proxy figure, you take the number of women you have had intercourse with. First, there are more proxy figures related to this ultimate aim, such as the number of women you have had a date with, or the number of women who enjoyed being on a date with you. But this aside, you may feel your dating and conversation skills are so poor that you have absolutely no chance. However, if you have made becoming a successful Casanova you life's ultimate aim, all your resources—time, money, attention, even pain—should be summoned to support your aim. You should read books on how to become a Casanova. You should take classes if there are some. You should write down how you think could be possible to become a Casanova. You may practice on your own. You may imagine you are about to invite a lady or a girl to a date, and say out loud what you are going to say. You may ask your friends to help you. You may hang a poster in your room reminding you that becoming a Casanova is the most important thing for you. You may come up with all kinds of options that I have failed to mention because of my lack of imagination and know-how. With the progression of time, your documentation and experience with aiming at the goal will grow. You will have found out what does not work for you.

Whatever breakdown of the larger goal into subgoals you are going to pick, you always need to take care of yourself, apart from your life program. Dead and poor people are poor hosts of life programs, which is not to say that you should turn into a financial manager. Regardless of the wording of your ultimate aim, you will need generic means: skills, money, reputation, and network of family, friends and colleagues. Depending on your ultimate aim, some may be more needed than the others.

When you start to write everything down, keeping lists of to-do items, and documenting all kinds of things, you may at some point run into limits of your mind and memory. The limits can be shifted using computers, but they are still going to be there. This may require you to reduce the variety of activities and projects that you are taking part on, or reduce the amount of detail that you are writing down. Information overload can lead to unpleasant mental states; keep in mind that there is such a thing and learn to manage it.

A lot of information work is done for you by your brain in the night. While you sleep, the mind is trying to tackle the problems you were trying to solve during the day, to file new things you have learned, to link them with your previous knowledge. Getting enough sleep is key to let the brain get these things done. On the other hand, there is not so much need of sleep after a boring day.

You will need to develop many skills. Which skills to develop depends on your ultimate aim. Still, some skills are more universal than other skills. For instance, the ability to talk convincingly is more universal than the ability to solder. The universal skills include the ability to read, write, listen and talk; the emotional stability under stress, and general physical health; you need not be an accomplished athlete though. Depending on how much money you have, you may gain skills on your own with the help of books, hire a private teacher, attend classes, or learn from a self-professed teacher willing to teach you not for money but in exchange for some service that you provide to him. Almost everyone has something to teach you.

Apart from finding out what to do, written down in your life plan, it is also important to find out what not to do, what to avoid, not because of its harm, but because it steers you away from your major aims. Things in themselves harmless yet of secondary importance take away your time, but, sometimes more importantly, also your attention and energy, including your limited short-term memory, your ability to think things through in your mind during the sleep, and your ability to do it during the waking hours in the background of your head. 

If at first you have no time left beyond making living and feeding all planned and running activities, you cannot do anything in addition, regardless of how useful the additional activity might be. To get started, you need to find at least a small time slot to begin with. As you find ways to become more effective in what you're doing, your time available for whatever it is you aim at will expand. 

Better than reading this sketch of a chapter, you may consult popular literature that focuses on or covers execution—turning plans into action, such as Stephen R. Covey's the ''7 Habits of Highly Effective People'' and David Allen's ''Getting Things Done''.

== Managing Emotions ==
There is a false dichotomy between emotions and reason, easily misleading people into believing that they have to say either yes or no to emotions. However, there are various things you can do with emotions: suppress them, let them guide you, discharge them, show them or hide them, or feel guilty because of them. To what degree and whether you want to do these things with emotions can be decided by you basically independently for most of these actions, and also depending on the kind of emotion in question. You may want to show happiness, suppress anger when in public and discharge it when alone, and let yourself be guided by regret.

Assuming that emotions are driven by outdated parts of the human brain, and that you decide to aim at things unrelated to emotions, nowhere does it follow that you need to suppress your emotions or that you should never take them as a clue for action. Instead, emotions need to be managed, like a sometimes naughty, sometimes nice, funny and creative child, which you cannot easily get rid of, and even if you did, the consequences could easily hurt your aims, like you would have difficulty getting along with people. Further, even if you choose to aim at a particular emotion such as happiness or love, you will need to manage the other emotions.

Emotions like love, anger, joy, or sadness should not be confused with rational intuition, with an idea that occurred to you, felt certainty, or seeing certain things as apparent. Your brain is able of doing a lot of thinking for you in the background, and lets you know the results of that thinking once in a while. To recognize the contribution of that background thinking is not to attribute it to emotions, regardless of the accompanying emotions such as the joy of discovery or insight that you may feel when you get the results delivered.

Emotions are only under your imperfect control. When you decide to move your hand to the right, you just do it. When you decide to calm down, that may fail. However, emotions are obviously not completely out of our voluntary control. To an extent, you may control emotions directly just like you control your muscles, but you have to learn that. A child has to learn how to coordinate and control muscles, by mentally trying to do various things and observing the results. Likewise, you can learn how to control emotions at least partially, by focusing on the required resulting emotion and letting your background self try various mental things to achieve that result. There is no way I can describe this method any further, just as I cannot describe how to coordinate your muscles. Furthermore, you can also control your emotions indirectly. By reading a book that you know will make you angry, you are ensuring you will be angry. By going to a calm place that you have associated with tranquillity, you can calm down. By drinking alcohol, you ensure that you are going to get relaxed, if you usually get relaxed by alcohol.

== Decision Making ==
While executing your life plan, you will need to make decisions. This section treats them in a general way. There are various approaches to personal decision making, ranging from the completely intuitive one, based on immediate sense and perception of what is the best option, without being able to explain why, and a decision made based on words, measured numbers and estimated numbers. If you would want to decide everything in your life intuitively, on the spot, without previous collection of information, you would not probably be reading this book. I assume that at least certain decisions are important and difficult enough to deserve a non-intuitive approach.

Types of decisions vary in their complexity and importance. Choosing the yogurt is of little importance and consequence; you can review the yogurt decision often, it has high degree of repetition, and both yogurts and the consequences of choosing a bad one are cheap. The really interesting decisions are the big ones, like choosing a spouse, house to buy, occupation, and the general direction in life. They may take a lot of research and preparation, and are executed in short time compared to the time of preparation, with major consequences.

There are mutual dependencies between the important decisions in your life; the results of one decision influence the options available for the other ones. A decision is important if the options available to many other decisions depend on it. Choosing the place to live influences your job choice and other opportunities.

Trying to make a big decision in the absence of personal experience can be painful. Unfortunately, big decisions in life provide little opportunity for learning from your direct experience. If possible, you can try a test run. First go for a vacation, then marry; first rent an apartment in an unknown quarter, then buy it. The sources of information include your experience, typically unavailable, reports of friends and acquaintances and family, printed information, information available through telephoning, and counseling such as career counseling. You may also rely on one of the time-tested philosophies, propounded by various religions.

Sophisticated methods include listing of available options, listing numeric attributes of the options and their weights, estimating the values of the attributes, and computing which one is the best, with the help of spreadsheet. This method can be simplified to several variants, such as plainly listing pros and cons and counting them. The simplest method is making the choice based on previous similar choices, without considerations. Even if the sophisticated methods seem too complex for you, you may give it a try anyway, try to estimate the values of attributes, and feel the pain of the brain trying to estimate something for which it has no clear definition and no clear input information. Repeat the method several times, making several weeks lasting pauses before the iterations, and see how the estimates and results change. Find out what more information can be gained in this way.

Research. Although quite fast, estimation relies only on that information that its author already has available in memory, even if buried in the long-term one. The really big and important decisions in industry and organizations require research, including field research and desk research. Desk research means that you research and collate sources of textual information and try to analyze and put the things together. In field research, you observe the world or people, and possibly inquire yourself. Some of your life's major decisions are important enough to deserve research.

The results of research need to be collected systematically, unless you have an exceptionally good memory. Technological options include paper and computers. With paper, organize the material alphabetically, and pay attention to choosing the keywords under which you file, so that you are able to find the material later.

Review. Document your planned decisions and review them with someone whom you trust, if there is such a person. Different decisions have different degrees of personality and need of privacy; there probably are at least some decisions whose documentation you would show to close to anyone. Reasons for the need of privacy include exposition of one's convictions, and disclosing of one's lack of skill, knowledge, information, or experience.

== Life Decisions ==
During the execution of your life program—a statement of what to value and what overarching aim to have—and based on your life plan—a more concrete fleshing out of the details of your life, much more individual than the life program—you will need to make some major decisions; a decision where to go for a vacation is not such one. Although execution is out of the main focus of the book, the following chapter covers the major decisions you will need to make in your life, helping you to identify the areas in which to search for them.

The most important decision in life is whether to live at all. This decision is entirely in their hands for most people.

More mundane and relevant decision areas are the choice of the source of making livelihood, which affects the choice of education, occupation or business; of relationships including marriage and friendships; of place of living including the country of living and the city, town or village; there are major health decisions like whether to undergo a surgery or induced abortion. For the luckier, there are major financial decisions like the choice of a house to purchase or the investment into which to place the savings.

For a major decision, you should begin the preparation and information gathering long before the decision is made and executed. Important decisions with considerable impact on your future may require extensive research and burning your fingers, like executing them in a test mode. 

The three major sources of information for your decisions are your own experience, the experience and expertise of living people, and what is written in the books, magazines, the Internet and other sources of written information that is publicly available for purchase or free of charge.

I propose what many don't like to do: to document your major decisions. Write down the options that you had, which options you ruled out, and what the pros and cons of the options were. The approaches range from informal and hazy to formal, but the least that you can do is write your verbal thoughts about the decision down. Review your decisions with other people. Get ready to feel hurt by their reactions and views; the point is to solicit disagreement from them rather than agreement. 

Try to commit the decision in a test run. Like, when you are ready to make the decision at one day, write it down, perform a rite or physical transformation representing that decision, and let the decision ripen for some more time.

Livelihood. One of the major difficult decisions is the choice of livelihood, which influences your education, your occupation or business, but also the kind of people you are going to meet, and the amount of time you will have for your family, friends, and hobbies. This decision does not need to be executed at once, unlike some of the decisions influenced by it. You may study one field at university and later work in another field; along with specific skills, most university programs teach you some universal thinking skills, as a side-effect. A key distinction is how the livelihood is planned to contribute to your life program—it can contribute merely as a source of livelihood or it can contribute directly. Important aspects of a source of livelihood include money, fascination, enjoyment, social power, prestige, leisureliness, people, and security of employment. Considered broadly, it is the lucky people who can consider all the various aspects and choose rather than being happy to earn their living. What of these components is important for you depends on your life program; money always matters though, as it is a universal means, unlike social power, prestige or fascination that you derive from the work. 

Finance. People blame money for inflation. Still, it is not only money but also other results of human work that are subject to depreciation, including bread, apples, hammers, machines, computers, and buildings. Compared to all these, money is still a good place where to store the results of your work. An alternative to money are various types of investment possibilities, which differ in security—how secure they are against loss, liquidity—how fast you can pick your money out of them, and profitability—how much yield they provide. What they also differ in is the amount of your attention that they require on daily, weekly, and monthly basis, and the amount of attention and mental effort they require you to take upfront, before you commit the investment. Before you commit an investment, you should test your investment strategy at least by evaluating its performance on past events, as if you had chosen the strategy in the past. However, in finance more than elsewhere, the future may be much unlike the past.

== Relationships ==
While making your life plan happen, based on your life program, you will rely on and cooperate with a number of people, unless you choose an isolated, solitary life program such as those that require people to live in a lonely cottage in the mountains.

The kind and degree of cooperation varies vastly. By buying food in a supermarket, you surely directly and indirectly cooperate with the selling person, the producers of the food, the managers of the supermarket, those of the chain, and the like. However, there is nothing tricky about that cooperation. The communication is almost absent, so there is negligible risk of misunderstanding. What you need to learn about the food you find printed on the labels. When buying industrial goods, there is mostly little or no negotiation with the seller, and there is a guarantee provided. The cooperation gets critical when there are no formal standards and there is the need for a lot of communication or negotiation; as is the case in family relationships, working relationships, the one with a landlord, or in business partnerships.

You need to be clear about what you say and what you don't say to other people. You need to understand what information to pass and what to keep secret. Your life program may be such that you may want to keep it completely private, not telling a single person about it.

Communication skills are key to all kinds of purposes. There is a considerable variety, with different kinds of skills coming easy to different kinds of people. One kind is the ability to describe things exactly, listing the details of things, with precision that prevents misunderstanding, but also accuracy, in align with reality. A contrary and complementary skill is the ability to describe things vaguely or indirectly using figures and hints, so that only certain people are able to discern the message. Related are the ability of giving praise in the right time and quantity while avoiding flattery, and of giving inconspicuous, discreet, sometimes indirect criticism, or, difficult for some people, calm and non-angry expression of disagreement. To make things more difficult, communication is not only verbal but also non-verbal. Your ability to describe things with precision may be perfect but the overall effect may be worsened if you communicate fear through your eyes, face, tone, body, and gestures.

Communication is closely related to negotiation, the ability to describe what you want, explain it, disclose not too much, and in the end, get what you want without letting the other party give too much in. It requires that you do your homework, clarifying your requirements, sometimes painfully discovering them, writing them down, illustrating them with vivid examples, and writing everything down and yet being able to remember great part of it. It involves the art of not attacking people, as much they may seem to deserve it by what they say and how they behave. Required is the ability to distinguish what part of your partner's argument pertains to logic and what part only vividly describes something intense in order to stir emotions, and still telling it the finding to the partner in a non-assaulting way. Controlling anger may be particularly difficult when the partners use tricks against you, such as an overheated room, or an environment that in other way makes you hurry up the negotiation and the involved decisions.

As long as you do not need tight integration, above all negotiation, you are basically in privacy.

It may be difficult to avoid offending other people. If you do, and you feel you should not have, apologize.

Apology is understood by various people in various ways. In the most generic meaning, an apology is letting the other people know that you are aware of an error or offense that you have made, that you are willing to compensate the other party for that error immediately, and that you will try to avoid making a similar error in the future. Even acknowledging an error is important; you could as well have been unaware of the error. Still, it does not mean that you will be able to prevent the error next time around. It is a bit like parents apologizing for the misbehavior of their children: the parents will try to prevent their offspring from misbehaving again, but they have only imperfect control over them, so no perfect guarantee can be made.

An apology can be accompanied with a remedy or a compensation. If you destroy a thing that can be bought for 10 €, the apology can be accompanied with a provision of the same thing or a replacement.

An insincere apology stands chance of being rejected and decreases the chance that future apologies will be accepted by the hurt person. Apologies do not need to be done publicly and often should not; ideally they should be done discreetly. If a face-to-face apology does not work, write a letter. Even if trying face to face, you can write a letter as an exercise before.

An important part of your dealing with other people is managing your emotions. That has been covered in the &quot;Managing Emotions&quot; chapter.

Buy services of other people if you can. Buying services can be more complex than buying goods, depending. Goods are often highly standardized, under tight industrial quality control, so that items in one category of goods are much more alike than items in one category of services. Service can leave an imprint in your head, leading to recollection or a wound that you would prefer not to have. Consider for how long you will be in contact with the person providing the service, how intense the emotions will possibly get and whether there is a way of terminating the service in the middle. A haircut is a service that lasts only shortly and won't leave you scared, unlike poor driving lessons.

Make friends. Distinguish friends from buddies, who come in certain period of life, quite automatically, and then go away, and from acquaintances. Aristotle thought that in each friendship, three ingredients are present in various degrees: friendship for pleasure, friendship for utility, and friendship for what I would rephrase as respect. Learn to distinguish those. When you enjoy the other person, that's pleasure; when that person knows some contacts important for your aims or can help you, that's utility; when you have high regard for the person above all, and find way to talk to him in spite of occasional pain, that is respect. 

== Learning ==
Whatever you are going to aim at, you will need to learn—to gain skills and knowledge. How to learn depends a lot on the specific area of learning: learning maths is vastly different from learning a foreign language or learning to swim. Still, let me show you some general considerations that can improve your ability to learn in a great variety of areas, depending on how skilled in learning you already are.

First, there are major differences between leaning of academic subjects and learning of skills, such as the ability to write well. Let me first focus on learning of knowledge in an academic way. Although learning of skills is different, even that benefits from having learned by heart some facts that help during the learned activity.

A typical way of acquiring academic knowledge is at schools and courses. The result of such a learning is your ability to answer certain groups of questions to the satisfaction of the examiner or your own. Some questions can be answered immediately, other require preparation or calculation; some questions require an elaboration, other are answered with one sentence, or with a plain or hierarchical list.

Some of the most useful aids for learning of verbal knowledge are hierarchical outlines. Whether you are going to learn knowledge at school or on your own, you will need to verify whether you know what you should have learned, and to be able to tell what there is to cover in the first place. The hierarchical outline contains heads about which you should be able to talk, or terms that you should be able to define or explain. The outline contains keys to which your memory should be able to associate some material. Once you have such an outline in your hands, it may look boring enough, surely not something you would want to read for fun. Still, the task of creating such an outline is a major one, which, if you go through it, will teach you to appreciate the amount of information and hard organizing work that a good outline contains. It is you who, upon review, should provide the flesh to the skeleton that the outline presents. You can get an outline from a textbook, where you can also find a list of questions to be answered, or you can create it yourself from a teaching text, which has the advantage that, in that outline, you can use such keywords that you find most telling. Although unpleasantly resembling examination in school, reviewing and testing what you have learned is key. Unless you are exceptional, there is no way to actually learn some knowledge by plain listening or reading. You have to verify that you have actually learned the material.

If textbooks or other learning materials are not available, and there is no course that you can attend or you cannot afford it financially, you have to be much more creative and the whole process is going to cost you a lot more attention and research. In that case, the academic knowledge still has to be located somewhere, but it may only be at scientific articles or books that are difficult to read. The whole subject may be poorly organized, with texts scattered and using inconsistent terminology and structuring the subject differently. The task of learning becomes much more of the demanding task of secondary research.

The other type of learning is the one of learning skills, such as swimming or good writing. For most skills, there is some verbal knowledge to be learned by rote that is helpful, but it alone will not do. Skills require the gaining of habits—automatic reactions to certain stimuli, which you do not need to focus on consciously. That is clear in shifting gears of a car; you only have to think of &quot;gear up&quot; and the rest kind of happens on its own, without your intervention. It is as if you have trained your internal dog to react in a certain way, the dog doing the work for you. But the dog only does the work after you have trained it. Also, the terms of the theoretical knowledge about skills may be difficult to apply before you actually experience the learned activity. Many things are much easier to show than to describe. Especially with motor skills such as those needed in sports, learning happens even if you just practice without paying much attention to it.

An important part of learning of skills is learning from mistakes. Extending the dog metaphor, your internal dog learns from mistakes even without your intervention. But there are kinds of mistakes that it does not even recognize as mistakes and thus cannot learn from. You can improve your performance in any activity by actively, deliberately reviewing your recent past activity, searching for mistakes and pondering their remedies. A future mistake can be either altogether avoided or at least a measure taken to limit its impact. In a more sophisticated vein, a future mistake can be seen as a future risk and managed using the methods of risk management. 

Active search for mistakes has some drawbacks, though. It takes time and it takes away part of your attention—your memory and thought—that you could have devoted to the learned activity otherwise. Also, it changes the way the dog behaves next time around. As the dog expects another review, it becomes more careful. That is a good thing only if the dog still has reserves. In effect, you are instructing the dog to take away part of your attention for preventing mistakes in the future. 

It may be difficult to distinguish a mistake from a non-mistake. Often, people can realize something has gone wrong, but an undesirable result does not make the action that lead to it automatically wrong. If you bet in a 1:1 rate that a dice will not roll 6 and it does, you have still chosen the right strategy, just that you were unlucky. To recognize a mistake, you need to know what causes what, and that in general requires experience or expertise. 

A reviewer can help a lot with finding mistakes. Even with best efforts, you may be unable to see a mistake that another person spots immediately, as is the case with poor pronunciation of a foreign language that can quickly be corrected by a native speaker. 

Learning from mistakes requires your willingness to accept that you make mistakes, which may be an emotionally painful process. Admitting a mistake to yourself is difficult enough; admitting your goof to another person or even publicly more so.

Learning in privacy is vastly different from learning in a group, and that further vastly differs between a tamed group of note taking students, with clear subordination to the teacher, with close to no cooperation and mutual interaction, and a group of peers working together to solve some problem, with unclear power structure. The presence of the group consumes part of your available attention, the more so, the more there is to learn about the group. Errors that you make in privacy are not exposed to other people. 

Many skills can be practiced in privacy, including those whose ultimate results are going to be shown publicly. Such is the case of an aspiring speaker, who practices public speaking in privacy in a barn, imagining his fictional audience. He can learn a lot even if certain aspects of public speaking are left unexposed, including the stage fright. Another case is a group of actors rehearsing for a public performance; among themselves, the actors are in privacy as compared to the ultimate public show. 

Imagination can be a powerful helper in learning. The effect of imagination can be likened to the effect of a physical driving simulator, which helps people to learn to drive, or at least to automatically shift gears. Imagination can help to create a mental simulator of sorts, one that is physically absent but can still be used to produce your required reaction. For instance, you can sit on a chair, close your eyes, put your hand where you expect the gear handle to be, and ask yourself to change to various gears, and see whether your hand automatically moves to where you expect it to. Parts of this model can be taken over to other situations. 

Observing other skilled people is an important method too. You may ask yourself what it is that they are doing and you are not doing, and why. Sometimes, just being around experienced people suffices for picking some of their ways subconsciously. However, this method mostly fails with teachers, unless the skill that you want to pick is teaching.

You can learn on your own, enroll in a university, buy a course, or join or organize a self-organized group of learners. Each approach has its own benefits and drawbacks, so they are best combined. Formal education provides you with a degree, standardized curricula and teachers who provide instruction, assign tasks, and correct your errors. Degrees and certificates are recognized by hiring people. A standardized curriculum, even if too extensive, makes sure you have a basic coverage of knowledge and skills in the given area. Grades provide an aim against which to measure your performance, even if grading is an imperfect process. Classes lead by professional teachers are tested by the participants. The teachers correct your mistakes and provide praise and blame, increasing your motivation. 

Many skills can be learned on your own. Before you decide to learn on your own, you should consider the alternatives: taking classes and learning in a self-organized group. Self-teaching should be distinguished from the homework and practice that classes and courses require. With self-teaching, you are completely on your own. You need to decide which textbook to buy, what exercises to make, what kind of and how much practice to take. When you're learning alone, instruction materials such as textbooks and workbooks help a lot. Many skills cannot be learned exclusively in classes. Especially learning of foreign languages requires a lot of practice on your own, your own attempts to speak and write. If there are no textbooks, as is the case especially with lucrative kinds of knowledge and know-how, the expertise can come from instruction manuals, which are not tailor-made to students. Although learning on your own may be a lot of joy, there are some risks too. You may miss the conventions that the field uses, such as the letter &quot;v&quot; for velocity. You may assign too much work to yourself, leading to excessive practice. In the absence of other practitioners, you may lose motivation and a sense of where you stand as compared to other people, leading to possible underestimation or overestimation of your achieved level. The benefits of learning on your own are considerable too. You may learn in the tempo and learning style of your own. You may pick your own time and scope of learning. You may decide what is relevant for you and what is not. And importantly, you may learn skills and knowledge that are difficult to gain from courses or the courses are expensive. 

Apart from learning on your own and taking classes, another model is the one of a self-organized group. That is, a group of people plan to come together on a regular schedule and present or discuss certain topic of academic knowledge. The task of determining the scope and the best learning materials can be divided between the members, as can be the task of presenting the matter to other participants. Compared to self-teaching, you have much less autonomy as an individual learner, but you do not carry all the organizing work on your shoulders, and more of the discipline to keep the regular schedule comes from the outside of you. Downsides include that the participants may vary in their starting knowledge, their speed of learning and their preferred learning styles, leading to all kinds of frustrations.

== Yourness ==
You may want your life program to be truly yours. It is unclear what &quot;yours&quot; means exactly, but a life program that you have written yourself is more yours than one that you have taken over from someone else. But even a life program that you have written yourself may contain ideas or suggestions from other people or books that you have read and have forgotten what they said. That touches on the question of where the life program that you have written comes from. You may use your own words, but are they truly yours? What makes you accept one life program in favor of another one? For an external observer of you, the life program or its choice results from the combination of your innate faculties, tendencies, and motives in you, and all your past experience that have shaped your mind, including parents, close family, books, movies, buddies, friends, teachers, and other people and media.

== Individual Impact ==
If you have been considering one of the universal life programs, those expressed in terms that span not only the earth but also the universe, such as the power of life over matter, a seed of doubt could creep in. Making a difference on Earth is hard enough. The groups of living things possibly living on distant planets threaten to overshadow any impact that you alone or even the whole of humankind could make on the chosen universal goal. It is a matter of probability. As we do not know whether life is present elsewhere in this universe, there is a chance that the impact that you can make on Earth actually does matter universe-wide.

Even if you do not fear the doubt resulting from considering other civilizations in the universe, you may still feel that you cannot influence such planetary goals as maximizing the gross world product or minimizing the world illiteracy. There are situations such as the one of a dying person in which influencing them seems indeed impossible. But a small influence is almost always possible. Even a cleaner in a hospital contributes a small share to the result of the whole organization, and if the cleaner sees the furthering of health as his larger goal, contributing in this way is still better than not contributing at all. One sentence that you pass to another person stands a chance, as small as it can be, of making a difference in what matters most to you in the long run. 

Let us consider the various kinds of contributions to your larger goals that you can make. Many people take part in the production of physical objects including tools, houses, and cars. Other produce information objects such as books, movies, reports, documentation or software. Great many people make it to leave offspring, an important contribution to almost any global goal, as a goal without hosts is a dead goal. Other people help shape the minds of the future generations. Some people maintain what has already been discovered and developed, other develop new designs, still other manufacture them.

It is pleasing to see the results of your efforts during your lifetime. But if your goals are large and spanning the Earth or the universe, you may be satisfied with supporting the chance that your goal will be achieved in three hundred years time. Many a notable person has become influential through their writings only after their death.

It is nice to see that your individual impact was unique, different in kind from that of other people. But the impact does not need to be unique. The point is to aim at the larger goal, even if your influence on that goal is of the same kind as the influence of other people. If your goal is to let as many books as possible to make it from the imaginary Borges library of all conceivable books into this world, then the fact that the book that you have written is completely unexceptional does not diminish your contribution to that goal.

I run the risk of repeating a cliché by saying that there is always hope of affecting the chosen aim. We know nothing for perfectly sure. Purely theoretically, the laws of the world can change in the next moment. This may seem unreasonable to human intuition, but that is exactly what the laws of logic say. Put differently, there is no perfect guarantee that the future will be like the past in any regard. This is not a suggestion to rely on a divine intervention, only a recognition of our ignorance. Also, our understanding of the laws of the world is limited. For the world to violate the laws as we know it, it does not need to violate the real laws. There are times when scientific theories change drastically. At these times, it is not the world that changes, only our image of the world. Thus, everything considered, and strictly logically speaking, even a dying person has a minute hope of acting to affect his distant long-term goal.

== Free Will ==
Some people object that they cannot write and turn into action any life program, because their life is already determined. They believe the world is governed by physical laws and so are their decisions, as they get made in their brains. Even on this account, if you are such a person, the text that you are currently reading stands the chance of influencing you to write a life program, or to choose a specific method of creating it. The idea that we make choices, well known from everyday experience, is in no logical contradiction to the idea that the future course of the universe is already determined; it is determined by the choices that we make, that can possible determined, but we do not know them. If you will, you can read it as that we do not make our choices, we discover them.

For your choice and execution of a life program, what matters is that you actually have the option to choose, not how the choice is done in your brain. Imagine a glass of water standing on your writing desk. You can choose to move the glass to another place on the desk, or let it stand where it is. Choosing your life program is much more complex than choosing whether to move a glass, consisting of a myriad of subdecisions, but ultimately, the alleged problem of free will does not depend on the complexity of the decision but on the fact that a decision is being made at all.

That said, your freedom of action is limited. There are things which you know you most probably cannot do, no matter what life program you choose and what set of strategies and tools you use for turning it into action. But that has nothing to do with the fact that you can make choices. A prisoner has his freedom of movement drastically limited and yet can to an extent choose the verbal ideas running through his head.

At times, the strength of your will can be put to a test. A strong urge, an impulse to do something you have previously decided not to do, can seem irresistible. Also, the pressure on you other people create may have a similar effect. This however does not diminish the possibility of the will, only its strength. For one thing, you can make your will stronger if you regularly exercise it. For another one, if an urge, impulse or drive was at some point stronger than all your concentrated will, then what you were trying to achieve using your will was in fact not possible, at least not in that moment.

Some people could argue that all your action is merely a combination of external pressure and internal impulse, but in order to adjudicate the two, you need some other source of information, some other principle than those coming from those two sources.

== The Big Picture ==
Unless you choose to focus all your efforts on the time scale of your life, you may express your life program in terms of larger time scales and larger areas and groups of beings, including centuries and millennia, collective enterprises, grand causes, human cultures, the human species, or the biological life on the Earth. If you do, a fundamental obstacle you are going to face is that long-term prediction is difficult and very long-term one borders on impossibility, and so is influencing distant future through present deeds. Although direct aiming at very long-term goals is impossible, what you can do is to aim at those short-term goals that are likely to create stepping-stones to very long-term goals. The obvious short-term goals are various means to long-term ends, such as further existence of people, maintenance and growth of knowledge and technology, or keeping and growing of human culture. 

Any entity or process you choose to focus on or identify with is exposed to threats, close and more distant. The life on Earth is exposed to threats, also other threats than the technological activity of humankind. The Sun is going to expand, and before that, there is going to be a new ice age. There is the possibility that life is going to expand from the Earth to other planets. Humankind can be helpful in this expansion. Without human technology, it is unobvious how biological life will leave the Earth. No form of biological life that we know, neither all the forms of biological life taken together as a whole when humankind is excluded, has as far as we know ever managed to leave the Earth.

At some point of time, all the living things on Earth are going to die. At that point, the game of life will be over. But so far, the game of life is on. Go and play it.

== The Power of Life Programs ==
I have endeavored to help you with writing your own life program. You may have believed that you should then execute it. If you imagine people executing various life programs, of their parents, of their own making, or of whom they consider their superiors, you may start to see that it is the life programs that control the people. Many people zealously distribute basic tenets of their life programs, threatening those who won't accept with eternal torture while promising those who join them an eternal life. Seen from a different perspective, it is the life programs that ask their hosts to reproduce them, to get copied from minds to books and from books to minds, in search of their new hosts.

Apart from conscientiously executing a life program, you have another, difficult option. Do your own thing. By writing your own life program, you make a step in that direction. Still, you also step in the direction of being controlled by your own life program.

You may try to rebel against any life program. However &quot;to rebel against any life program&quot; is a life program of sorts too. You may exclude this particular one from your rebellion. That comes quite close to being capricious and unpredictable.

== Ethics ==
In the following, by ethics I mean the investigation of right and wrong, acceptable and unacceptable, rather than the investigation of what is a good life. An ethical norm is exemplified by the ought-statement: one ought not make an arbitrary killing of a human. That is a very weak statement and we usually have much stronger requirements concerning killing of a human; its purpose is to anchor the concept of ethics to an example. The kind of ethics investigated in Aristotle's Nicomachean Ethics is something else.

Most very simple life programs are unethical: their specified aim, being the sole ultimate one, overrides any ethical concerns unless they happen to be instrumental to that aim. The only way for a very simple life program to be ethical is to have ethical requirements be derivable from it with the use of logic. If one wants genuine ethics, as many of us do, it seems one has to explicitly codify ethics as part of the life program. Thus, the life program has to specify the ultimate objective but also ultimate constrains on how one is allowed to achieve the objective. However, one can have quasi-ethics as something serving as an instrument for a large aim. Thus, if one aims at maximizing the copies of one's genes (approximately, have as many descendants as possible), one can probably derive kin altruism, reciprocal altruism and display altruism from this aim. Thus, one can be motivated to show ethical and altruistic behavior by realizing the other person is a relative, by expecting a reciprocation of a favor, and by accepting other benefits from ostensive display of ethical conduct. The genuine ethics gets revealed from how one accepts or refuses to take an unethical advantage of opportunities when no one is looking and one cannot be found out, as well as in the situations where the only witnesses are accomplices in an unethical act.

A solution used by some religions to the problem of genuine ethics, meaning ethics as revealed in private dealings, is to abolish privacy by positing a constant observer capable of administering very harsh punishment in hedonistic terms, that is, eternal pain with no relief. However, this trick does not seem to work very well, as the Christian European conquest of South America, North America and Australia suggests; true believers would seem to be afraid to commit violence for the fear of the eternal damnation. By contrast, if the invaders use Christianity as a mere pretense cloak, and are in fact driven by the selfish-gene-coded hidden desire to acquire natural resources instrumental for supporting more bodies to carry these genes further, things make sense.

One thing we can do is develop various well-designed ethical codes together with justifications and debates serving as quasi-proofs. This way, those who happen to care about being ethical can access decent ethical codes to start with without having to invent their own. As for those who could not care the least about being ethical, ethical codes seem powerless against them, and the prospect of scaring them by untrue stories into ethical conduct seems very uncertain.

== Politics ==
Your chosen life program may have political consequences. I have proposed from the very beginning that you respect political freedom. It is the political freedom that you have, if you in fact have it, that makes a search for a life program so much meaningful and acute, although it is basically meaningful even without political freedom. Also, it is the value of thinking in align with truth that makes such a search meaningful. If you do not honor knowing and finding truth, you do not need to honor the meaning of the words in your life program either.

==Tentative eclecticism==
Instead of writing a rigid life program, one can take a stance that involves tentativity and eclecticism while still recognizing the value of a written life program.

As for tentativity, one can say: I am not going to stick to any fancy set of doctrinaire ideas, echoing phrasing of Robert Pirsig. Any life program expressed in words is tentative, and open to revision. If a life program were a declarative/descriptive object rather than imperative, one could say it is conjectural.

As for eclecticism, one's position may be this: I am not going to name a single primary concept to drive my life. I will not seek the ultimate but rather something like multiple penultimates or ultimates that appear to be ones only because they are the last items seen on the current horizon, but there are in fact deeper ultimates beyond the horizon. Thus, I may pick goodness, virtue, excellence, kindness, live-and-let-live, intellectual honesty, personal longevity, personal health and other items as desiderata, realizing that they are in conflict and need some balancing. Moreover, I will realize that it is fine for different people to put emphasis on different desiderata.

An objection to eclecticism is this: it is unclear what brings the parts into a coherent whole. The culture spreading the commonly recognized desiderata may well be wrong about them.

== Literature ==
The following literature played the role of an inspiration and source of ideas:
* Berne, Eric. ''What Do You Say After You Say Hello''. 1964.
* Cameron, Donald. ''The Purpose of Life''. 2001.
* Covey, Stephen. ''The 7 Habits of Highly Effective People''. 1989.
* Dawkins, Richard. ''The Selfish Gene''. 1976.
* Durant, Will. ''The Story of Philosophy.'' 1926.&lt;!-- Pocket Books. ISBN 0-671-73916-6. --&gt;
* Frankl, Viktor. ''Man's Search for Meaning''. 1946.&lt;!-- Pocket Books. This translation first published by Beacon Press, 1959. ISBN 0-671-02337-3. Also read in Czech, A přesto říci životu ano. --&gt;
* The Encyclopedia Britannica, 1911 edition online in Wikisource
* Hofstadter, Douglas. ''Gödel, Escher, Bach''. 1979.
* Mander, Jerry. ''In the Absence of the Sacred''. 1992.
* Moravec, Hans. ''Mind Children''. 1988.
* Pirsig, Robert. ''Zen and the Art of Motorcycle Maintenance''. 1974.
* Poincaré, Henri. ''The Value of Science''. 1913.
* Popper, Karl. ''Open Society and its Enemies''. 1945.
* Popper, Karl. ''Alles Leben ist Problemlösen''. 1994, Ausgabe 2002.
* Stanford Encyclopedia of Philosophy online</text>
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    <title>User:Dan Polansky/Czech national identity</title>
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      <comment>Atcovi moved page [[Czech national identity]] to [[User:Dan Polansky/Czech national identity]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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Author: Dan Polansky

This article investigates what kind of things could constitute Czech national identity. The result is very tentative and probably subjective.

One candidate is this: Czechs are the nation of Jan Hus, who was burned at stake in 1415 for his teachings and his refusal to recant. Hus emphasized the value of truth. As Britannica points out&lt;ref&gt;[https://www.britannica.com/biography/Jan-Hus Jan Hus], britannica.com&lt;/ref&gt;, Hus &quot;anticipated the Lutheran Reformation by a full century&quot;. (By contrast, Galileo chose a different strategy, of insincere recanting; not so Giordano Bruno.)

This brings us to another item: the standard (flag) of the president of the Czech Republic states &quot;truth prevails&quot; (&quot;pravda vítězí&quot; in Czech). The slogan is not literally true but it points to a wish for truth to prevail and to importance of striving for truth to prevail, even at the cost of one's life. The slogan was on the presidential standard since the time of Masaryk, the first Czechoslovak president. The emphasis on the value of truth was reinforced by a phrase popularized by the internationally renowned Czechoslovak and then Czech president Václav Havel, about truth and love to prevail over lies and hatred.

Other characteristic property of Czechs is that they were under German-language administration for over 300 years, from the Battle of the White Mountain in 1620 to creation of Czechoslovakia in 1918. (It remains to be clarified to what extent German dominated to some extent even before 1620.) It was the Czech national revival (a form of nationalism) that brought Czechs out of the German-dominated state, together with post-World War One intervention by the U.S. president Woodrow Wilson and his doctrine of national self-determination.

Czechs never had a colony. The empire Czechs were part of, the Austrian and later Austrian-Hungarian monarchy, had almost no colonies. If anything, Czechs were emancipated from under a yoke. (On the other hand, part of Slovaks considered Czechs to be too dominant in Czechoslovakia, which drove Slovakia to separate from Czechoslovakia. Somewhat similarly, some of those who identify as Moravians as a distinct ethnicity or nationality see Czechs as dominating them from Prague.)

Czechoslovak failure to militarily resist Hitler in the wake of Munich Agreement is likely to have left something of a stigma on Czechs as cowards who do not fight, unlike the Polish. (Not that the Polish fighting made much of a difference against Hitler.) A similar picture emerges from the 1968 Warsaw Pact invasion of Czechoslovakia, when Czechs and Slovaks did not militarily resist the massive military superiority of the Soviet Union (Russia et al.) joined by other Warsaw Pact countries. This stands in contrast to the 15th century military resistance of Bohemian Hussites (followers of Jan Hus) lead by Jan Žižka against Sigismund-lead crusading armies that were trying to suppress religious freedoms.

Czechia leads the list of countries by beer consumption per capita by far, followed by Austria. This could contribute to the view of Czechs as a beer nation, who, anecdotally, endlessly debate all sorts of possible and impossible things in their pubs.

Czech legal culture is that of a codified law. Czechoslovakia had a codified constitution since 1918.

Another item adding to what constitutes a Czech is a list of role models Czech can naturally select from. Some famous Czechs (having an article in Britannica is one criterion):
* Charles IV, an emperor
* Bedřich Smetana, a music composer
* Antonín Dvořák, a music composer
* Leoš Janáček, a music composer
* Jan Hus, a religious reformer and martyr
* John Amos Comenius, an educator
* František Palacký, a historian and politician
* Tomáš Garrigue Masaryk, a philosopher and the first Czechoslovak president
* Václav Havel, a dissident and a politician
* Václav Klaus, a free-marketeer politician and climate skeptic
* Božena Němcová, a writer&lt;ref&gt;https://www.britannica.com/biography/Bozena-Nemcova&lt;/ref&gt;&lt;!-- mentioned in Britannica, but without dedicated article --&gt;
* Jan Neruda, a writer&lt;ref&gt;https://www.britannica.com/biography/Jan-Neruda&lt;/ref&gt;&lt;!-- mentioned in Britannica, but without dedicated article --&gt;
* Jaroslav Hašek, a writer
* Milan Kundera, a novelist
* Bohumil Hrabal, a writer&lt;ref&gt;https://www.britannica.com/biography/Bohumil-Hrabal&lt;/ref&gt;
* Jaroslav Seifert, a writer&lt;ref&gt;https://www.britannica.com/biography/Jaroslav-Seifert&lt;/ref&gt;
* Miloš Forman, a film director&lt;!-- e.g. ''One Flew Over the Cuckoo's Nest'' --&gt;&lt;ref&gt;https://www.britannica.com/biography/Milo-Forman&lt;/ref&gt;
* Emil Zátopek, a long-distance runner&lt;ref&gt;https://www.britannica.com/biography/Emil-Zatopek&lt;/ref&gt;
* Martina Navrátilová, a tennist&lt;ref&gt;https://www.britannica.com/biography/Martina-Navratilova&lt;/ref&gt;
* Jaromír Jágr, an ice hockey player&lt;ref&gt;https://www.britannica.com/biography/Jaromir-Jagr&lt;/ref&gt;
* Věra Čáslavská, a gymnast&lt;ref&gt;https://www.britannica.com/biography/Vera-Caslavska&lt;/ref&gt;
* Dominik Hašek, ice hockey goaltender&lt;ref&gt;https://www.britannica.com/biography/Dominik-Hasek&lt;/ref&gt;
* Ivan Lendl, a tennis player&lt;ref&gt;https://www.britannica.com/biography/Ivan-Lendl&lt;/ref&gt;
* Alphonse Mucha, a painter&lt;ref&gt;https://www.britannica.com/biography/Alphonse-Mucha&lt;/ref&gt;
* Karel Čapek, a playwright&lt;ref&gt;https://www.britannica.com/biography/Karel-Capek&lt;/ref&gt;
* Jaroslav Heyrovský, a chemist&lt;ref&gt;https://www.britannica.com/biography/Jaroslav-Heyrovsky&lt;/ref&gt;
* Jan Evangelista Purkyně, a physiologist&lt;ref&gt;https://www.britannica.com/biography/Jan-Evangelista-Purkinje&lt;/ref&gt;

Some famous people, non-Czech by ethnicity, having lived or worked in Czech lands (Bohemia and Moravia):
* Tycho Brahe, a Danish astronomer (was multiple years in Prague)
* Johannes Kepler, a German astronomer (was multiple years in Prague)
* Franz Kafka, a German-speaking novelist
* Gregor Mendel, the German-speaking scientist behind the Mendelian gene theory
* Kurt Gödel, a German-speaking logician
&lt;!-- https://www.britannica.com/biography/Sigmund-Freud; Freud was born in Moravia, but he moved to Leipzig as a child ==&gt; tentatively rejected from the list --&gt;
* Edmund Husserl, a German-speaking founder of phenomenology, having been born and studied in Czech lands&lt;ref&gt;https://www.britannica.com/biography/Edmund-Husserl&lt;/ref&gt;

==References==
&lt;references /&gt;

==Further reading==
* {{W|Czech Republic}}, wikipedia.org
* [https://www.britannica.com/place/Czech-Republic Czech Republic], britannica.com
* {{W|Jan Hus}}, wikipedia.org
* [https://www.britannica.com/biography/Jan-Hus Jan Hus], britannica.com
* {{W|Truth prevails}}, wikipedia.org
* {{W|Bohemia}}, wikipedia.org
* [https://www.britannica.com/place/Bohemia Bohemia], britannica.com
* [https://english.radio.cz/how-hussitism-served-first-republic-8146956 How Hussitism served the First Republic], 2018, english.radio.cz
* {{W|Austrian colonial policy}}, wikipedia.org
* {{W|Munich Agreement}}, wikipedia.org
* {{W|Warsaw Pact invasion of Czechoslovakia}}, wikipedia.org
* {{W|List of countries by beer consumption per capita}}, wikipedia.org
* {{W|List of Czechs}}, wikipedia.org
* [https://knihovna.obecmokre.cz/slavni-cesi-historie Slavní Češi historie], knihovna.obecmokre.cz (in Czech)

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    <title>Anxiety disorders</title>
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Though occasional anxiety as an emotion is considered healthy, an anxiety disorder occurs when said anxiety and fear is pervasive, irrational, and impairs one's quality of life for around six months. According to the DSM-5, those with anxiety are more likely to think about, attempt, or commit suicide.&lt;ref&gt;DSM-5&lt;/ref&gt;

== Generalized Anxiety Disorder ==
G.A.D. is the most common anxiety disorder, normally referred to as simply anxiety.

=== Diagnostic Requirements ===
Excessive fear, fatigue, difficulty concentrating, irritability, sleep disturbance and muscle tension that lasts for six months and can not be better explained by medications, circumstances, or another disorder

[[Category:Anxiety|disorders]]</text>
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Though occasional anxiety as an [[emotion]] is considered healthy, an anxiety disorder occurs when said anxiety and fear is pervasive, irrational, and impairs one's quality of life for around six months. According to the DSM-5, those with anxiety are more likely to think about, attempt, or commit suicide.&lt;ref&gt;DSM-5&lt;/ref&gt;

== Generalized Anxiety Disorder ==
G.A.D. is the most common anxiety disorder, normally referred to as simply anxiety.

=== Diagnostic Requirements ===
Excessive fear, fatigue, difficulty concentrating, irritability, sleep disturbance and muscle tension that lasts for six months and can not be better explained by medications, circumstances, or another disorder

[[Category:Anxiety|disorders]]</text>
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    <title>Machine Intelligence Quotient</title>
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= '''Machine Intelligence Quotient''' =


Intelligent agent-based systems (IABSs) are a common type of intelligent systems. An IABS could be an intelligent agent (IA) which solves problems individually, or an intelligent cooperative multiagent system (ICMS) where the agents cooperate in problem-solving. The health sciences employ intelligent systems for a wide range of tasks, including to solve complex medical diagnosis problems &lt;ref&gt;Iantovics, L.B.: Agent-Based Medical Diagnosis Systems, ''Computing and Informatics'', 27(4), 2008, 593-625. &lt;/ref&gt;&lt;ref&gt;{{Cite book|url=http://link.springer.com/10.1007/978-3-319-70090-8_92|title=Next Generation Hybrid Intelligent Medical Diagnosis Systems|last=Arik|first=Sabri|last2=Iantovics|first2=Laszlo Barna|date=2017|publisher=Springer International Publishing|isbn=978-3-319-70089-2|editor-last=Liu|editor-first=Derong|volume=10636|location=Cham|pages=903–912|doi=10.1007/978-3-319-70090-8_92|editor-last2=Xie|editor-first2=Shengli|editor-last3=Li|editor-first3=Yuanqing|editor-last4=Zhao|editor-first4=Dongbin|editor-last5=El-Alfy|editor-first5=El-Sayed M.}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Abdellatif|first=Alaa Awad|last2=Mhaisen|first2=Naram|last3=Mohamed|first3=Amr|last4=Erbad|first4=Aiman|last5=Guizani|first5=Mohsen|date=2023-12-15|title=Reinforcement Learning for Intelligent Healthcare Systems: A Review of Challenges, Applications, and Open Research Issues|url=https://ieeexplore.ieee.org/document/10162185/|journal=IEEE Internet of Things Journal|volume=10|issue=24|pages=21982–22007|doi=10.1109/JIOT.2023.3288050|issn=2327-4662}}&lt;/ref&gt;. &lt;ref&gt;{{Cite journal|last=Wang|first=Ge|last2=Badal|first2=Andreu|last3=Jia|first3=Xun|last4=Maltz|first4=Jonathan S.|last5=Mueller|first5=Klaus|last6=Myers|first6=Kyle J.|last7=Niu|first7=Chuang|last8=Vannier|first8=Michael|last9=Yan|first9=Pingkun|date=2022-11-15|title=Development of metaverse for intelligent healthcare|url=https://www.nature.com/articles/s42256-022-00549-6|journal=Nature Machine Intelligence|language=en|volume=4|issue=11|pages=922–929|doi=10.1038/s42256-022-00549-6|issn=2522-5839|pmc=PMC10015955|pmid=36935774}}&lt;/ref&gt;defines the novel idea of the metaverse in intelligent healthcare. In the context of intelligent systems, measuring problem-solving machine intelligence becomes of utmost importance. There are very few studies that present results related to the subject of measuring machine intelligence &lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://link.springer.com/10.1007/978-981-19-7842-5_7|title=Measuring Machine Intelligence Using Black-Box-Based Universal Intelligence Metrics|last=Iantovics|first=Laszlo Barna|date=2023|publisher=Springer Nature Singapore|isbn=978-981-19-7841-8|editor-last=Kountchev|editor-first=Roumen|volume=332|location=Singapore|pages=65–78|language=en|doi=10.1007/978-981-19-7842-5_7|editor-last2=Mironov|editor-first2=Rumen|editor-last3=Nakamatsu|editor-first3=Kazumi}}&lt;/ref&gt;. Machine intelligence metrics presented in scientific literature rely on different philosophies, which hinders their effective comparison. There is no standardization on what machine intelligence is and what should be measured to quantify it.

== '''Universal black-box-based machine intelligence metrics''' ==
To ensure the universality of machine intelligence metrics, a feasible general approach consists of the black-box-based intelligence modeling used to measure the central intelligence tendency of intelligent agent-based systems. Such metrics should treat aspects like the variability in intelligence, and anomalies (outliers) in intelligence measurements. Statistically grounded universal methods with these properties presented for measuring the machine intelligence quotient of intelligent agent-based systems (IABSs) consist of MetrIntPair &lt;ref name=&quot;:1&quot;&gt;{{Cite journal|last=Iantovics|first=Laszlo Barna|last2=Rotar|first2=Corina|last3=Niazi|first3=Muaz A.|date=2018-03|title=MetrIntPair -A Novel Accurate Metric for the Comparison of Two Cooperative Multiagent Systems Intelligence Based on Paired Intelligence Measurements|url=https://onlinelibrary.wiley.com/doi/10.1002/int.21903|journal=International Journal of Intelligent Systems|language=en|volume=33|issue=3|pages=463–486|doi=10.1002/int.21903}}&lt;/ref&gt;, MetrIntPairII &lt;ref name=&quot;:2&quot;&gt;{{Cite journal|last=Iantovics|first=László Barna|date=2021-03-22|title=Black-Box-Based Mathematical Modelling of Machine Intelligence Measuring|url=https://www.mdpi.com/2227-7390/9/6/681|journal=Mathematics|language=en|volume=9|issue=6|pages=681|doi=10.3390/math9060681|issn=2227-7390}}&lt;/ref&gt;, MeasApplInt &lt;ref name=&quot;:3&quot;&gt;{{Cite journal|last=Iantovics|first=László Barna|last2=Kovács|first2=László|last3=Rotar|first3=Corina|date=2019-10|title=MeasApplInt - a novel intelligence metric for choosing the computing systems able to solve real-life problems with a high intelligence|url=http://link.springer.com/10.1007/s10489-019-01440-5|journal=Applied Intelligence|language=en|volume=49|issue=10|pages=3491–3511|doi=10.1007/s10489-019-01440-5|issn=0924-669X}}&lt;/ref&gt; and MetrIntSimil &lt;ref name=&quot;:4&quot;&gt;{{Cite journal|last=Iantovics|first=Laszlo|last2=Dehmer|first2=Matthias|last3=Emmert-Streib|first3=Frank|date=2018-02-14|title=MetrIntSimil—An Accurate and Robust Metric for Comparison of Similarity in Intelligence of Any Number of Cooperative Multiagent Systems|url=http://www.mdpi.com/2073-8994/10/2/48|journal=Symmetry|language=en|volume=10|issue=2|pages=48|doi=10.3390/sym10020048|issn=2073-8994}}&lt;/ref&gt;. &lt;ref name=&quot;:0&quot; /&gt; presents a guide for choosing the most appropriate black-box-based intelligence metric for measuring the intelligence of a set of studied IABSs, classification of IABSs in intelligence classes, and detection of the IABSs with statistically low and high outlier intelligence. The general idea of these intelligence measuring methods consists in the fact that each of them can be applied to a set of studied intelligent systems, whose problem-solving intelligence is intended to be measured. Initially, an intelligence measurement of the studied systems is performed on a set of difficult testing problems. After this, as a second step, the obtained intelligence measurement data is analyzed based on advanced statistical methods. As a result, the Machine Intelligence Quotient (MIQ) that represents the so-called machine intelligence tendency is calculated using advanced statistical methods. The calculated MIQs are comparable.

== '''Pairwise measuring intelligence of agent-based systems''' ==
MetrintPair &lt;ref name=&quot;:1&quot; /&gt; is an intelligence metric that can be applied to two studied IABSs. IABSs with statistically the same intelligence are classified in the same class. The specificity of the measurements consists in the fact that they are made pairwise (a difficult problem is chosen and the problem-solving intelligence of both systems for the respective problem is measured). A limitation of the metric consists in the fact that it can be applied to only two studied IABSs. In the case of application of more than two IABSs, a so-called family-wise error rate (FEWER) statistical error appears. To eliminate this disadvantage, MetrIntPairII &lt;ref name=&quot;:2&quot; /&gt; intelligence metrics, was developed, having the same properties as MetrintPair; it can be applied to any number of IABSs.

== '''Non-pairwise measuring intelligence of agent-based systems''' ==
MeasApplInt &lt;ref name=&quot;:3&quot; /&gt; is a similar intelligence metric to MetrintPair, being applicable to two studied IABSs. The applicative difference consists in the fact that the experimental problem-solving evaluation does not require pairwise problem-solving intelligence measurements. MetrIntSimil &lt;ref name=&quot;:4&quot; /&gt; extends MeasApplInt, being applicable to intelligence measuring of any number of intelligent systems. The systems with the same intelligence are classified in the same class. The difference between MetrIntSimil versus MetrIntPairII consists of the specific statistical data analysis since the experimental problem-solving intelligence in the case of MetrIntSimil is not made pairwise.

== References ==</text>
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      <comment>Atcovi moved page [[Survivalism]] to [[User:Dan Polansky/Survivalism]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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In the following article by Dan Polansky, let survivalism refer to various attempts to reduce philosophical problems to the concept of survival, or continuing existence, of various entities such as humans, their genes and their ideas. An alternative name could be viabilism, referring to viability of entities. The problems may include those in epistemology, ontology and ethics. Wikipedia has a different concept of survivalism; on the other hand, Merriam-Webster's &quot;an attitude, policy, or practice based on the primacy of survival as a value&quot;&lt;ref&gt;[https://www.merriam-webster.com/dictionary/survivalism survivalism], merriam-webster.com&lt;/ref&gt; is close enough to the concept chosen in this article.

The word &quot;survival&quot; contains the morphological/etymological elements of sur- + viv- + -al, perhaps pointing to staying alive past an event endangering life. For our purposes, it creates a slightly misleading effect since the entities whose continuing existence is analyzed need not be living things/organisms; they can be e.g. genes or elements of culture. Furthermore, the concept of survival seems to point to some event or accident that is to be survived, but there are also uses of the word where the reference dangerous event is not pointed to.

The word &quot;survival&quot; appears in the phrase &quot;the survival of the fittest&quot; in the fifth edition of Darwin's ''On the Origin of Species''.&lt;ref name=eb&gt;[https://www.britannica.com/science/survival-of-the-fittest Survival of the Fittest], britannica.com&lt;/ref&gt; Darwin borrowed the phrase from English philosopher Herbert Spencer.&lt;ref name=eb/&gt; There may be some connection between survivalism and various concepts or ideas named by a phrase containing the word &quot;Darwinism&quot;.

The first application of survivalism is to skepticism. A person who is a deeply radical skeptic may refuse to believe there is a hole before their eyes, but once they fall into the hole, they may realize this form of skepticism is impractical. A person whose radical skepticism leads to their premature death cannot realize as much, provided there is no afterlife. The person who has fallen into a hole may maintain that they do not mind and that that is fine; a person who has died does not have this option. The only widely adopted genuinely held epistemic stances are those that do not result in quick death of their holders.

The second application of survivalism is to the problems of value and ethics. Persons can debate what is intrinsically valuable and ultimately morally good, but only as long as they are alive. Put differently, dead people do not debate what is valuable, worthwhile, morally good, meaningful, etc. This appears to skew all debates about these things toward an implied objective of the continued survival or existence of the debate participants. However, a more careful analysis reveals that also those incapable of speech do not debate these things, implying an objective of the continued ability to speak, or more specifically, to participate in the debate. Therefore, as a general principle, debates about values, goods and morals appear to be biased toward the continued ability of the debate participants to debate. Thus, one might think that values of idle debaters will be better represented in the debates than the values of more busy people.

However, debates about what is good are not the only means by which value stances are revealed. Other actions, including purchases of goods and services on the market, also reveal what people value. Using similar analysis as above, these will tend to be biased toward the ability to participate on these purchases rather than being as if unbiased and random.

Another connection can be made between survival and the concept of good, namely the survival of a particular rendering of the concept of good itself in a particular culture. One approximation of that rendering may be phrases and sentences pointing to that rendering, but they are not the only item of the sort. What it tells us is that some concepts of good are viable in that the cultures hosting them are viable. What it does not tell us is that the survival of a particular concept of good is a good thing or the true ultimate objective. At some level of analysis, the choice of the ultimate good or the ultimate objective to pursue appears open; what is not open are the consequences of the choice.

One thing the various forms of survivalism appear to have in common is that they appear connected with the notion that might makes right, but that needs to be clarified:
* The notion of ''might makes right'' is ambiguous and requires an explication. Based on that explication, we would see whether the result is a form of survivalism.
* The concept of ''morally right'' may be different from ''morally good''; this requires a clarification.
* There is possibly a concept of ''objectivelly morally right'' to which the various cultural concepts are mere approximations or variations. If so, an entity having a might can be in the position to control or dictate statements about ''right'', but not the concept of ''objectively morally right''.
* The survival of an individual, the copying of genes and the copying of concepts of the good are three distinct things and it is unclear why they would all point to the single concept of ''might makes right''.

It appears that the various forms of survivalism fail to lead to satisfactory epistemic and moral philosophies, yet they appear not completely irrelevant:
* The accuracy of a model of reality (e.g. Newtonian physics) does not appear to be guaranteed by the fact that the model serves survival or practical applications well; the concept appears to involve more than that. (A model of empirical reality can be more or less verisimilar or truth-like, or empirically adequate.) If a falsifying (refuting) observation against the model is known and unresolved, we do not think the model is accurate as long as we survive well; rather, we consider the falsifying observation to be a problem showing the model to be imperfect.
* The validity of a set of norms does not appear to be justified by the fact that the set serves the survival of the holder or holders of the norms well. In particular, the norm that one ought not kill another for one's benefit only because no one is looking and will never find out does not seem derived from the objective of one's survival, and is sometimes contrary to it.

Thus, it appears that the concepts of truth of a statement, accuracy or verisimilitude of a model and validity of a norm are ''transcendent'' in some sense, going beyond the requirements of survival. And yet, believing the Darwinian and Dawkinsian theory, the brain structures able to identify or recognize things as true, accurate or valid have originated through Darwinian evolution by natural selection, by variation and elimination of various entities, including genes, gene complexes, patterns of organ growth, organ structures, functional designs, traits, and other entities we may have poor understanding of.

Let us clear some misconceptions about the kinds of entities that are to survive:
* The fittest. This is ambiguous, given the various meanings of &quot;fit&quot;.
* The most genetically fit.
* The strongest.
* The most adapted.
* The most able to survive in various niches that keep on appearing and disappearing as the world is changing.
The last answer seems to be correct even if it approaches a tautology, a statement with no empirical content.

The following sources seem to point to some form of survivalism in relation to some entities:
* Herbert Spencer talks positively of &quot;the survival of the fittest&quot;.
* Charles Darwin used the phrase &quot;the survival of the fittest&quot; in the 5th edition of ''The Origin of Species''.
* Henri Poincaré: A quotation from Poincaré about aborigines loving loud colors and sounds of the drum, but the world being ruled by the lovers of intellectual duty, seems to point to survivalism.
* Karl Popper: His consideration about an Indian tribe that considered tigers so sacred that killing them would be prohibited, and then, the tribe would be killed by the tigers, points to ethical survivalism, whether genetic or rather cultural one. The relevant quotation is this:
*: &quot;[https://books.google.com/books?id=iXp9AwAAQBAJ&amp;pg=PT89]The method of trial and error is not, of course, simply identical with the scientific and critical approach--with the method of conjecture and refutation. The method of trial and error is applied not only by Einstein but, in a more dogmatic fashion, by the amoeba also. The difference lies not so much in the trials as in the critical and constructive attitude towards errors; errors which the scientist consciously and cautiously tries to uncover in order to refute his theories with searching arguments, including appeals to the most severe experimental tests which his theories and his ingenuity permit him to design.
*: &quot;The critical attitude might be described as the result of a conscious attempt to make our theories, our conjectures, suffer in our stead in the struggle of the survival of the fittest. It gives us a chance to survive the elimination of an inadequate hypothesis--when a more dogmatic attitude would eliminate it by eliminating us. (There is a touching story of an Indian community which disappeared because of its belief in the holiness of life, including that of tigers.) We thus obtain the fittest theory within our reach by the elimination of those which are less fit. (By 'fitness' I do not mean merely 'usefulness' but truth; see chapters 3 and 10, below.) I do not think that this procedure is irrational or in need of any further rational justification.&quot;
* Eric Berne: There could be something pointing to survivalism in Eric Berne, but I would have to find what it is.
* Ayn Rand: The following quotation from ''Philosophy, Who Needs It'' is suggestive: &quot;Man's life is the standard of morality, but your own life is its purpose. If existence on earth is your goal, you must choose your actions and values by the standard of that which is proper to man—for the purpose of preserving, fulfilling and enjoying the irreplaceable value which is your life.&quot; The quotation and its context can be found in amberandchaos.net.&lt;ref&gt;[https://amberandchaos.net/?page_id=73 John Galt’s Speech from Ayn Rand’s “Atlas Shrugged”], amberandchaos.net&lt;/ref&gt; Here, ''Philosophy, Who Needs It'' quotes ''Atlas Shrugged''. amberandchaos.net features inter alia the following: &quot;A being who does not hold his own life as the motive and goal of his actions, is acting on the motive and standard of death.&quot; Comment: From the gene-selfish/Dawkinsian perspective, it is not clear why one's own life would be the objective rather than, say, replication of the genes, which would often lead one to self-sacrifice to save one's children.

One may focus on the survival of humankind rather than human individuals, their genes or elements of human culture. Green 2019 sees the survival of humankind as a foundational ethical obligation.&lt;ref&gt;[https://www.sciencedirect.com/science/article/abs/pii/S0016328718303173 Self-preservation should be humankind’s first ethical priority and therefore rapid space settlement is necessary] by Brian Patrick Green, 2019&lt;/ref&gt; Similar idea is aired at Philosophy Stack Exchange.&lt;ref&gt;[https://philosophy.stackexchange.com/questions/54569/is-promoting-the-survival-of-humanity-a-simple-formula-for-assessing-whether-a ethics - Is &quot;promoting the survival of humanity&quot; a simple formula for assessing whether a decision is ethical?], Philosophy Stack Exchange&lt;/ref&gt;

An application of survivalism to ontology could be this. An ontological imprecision is acceptable as long as it does not threaten the survival of those making the mistake. A different take could be this. The innate brain structures that lead to ontological intuitions are a result of variation and elimination of the genes coding these structures, so the objective of survival (of the genes) is implied in them. On the other hand, if one distinguishes a gene occurrence from a gene copy, it is much more about gene copying than survival alone (compare token vs. type distinction). And then, we could use one of the words ''gene-copyism'', ''gene-replicationism'' or also ''replicationism'' (which would refer not only to genes but also to memes/elements of culture).

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Survivalism}}, wikipedia.org
* {{W|Survival of the fittest}}, wikipedia.org

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This article by Dan Polansky looks at the role of Tomas Pueyo (also spelled Tomás Pueyo&lt;ref&gt;[https://fr.linkedin.com/in/tomaspueyo Tomás Pueyo - Uncharted Territories], fr.linkedin.com&lt;/ref&gt;, identified on Amazon as Tomas Pueyo Brochard&lt;ref&gt;[https://www.amazon.com/stores/Tomas-Pueyo-Brochard/author/B074P8X2L6 Tomas Pueyo Brochard], amazon.com&lt;/ref&gt;) as relates to COVID-19 in 2020. It critically reviews his two key articles from a perspective of someone who is not an epidemiologist but rather a software engineer who reviewed and moderated fairly many engineering documents. A properly qualified reviewer could produce much better list of issues/defects.

This seems rather relevant since, the article &quot;Why You Must Act Now&quot; by Tomas Pueyo from 10 Mar 2020 had over 40 million views (believing the article page itself) and probably influenced politicians toward lockdowns. The article &quot;Coronavirus: The Hammer and the Dance&quot; by Tomas Pueyo from 19 Mar 2020 had over 10 million views (per the article page itself) and also stood a chance to influence Western policy makers. Pueyo has no credentials specifically for the data analysis he performed in the article, and one should analyze the risk that the lack of credentials and experience would lead to grave errors in his analysis. Also problematic was that his articles were not reviewed; generally, serious reviewing of artifacts greatly contributes to reduction of mistakes, to the extent that reviewers can sometimes be considered to be de facto co-authors.

==Article: Why You Must Act Now==

===Issues===
1.1) (Relatively minor) The article has no table of contents. That makes it harder to review whether the structure of headings is adequate for the analysis undertaken.

1.2) The article starts with something like an agitation/propaganda. This should perhaps send a warning signal that the material is low-grade.

1.3) Re: &quot;Exhausted healthcare workers will break down. Some will die.&quot;
* What is the quantification? Some? Many? At least two, per plural?

1.4) Re: &quot;The only way to prevent this is social distancing today. Not tomorrow. Today.&quot;
* Clearly untrue, on literal reading. This would mean that if countries do not implement state-enforced social distancing on the day of publication, they will not prevent &quot;this&quot;. But surely the author cannot expect governing bodies to act on his advice within 24 hours.

1.5) Re: &quot;Will I hurt the economy too much?&quot;
* The author pretends to understand worries of decision makers in power, by asking this question. But the question is not addressed in the rest of the article. Therefore, the question is asked and then implicitly dismissed.

1.6) Re: &quot;This works extremely well when you’re prepared and you do it early on, and don’t need to grind your economy to a halt to make it happen.&quot;
* The worry is not about ''grinding economy to a halt'' but rather badly damaging the economy. The employed rhetorical technique is of hyperbole. Moreover, the concern is not just with economy in the abstract but e.g. with those ''people'' who become unemployed.

1.7) Re: &quot;But in 2–4 weeks, when the entire world is in lockdown, when the few precious days of social distancing you will have enabled will have saved lives, people won’t criticize you anymore: They will thank you for making the right decision.&quot;
* This predicts that in 2-4 weeks, the ''entire'' world is going to be in lockdown, a strongly quantified statement that was unlikely to be true and that turned out to be untrue. As per  [[W:COVID-19 lockdowns by country]], &quot;A few countries and territories did not use the strategy, including Japan, Belarus, Nicaragua, Sweden, South Korea, Hong Kong, Taiwan, Tanzania, Uruguay, two states in Brazil and certain United States states.&quot;
* As for &quot;people won’t criticize you anymore&quot;: which people? Surely ''some'' people are going to criticize the lockdown in part since they will have different priorities, risk aversions, biases, etc. And that really happened in 2020 and later: in many countries, there was a continuing debate concerning the lockdowns, with various parties sharply criticizing the lockdowns.

1.8) Re: &quot;South Korea cases have exploded, but have you wondered why Japan, Taiwan, Singapore, Thailand or Hong Kong haven’t?[...]Taiwan didn’t even make it to this graph because it didn’t have the 50 cases threshold that I used. Many of them were hit by SARS in 2003, and all of them learned from it. They learned how viral and lethal it could be, so they knew to take it seriously. That’s why all of their graphs, despite starting to grow much earlier, still don’t look like exponentials.&quot;
* The language of &quot;knew to take it seriously&quot; contains no observable or clearly testable predicate. It tells us very little.
* Expanding on the above, there is no description of e.g. what exactly did Japan do to prevent the growth of cases.

1.9) The article does not contain the words/phrases &quot;economic&quot;, &quot;long-term&quot;, &quot;liberty&quot;, &quot;human right&quot; and &quot;overreach&quot;. It does not seem serious about any concern other than the immediate or near-future saving of lives. One could well conclude that certain economic concerns are to be overriden, but to do so, one would have to take economic concerns into account in the first place. Despite that, the beginning of the article indicates lockdowns to be &quot;the right decision&quot;.

1.10) Expanding on the above, there are different political positions on what is right and important. There is Millian utilitarism with the greatest happiness of greatest numbers; there is libertarianism with its emphasis on liberty. The article makes claims about &quot;the right decision&quot; without acknowledging that it is making an unspoken assumption of what is ultimately important. The assumption that human death avoidance is the sole thing of ultimate importance is untenable since to achieve that, one can sterilize the Earth's population and make sure there are no longer any  human deaths after a point in foreseeable future, but that is hardly an acceptable or attractive prospect.

1.11) Re: &quot;The total number of cases grew exponentially until China contained it. But then, it leaked outside, and now it’s a pandemic that nobody can stop.&quot; [...] &quot;But they aren’t enough to get us below 1 for a sustained period of time to stop the epidemic.&quot;
* A contradiction: on one hand, nobody can stop the pandemic, on the other hand, governments are allegedly not doing enough to stop the epidemic and should do more.

1.12) Re: &quot;Here’s what I’m going to cover in this article, with lots of charts, data and models with plenty of sources&quot;:
* This suggests that &quot;lots of charts, data and models with plenty of sources&quot; is in itself something good enough to bring about validity. It isn't.

1.13) The article does not seriously reckon with any potential negative impacts of a lockdown. This was hinted at in 1.4); in addition to that, there is no mention of additional suicides, missed visits to medical doctors, etc. The article should have at least acknowledged existence of these items.

1.14) The article does not mention or refer to any existing epidemiological plans. If it did, it would need to explain why the existing plans and the pre-pandemic positions of epidemiological experts on the suitability/propriety of lockdowns were incorrect.

===Impact===
As per the article itself, the article got 40 million views in a certain week; and over 40 translations were created and attached to the article.

===Endorsements===
The article has attached a list of endorsements[https://medium.com/tomas-pueyo/coronavirus-articles-endorsements-fdc68614f8e3], featuring many notables.

===Critics from comments===
Selected critics from comment section in Medium:
* Margaret Menzin, Professor of Computer Science and Mathematics and Program Director of Mathematics and Statistics
* Bastian Schoell
* Don Planck
* L.S. Mech
* Robert Dartt Webster

==Article: The Hammer and the Dance==

===Issues===
2.1) Re: &quot;Countries have two options: either they fight it hard now, or they will suffer a massive epidemic. If they choose the epidemic, hundreds of thousands will die. In some countries, millions.&quot;
* The specific quantitative meaning of the above is very unclear. &quot;hundreds of thousands&quot; are going to die where? In some countries? In most countries?

2.2) Re: &quot;We will be locked in for weeks, not months.&quot;
* It is unclear from which statements this conclusion follows. It was not borne by actual experience of the countries that did lockdown.

2.3) The article states that in &quot;do nothing&quot; scenario, 10 million people will die in the U.S., but it does not derive the figure in any way but rather defers the figure to &quot;epidemic calculator&quot; http://gabgoh.github.io/COVID/index.html. The calculator itself contains no data validating that calculator. The calculator states: &quot;This calculator implements a classical infectious disease model — SEIR&quot;; this is a simplistic model that, as far as I know, has never been shown to be numerically adequate to real-world development of epidemics.
* Actual U.S. COVID deaths as for Jan 2024 reached over 1,100,000 per various sources. It seems unlikely that without lockdowns, the figure would have been 10 times worse.
* In a proper exercise, Pueyo would have named the model as &quot;SEIR&quot;. He should have pointed to sources establishing numerical adequacy of this model in relation to real world.
* Moreover, Pueyo should have analyzed the credibility of http://gabgoh.github.io/COVID/index.html rather than taking it automatically to be a correct implementation of a model.

2.4) Re: &quot;So why is the fatality rate close to 4%? If 5% of your cases require intensive care and you can’t provide it, most of those people die. As simple as that.&quot;
* Nothing is simple or obvious about it. It is not clear what &quot;most&quot; refers to quantitatively, how exactly was the input figure 5% obtained and then where the factor reducing 5% to 4% came from. This is not scientific or science-like writing, nor serious engineering writing.

2.5) Chart 7 indicates the figure under &quot;suppression&quot; strategy to be 4000 (four thousand).
* The figure is probably for the U.S. Since the chart does not clearly state &quot;for the U.S.&quot; or the like, it could be dismissed purely on formal grounds.
* The figure is confirmed in the statement &quot;Under a suppression strategy, after the first wave is done, the death toll is in the thousands, and not in the millions.&quot;
* It is hard to believe that the death figure for the U.S. could have been so low even under some radically tightly executed suppression strategy.
* Even in Taiwan noted for its early successful suppression, as of Jan 2024 there are 19 000 COVID confirmed deaths, given population of over 23 million.

2.6) Re: &quot;Unbridled coronavirus means healthcare system collapse, and that means mass death.&quot;
* The phrases &quot;healthcare system collapse&quot; and &quot;mass death&quot; are likely to be free from any specific meaning useful for a serious analysis.
* The term &quot;collapse&quot; would, in a house, indicate elimination of its residential capacity. An analogue in healthcare would be a drop to healthcare performance to zero, but that is obviously not meant. What is meant is a reduced ability to serve all the needs that would be served otherwise. To use the vivid verbal image of &quot;collapse&quot; for something that is nothing like that is not serious.
* The virus is nearly certainly going to cause &quot;mass death&quot;, as does influenza, as long as the deaths are at least in the thousands.
* The above statement is in a large font as if it was some kind of important takeaway, but this is 1) inappropriate for a scientific article, 2) as just pointed out, there is almost no takeaway but rather empty rhetoric.

2.7) Re: &quot;Put in another way: the mitigation strategy not only assumes millions of deaths for a country like the US or the UK.&quot;
* Now we also get millions of deaths for the UK, which means at least 2,000,000 (given the plural). The actual death count as of Jan 2024 is over 230,000.

2.8) Re: &quot;So once we’re done with a few million deaths, we could be ready for a few million more — every year. This corona virus could become a recurring fact of life, like the flu, but many times deadlier.&quot;
* Incredibly, we are told that because the virus is going to be highly mutable, there could be a million deaths per year, going forward indefinitely. But downwards, he states &quot;until we have a vaccine&quot;, so then, not really indefinitely.
* More on a point down below: If the virus is so highly mutable, as he says, are the vaccine makers going to be able to keep up with the new mutations?

2.9) Re: &quot;The US (and presumably the UK) are about to go to war without armor.&quot;
* Metaphors like this are a tool of political rhetoric, not science and engineering.

2.10) Re: &quot;Wouldn’t it be dumb to commit to a strategy that throws us instead, unprepared, into the jaws of our enemy?&quot;
* More of empty rhetoric.

2.11) Re: &quot;On the other, countries can fight. They can lock down for a few weeks to buy us time, create an educated action plan, and control this virus until we have a vaccine.&quot;
* It seems unlikely that one could have known that the &quot;suppression&quot; as opposed to &quot;mitigation&quot; lockdown would require only &quot;a few weeks&quot;; and in most countries that went for lockdown, it did not.

2.12) Re: &quot;What if Churchill had said the same thing? “Nazis are already everywhere in Europe. We can’t fight them. Let’s just give up.” This is what many governments around the world are doing today. They’re not giving you a chance to fight this. You have to demand it.&quot;
* More empty rhetoric with no added informative value.

2.13) There is no mention in the article that part of the confirmed case growth is due to the growth of available and performed tests.

2.14) Re: &quot;Here’s what we’re going to cover today, again with lots of charts, data and models with plenty of sources&quot;
* As with the other article, lots of charts, data and models do not establish validity.
* The article does not really present &quot;models&quot;, their analysis and validation; for instance, it derives its 10 million deaths figure with the use of model that it does not name and whose mathematical formula it does not state, merely linking to http://gabgoh.github.io/COVID/index.html. (A similar defect is in the first article). The page http://gabgoh.github.io/COVID/index.html states this: &quot;The clinical dynamics in this model are an elaboration on SEIR that simulates the disease's progression at a higher resolution, subdividing I,RI,R into mild (patients who recover without the need for hospitalization), moderate (patients who require hospitalization but survive) and fatal (patients who require hospitalization and do not survive). Each of these variables follows its own trajectory to the final outcome, and the sum of these compartments add up to the values predicted by SEIR. Please refer to the source code for details. Note that we assume, for simplicity, that all fatalities come from hospitals, and that all fatal cases are admitted to hospitals immediately after the infectious period.&quot; Directing a reader to the source code is not a proper way to specify a model for reviewers; in a properly conducted exercise, the calculation method/detail has to be available in English. Moreover, the page does not seem to link to the source code; from using Google and browsing around, one can guess that the source code is at https://github.com/gabgoh/epcalc, but the page does not seem to explicitly link there. The author of the page is Gabriel Goh[https://gabgoh.github.io/], currently &quot;machine learning researcher at OpenAI&quot;.

Overall, Tomas Pueyo cannot know all these things he is putting forth with so much confidence, and so much urgency. The article does not provide proper traceability for most of its key statements: we do not know which statement is supported by which other statements.

Could the public know the article was wrong? Public could have used its strategy of relying on properly published peer-reviewed science. People could have thought: I do not have enough expertise in reviewing epidemiological articles to find whether the modeling and calculation it uses is completely wrong. But even that is probably not quite true: even a surface review as the one above could have dismissed the article mostly on relatively easily accessible grounds. 

Instead of sounding an alarm about the article, many people endorsed the article, some collaborated on it, and some have translated it into other languages.

Why did the article need to be translated into other languages? Would it have been because political decision makers do not know English enough? A more likely explanation is that the article was addressed to the general public, which should have put pressure on politicians to adopt a suppression lockdown strategy. The tone of the article seems to be this: you, the general public, can see that the article is written with lots of data, charts and models and as you can see, its conclusions are a no brainer. You should be convinced by the superficial persuasion techniques; you do not need to be worried that you do not have the expertise to judge the matter.

===Endorsements===
The article links to a list of endorsements[https://medium.com/tomas-pueyo/coronavirus-articles-endorsements-fdc68614f8e3]. The list feature Tim Berners-Lee, Steven Pinker, and Daniel Dennett. And yet, arguably, the article should have been dismissed on relatively easily accessible grounds.

== Article: The Fail West ==
This article is covered here as something of an aside: it was not part of the two key 2020 articles with millions of viewers that probably influenced Western policy makers.

Link: https://unchartedterritories.tomaspueyo.com/p/the-fail-west; 6 May 2021

Pueyo compares the lives lost in the West with those in Asia-Pacific.

Start of the article:
: &quot;Soon, over 1.5 million people will have died of COVID in Western countries.
: &quot;1.5 million futile, needless deaths. 1.5 million wasted lives.
: &quot;Meanwhile, in a block of Asia-Pacific countries with a population over twice as big, they lost 18,000 people.&quot;

=== Issues ===
3.1) In the first half of 2021, the pandemic was far from over. It was not the time on which to do the reckoning/accounting. This is especially obvious in retrospect since we know China had its late Covid wave much later, in 2022 per [[Wikipedia: COVID-19 pandemic in mainland China]]. But it was also obvious in 2021 since it was already in 2020 that Anders Tegnell pointed out that Covid needs to be managed in the long run rather than in mere several weeks or months.

3.2) It is not clear that data collection in Asia-Pacific is comparable in its thoroughness with the West. In particular, the data from China could back in 2021 be safely assumed to be completely wrong. Even today in 2024, we do not know the covid-positive deaths from China (or do we?) and we do not have all-cause deaths for China (or do we?). By contrast, we have solid all-cause death data for the West. Thanks to Karlinsky &amp; Kobak&lt;ref&gt;https://github.com/akarlinsky/world_mortality&lt;/ref&gt;, we have all-cause mortality also from other parts of the world, including South America and Russia, but it is Asia-Pacific that is conspicuously absent from the coverage of that data set.

3.3) The folowing pleonastic statement is pure empty rhetoric or theatricals: &quot;1.5 million futile, needless deaths. 1.5 million wasted lives.&quot;. One could have as well said &quot;1.5 million lives needlessly lost&quot; and be done with it. And a life lost is not automatically a live that is futile or wasted.

A more thorough review is pending; the above issues were found in quick first-impression review.

==Responsibility==
In the subject of responsibility of intellectuals, one can ask to what degree and in what way can the author be held responsible/accountable for this kind of articles, which, given a calm analysis available in retrospect, easily fits into the &quot;spreading misinformation&quot; category.

On a tangential yet somewhat related note, those eager to censor misinformation are all too likely to censor information and let misinformation flourish. But that is for a separate debate.

==Online criticism==
Some criticism can be found in the comment sections of the articles. In so far as the author did not post replies to these comments there, he failed to address them. Should I take an imaginary role of a review moderator, I would need to prevent closure of the review since not all comments have been addressed (accepted, rejected with an explanation, etc.). The documents would need to be put into the state of review still open, not all comments processed, not ready for publication or consumption.

A 2023 critical review is Senger 2023, in further reading.

==Mainstream media==
According to fortune.com, 'Donald McNeil, the eminent health writer for The New York Times, referenced “The Hammer and the Dance.” CNN’s Anderson Cooper invited Pueyo to speak on TV.'&lt;ref&gt;[https://fortune.com/2020/08/10/the-overnight-coronavirus-expert/ The overnight coronavirus expert] by Adam Lashinsky and David Z. Morris, 10 Aug 2020, fortune.com&lt;/ref&gt;

One should perhaps not be surprised to find that mainstream media authors speak positively of things they are not qualified to properly critically evaluate. This is corroborated e.g. by the laudatory mainstream media response to lobotomy.

==Conflict of interest==
One critic pointed out that Tomas Pueyo, a stakeholder in a company publishing online courses, stands to benefit from various countries going into lockdown and the demand for these courses increasing. Could Pueyo's psyche unconsciously contribute to the mistakes and biases in his article? It seems hard to believe, but could human psyches be like that?

==Personal note==
I sent a link to Tomas Pueyo's &quot;Coronavirus: Why You Must Act Now&quot; to a family member via email. I am not beyond reproach. We are all fallible.

==References==
&lt;references/&gt;

==Further reading==
By Pueyo:
* [https://tomaspueyo.medium.com/what-you-can-do-to-curb-the-coronavirus-9f878d5982f2 How Bad Is the Coronavirus?. And Everything Else You Need to Know…] by Tomas Pueyo, 1 Mar 2020, tomaspueyo.medium.com
* [https://tomaspueyo.medium.com/coronavirus-act-today-or-people-will-die-f4d3d9cd99ca Coronavirus: Why You Must Act Now] by Tomas Pueyo, 10 Mar 2020, tomaspueyo.medium.com
* [https://tomaspueyo.medium.com/coronavirus-the-hammer-and-the-dance-be9337092b56 Coronavirus: The Hammer and the Dance] by Tomas Pueyo, 19 Mar 2020, tomaspueyo.medium.com
* [https://unchartedterritories.tomaspueyo.com/p/what-most-people-still-get-wrong What Most People Still Get Wrong About COVID Management] by Toma Pueyo, 23 Jul 2023, unchartedterritories.tomaspueyo.com
* [https://unchartedterritories.tomaspueyo.com/p/covid-end-game Coronavirus: Game Over] by Tomas Pueyo, unchartedterritories.tomaspueyo.com

Featuring Pueyo:
* [https://www.youtube.com/watch?v=C98FmoZVbjs Coronavirus special: Are we doing enough?] by Channel 4 News, 13 Mar 2020, youtube.com -- with Tomas Pueyo and John Edmunds
* [https://www.youtube.com/watch?v=m4FFNKo0kfQ Anderson Cooper talks with Tomas Pueyo on May 26th 2020 about coronavirus, opening states &amp; churches], youtube.com

Other:
* [https://brownstone.org/articles/tomas-pueyo-returns-the-mba-who-shut-down-europe-on-masks-and-the-cochrane-review/ Tomás Pueyo Returns: The MBA Who Shut Down Europe on Masks and the Cochrane Review] by Michael Senger, Mar 2023, brownstone.org
* [https://www.sheffield.ac.uk/ihuman/blog/what-does-covid-19-mean-expertise-case-tomas-pueyo What does Covid-19 mean for expertise? The case of Tomas Pueyo] by Warren Pearce, sheffield.ac.uk
* [https://www.reddit.com/r/sanfrancisco/comments/fhk4nu/coronavirus_why_you_must_act_now_tomas_pueyo/ Coronavirus: Why You Must Act Now - Tomas Pueyo - Medium : r/sanfrancisco], 12 Mar 2020, reddit.com
* [https://fortune.com/2020/08/10/the-overnight-coronavirus-expert/ The overnight coronavirus expert] by Adam Lashinsky and David Z. Morris, 10 Aug 2020, fortune.com
* [https://news.ycombinator.com/item?id=27820509 Delta Variant], Hacker News -- comments on Pueyo's article/post Delta Variant but also about his TV performance in 2020
* [https://medium.com/@StephanieMae/coronavirus-why-you-must-not-believe-everything-you-read-on-the-internet-7c3fd9c03b5b Coronavirus: Why You Must Not Believe Everything You Read on the Internet] by Stephanie Mae, 15 Mar 2020, medium.com -- an article critical of Pueyo's article, by no one of note (it seems)
* [https://childrenshealthdefense.eu/eu-affairs/a-single-man-is-behind-the-global-corona-measures-and-nobody-knows-him/ A single man is behind the global corona measures - and &quot;nobody&quot; knows him] by CHD Europe Editorial Team, 25 Mar 2024, childrenshealthdefense.eu

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This article by Dan Polansky looks at the categorical imperative, a principle devised by the German philosopher Immanuel Kant.

A motivation is that I find the principle quite interesting, with interesting applications, even if somewhat problematic and open to objections.

The imperative was given multiple formulations by Kant. I will consider above all the first formulation, which [[S:Groundwork of the Metaphysics of Morals]], translation by Thomas Kingsmill Abbott, renders as follows (Wikipedia has a minor modernization of it):
: (1) &quot;Act only on that maxim whereby thou canst at the same time will that it should become a universal law.&quot;

What I take from this is the following application, which is possibly not entirely Kantian. Let us have a situation where I am pondering an action, for which I have a rationale or urge, but am not sure of its acceptability from an ethical or quasi-ethical standpoint. Here, I intend to design a good gate: a statement allowing something. I will act on the rationale or urge only if the gate designed by me allows it. The allowance/gate shall have a reasonable universality; in particular, it is generally not allowed to arbitrarily invoke concrete individual entities, e.g. individual people (to be explained/detailed later). A key criterion on the gate is this: I must be able to support the gate's becoming a part of the physical law. If a gate is part of the physical law, no one can break it, not because there is a harsh punishment (e.g. eternal pain in hell) but because it is physically impossible.

This can be applied to a project or situation with poor or poorly defined rules. Any breaking of the rules is potentially problematic, but I can design a rule update (corresponding to that intended breaking) that I could wish to become an official rule of the project. Another problem is an action that is potentially problematic but a rule is missing. Then, I can try to figure out putative rules governing the admissibility of the action and determine whether the rules could become part of official rules.

We can make a trivial application of the imperative to what one might call contextual or situational ethics, in the context of a wiki. Let us have an editor with the right to delete pages who is pondering to pick a random/arbitrary page and delete it without any rationale or reason. The putative rule we are considering is this:
: (2) Any editor with the right to delete should feel free to arbitrary delete a page on a whim, with no deletion summary.
We immediately see that this rule is absurd. Clearly some allowances are unacceptable; no wiki could reasonably accept such a rule/allowance.

Another trivial application is to, say, stealing in a supermarket. We can again consider an absurd rule:
: (3) Any person in a supermarket (hungry, not hungry, poor, rich, etc.) should feel free to steal an item, on a whim.

One thing that makes these applications not so convincing is the triviality. At least, we have shown that situational ethics is doable and non-empty at least for some allowances/prohibitions.

Let us consider a more challenging application, by considering the following putative rule:
: (4) A person who is hungry and starving (has not eaten for days), in a country that has no food stamps and no refuge/support for such people, not even a charitable chuch support, should feel free to steal reasonable amount of food matching the needs from someone or some entity that has food in excess.
This rule violates the prohibition of stealing but is no longer patently absurd. Here, the categorical imperative does not seem to directly help, or it perhaps helps those whose ethical instincts or sensibility will reject the rule. But what the categorical imperative still does is invite rule making and principle exploration and it invites formulation of reasonably detailed principles. This we can see by omitting some of the differentiating criteria:
: (5) A person who is hungry and starving (has not eaten for days) should feel free to steal reasonable amount of food matching the needs from someone or some entity that has food in excess.
This principle is now open to objection: all hungry people in the U.S. have access to state food stamps and therefore, no one is forced by hunger to steal. We do enter the realm of rationality, of rule conjectures and refutations/criticism, even if in part inconclusive. This stands in stark contrast to an unethical position like the following: I will do whatever I want in whichever way I deem fit regardless of ethical principles or some imaginary imperatives conjured up by a continental pseudo-philosopher as long as I can get away with it, and sometimes even when I cannot entirely get away with it as long as the penalty is just the cost of doing business. Thus, for instance, if I am in the business of illegally marketing drugs/medicines off-label, I will proceed anyway and regardless of any harm to patients since any penalty the company risks incuring is handsomely compensated by profits.

I have noted that there was something contextual or situational about the ethics considered. There was no attempt to state ultimate value assumptions implied in the situation. In the wiki example: an arbitrary/whimsical deletion of a page can still be undone so does not do much harm. But it does create some overhead/disruption. The implied rule is this: do not create avoidable overheads for wiki editors and administrators. And more generally: act in such a way as not to harm objectives of the project (wiki or other project). The question why is left unanswered. Be it as it may, for many applications, situational ethics is all we need. And something like the categorical imperative is behind the idea of ethical rule making, as contrasts to unarticulated ethical intuitions. An anti-articulationist/anti-rulist could say: each situation is unique and therefore it cannot be covered by rules. We may find some tentative rules, but they are all too likely to be incomplete, reflecting our limited imagination, experience or rule-design skill. By saying so, the anti-articulationist has already entered the articulation game. A more radical anti-articulationist could just say, forget it. An even more radical one could just stay silent.

The other formulations of the categorical imperative are here left unexplored; they may be explored later.

A related subject is, based on memory, Kant's idea that all action can be reduced to fulfilling duty. If this is correct, one would no longer be just building ethical gates to block some urges/springs to action; rather, all action would be driven by maxims discovered with the help of the categorical imperative. This is left here largely unexplored.

Ayn Rand is an example of a philosopher opposed to Kant's categorical imperative. Exploring her criticism could be worthwhile.

== Further reading ==
* {{W|Categorical imperative}}, wikipedia.org
* [https://www.britannica.com/topic/categorical-imperative Categorical imperative], britannica.com
* [https://plato.stanford.edu/entries/kant-moral/ Kant’s Moral Philosophy], Stanford Encyclopedia of Philosophy

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      <text bytes="3227" sha1="r962ly0lz3iwdu79i51wuk352oju6ou" xml:space="preserve">==Alternative term: existentialism ==
(May be incorporated later; now at least on the talk page)

Instead of survival, we can talk of continuing existence, as opposed to cessation of existence. Some literature uses the phrase &quot;struggle for existence&quot;, e.g. [[S:Darwinism (Wallace)]]. Thus, instead of survivalism, we could talk of existentialism (omitting the word and concept of struggle).

Alas, the word existentialism is already in use. We would need to figure out whether the customary use of the word has any bearing on the analysis I am trying to undertake here. From reading of Britannica's article on existence, the customary use of ''existentialism'' goes into a different direction.

We could also emphasize struggle (and omit &quot;for existence&quot;), and get something like strugglism. But then, replicators do not really need to ''struggle''; they just need to do whatever it takes to be here/to have copies here, to survive adverse events.

We could also note the phrase &quot;struggle for life&quot;, used by Darwin in [[S:Origin of Species]]. We already considered the word &quot;struggle&quot;; what remains to consider is the word &quot;life&quot;. We could get &quot;lifeism&quot;, but we already have &quot;viabilism&quot;, from &quot;viable&quot;.

Links:
* [https://www.britannica.com/topic/existentialism existentialism], britannica.com

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:25, 11 October 2024 (UTC)

== Gene-survivalism ==
I am pondering what a gene-survivalism would be or what it is for a gene (actually an allele?) to survive. One could see a particular gene as a collection of all its occurrences/copies (and thus, the gene would be a type, not a token). And then, unless the gene goes extinct in the sense that it is completely eliminated from the gene pool, the gene survived. Here, one can contrast the objective of survival/non-extinction with the objective of maximizing the number of copies of the gene. The latter seems helpful/instrumental for the former, but not the same objective.

One could consider an analogy to books. The book ''Ivanhoe'' would not go extinct until all its copies go extinct/disappear. An effort to preserve the book would not be the same as an effort to maximize the number of copies in existence. That is obvious especially if one considers electronic copies as also being copies; to maximize the number of copies of ''Ivanhoe'', one could buy huge digital storage and store countless copies there. From the point of view of Ivanhoe not going extinct, that would be rather silly; one should diversify storage rather than maximizing the number of copies. And thus, some copies should be in paper, some electronic but on geographically distributed servers, etc.; the mere number of copies does not seem to be an interesting metric, from this perspective. It is not clear what the analogy for diversification would be for the gene. Perhaps the gene, to not become extinct, should geographically diversify or something; storing some copies on an isolated island is perhaps a decent idea. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:48, 28 February 2025 (UTC)</text>
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This article by Dan Polansky contains considerations concerning the design of dictionary definitions. Dan Polansky studied mathematics and mathematical fields, noted for their extensive use of definitions. Moreover, he is an experienced translation lexicographer, as for entering mappings between Czech and English into the English Wiktionary. However, this activity does not cover definition design. As a result, this article is written by someone with almost no experience in dictionary definition design.

==Dictionary definitions vs. mathematical definitions ==

Let us start by demarcating the subject from related fields. Above all, dictionary definitions are very different from mathematical definitions. In general, mathematical definitions are fairly often much longer than the short dictionary format allows. But not always; some mathematical definitions fit the dictionary format well, e.g. a definition of a prime number. Metric space is an example of a mathematical concept that fits the dictionary format relatively poorly. Moreover, dictionary defintions are ''descriptive'': they describe facts of usage. By contrast, mathematical definitions are a mixture of stipulative and descriptive. An author of a mathematical article can ''stipulate'' a definition of a term any way he wants. When that terminological choice becomes conventional, the definition becomes not only the author's stipulation but rather part of common usage and thereby ''descriptive'' of common usage. There are also ''prescriptive'' definitions, but these would require a separate investigation, and clarification whether they are the same thing as stipulative definitions. Coming back to metric space, M-W&lt;ref&gt;https://www.merriam-webster.com/dictionary/metric%20space&lt;/ref&gt;defines it as &quot;a mathematical set for which a metric is defined for any pair of elements&quot;, complementes by M-W:metric&lt;ref&gt;https://www.merriam-webster.com/dictionary/metric&lt;/ref&gt; That seems to actually do the job (needs a double check)? One can compare the definition to that given by Britannica.&lt;ref&gt;https://www.britannica.com/science/metric-space&lt;/ref&gt;

==Genus proximus vs. defining vocabulary==

Let us continue with a consideration of two different concepts: one is relying nearly exclusively on defining vocabulary, another on the Aristotelian genus-differentia definitions (genus proximus, differentia specifica). In the Aristotelian concept, one should identify the genus proximus. Such a genus should be proximal or nearby; it should not be unnecessarily distant. For example, the domestic cat can be defined as a certain kind of domestic ''feline'' animal. Here, once relates to scientific taxonomy to figure out the genus proximus (genus in the linguistic sense, not taxonomic sense; the &quot;genus&quot; can be e.g. a family, in the biological taxonomical terminology). By contrast, one can decide to base all definitions of the defining vocabulary and define cat in a way that does not depend on ''feline''. There, one would not worry about the genus being proximus but rather the genus being part of the (relatively small) defining vocabulary. But the plan to base all definitions exclusively on defining vocabulary is extremely impractical especially for trivial derivatives such as adverbs derived by affixing -ly, -ness words, agent nouns, etc. Since, to define, say, a -ly adverb, one would not in general be able to use the base adjective in the definition. A solution chosen by Merriam-Webster online is not to define trivial derivatives at all and merely list them next to the base word in the base word entry. But this is probably only one complication of using only defining vocabulary; the plan, while interesting, may prove impractical for other reasons.

==Trivial derivatives and use of macros==

We touched on the subject of trivial derivatives. For them, what I call a ''macro'' is relevant, a definition that is not really a definition proper but rather something like a macro whose expansion provides the definition proper. Let us take the word ''blueness'', defined as the quality or state of being blue. But blue in which sense? In any sense. As soon as one tries to enters a mapping to different languages (as one does in a multilingual dictionary), one sees how this breaks down: different senses of blue generally map to different translations, and therefore, there are also different mappings of ''blueness'' to words in other languages. One seems forced to split a -ness word into as many senses as the base adjective has. Merriam-Webster is a monolingual dictionary and does not have this problem; it merely lists -ness words next to the base adjectives, e.g. for ''blue''&lt;ref&gt;https://www.merriam-webster.com/dictionary/bluen&lt;/ref&gt; By doing so, Merriam-Webster avoids a massive duplication from ''blue'' to ''blueness''. In a multilingual dictionary, this duplication creates a considerable maintenance overhead: any change of definition in the base word should theoretically be reflected in the definition of the trivial derivative. A solution is to start with macros and only replace them with definitions proper as need arises, possibly even allowing a mixed state of affairs.

==Minimum definition vs. encyclopedic extension: chemical elements==

The definitions of chemical elements present an interesting question from the logical point of view and encyclopedicity: to what extent should definitions be extra-logical (extra-minimal?) and encyclopedic? This case suggests that a certain degree of encyclopedicity is unavoidable unless we want the dictionary to be quite peculiar. Since, a chemical element is identified by its atomic number and once this is stated, the definition is complete. By contrast, Merriam-Webster:gold states the atomic number but also provides some key characteristics.&lt;ref&gt;https://www.merriam-webster.com/dictionary/gold&lt;/ref&gt; A similar concern pertains to names of chemical compounds: one perhaps wants to not only identify them/define them but also characterize them. From a logical point of view and history, godl is not defined by its atomic number; rather, gold was discovered to be a chemical elements with a certain atomic number. Even gold's being a chemical element may be a discovery rather than part of the historic definition reflecting the cognitive access to gold. One is reminded of Kripke's ''Meaning and Necessity''; deeper deliberations could be picked from there.

==Circularity of definitions==

There is a concern with circularity of definitions. Circularity arises not only in a single entry but between entries. Circularity cannot be completely removed (the dependency graph needs to have something like a source or a sink, depending on which direction of the edges one considers) but it can be restricted to definitions of the ''defining vocabulary''. The defining vocabulary is a set of words such that all other words can be defined with them without any circularity. One can verify that this is satisfied by taking a candidate definition of a word outside of defining vocabulary and expanding its components until one gets a definition that uses exclusively words from the defining vocabulary.

==Basing definitions on quotations of use==

Theoretically, one determines the definitions of words with the use of citations/quotations of use. How this works is not entirely clear. But one can get an idea. Let us consider a putative word X_NOUN, knowing it is a noun. And we find the following sentence in use: &quot;X_NOUNs turned red, orange and yellow and the floor under the trees were full of them&quot;. We find an additional sentence: &quot;connifers do not have X_NOUNs&quot;. We can already guess tha X_NOUNs are leaves. This presupposes we note certain classes in the world as cognitively significant, worth tracking as classes. We track the concept of a ''leaf'' (of a tree) but not ''leaf that is on the floor, is yellow and has been split by a human in half''. Something like pre-linguistic cognitive ontology provides candidate classes, attributes, relationships, operations, etc., to the child. The child must be able to build something like an ontology (classes, attributes, relationships, etc.) even before it learns words, but maybe there is some iterative interplay, in which an initial very naive ontology gets refined by interaction with language. Be it as it may, this consideration suggests the problem of extracting semantic meaning from word usage is not entirely intractable (if it was, definition lexicography would be impossible?).

Section [[#Definitions of lay names in biological taxonomy|Definitions of lay names in biological taxonomy]] quotes a remarkably sophisticated definition of ''fish'' from M-W. It is hard to imagine this is a result of examination of ''uses'' of the word fish, let alone the English Wiktionary's required mere 3 uses.

==Word with many meanings==
Some words have great many meanings, especially some English verbs. How anyone is able to figure out and sort out all these meanings is something of a mystery.

==Duplication reduction via definition by synonym==
Another concern is with avoidance of repetition of definitions of synonyms. Here, polysemy (words genereally having multiple meaning) creates a hurdle. The modern version of Merriam-Webster online often defines senses by stating a single synonym and providing the sense number of the defining synonym. This may well be supported by a reasonably sophisticated software. It ensures excellent consistency and avoids maintenance overhead but can be rather challenging as for implementing changes. Since, once one changes the sense structure in a word used to define other words, in general, all the words depending on the defining word need to be updated. This may require something like a fairly complex change request, stating items affected, describing changes in them, etc.; or maybe the supporting software handles this in some way.

==Definition by synonym, an ambiguity==
A definition by synonym is in general problematic because of polysemy. This can be handled as mentioned above, by indexing of senses. Some Czech dictionaries sometimes define words by listing a set of quasi-synonyms; these leave a lot to wish.

==Approximate definitions vs. precise definitions==
Some definitions are probably merely approximate and not perfectly accurate. But not all: as mentioned, since a chemical element is uniquely identified by its atomic number, a definition stating the atomic number does a perfect job of picking its referent, at least in this world (as opposed to possible worlds). Moreover, e.g. defining a -ly adverb via its adjective often seems perfectly accurate; similarly for other trivial derivatives.

==Definitions of natural kinds==
Definitions of natural kinds (e.g. biological species) probably present a special problem. One has to pick the uniquely selecting characteristics but what these are may be not entirely clear and one may veer into encyclopedicity (the result is not so much a definition as characterization). And it may be unclear whether they work well across possible worlds. This would also be a problem for chemical elements (these are natural kinds) when one would not be able to use the atomic number. But one could also ask: if one picks gold by its physical and chemical characteristics, could its atomic number be different in a possible world? On the other hand, the question is perhaps a bit silly since the physical and chemical characteristics of gold are determined by the particle composition of the nucleus. One may find relevant considerations in Stanford Encyclopedia of Philosophy.

==Encyclopedicity of definitions==
One complaint sometimes raised against definitions in the English Wiktionary is that they are encyclopedic. As pointed out above in relation to chemical elements, this is better not avoided to some extent (defining via atomic number alone would work, but would be hardly reader friendly). The definition of &quot;gold&quot; in M-W veers on encyclopedic and is marvellous: &quot;a yellow metallic element with atomic number 79 that occurs naturally in pure form and is used especially in coins, jewelry, and electronic&quot;. One learns: 1) the atomic number, which would be enough for unique selection/picking out; 2) some of the physical and chemical properties; 3) the social significance. Sure enough, one does not want to have a paragraph-long encyclopedic summary instead of a definition, but the problem in such a case would be excessive length, not the encyclopedic character. A more limited definition/characterization of gold would do the job well enough, but this wealth of characterization arguably makes the definition better, not worse.

Moreover, the very concept of encyclopedicity is dubious and vague. Since encyclopedia articles often start with a definition or a characterization, there is necessariy an overlap between information found in encyclopedia and that found in a dictionary. The question should not be whether a dictionary definition is encyclopedic but rather whether it contains too much extraneous information and is overlong. The word ''encyclopedic'' seems pushed to serve this different concern (too long or detailed a definition/characterization), as some kind of shortcut label, but it creates an analytical confusion.

The point above chemical elements above applies equally well to chemical compounds, as one would expect. Merriam-Webster defines TNT as &quot;a flammable toxic compound C7H5N3O6 used as a high explosive and in chemical synthesis&quot;&lt;ref&gt;https://www.merriam-webster.com/dictionary/TNT&lt;/ref&gt;; from a purely logical point of view, the chemical formula would probably be enough for identification.

==Etymology is not semantics==
Etymology is not semantics. While it is true that something like etymological quasi-semantics is often readily available to interpret an utterance to the mind of the interpreter (if he knows the etymology, which is the case in the transparent morphology), one generally does not find this kind of quasi-semantics in uses, unless the etymology becomes lexicalized or happens to match the semantics. And there is no point in repeating etymology as a definition, or multiple definitions.

==Trivial all-sense-encompassing quasi-semantics==
Trivial all-sense-encompassing quasi-semantics is pointless to enter into a dictionary. I mean something like this: A definition of cat: &quot;Any thing labeled by the English word 'cat' in any of its senses&quot;. Yes, such a quasi-sense may sometimes be used (even if rarely) but it is entirely trivial and uninteresting. (However, such a construction can be cognitively interesting. For instance, one may learn from a German speaker that he saw a Grunzbetricht, and have no idea what that is. A report can be as follows: &quot;Person so-and-so saw what they referred to using the German word Grunzbetricht&quot;, or in an abbreviated and non-explicit form, &quot;Person so-and-so saw Grunzbetricht&quot;. Needless to say, I made the word Grunzbetricht up.)

==Sense nesting==
Nesting of senses is used in some English dictionaries online, but not by Czech dictionaries. In the English Wiktionary, this produces some really bad outcomes, by my assessment, in part since it requires talents and attention to detail that few possess. Merriam-Webster online often merely groups senses rather than nesting them; that is, if there are senses 1a, 1b and 2, there is not definition for sense 1. But sometimes even Merriam-Webster creates an outright subsense structure.

==Definitions with optional elements==
The role of &quot;especially&quot;, &quot;typically&quot;, &quot;usually&quot; etc. in definitions is unclear. From a logical point of view, it seems like nonsense: if a sign is not essential in the definition, it is not part of the selector. But it does make some sense. If we consider, say, ''bird'', this is an entity that typically can fly, even stereotypically, but not all birds can fly. Merriam-Webster's bird entry says nothing about flying in the relevant sense: &quot;any of a class (Aves) of warm-blooded vertebrates distinguished by having the body more or less completely covered with feathers and the forelimbs modified as wings&quot;. For birds, we may argue that the definition is not meant to select a bird individual (distinguish it from other biological individuals) but rather the class; and thus, if we consider the class of all birds, it is perhaps true that most individuals of that class can fly, or considered differently, most taxa within the class are flying taxa (switching from individuals to taxa can affect the effect of the word &quot;most&quot;).

==Definitions of proper names==
Definitions of proper names (proper nouns and phrases acting as them) present perhaps a special case. Some considerations are in my [[Proper name]] article. Questions that arise include: which characteristics should one pick as somehow defining an individual entity such as a city? Theoretically, stating the latitude and longitude of some time-invariant part of the city (come kind of city center) should do and the rest is encyclopedic. Do definitions of proper names tend to be encyclopedic characterizations or summaries that fail to work across possible worlds, especially in view of Kripke's ''Meaning and Necessity'' and its idea of proper names being rigid designators, standing in contrast to Russell's theory of descriptions? Should the definition be phrased as a definite description, starting with &quot;the&quot; rather than &quot;a/an&quot;? Can one use the word &quot;certain&quot; in the definition to avoid bearing the responsibility of providing a uniquely selecting criteria? Or should one take &quot;certain&quot; to be implied? Let us consider's M-W Darwin entry&lt;ref&gt;https://www.merriam-webster.com/dictionary/Darwin&lt;/ref&gt;. The leading sense says: &quot;Charles Robert 1809–1882 English naturalist&quot;. The year range is uniquely identifying, but one also wants to know that he was an English naturalist. Interestingly, no mention is made of evolution by natural selection for which he is so famous, so here, encyclopedicity is avoided. Let us look at the second definition, &quot;Erasmus 1731–1802 grandfather of Charles Darwin English physiologist and poet&quot;. Here, in contrast to the first definition, significance is indicated by the part &quot;grandfather of Charles Darwin&quot;; why is significance not indicated in the first definition? There is also a geographical name: &quot;city and port in northern Australia on Port Darwin (an inlet of the Timor Sea); capital of the Northern Territory population 103,016&quot;, which does not start with an article and thereby avoids the &quot;the&quot; vs. &quot;a/an&quot; conundrum. The statement of the precise population seems rather encyclopedic and creating maintenance overhead, which could be reduced by stating &quot;population over 100,000&quot;.

==Definitions of lay names in biological taxonomy==
There is something called ''vernacular'' names. These seem to contrast to scientific names. Lay names are either the same thing as vernacular names or not. In any case, something like lay names seem often confusingly mapped to taxa, in part probably since lay people either do not care all that much about precise biological taxonomy or they lack the requisite know-how.

Fly agaric is an example of a name that is unproblematic, mapping directly to ''Amanita muscaria''. M-W defines fly agaric as &quot;a medium to large poisonous amanita mushroom (''Amanita muscaria'') with a usually bright red cap&quot;.&lt;ref&gt;https://www.merriam-webster.com/dictionary/fly%20agaric&lt;/ref&gt;

A good example of a problematic or confusing name is missing, but based on experience from the English Wiktionary, they do exist. They would probably also be reflected in some way in Wikidata.

One slightly confusing name is &quot;fly&quot;, which, per Britannica, 1) maps to &quot;order Diptera&quot;, 2) is used &quot;for almost any small flying insect&quot;.&lt;ref&gt;https://www.britannica.com/animal/fly-insect&lt;/ref&gt;. [[Wikidata:Q859257|Wikidata:fly]] has the description &quot;common name of small flying insects, especially Diptera&quot;, which is peculiar since Wikidata items normally stand for named entities rather than names. Other such cases can be found by searching for items linking to [[Wikidata:Q55983715|Wikidata:organisms known by a particular common name]].

Fish is an example of a name that does not seem to refer to a taxon, believing Britannica, as per &quot;It describes a life-form rather than a taxonomic group.&quot;&lt;ref&gt;https://www.britannica.com/animal/fish&lt;/ref&gt; The main definition of fish given by M-W seems to be a marvel of definition engineering, suggestive of remarkable expertise: &quot;any of numerous cold-blooded strictly aquatic craniate vertebrates that include the bony fishes and usually the cartilaginous and jawless fishes and that have typically an elongated somewhat spindle-shaped body terminating in a broad caudal (see caudal sense 2) fin, limbs in the form of fins when present at all, and a 2-chambered heart by which blood is sent through thoracic gills to be oxygenated&quot;&lt;ref&gt;https://www.merriam-webster.com/dictionary/fish&lt;/ref&gt; By contrast, the English Wiktionary does with &quot;A cold-blooded vertebrate animal that lives in water, moving with the help of fins and breathing with gills.&quot; It is unclear whether fish is really a lay name/vernacular name; it is in any case a name not mapping to a taxon.

Further reading:
* {{W|Common name}}, wikipedia.org

==Duplication between perfective and imperfective==
For Slavic languages such as Czech, there is an opportunity for definition duplication between perfective and imperfective variants of verbs. One solution is to avoid the duplication and mark one of the variants as a mere imperfective (or perfective, respectively) form of the other. Thus, e.g. ''dávat'' (give) can be defined as an imperfective form of ''dát''. Some Czech dictionaries opt for duplication. However, about ''dávat'' specifically, there may be not an exact correspondence between the senses of the two forms, which may be a rationale for duplication.

==Incomplete definitions for work in progress==
For a dictionary in the making (e.g. Wiktionary), it may be sometimes acceptable to provide incomplete definitions lacking some differentia (missing genus would be suspect). This may be okay as long as it is clear which sense is meant and the only question that remains is how to best design the definition. For chemical elements, one could only state the atomic number and leave further characterization for later. For a proper name, one could only state e.g. &quot;the capital of the U.K.&quot; and leave expansion for later, e.g. to something like M-W's &quot;city and port on both sides of the Thames River in southeastern England; capital of the United Kingdom formerly constituting an administrative county; comprises the City of London (approximately coextensive with ancient Lon*din*i*um \ län-​ˈdi-​nē-​əm How to pronounce London (audio) , lən-​ \ ; population 7400) and 32 other boroughs, which together are referred to as the metropolitan county of Greater London (area 632 square miles, or 1637 square kilometers, population 8,174,000) &quot;. Although here, one may wonder whether M-W does not err too much on the encyclopedic side anyway. In the two cases mentioned, the definitions are not even incomplete from the logical point of view. By contrast, one could define a geographic name refering to many smaller places as e.g. &quot;One of multiple municipalities in the U.S.&quot; and expand that later if desired.

==Quasi-definitions of given names==
Definitions of given names of the form e.g. &quot;An English given name&quot; are arguably not definitions proper: they refer to the word itself and its function as a given name rather than providing a key for how to get to referents (a selector of referents). But it makes no sense to list all bearers of the given name, e.g. all Peters, as individual senses. A similar consideration applies to surnames, but here, one may want to list very notable bearers as senses.

==Definitions of eponymic adjectives==
For eponymic -esque and -ian/-ean/-an adjectives, one has to figure out whether to only identify the person who gave name to the adjective or whether to further characterize the matter. Thus, e.g. for ''Kafkaesque'', one can state &quot;or or relating to novels by Kafka&quot;; that is correct, but everything else has to be found out in an encyclopedia. Here, M-W does both&lt;ref&gt;https://www.merriam-webster.com/dictionary/Kafkaesque&lt;/ref&gt;: &quot;of, relating to, or suggestive of Franz Kafka or his writings&lt;br&gt;especially : having a nightmarishly complex, bizarre, or illogical quality&quot;.

To take another example, for ''Euripidean'', M-W just places the word next to the base word, Euripides, defined as &quot;''circa'' 484–406 b.c. Greek dramatist&quot;. About Euripides, we learn almost nothing.

As for ''Orwellian'', we learn a little bit more from M-W&lt;ref&gt;https://www.merriam-webster.com/dictionary/Orwellian&lt;/ref&gt;:&quot;: of, relating to, or suggestive of George Orwell or his writings&lt;br&gt;especially : relating to or suggestive of the dystopian reality depicted in the novel 1984&quot;. In what way the reality was dystopian, we do not learn. Compare the English Wiktionary: &quot;Resembling the totalitarian political methods decried in the works of writer George Orwell, particularly in the dystopian novel Nineteen Eighty-Four; characterized by use of misleading terminology, propaganda, censorship, surveillance and repression.&quot; Here, we learn a little more, without the definition thereby becoming excessively long. Needless to say, creation of such a definition/characterization is much more challenging.

A tentative reasonable approach could be this: in general, define eponymic -esque and -ian/-an adjectives merely by referring to/identifying the name-giving person, without an attempted additional characterization. In justified exceptional cases, provide a more extensive characterization. This may be the approach taken by the English Wiktionary (requires verification). This approach also seems taken by M-W as per above, although the sample taken is very small.

==Definitions of agent nouns==
An agent noun such as ''swimmer'' could be defined as follows:
* a human that swims
* a person who swims
* one who swims
The first definition restricts the subject to humans, but non-human persons (Martians, other extraterrestrial aliens, hobbits) can swim as well, so it is imperfect.

M-W defines ''swimmer'' as &quot;a person or animal that swims&quot;&lt;ref&gt;https://www.merriam-webster.com/dictionary/swimmer&lt;/ref&gt;, covering also animals. M-W does not define ''perpetrator'' but merely lists it next to ''perpetrate''&lt;ref&gt;https://www.merriam-webster.com/dictionary/perpetrator&lt;/ref&gt;.

Above, a rationale for the use of &quot;person&quot; was given, namely that there are non-human persons. However, M-W does not have a correspondingly broad sense for ''person''.&lt;ref&gt;https://www.merriam-webster.com/dictionary/person&lt;/ref&gt; For ''one'', M-W includes the sense &quot;2 a : an individual of a vaguely indicated group : anyone at all&quot;, with the example &quot;one never knows&quot;, but it is not clear whether ''individual'' includes e.g. Martian individuals.

Be it as it may, personal pronouns such as ''who'' do not only refer to human persons, but also to Martians, hobbits, etc.

For ''presenter'', the lead sense in M-W is &quot;one who presents something : a person who formally gives or bestows something (such as an award) or who brings something before the public&quot;. M-W could have used &quot;human&quot; but uses &quot;person&quot;. The M-W rationale is unclear; it is unclear whether M-W intends to include Martians under this definition.

See also [[An analysis of the concept of person]].

==The definition of human==
Let us have a look at the definition of the noun human (and German Mensch and Czech člověk) in various dictionaries, with the hope that this one case is going to reveal something about definition design.

Definitions:
* M-W: &quot;a bipedal primate mammal (Homo sapiens) : a person : man sense 1c—usually plural&quot; (there is another sense, here omitted)
* AHD: &quot; A member of the primate genus Homo, especially a member of the species Homo sapiens, distinguished from other apes by a large brain and the capacity for speech.&quot;
* Collins: &quot;You can refer to people as humans, especially when you are comparing them with animals or machines.&quot;
* German Duden: &quot;mit der Fähigkeit zu logischem Denken und zur Sprache, zur sittlichen Entscheidung und Erkenntnis von Gut und Böse ausgestattetes höchstentwickeltes Lebewesen&quot;
* Czech ASSČ: &quot;nejvyspělejší živá bytost, lidský jedinec (muž, žena nebo dítě)&quot;; &quot;rod a příslušník rodu z čeledi hominidů charakterizovaný zejména rozvojem mozku a ruky&quot;

Observations about individual dictionaries:
* M-W and AHD take a biological look and try to identify the sense with taxa.
* M-W only identifies/characterizes the taxon Homo sapiens only by &quot;bipedal primate mammal&quot;; AHD, states more distinguishing characteristics.
* Collins defines ''human'' via ''person''.
* Duden make no taxonomic statement or identification. Interestingly enough, Duden singles out moral capacity and the capacity to distinguish good from evil, a characteristic that a biologist probably would not pick?
* ASSČ first singles humans out as &quot;most advanced&quot;, a characterization that an English-speaking biologist (especially Gould) probably would not pick; it seems very non-objective/anthropocentric. ASSČ then also provides a more biological definition. It is not clear why ASSČ has two distinct definitions.

What we see above is part of the definition design space available to the definition designers. The design is not cross-culturally objectively given; rather, it reflects a certain design strategy or attitude. Moreover, for identification purposes, stating the Latin taxon name (or taxa) would suffice, but additional characterization is provided by M-W and AHD (which reminds of the consideration about chemical elements being characterized in addition to stating the atomic number).

Furthermore, we see definitions that, barring the identification with a taxon or taxa, are not going to work across possible worlds. Let us take &quot;bipedal primate mammal&quot;. It should not be too hard to a competent designer of a modern computer game (using today's high-performance personal computers) to create a human-like creature using 3D graphics that looks distinctly non-human, perhaps some kind of orc, yet apparently is bipedal, primate and mammal. AHD's definition does not save the matter; an orc is going to have a large brain and the capacity for speech. What does save the matter are the taxa as individual entities (who Latin names are considered to be proper names) whose cross-world identity is unclear and subject to philosophical discussion. By referring to taxa, the definition designer identifies humans with certain natural kinds, thereby bringing in the philosophy of identity of natural kinds across possible worlds.

==Choice of dictionary==
About the choice of the dictionary consulted: I chose M-W as a respected popular American dictionary freely available online (still copyrighted!). I could choose the British OED as another very respected dictionary, but the current online version requires a registration. I think OED2 can be found freely available online, but it is sometimes tricky to find the entries. In case of doubt, one could consult other dictionaries available from OneLook.

== References ==
&lt;references/&gt;

== See also ==
* [[Definitions/Theory]]
* [[Dominant group/Genus differentia definition]]</text>
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This article by Dan Polansky investigates the concept of person. It aims to illuminate certain quandaries. One quandary or dissatisfaction is a surprise in finding that a range of serious sources suggest that a person is by definition a human.

== Main analysis ==

Let us start with the observation that that pronoun ''who'' belongs to what are called ''personal'' pronouns. This would suggest that answers to ''who'' would be persons. If so, not only humans but also other agents capable of speech would probably be persons, including Martians, Ancient Greek gods, elves and hobbits. The need to introduce a head for possible answers to the question ''who'' could explain the introduction of the concept of person contrasting to human. This gives us the following putative definition:
* A person is an entity that can be given as an answer to a question using ''who'', such as ''who did it?''
This definition is linguistic in that it does not answer what kind of entities can be referred to as ''who'' (or ''someone'') but delegates this question to language users.

Christian God may also be thought of as a person.&lt;ref&gt;[https://www.cambridge.org/core/journals/religious-studies/article/abs/is-god-a-person/CB6CCB84D6544F2FDDDBB13582BF3199 Is God a Person?], cambridge.org&lt;/ref&gt; If so, this reinforces the idea that a person does not need to be a human. This reinforcement is there even if one is merely in doubt about God being a person; if a person were by definition a human, God's not being a person would follow immediately from definition and not be subject to analysis or debate.

The above notion that there may be non-human persons including aliens is supported by an MU School of Medicine article.&lt;ref&gt;[https://medicine.missouri.edu/centers-institutes-labs/health-ethics/faq/personhood Concept of Personhood], MU School of Medicine, medicine.missouri.edu&lt;/ref&gt;

[[Wikidata:Q215627|Wikidata:person]] could be a candidate entry for the concept. However, it traces e.g. to Library of Congress authority entry[https://id.loc.gov/authorities/subjects/sh85100163.html] that says &quot;Here are entered general works on human beings as individuals. Works, primarily of an anthropological nature, on humanity in the collective sense are entered under [Human beings.]&quot; This is not the sought broader sense.

Merriam-Webster's person entry[https://www.merriam-webster.com/dictionary/person] does not have a corresponding broader sense; its lead sense is &quot;human, individual—sometimes used in combination especially by those who prefer to avoid man in compounds applicable to both sexes&quot;. M-W's entry on the noun human features &quot;a bipedal primate mammal (Homo sapiens) : a person : man sense 1c—usually plural&quot;; this is curious since the concept of a person should rather be explicated with the help of the concept of human than the other way around.

In Google Ngram Viewer, the combination ''human person'' sees considerable use.&lt;ref&gt;[https://books.google.com/ngrams/graph?content=human+person&amp;year_start=1800&amp;year_end=2019&amp;corpus=en-2019&amp;smoothing=3 GNV]&lt;/ref&gt; But then, this implies there are non-human persons; indeed, also ''non-human persons'' sees considerable use&lt;ref&gt;[https://books.google.com/ngrams/graph?content=non-human+person&amp;year_start=1800&amp;year_end=2019&amp;corpus=en-2019&amp;smoothing=3 GNV 2]&lt;/ref&gt;.

If humans are persons, one can ask whether some non-human animals are also persons, or at least quasi-persons. For instance, chimpanzees (some of the closest human relatives) could be considered as quasi-persons. Peter Singer is a philosopher who considers some animals to be persons: &quot;Because Singer believes that animals are sentient persons and sentient person have rights, including a right to life, Singer has been an advocate for a granting a “right to life” to Great Apes, dolphins, dogs, and other species.&quot;&lt;ref&gt;[https://erlc.com/resource/what-defines-personhood/ What defines personhood?] by Ben Mitchell, erlc.com&lt;/ref&gt; This some animals encompassing concept does not seem to match the definition via ''who'' (as ''someone''); if one says &quot;someone is there&quot;, it would be surprising to learn that in fact a chimpanzee is there (similarly probably for ''who'').

Under the position that non-human animals are never persons, and assuming Darwinian theory, the concept of persons gets blurry edges. Since, there is the assumed evolutionary continuity between the non-human ancestors of humans and humans. This line of reasoning is mentioned in a philosophynow.org article.&lt;ref&gt;[https://philosophynow.org/issues/144/Nonhuman_Persons Nonhuman Persons] by Gerard Elfstrom, philosophynow.org&lt;/ref&gt; On a different note, it is not clear why a putative post-human descendant organism of humans, possibly having improved cognitive and moral faculties, should not count as a person.

In law, there is the concept of ''legal person'', which is not constrained to humans but also covers certain kinds of organizations. It would have to be clarified whether human children are legal persons; they do not have all the rights of adults.

Stanford Encyclopedia of Philosophy does not have an article titled Person.

Some concept of a person has an application in abortion debates. One position distinguishes a person from a human and argues that a first-trimester fetus does not have enough of personhood to be protected. A more radical position even distinguishes degrees of personhood after birth. See also [[Should infanticide be legal?]].

Tracing the etymology of the English word ''person'' could be interesting. M-W traces the word to words meaning mask (and other things), including Latin persona. According to Rejzek, Czech ''osoba'' traces to phrase ''o sobě'', per se or on its own; other Slavic languages have a similar word.

One related concept contrasted to person is ''agent''. For one thing, agent also refers to chemicals. For another thing, some entities in computers are called agents without much ado, whereas calling entities in computers persons would be strage, except perhaps--even if controversially--an instance of general artificial intelligence.

Webster 1913's most pertinent definition is perhaps this: &quot;3. A living, self-conscious being, as distinct from an animal or a thing; a moral agent; a human being; a man, woman, or child.&quot;&lt;ref&gt;[https://www.websters1913.com/words/Person Person], websters1913.com&lt;/ref&gt; Animals are excluded. But except for the final parts &quot;a human being; a man, woman, or child&quot;, this definition could fit a broader concept that includes Martians.

Wikipedia's definition in its Person article is this: &quot;a being who has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility&quot;. It traces to four sources. It could be interpreted as including Martians. Wikipedia also has a dedicated [[Wikipedia: Personhood]] article, much more detailed and covering much more than the Person article.

Some rivers are now being granted legal personhood status, as per [[Wikipedia: Personhood]] as well as reliable sources&lt;ref&gt;[https://www.theguardian.com/environment/2021/jul/25/rivers-around-the-world-rivers-are-gaining-the-same-legal-rights-as-people Should rivers have the same rights as people?], theguardian.com&lt;/ref&gt;. I argue that this deviates from the non-legal concept of person too far. To be a person, an entity has to show goal-directed behavior, as a minimum; rivers do not do that. The desire to protect an entity does not warrant conferring a status on that entity that is completely foreign to it.

As for the plural, the correct plural for the purpose of this analysis is persons, not people; people refers to humans.

== Applications ==
This analysis is not just a theoretical exercise but has at least the following applications:
* In the ethics of abortion of human fetuses (or babies, as the critics would have it), the contrast between a human individual and a person can be used to justify the acceptability of first-trimester abortion.
* In the ethics of animal torture and experiments on animals, claiming that some animals are persons or quasi-persons may impact the result of the analysis.
* In the definitions of agent nouns in a dictionary (e.g. doer, swimmer, experimenter, and analyst), one may want to allow non-human persons and then, if one uses the word &quot;person&quot; in the definition, one has to require persons to be possibly non-human.
* In the environmental protection, some want to expand the concept of legal person to include rivers, resulting in a certain form of protection.
* When a human is seen as possible multiple persons, the concept of a person needs to be different from the concept of a human.

== Words person and human in English ==
In English, the word ''person'' seems much more natural to refer to humans than ''human''. For instance, one would say &quot;I am not that kind of person&quot; but not really &quot;I am not that kind of human&quot;. Therefore, a dictionary would probably need at least two senses for ''person'': 1) human, 2) referent of a personal pronoun. Another word often used for humans is ''man'', which ambiguously refers to males as well as humans regardless of sex, and which seems to be often displaced by ''person''.

The U.S. constitution uses the words ''people'' and ''person'', and never ''human''.&lt;ref&gt;[https://www.archives.gov/founding-docs/constitution-transcript The Constitution of the United States: A Transcription], archives.gov&lt;/ref&gt;

== Dictionaries ==
We already covered M-W: it defines person as a human.

German Duden defines the relevant sense of ''Person'' as a human (''Mensch'') as well.&lt;ref&gt;https://www.duden.de/rechtschreibung/Person&lt;/ref&gt;.

== Google Gemini ==
Google Gemini answered the following questions in the affirmative:
* Is Sherlock Holmes a fictional person?
* Is Eru a fictional person?
* Is Bilbo a fictional person?
* Is Smaug a fictional person?
* Is Spock a fictional person?
* Are Huey, Dewey and Louie fictional persons?

The following is answered in the negative:
* Is Sherlock Holmes a person? (Dropping &quot;fictional&quot; changes the answer.)
* Is Smaug a person? (Dropping &quot;fictional&quot; changes the answer.)
* Is Scooby-Doo a fictional person? (Why? If a talking dragon is a fictional person, why not a fictional talking dog? And fictional ducks were persons above. Asking &quot;Ok. Why is Huey a fictional person (a duck) but not Scooby-Doo?&quot; does not lead Gemini to change its mind.)
* Is a centaur a mythological person?

The following is answered ambiguously:
* Is Christian God a person?
* Is Christian God multiple persons? (The answer is yet according to a certain doctrine/tradition.)

A reservation: it is not clear what conclusions one may draw from this. Generative AI is generally unreliable.

== Entity that can give consent ==
We can consider the following definition of some concept relating to the concept of person:
* An entity that can give consent.
It is not perfectly clear what give consent refers to, but it seems to exclude babies in the womb. And therefore, this concept cannot be the concept of person useful for the ethics of abortion analysis, unless one wants to grant all before-birth abortion (including late-term abortion) as freely available. This concept does include young children who understand questions being asked, as well as fictional characters (in the capacity of ''fictional'' persons) and human-like talking aliens. One would have to figure out whether it could include chimpanzees; animals cannot give consent to a verbally made proposal, but they can perhaps indicate consent in some way to a proposal made without verbal means. One would have to clarify whether &quot;give consent&quot; means &quot;give a verbal consent to a verbally formulated proposal&quot;. But then, a mute human would not be a person, unless perhaps he could write.

It is perhaps true that a human who cannot talk is seen as less of a person. This may also be true of a human whose ability to make their own decisions about themselves and their own body has been legally removed.

==Grammatical person==
A grammatical person is a distinct concept. For instance, in the sentence &quot;the sun rises&quot;, the verb ''rise'' is in the 3rd grammatical person. The sun does not seem to have anything to do with the concept of person outside of grammar. Then, one might ask why the label ''person'' is applied to the name of the concept of grammatical person. It may have to do with the three distinguished grammatical persons corresponding to I/we, you, he/she/they, all referring to persons. It is only the 3rd grammatical person that can refer to non-persons, not the 1st and 2nd person (except in poetic and similar uses, when one may address oneself to non-persons as if they were persons or let a non-person speak using I, e.g. &quot;I, the sun of the earth, herewith declare that I am the brightest and shiniest&quot;).

This ties in well to the initial consideration of persons as referents of personal pronouns. In particular, it is not suprising to see fictional characters (arguably thus fictional persons), human as well as non-human, use the words I/we, you and he/she/they in refering to themselves.

Further reading:
* {{W|Grammatical person}}, wikipedia.org

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Personhood}}, wikipedia.org
* {{W|Person}}, wikipedia.org
* {{W|Great ape personhood}}, wikipedia.org
* {{W|Environmental personhood}}, wikipedia.org
* [[Wikisource: Catholic Encyclopedia (1913)/Person]], wikisource.org
* [https://medicine.missouri.edu/centers-institutes-labs/health-ethics/faq/personhood Concept of Personhood], MU School of Medicine, medicine.missouri.edu</text>
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This article by Dan Polansky is a brief review of a self-published book ''Developing a Universal Religion'' by David Hockey, 2003. The reviewed text is currently available here: [[:File:Developing a Universal Religion Parts 1-2-3 &amp; 4.pdf]] and was previously available at [[Wikibooks: Developing A Universal Religion]]. Even if self-published, the book seems interesting enough to be reviewed.

The book's key tenet is that we should adopt as a ''surrogate'' purpose of life to &quot;support life’s continual evolution and focus upon helping it to achieve an omnipotent ability&quot;. &quot;Given that there is no detectable purpose pre-designed into life or the universe, then, if we must have one, we must adopt a surrogate. To my mind, the only viable option is to support life’s continual evolution and focus upon helping it to achieve an omnipotent ability. Such a purpose is universal and rational; it is a purpose that will last as long as life itself lasts. It accommodates the whole of life, and shows that we care about more than just our own well-being. It declares that we value life for its own sake and think little about the death that must follow, taking it simply as the price to be paid for living.&quot;

The book contains multiple questionable claims about life's omnipotent potential. Not only can life not become omnipotent but it cannot become ''nearly'' omnipotent either. To begin with, given our current knowledge, there is no chance life could ever inhabit planet Pluto and the book does not support this idea in any way; and there is no way life can spread from the Earth to the Earth's nearest star given our knowledge. One can find multiple such claims and I will quote just one: &quot;This  omnipotent  consequence  of  evolution  is  just  that—a consequence.&quot; It is trivial to come up with capabilities that life including humankind may never achieve; one needs just a little bit of imagination. The argument that our ancestors could not have imagined our present capabilities has very little force to support the idea of future near omnipotence. A relevant link is [https://www.quora.com/Is-evolution-omnipotent? Quora: Is evolution omnipotent?].

The book examines some of the ethical consequences of its proposed ultimate purpose, e.g. in chapter &quot;Killing&quot;. Its examination in unconvincing. For instance, it says &quot;The rationale for stating that it would be wrong to kill an individual is easy to state: any individual’s actions may contribute to the objective of supporting Life’s continued evolution, thus each life is valuable and should be preserved&quot;, but it is not obvious that each and every human including those severely disabled can contribute to Life's continuing evolution, so it does not follow that each human life should be preserved. Those following the stated purpose could decide to exterminate a technologically weak nation and take its resources and there is nothing obvious in the stated purpose to prevent them from doing so; the author does not seem to realize that.

The book presents a ''philosophy'' of the purpose of life and ethics, not a ''religion''. The book does not involve God or gods except that it portrays evolution and the life on the Earth as a quasi-god for being alleged potentially ''omnipotent'' and by its occasional capitalization of &quot;life&quot; as &quot;Life&quot;. It is not true that any philosophy of purpose of life is a religion and the book does nothing to distinguish itself from philosophy as a religion.

See also [[A purpose of life: The power of living things]]. The criticism contained in that article largely applies to David Hockey's surrogate purpose.

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This article by Dan Polansky looks at the problem of the arrow of time in physics.

One formulation of this problem is this: since physical laws are symmetric as for the arrow of time, why is it that we see arrow of time in events? Put differently, why is it that we can distinguish a movie played forward from a movie played backward?

A first response is this. Is it really true that all fundamental physical laws are symmetric? Among the currently recognized fundamental forces/interactions, there are repulsive forces. And a repulsive force does not seem to be symmetric as for the arrow of time. To see this, let us consider two material points located at a certain distance (not mass points since we make no assumption about mass and gravitational force) and let there be a single force only, a repulsive force. Let them be stationary, not moving. Let us press &quot;play&quot; on a simulation. Then, the repulsive force makes the two points move apart. At no point in time does this change: they will keep moving apart indefinitely. And then, anyone seeing a movie of the two points will be able to tell whether the movie is being played forward or backward. The situation changes with a mixture of attractive and repulsive forces, but it is not clear that the result will be symmetric in time given the presence of at least one repulsive force. (To be more specific, two electrons are subject to repulsive electromagnetic force. So are two protons; they are kept together in an atomic nucleus by an attractive force stronger than the repulsive electromagnetic force.)

The above paragraph is now criticized at the talk page, [[Talk:One man's look at the arrow of time]]. The criticism points out that the apparent detectability of the arrow of time (direction of the movie replayed) is there only if we know the initial condition of the system. As for a system that combines, say, the repulsive electromagnetic force on two electrons and the attractive gravitational force, this would require a closer look, but if we believe the sources that say that the fundamental laws are symmetric in time, one would assume the result to be that one cannot detect the direction of the movie either.

It can be admitted that simulating only the gravitational force for two points will lead to symmetrical behavior. This is so if we assume that the two points cannot touch, having no extension (extension would be explained by something like a repulsive force). Thus, initially, the two points do not move and are at a distance, then, they accelerate toward each other, and then they slow down again until they end up with zero velocity and their original locations swapped. Then the behavior gets cyclic. The behavior is perfectly symmetric in time. This reminds of a different thought experiment: one drills a hole through the Earth and lets a body drop into the hole. The body accelerates toward the center and then decelerates, ending up at zero velocity at exactly the opposite point. This, of course, assumes that the Earth is perfectly symmetric along the drilling axis and that the center of the Earth is solid (and therefore fit for drilling a hole), which is probably not the case. (The accuracy of this paragraph is now challenged at [[Talk:One man's look at the arrow of time#Two initially not moving Newtonian point masses approaching their mutual center of mass]].)

The above consideration was for two points but we can also consider multiple points subject to gravitational force. This then seems related to the three-body problem ([[W: Three-body problem]]). One would have to figure out whether this is really symmetric in time or whether the points being more than two make a difference.

Another formulation of the problem of the arrow of time concerns only thermodynamic systems. This is technically a different problem. The formulation can be this: the microscopic laws of statistical thermodynamics are symmetric in time. How does it happen that the macroscopic classical thermodynamics has the second law? A response is this. Is it really true that the microscopic laws are symmetric, given repulsive forces are at play at microscopic level? But my understanding of the technicalities of this problem is possibly poor, and there could be something to render this response invalid. Be it as it may, a problem concerning a purely thermodynamic system cannot have a direct bearing on a cosmological problem of arrow of time since the world has the gravitational force, which is not represented in a purely thermodynamic model.

There is some talk about tendency of increase of entropy in relation to the arrow of time. First of all, this is merely a tendency, not an inexorable law of increase. Moreover, we need to consider which concept of entropy we are dealing with since there are multiple of them. In the context of thermodynamics, this could be thermodynamic entropy, either classical thermodynamic entropy or statistical thermodynamic entropy.

We can also investigate an increase of mixing entropy, a different concept. Let us consider a pack of cards. Let us consider the ordering of colors to define the mixing entropy (we do not consider the other values such as king vs. queen to avoid the charge that ordering of these is arbitrary). Let the cards be initially ordered by colors, that is, there is a sequence of cards of one color, then the second color, etc. Let us consider the mixing operation of swapping two randomly chosen cards. By iterating this operation, the system will tend to move away from the initial state. But if we wait long enough, it is very likely (nearly certain) to eventually return to the perfectly ordered state in terms of order of colors. The arrow of time is given in the thought experiment; it is not something that we detect by measuring the mixing entropy increase. But let us suppose that there is a mechamism that allows some entity to revert the arrow of time, in the sense that there will be a undo. But it is not known when or how often such an intervention occurs. And let us only be able to observe the sequence of the states of the system. Then, we could indeed try to infer that such intervention is happening by oserving a suspect decrease of entropy such as a move from a well mixed state to the perfectly ordered state by a minimum length sequence of swaps. Here, we still have the observer's arrow of time fixed, but we emulate something like another arrow of time by representing the undo intervention. Then, it would make sense to think of an observer trying to detect whether the arrow of time is being swapped. On the other hand, a particular sequence of swaps leading to a perfectly ordered state is as improbable as any other particular sequence of swaps. This could shed doubt on the observer's ability to detect the undo interventions. It is perhaps something of a puzzle.

We can consider another discrete model of entropy, that of Kolmogorov complexity of a sequence of zeros and ones. Let the system with a state of length n start at all zeros and let each change in state consist in a random flip of a randomly chosen bit. Then, as time passes, it seems that the system will tend to move away from all zeros or all ones. However, Kolmogorov complexity (the length of the program generating the sequence) stands in sharp contrast to Shannon entropy, which is probabilistic. It is not clear how a theorem about a tendency of increase of Kolmogorov complexity in the our system would look like (especially how to specify what &quot;tendency&quot; means), whether there is such a theorem and which sources cover it. There is a related stackexchange.com question.&lt;ref&gt;[https://physics.stackexchange.com/questions/606778/is-the-universes-kolmogorov-complexity-growing-over-time Is the universe's Kolmogorov complexity growing over time?], physics.stackexchange.com&lt;/ref&gt;

Concerning time being part of space-time and therefore something like an analogue of a space coordinate, Popper points out that the axis of time is clearly given while no particular axis (there are three of them) of space is clearly given. This does not concern the ''arrow/direction'' of time, though, so is perhaps something of a tangent. Esfeld 2005 discusses Popper's views on the arrow of time.&lt;ref&gt;[https://www.researchgate.net/publication/36444442_Popper_on_irreversibility_and_the_arrow_of_time Popper on irreversibility and the arrow of time] by Michael Esfeld, 2005&lt;/ref&gt;

My tentative take, one that I cannot formally substantiate, is this: the physical time has the same direction as the psychological time (but not the same rate of flow). There is no need to try to track the direction of time using some quantity or characteristic of the world. A characteristic of the word can have a tendency to change in a certain direction as the time passes, but this does not define the arrow of time, and merely tends to be associated with it.

But from a different angle, something like the initial question has not been answered: what is it about the world we are living in that makes movies played forward so different from those played backward? This question does not question the existence of the real arrow of time independent of states of the world; it nonetheless puzzles about the kind of changes that happen in time. This apparent phenomemon is detectable without considering chemistry, biology or sociology; physics alone will do. Since, we can observe a piece of rock fall onto the Moon, but we do not expect a rock lift from the surface of the Moon.

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Arrow of time}}, wikipedia.org
* {{W|T-symmetry}}, wikipedia.org
* [https://iep.utm.edu/arrow-of-time/ The Arrow of Time], Internet Encyclopedia of Philosophy
* [https://plato.stanford.edu/entries/time-thermo/ Thermodynamic Asymmetry in Time], Stanford Encyclopedia of Philosophy
* {{Cite book|title=[[W:Time Reborn|Time Reborn]]|last=Smolin|first=Lee|year=2013|publisher|Houghton Mifflin Harcourt|isbn=978-0-547-51172-6|title-link=W:Time Reborn|author-link=W:Lee Smolin}}</text>
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      <text bytes="5444" sha1="rzqxku8vpf5ei0fjheth5btc1585wqu" xml:space="preserve">== Repulsive electromagnetic force and two electrons ==
(To be incorporated later in some form.)

In the article (later to be corrected), I considered a thought experiment in which we have two electrons and only the electromagnetic force, no other forces, especially no gravitational force and no other attractive force. (Electromagnetic force can be attractive e.g. for an electron and a proton, but not for two electrons.) As the initial state, I took the electrons to be at rest (zero velocity) and at a fixed distance, say, 1 meter. Then, as I let the system develop in time (or press play/run on a simulation), the electrons start to move away from each other and never return. I thought this shows an arrow of time: if the electrons are moving away from each other, the film someone took of them is moving forward, if they are moving toward each other, backward.

But this seems wrong. It is true if we fix the ''initial condition'', that is, if we know that the system (or our little universe) started with the two electrons being at rest. But how can an observer know the initial condition? If we, by contrast, assume the initial condition to be unknown, the film being played backward seems plausible/compatible with the repulsive force. Since, the film starts with the electrons moving toward each other with a non-zero speed (their speed vector is exactly the opposite of the one at the end state of the simulation run forward) and they slow down as a consequence of the repulsive force, eventually becoming at rest, which is where the movie played in reverse ends. (If this continued, which is not part of the reverse movie, they would start moving away from each other.) Thus, the observer does not know that the movie is being played backwards. But if the observer knew the initial condition was the two electrons being at rest, the observer would in fact know: it would be impossible for the electrons to find themselves moving toward each other.

As an aside: if we take time to have a start and no end, then a system with an initial condition of the two electrons moving toward each other will spend only finite time in them moving toward each other but infinite time in them moving away from each other. An observer whose goal would be to determine the unknown direction of the film could argue that it is much more probable for electrons to be moving away from each other than toward each other, and that if we see electrons moving toward each other, our best guess (if we have to make it) is that the film is moving backward.

Not knowing the initial condition is plausible enough if we consider the observed system to be a universe, something causally isolated from everything else (but still being able to be observed). If we take humans as observers of our universe, we are observing the universe process somewhere in the middle; we do not ''directly'' observe or know the initial condition.

This thought experiment is made using classical physics: the two electrons are electrically charged infinitely thin points (having no extension) having a precise location in space; there is no Einsteinian/relativistic limit on velocity and there are no quantum mechanical effects. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:33, 31 October 2024 (UTC)

==Two initially not moving Newtonian point masses approaching their mutual center of mass==
I am now unclear about what happens to two initially not moving Newtonian point masses, both having the same mass. For instance, let them start 1 meter apart at rest, each having the mass of 1 kg. They start moving toward each other, but what happens as they approach their mutual center of mass? From the formula of the Newtonian gravitation force, the force would approach infinity as the points approach each other, and thus, the acceleration would approach infinity. It seems that the moment of meeting would be some kind of singularity. It is not clear to me whether this would result in arbitrarily large speeds near the shared center of mass. (I am not that good at calculus and systems of continuous time, having studied computer science and not physics at a university level.)

Of course, real particles have also electrical charge, and there are repulsive forces that get very strong as particles get very close to each other. Moreover, Newton is superseded by Einstein. And perhaps the concept of a particle is not particularly apt either and should rather be replaced with something like an entity with a dual particle-wave character, and quantum mechanics should kick in. But that is not the analytical exercise here. The question is what happens in a purely Newtonian system that has only the Newtonian force. Thus, in a sense, the question is more mathematical than physical.

Links:
* {{W|Two-body problem}}, wikipedia.org
* [https://physics.stackexchange.com/questions/113660/infinities-in-newtons-law-of-gravity-for-point-particles newtonian mechanics - Infinities in Newtons law of gravity (for point particles)], physics.stackexchange.com
* [https://physics.stackexchange.com/questions/126675/singularity-in-newtons-gravitational-law newtonian gravity - Singularity in Newton's gravitational law], physics.stackexchange.com

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:14, 3 November 2024 (UTC)</text>
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      <text bytes="17690" sha1="tphltm6zvntpcsmaoycurhonw58wn0b" xml:space="preserve">==Reinhold Messner==
(Perhaps to be incorporated later.)

I must have heard Reinhold Messner, perhaps at Markus Lanz, state something to the effect that he is mountain climbing since it is most meaningful (something like ''sinnvollste'') while at the same time most useless (something like ''nutzloseste'') (the German spellings may need checking).

One can find Messner talk like this: &quot;It’s the conquering of the useless.&quot;&lt;ref&gt;https://www.forbes.com/sites/jimclash/2014/09/24/reinhold-messner-on-his-legacy-climbing-is-the-conquering-of-the-useless/&lt;/ref&gt; Similar language is used in an Independent article.&lt;ref&gt;https://www.independent.co.uk/life-style/reinhold-messner-mountaineer-b2422306.html&lt;/ref&gt;

I find this idea interesting, though from a logical point of view, I have some doubts about it. He also must have said something to the effect that he goes to places where he can die not to die. He uses the words ''Grenzgang'' and ''Grenzgänger''&lt;ref&gt;https://reinhold-messner.de/de/lebenspanorama/der-grenzgaenger/&lt;/ref&gt;.

A question for generative AI: What does Messner say about the most useless while most meaningful?

References:
&lt;references/&gt;

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:38, 3 November 2024 (UTC)

==Whence the concept of life program==
I wondered where I got this concept of life program from, including the name for the concept.

One candidate is Eric Berne, who speaks of ''life plan'', also known as ''script''. And as a computer programmer, I easily interpret ''script'' as a certain kind of program (as in Unix shell script), although that is not necessarily what Berne had in mind. I seem to recall Berne speaks of ''parental programming''.

Moreover, I seem to recall the phrase ''životní program'' (life programs) being used in a Czechoslovak film whose screenwriter could have been Zdeněk Svěrák. I seem to recall that the film makes fun of someone who lives their life in a very planned way, someone working as a computer programmer. I would need to check.

One could make a Google search for Czech ''životní program'' and figure out the life of this phrase. It could be used quite differently from English life program; perhaps it does correspond to ''life plan''.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:05, 22 November 2024 (UTC)

==Well-being==
Interestingly, ''well-being'' is not mentioned. On the other hand, happiness and pleasure are mentioned. But well-being can be contrasted to happiness. If, say, someone has an early stage of cancer and does not know that, they may be happy (ignorance is bliss), but they are not ''really well''.

Relating to well-being is health, which is mentioned. Also related is psychological well-being, which is not mentioned; one could perhaps claim psychological well-being is same thing as happiness, but that would require more carefully analysis.

There is an implied contrast between well-being and well-having. Of course, one can proclaim having to be a species of being, as in &quot;having X&quot; is &quot;being an entity that has X&quot;; still, this can be probably dismissed on grounds yet to be articulated and a contrast can still be maintained.

Another contrast could be between well-being and ''well-feeling''. Thus, one would argue that to ''be well'' and to ''feel well'' are different; one who has an early stage of cancer without knowing it is not really well, but they may still feel well. Under this interpretation, well-being is something more substantial (whatever that means) than well-feeling. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:36, 25 November 2024 (UTC)

==Immortality==
Immortality is not mentioned. It may be because such an objective may have seemed to me not to be taken seriously. From a gene-copying Dawkinsian perspective, it may even seem absurd: the genes &quot;care&quot; about being copied from a body to a body, not about immortality of the individual body.

1) The direction of immortality is the same as longevity. And longevity is now covered.

2) If one takes one's children to be quasi-identical to oneself (or some other weakening or alienating prefix other than quasi-), one can aim in the direction of immortality by aiming at having children, grandchildren, etc. Someone might want to invent a cloning device, to achieve genetic identity (since he would be dissatisfied with the loss of genetic identity resulting fom genetic recombination). The doctrine of quasi-identity seems peculiar or bizarre, but perhaps someone may want to adopt it anyway.

3) Some people such as Hans Moravec seem to want to achieve extreme longevity by uploding themselves into human-like robots. More such people are featured in the film [[W:TechnoCalyps]]. See also [[Mind Children]].

4) Some may consider immortal fame to be a form of immortality. One can think in this way: the spirits of Ancient Greek philosophers are still with us. They get activated or strengthened whenever someone reads their works. I have some qualms with this line of reasoning, but let it be mentioned nonetheless. Immortal fame is now covered in &quot;Fame&quot; section.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:13, 29 November 2024 (UTC)

==Nature preservation==
This item is not covered. It perhaps did not seem like a candidate ''ultimate''. But if one considers a multi-element, eclectic life program, nature preservation can well fit in. One can perhaps ask why one would go for nature preservation, but in a sense, no such question is allowed concerning ultimates. Alternatively, one may consider nature preservation to be not an ultimate aim but rather an intermediate one, relating to causing irritation in someone who cares about it; and thus, actions aiming at nature preservation would be certain kind of hedonic actions.

Nature preservation includes preservation of both living and non-living nature. Perhaps paradoxically, Mars colonization is at odds with nature preservation, since Mars as it naturally is would be turned into something created artificially. Similary, turning deserts into gardens would be destruction/elimination of the natural form known as desert.

Nature preservation includes protection of biological species and biodiversity.

If one would aim at nature preservation and nothing else, extermination of humankind could be seen as a good plan. Thus, a curator of a natural museum could be happy, figuratively speaking. But a curator of the museum of arts or such would not be amused. What we currently have on Earth is results of both natural creativity and artificial creativity (this terminology may need clarification). Nature preservation as the sole objective disregards the latter as valuable.

This subject should perhaps be explored much deeper. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:24, 29 November 2024 (UTC)

== Negentropy and life as that which feeds on negative entropy ==
A key item is the power of life. In the section on the definition of life, there is &quot;OR life based on silicon digital storage, including robots&quot;. That is very uncustomary use of the word life. It seems rather unfortunate.

No serious genus-differentia definition of life is attempted or investigated. It seemed like a good idea back then, but now it looks like a deficiency. It is perhaps no way to do serious philosophy. On the other hand, one can argue that serious definitions or attempted characterizations of life are in online encyclopedias and do not need to be repeated here.

One characterization of life is from Schrödinger: that which feeds on negative entropy (see also [[W:Entropy and life]]). Popper criticizes this definition. (See also [[Technology as a threat or promise for life and its forms]].) It seems reasonable to reject this definition of life as leading to uncustomary results and uncustomary use of the word life. Nonetheless, it seems to be a definition of ''something''. We could call it negentropic system. This would lead to another item, the power of negentropic systems. Or it could be maximum negentropy generated by negentropic systems, if that makes any sense.

This deliberation or a similar one could have lead to the name Extropy, used by the Extropy Institute. The relating subject labels are transhumanism and posthumanism. A relating film is TechnoCalyps. I must have read in some analysis that it seems as if the transhumanists or posthumanists plan or want to turn the universe into a huge supercomputer. Put differently, they want to turn it into a huge pattern machine that can emulate sort of anything and thus, on the pattern level, save anything real and represent anything imaginary (see also [[Mind Children]]). Of course, not anything, since &quot;anything&quot; refers to too many patterns.

Another word that comes to mind is universalism, whatever that means outside this context. It seems that ''life'' is not broad enough for the taste of some; they want something broader, more general. The most general concept seems to be entity, but I have no idea what entitism would be.

Coming back to whether including robots as alive is too unconventional, some media seem to disagree. After all, &quot;Number Five is alive!&quot;, Short Circuit (1986) says. Nonetheless, it now seems to me that this extension of the concept of life is analytically fragile and unfortunate. One should use the word quasi-life if one has to go in that direction, but perhaps even that is too suggestive of life.

A major problem with these entropy-relating deliberations seem to be that entropy is not a single thing/concept and that thermodynamics does not capture the whole of physics, e.g. gravitational forces.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:47, 29 November 2024 (UTC)

See also [[One man's look at extropianism]]. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:53, 24 August 2025 (UTC)

== The implicit goal of survival ==

As for:
: &quot;Implicit in emotional goals is the goal of survival, which has shaped the process through which the parts of the brain responsible for the creation of emotions came about. The goal of survival as implicit in emotional goals is however twisted by suboptimal and only seemingly adaptive evolutionary process&quot;

That is incorrect or misleading. Let us consider the following candidate implicit goal specifications/descriptions:
* survival
* survival and reproduction
* reproduction
* copying one's genes
* having one's genes copied 

The final item seems to be most accurate. Adding reproduction to the picture is important, unless one claims that it is not the survival of the individual but rather e.g. of the species. But the latter is implausible per Dawkins.

We may perhaps even drop survival and only keep reproduction alone. That is, the purpose of survival would be to make sure one can engage in reproduction. But that is greatly oversimplified. At the end of the day, the implied purpose is that of making sure one's genes get copied down the generations, which includes not only concieving children but also protecting children, helping them to have their children, helping one's relatives to have children, etc.

The last two items are nearly the same. The item &quot;copying one's genes&quot; is suggestive of direct reproduction; by contrast, &quot;having one's genes copied&quot; points to alternative ways of having one's genes copied, e.g. by means of close relatives. And thus, by supporting close relative reproduction in some way down the generations, one supports the gene copying game.

I plan to modify the text accordingly but I need to figure out how to best do it. In the mean time, the defect description stays on the talk page.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:07, 24 February 2025 (UTC)

== The use of imperative ==
I now see the use of imperative as problematic. For instance:
: &quot;At some point of time, all the living things on Earth are going to die. At that point, the game of life will be over. But so far, the game of life is on. Go and play it.&quot;
I need to figure out whether to leave it as is or make some corrections. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:03, 26 February 2025 (UTC)

== Travel randomly around the United States ==
(An anti-plagiarism measure.) I have this idea from a theatrical play whose name I don't remember. From what I remember, in that play, a philosopher wants to demonstrate he has a free will by travelling randomly around the U.S. (He proves nothing of the sort, of course.) The play was played in some American military facility in Heidelberg, Germany; the group could have been called Roadside Theater. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:24, 28 February 2025 (UTC)

== Prosperity ==
Prosperity is not mentioned as an element of a life program. This is odd/suspect.

There is the following statement:
: &quot;Unfortunately, those old, simplistic parts are poor at distinguishing between information relevant to survival and prosperity and information that just appears to be relevant.&quot;
The statement implies that if entertainment is not instrumental to ''survival and prosperity'', it is thereby ''unfortunate''. The element of ''prosperity'' comes out of the blue; it is not anywhere else in the text.

Elsewhere, the claim is made that survival is an implied objective, but there is no mention of ''prosperity''.

On a different note, there is the phrase &quot;live long and prosper&quot;, apparently linked to a Vulcan salute. This phrase is used in John Walker's '''The Hacker's Diet''. If Vulcans are an epitome of rationality, it would imply that not one's survival, not having one's genes replicated but rather longevity and prosperity could be the rational ultimate objective. That this is not covered in the text in some form seems to be a defect.

On the other hand, there is the element of &quot;wealth&quot; mentioned. However, one would have to clarify whether wealth and prosperity is the same thing. Moreover, if one does conclude that wealth and prosperity are the same thing, the word &quot;prosperity&quot; should at least be added as a synonym to &quot;wealth&quot;. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:55, 1 March 2025 (UTC)

I now think that the word &quot;prosperity&quot; should be covered. If it is proposed to be just a synonym for wealth, it should be said explicitly. The word prosperity does appear in political &quot;programs&quot; (which is how we call manifestory in Czech) and it is quite plausible someone would want to incorporate into a life program. Perhaps the Czech word &quot;prosperita&quot; is more prominent in Czech than the English &quot;prosperity&quot; in English? I would have to find out.

For the time being, there is [[Wikipedia: Prosperity]], an article different from [[Wikipedia: Wealth]]. And there being two articles reinforce the idea that a separate section is worthwhile. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:31, 1 September 2025 (UTC)

== Einstein ==
In section Values of Philosophers, there is no mention of Einstein. That is perhaps a pity; he is not only a scientist but also something of a philosopher. See also [[User:Dan Polansky/Blog#Einstein about Jews]]. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:59, 10 April 2025 (UTC)

== The prominence of the power of life over matter ==
The life program ''the power of life over matter'' is prominent in the text. That does not match the book title &quot;Crafting Your Life Program&quot;.

I do not know how to fix this defect. One option would be to excise/remove this item from the book or to greatly reduce its prominence, but it is a key element of the book; it is one of the things the book is about. It sometimes happends that book titles show a poor match to content such as the famous 1974 novel ''Zen and the Art of Motorcycle Maintenance'' (ZMM). One can object that ZMM is a novel, unlike the present book, and a novel has more of an artistic license in title design. Right. Oh well. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:33, 13 April 2025 (UTC)

== Human vs. agent ==
Parts of the text use the term ''agent'' as more generic, parts use ''human''. The text should ideally be reviewed for the use of the term human to check whether it would be more appropriate to make the sentence more generic, by using agent. Surely not only humans but also entities that bear some resemblance of humans (persons? agents?) could host/execute a life program, e.g. extraterrestrial aliens with executive and cognitive capabilities similar to those of humans or better. World's mythologies feature all sorts of beings with such capacities as well, e.g. the Ancient Greek mythology. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:52, 14 April 2025 (UTC)</text>
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This article by Dan Polansky investigates what is ethics. An inspiration for this article is a suspicion that the subjects that Aristotle deals with in his Nicomachean Ethics are rather different from those usually considered to be the subjects of ethics in, say, the 20th century. (If someone wants to use this page title, the article can be moved to &quot;One man's look at what is ethics&quot; or &quot;What is ethics (Polansky)&quot;.)

== Initial considerations ==

Some questions asked by Aristotle:
* What objective do all human activities aim at?
* Is political life better than philosophical life?

Some questions asked by a differently scoped ethics:
* Is intentional killing of a human ever justified and why?
* Is theft ever justified and why?
* Under what conditions is lying permissible/acceptable, if ever?
* Is torture of animals inadmissible, and if not, why not?
* Is destruction of natural heritage inadmissible, and why?
* Are there positive ethical duties (duties requiring a positive action rather than abstinence from action), e.g. to try to save a drowning human?

The second set of questions could also be rephrased as: what is unethical and why? Since, the way the word ''unethical'' is usually used seems to point to the second set of questions rather than the first set.

If this analysis is correct, we get the strange situation that the name used by Aristotle in his work, of Ancient Greek origin, is now used in its Anglicized (and Germanized, etc.) form to refer to an inquiry that is quite different from Aristotle's inquiry.

We may further advance this inquiry by listing some of the key words/concepts with which ethics is or can be concerned. These can be above all good vs. bad and right vs. wrong. As a crude approximation, we may match good vs. bad with the first set of questions and right vs. wrong with the second set of questions. But once we introduce the word ''morally'', it may be hard to distinguish ''morally bad'' from ''morally wrong''. We can add admissible vs. inadmissible for disambiguation: right vs. wrong may pertain to e.g. a result of calculation, a different matter.

Ethics can be hard to delineate/distinguish from politics. Since, is the question whether first-term abortion should be legal an ethical or political one?

The above separation of questions can be perhaps captured as ''pull vs. gate''. Most people aim at various things (own health, own happiness, own wealth, etc.) but then are constrained by the means admissible in reaching these aims. The things aimed at (e.g. riches) are the pull, the constraints imposed are the gate. (Instead of ''pull'', we could say ''push'', but that is a terminological choice of little consequence. A cart is pulled by a horse, not pushed, and whether the cart can pass through a gate depends on the gatekeepers.)

== Key concepts ==
Let me single out some key concepts and words naming them of which the language of ethics could consist:

Adjectives:
* good and bad
* good and evil
* right and wrong
* admissible and inadmissible
* praiseworthy and blameworthy
* commendable and despicable
* desire, desirable
* valuable and worthless (I don't think so, but a candidate it is)

Nouns:
* action
* thought
* desire
* will
* outcome
* state of affairs

Verbs:
* seek vs. avoid
* praise vs. blame
* approve of vs. disapprove of
* love vs. hate
* prefer vs. disprefer

== Wittgenstein ==
Wittgenstein's Lecture on Ethics provides one hint on what ethics could be. Wittgenstein first quotes Moore as saying that &quot;Ethics is the general enquiry into what is good.&quot; But Wittgenstein has a broader conception: 'Now instead of saying &quot;Ethics is the enquiry into what is good&quot; I could have said Ethics is the enquiry into what is valuable, or, into what is really important, or I could have said Ethics is the enquiry into the meaning of life, or into what makes life worth living, or into the right way of living.' This broader conception can well be contrasted with an enquiry into admissibility and thus better matches the fist set of questions (those of Aristotle) than the second set of questions.

Further reading:
* [https://www.wittgensteinproject.org/w/index.php/Lecture_on_Ethics Lecture on Ethics - The Ludwig Wittgenstein Project]

== Inquiry into duties ==
One conception of ethics could be as inquiry into duties, both negative and positive duties. There would be duties not to murder, not to steal, not to lie (with exceptions), to try to save a drowning person, etc. There is even a word for that, ''deontology'', from Ancient Greek ''deon'', ''deont-'', obligation, necessity&lt;ref&gt;AHD&lt;/ref&gt;. And then, we could use that word instead of ethics. We could have e.g. &quot;medical deontology&quot; rather than &quot;medical ethics&quot;. And to be briefer, we could have ''medical deontics'', or in English, ''medical dutylore''. However, one can object that this is too narrow conception of ethics and that there is also consequentialism, an approach to ethics different from duty ethics.

== Inquiry into oughts ==
One conception of ethics could be as inquiry into oughts. This can turn out to be the same as inquiry into duties. Per M-W, the noun ought means &quot;moral obligation : duty&quot;.&lt;ref&gt;[https://www.merriam-webster.com/dictionary/ought ought], M-W&lt;/ref&gt; However, M-W auxiliary verb section covers not only obligation but also advisability, which could perhaps be interpreted as pointing to the distinction drawn out in the initial consideration. That section further covers epistemic (knowledge-relating) oughts, which do not belong to ethics.

The word ''ought'' features in Hume's is-ought distinction.

An auxiliary verb similar to ''ought'' is ''should''. A stronger verb is ''must''. A contrast can possibly be made, since ''should'' can possibly be interpreted weakly, as &quot;you (ideally) should not but you can&quot;. In particular, &quot;you must not murder&quot; (rule?) seems perhaps more convincing than &quot;you should not murder&quot; (recommendation, hint?).

== Inquiry into good and bad ==
One conception of ethics could be as inquiry into good (into what is good). This would perhaps fit customary usage if we limited the inquiry to good action, good conduct, good character, good person and good life. By contrast, the inquiries called ethics did not seem traditionally interested in what is e.g. a good knife (approximately, is instrumentally good for cutting) or good medical treatment (approximately, is very likely to improve health). This limitation could justify the terminological choise of ''ethics'' as relating to character, but this would require clarification. Even so, if the name of the field should be inquiry into ''good character'', one could incorporate the Greek word for good into the field name.

This inquiry would leave aside the contrast of right vs. wrong, focusing instead on good and bad.

== Inquiry into right and wrong ==
One conception of ethics could be as inquiry into (or study of) right and wrong. As pointed out in section [[#Britannica online|Britannica online]], one differentiator is missing, that of ''morally'' right and wrong vs. ''legally'' right and wrong. This line of inquiry seems to point to the second set of questions set out in the initial deliberation rather than the first set of questions, and thus, to duties and inadmissibilities. Since, it seems implausible that Aristotle's question whether philosophical life is better than political life is a question about whether, say, philosophical life is wrong. On the other hand, one could charge that philosophical life is wrong since it is a life of idle inquiry that does not meaningfully contribute to the community or polity.

== Inquiry into value ==
One might think ethics could have something to do with value. In [[An analysis of value]], I suggested that the adjective ''valuable'' could be reduced to the adjective ''good'', by this: X is valuable to the degree to which it is good to have. This reduction does not indicate semantic identity between valuable and good; there is a difference between ''is good'' and ''is good to have''; for instance, a knife that is good may be good to have or one may be indifferent since one already has enough good knives.

Ethics does not seem to be an empirical inquiry into the behavior of prices and other exchange rates; that is a subject to economics.

== Etymology ==
Following the etymology of the word ethics, it would be an inquiry into character, or characterology. But that is not what ethics is. Be it as it may, we may wonder whether matters would be improved if we replaced the label ethics with a label that better captures the investigated subject. Thus, if ethics is the inquiry into what is good, we could find an Ancient Greek word for good and make an -ology out of it. On the other hand, physics does not suffer from being an inquiry into nature by its name, while in fact excluding biology, an inquiry into living matter.

Other related words whose etymology can be of interest are ''moral'' and ''morality''. ''Moral'' is from Latin mōs, mōr-, custom&lt;ref&gt;[https://www.ahdictionary.com/word/search.html?q=moral AHD]&lt;/ref&gt;. Some sources indicate these words resulted from translation of Ancient Greek ethicos or something of the sort; needs a clarification and verification.

We can as if tap on the concept of ''custom'' (mentioned above) and see what we can get from it in relation to ethics. For one thing, it seems implausible that unethical/immoral would simply mean ''uncustomary'' (deviating from custom); surely various uncustumary behaviors are not bad enough to be generally considered immoral [an uncustomary use of brackets is {uncustomary enough} without being &lt;immoral&gt;, as confusing as it may be]. Moreover, in a tribe that practices cannibalism or infanticide, that practice being customary would not lead the Western speakers to conclude that that it is therefore morally admissible/morally right. (One may ponder whether the proverb &quot;When in Rome, do as the Romans do&quot; captures a moral principle or rather an immoral one, as in, when in Nazi Germany, do as the Nazis do, i.e. kill the Jews. On the other hand, we can provide a harmless variant or explanation: following local customs that violate no ethical norm is often advisable since it provides various benefits. For instance, in Italy, they have the custom of speaking Italian and speaking to them in good Italian can often be beneficial.)

== Moral philosophy ==
Some sources indicate that ethics is also known as moral philosophy.&lt;ref&gt;[https://www.britannica.com/topic/ethics-philosophy ethics] by Peter Singer, britannica.com&lt;/ref&gt;&lt;ref&gt;[https://researchguides.library.wisc.edu/c.php?g=178198&amp;p=1487671 General Philosophy : Ethics (Moral Philosophy) and Value Theory], wisc.edu&lt;/ref&gt;&lt;ref&gt;[https://www.bbc.co.uk/ethics/introduction/intro_1.shtml BBC - Ethics - Introduction to ethics: Ethics: a general introduction], bbc.co.uk&lt;/ref&gt; However, SEP's Moral Theory article indicates a possible contrast between the concepts of ''moral'' and ''ethical''.&lt;ref&gt;[https://plato.stanford.edu/entries/moral-theory/ Moral Theory], SEP&lt;/ref&gt; There is a related Stack Exchange question, in which some indicate equivalence and some difference.&lt;ref&gt;[https://philosophy.stackexchange.com/questions/297/what-if-anything-is-the-difference-between-ethics-and-moral-philosophy terminology - What, if anything, is the difference between ethics and moral philosophy?], philosophy.stackexchange.com&lt;/ref&gt; A related article is Britannica's What’s the Difference Between Morality and Ethics?.&lt;ref&gt;[https://www.britannica.com/story/whats-the-difference-between-morality-and-ethics What’s the Difference Between Morality and Ethics?], britannica.com&lt;/ref&gt;

== Britannica online ==
According to Britannica online (article by Peter Singer):
* &quot;ethics, the discipline concerned with what is morally good and bad and morally right and wrong. The term is also applied to any system or theory of moral values or principles.&quot;

This definition uses the word &quot;morally&quot;, presumably to differentiate. Thus, it is not any inquiry into good vs. bad and right vs. wrong but only specifically about what is ''morally'' relevant. However, the definition does nothing to define the word ''morally''. The use of the word ''morally'' appears somewhat circular; if we replace ''morally'' with its arguable synonym ''ethically'', we get that ethics investigates certain ethical matters, to which I say, sure thing, but what is meant by ''ethical''? One might add that the word ''moral'' was created as a Latin calque of the Greek root of ''ethical'' (sources to be provided). Whatever is meant by ''morally'', the need for differentiation is easy to discover: something can be ''legally wrong''--illegal, against the codified law--and at the same time ''morally right''. For an extreme example, a country can codify mass killing of certain human population groups into law, which makes that mass killing legally right, but nonetheless morally wrong.

Expanding on the above, we could start with the concept of ''legally wrong'' (being against the law) and try to derive ''morally wrong'' from it. We will need the concept of celestial (otherwordly) lawmaker, known as God. Then, something is morally wrong if it is prohibited by the celestial lawmaker, so it is ''celestially legally wrong''. This conception seems to point to the second set of questions indicated in the initial deliberation rather than the first set.

Greater clarity is brought by the following paragraph:
* How should we live? Shall we aim at happiness or at knowledge, virtue, or the creation of beautiful objects? If we choose happiness, will it be our own or the happiness of all? And what of the more particular questions that face us: is it right to be dishonest in a good cause? Can we justify living in opulence while elsewhere in the world people are starving? Is going to war justified in cases where it is likely that innocent people will be killed? Is it wrong to clone a human being or to destroy human embryos in medical research? What are our obligations, if any, to the generations of humans who will come after us and to the nonhuman animals with whom we share the planet?

The paragraph makes it clear that Singer's conception of ethics encompasses both sets of questions that we set out at the beginning as distinct, contrasting, or well separable. On one hand, it asks e.g. if we possibly should choose our own happiness as an (ultimate?) aim. On the other hand, it investigates whether it is sometimes admissible to be dishonest. As a point of doubt, it is not clear that the second set of questions above is &quot;more particular&quot; than the first set of questions. As a further doubt, the question about war could well be ranked as politics rather than ethics since it is a decision to be made by a polity.

== Britannica 1911 ==
Britannica 1911 gives us the following sentences that define or characterize ethics:
* &quot;ETHICS, the name generally given to the science of moral philosophy. The word “ethics” is derived from the Gr. ἠθικός, that which pertains to ἦθος, character.&quot;
* &quot;In its widest sense, the term “ethics” would imply an examination into the general character or habits of mankind, and would even involve a description or history of the habits of men in particular societies living at different periods of time. Such a field of study would obviously be too wide for any particular science or philosophy to investigate, and moreover portions of the field are already occupied by history, by anthropology and by the particular sciences (e.g. physiology, anatomy, biology), in so far as the habits and character of men depend upon the material processes which these sciences examine. Even philosophies such as logic and aesthetic would be necessary for such an investigation, if thought and artistic production are normal human habits and elements in character. Ethics then is usually confined to the particular field of human character and conduct so far as they depend upon or exhibit certain general principles commonly known as moral principles. Men in general characterize their own conduct and character and that of other men by such general adjectives as good, bad, right and wrong, and it is the meaning and scope of these adjectives, primarily in relation to human conduct, and ultimately in their final and absolute sense, that ethics investigates.&quot;
* From the above paragraph, let us single out the following: &quot;Men in general characterize their own conduct and character and that of other men by such general adjectives as good, bad, right and wrong, and it is the meaning and scope of these adjectives, primarily in relation to human conduct, and ultimately in their final and absolute sense, that ethics investigates.&quot;

There is more relevant material in the linked article. Here, we find the words mentioned in some of the above sections: good, bad, right and wrong, put in relation to human conduct.

Let us consider another quotation:
* &quot;When ethical speculation first begins, conceptions such as those of duty, responsibility, the will as the ultimate subject of moral approbation and disapprobation, are already in existence and already operative. Moral philosophy in a certain sense adds nothing to these conceptions, though it sets them in a clearer light.&quot;
This seems to read as an inquiry into duties and therefore the second set of questions from the initial deliberation rather than the first, Aristotelian, set.

Links:
* [[Wikisource: 1911 Encyclopædia Britannica/Ethics]]

== Aristotle's Nicomachean Ethics ==
Aristotle's Nicomachean Ethics sets out at least part of its inquiry rather clearly:
* &quot;If, then, there is some end of the things we do, which we desire for its own sake (everything else being desired for the sake of this), and if we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain), clearly this must be the good and the chief good. Will not the knowledge of it, then, have a great influence on life? Shall we not, like archers who have a mark to aim at, be more likely to hit upon what is right? If so, we must try, in outline at least, to determine what it is, and of which of the sciences or capacities it is the object. It would seem to belong to the most authoritative art and that which is most truly the master art.&quot;&lt;ref&gt;[[Wikisource: Nicomachean Ethics (Ross)/Book One]]&lt;/ref&gt;

Following this, ethics would be an inquiry into that which we (humans?) desire for its own sake rather than as a means for something else. And a label for this sought item would be &quot;chief good&quot;. (But what if all or most of our ''desires'' are bad or wrong? Would that which we desire for its own sake still be the chief good? But that is something of an aside; the subject of inquiry has been suggested clearly enough.)

Further reading:
* [[Wikisource: Nicomachean Ethics (Ross)]]
* [https://plato.stanford.edu/entries/aristotle-ethics/ Aristotle’s Ethics], Stanford Encyclopedia of Philosophy

== See also ==
* [[Ethics]]
* [[Introduction to ethics]]

== References ==
&lt;references/&gt;

== Further reading ==
* [https://www.britannica.com/topic/ethics-philosophy ethics] by Peter Singer, britannica.com

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This article by Dan Polansky looks at what is called generative artificial intelligence (GenAI) and large language models (LLM). Examples include ChatGPT, Gemini, Copilot and LLaMA.

== Introductory considerations ==

There are benefits, there are risks and there are costs.

An immediately obvious risk is inaccuracy. GenAI can easily generate inaccurate/untrue statements. This can be mitigated by awareness of the user. After all, users need to learn critical attitute toward sources that they read anyway; GenAI is far from the only offender as for being source of untrue statements.

A benefit is the use of GenAI as a source of ideas to be indepedently examined or verified. One use of this is for initial statement verification/probing: one can e.g. ask 'Is the following accurate: &quot;Adjectives are never capitalized in English.&quot;' and have the statement corrected. However, the above mentioned risk really needs an emphasis. It seems all too easy and tempting to trust the answer without independent verification.

One may wonder whether GenAI can be used as a form of psychotherapy. A remarkable feature is the limitless patience shown in answering questions, even stupid or annoying questions. One can practice asking questions, improving formulations of questions, thinking critically about the answers, etc.

GenAI can be charged to contribute to global climatic change via electricity use. The ethics of this aspect is for each prospective user to consider; governments have not prohibited GenAI for this reason and seem unlikely to do so, provided they did not for the most part even prohibitd cryptocurrency/cryptoasset mining. A serious analysis of this aspect would include a quantitative comparison of other dispensable uses of energy such as video streaming.

GenAI can also draw/paint/create images based on verbal description. For this use, the label large language model seems misleading or inaccurate, on the face of it.

Interestingly, GenAI seems rather inapt in even trivial calculation, as per Edmund Weitz video.

Tools providing complementary facilities to GenAI are e.g. Wolfram Alpha and Desmos Calculator. It would be interesting to see what would happen if one could somehow integrate genAI with e.g. Wolfram Alpha, that is, when genAI would delegate computational assignments to Wolfram Alpha (or equivalent).

One can ask whether the label generative artificial intelligence is appropriate. That is, one can ask whether this really is an intelligence, one that is artificial and generative. Very superficially, something suggestive of human verbal intelligence is there. Moreover, given the term artificial general intelligence (AGI), we may use the term artificial intelligence much more broadly to include specialized problem/task solving, and then, chess playing would be artificial intelligence. Generative artificial intelligence may even approach passing the Turing test. Paradoxically, the responses from GenAI are too fast to be human, which betrays the artificial origin. Be it as it may, GenAI does not really seem to understand what it is saying; but then, as a sinister note, too many humans speak as if they did not understand what they are saying either. And then, one may wonder whether part of the human brain does not really implement something like GenAI (such an idea is found e.g. [https://www.linkedin.com/pulse/why-you-more-like-genai-than-think-less-so-geoffrey-moore-gdxnc here]).

As for the mechanism of function, sources seem to indicate that textual GenAI just tries to determine the next word given the sequence of words (using artificial neural networks). I struggle to find this plausible and to understand how that principle could possibly produce the kind of behavior that we see, but what do I know. I would find it much more plausible if somewhether in the guts of textual GenAI, there would be something like OpenCyc ontology.

As for plagiarism. It seems to me that GenAI generally commits plagiarism: it does not attribute the sources from which it takes ideas. Plagiarism is not the same concept as copyright violation. Plagiarism is the use of ideas obtained from sources without attribution and presenting them as one's own. Some form of plagiarism is perhaps widespread anyway; attributing all ideas to sources seem to be a rather stringent requirement. One defense could be this: GenAI does not represent to have any ideas of its own; it attributes all ideas to sources, albeit unspecified ones. But from what I understand, failing to specify sources from which ideas are taken is still plagiarism. See also [[One man's look at copyright law]].

A terminological note about so-called hallucination. To label factually incorrect text as hallucination is to create a disanalogy to human psychology. Since, in human psychology, hallucinations are distinguished from delusions, hallucinations referring to sensory perceptions. More fit would be the label delusions. One could object that in humans, delusions are beliefs. But then, the external observer registers delusions merely by means of verbal behavior, so the label delusion seems good in application to textual artifacts.

Subjective assessment: I increasingly think that GenAI is pure genius, an incredible tool. It has to be used with great caution: one has to understand that the material may be incorrect and often is. On the other hand, it is perhaps good that one gets trained to read text critically, which one is sort of invinted to by GenAI. Many humans, including some academics, seem much worse than GenAI in their production of incorrect material and statement. As an aside, it seems to me that formal logical inference is leading us toward perfect knowledge (and via it, we are becoming more like God), whereas the artificial neural network is adding more of which is humanly frail, creating something that is very powerful while in some ways as stupid as human; and that I find scarry. (Although creating perfectly reasoning very powerful entity is also scary; it could well show no mercy with humans.)

== Abuse mode ==
I grew suspicious of the polite and praiseful mode in which Google Gemini comments on my writing when I propose it for consideration. To get a different result, I prefaced the writing with this:
: &quot;Can you comment of the following in something like an abuse mode, perhaps inspired by a Monty Python sketch?&quot;
The result is just perfect! The apparent wit of this mere machine is incredible.

== Mathematical calculation ==
The pure LLM technology had difficulty performing general simple calculation, e.g. multiplication of two arbitary integers, per Weitz video. That is, it have slighly inaccurate answers.

However, Gemini 2.5 Flash, when asked whether it can accurately calculate, responds that it can, by means of invoking Python interpreter. And when I asked it to multiply two specific arbitrary integers, it yielded a correct answer, part of which was a quasi-button &quot;Show code&quot; and it shows Python code.  I asked about &quot;sin(0.123456)&quot; and it gave an accurate answer to 5 decimal digits, and when asked for more digits, it gave the same answer as my local Python installation, 0.12314263218744217.

== Non-determinism ==
Gemini 2.5 Flash is non-deterministic in that the same prompt yields slightly different answer even when started from a new session. In the same session, it is more understandable that the same prompt, used successively, yields slightly different answers.

For instance, I asked 'What does &quot;2+5&quot; mean?' The two responses were somewhat different. They differed not only in wording but also in typography: the first response used &quot;2+5&quot; (using double quotes) while the second used '2+5' (using single quotes). One difference in wording was &quot;is a mathematical expression&quot; vs. &quot;a simple mathematical statement&quot; (I would not call this expression a statement). I asked &quot;Is it really a statement?&quot; and the response was '[...] Technically, no, it is not a &quot;statement&quot; on its own. It is more accurately called a mathematical expression.'

== Linguistic morphological analysis ==
I asked this: What are the morphemes in inscription? Gemini gave an interesting answer, breaking it down into -in, -script- and -ion. But run second time, it yielded -in + -scription, which I do not find compelling. It yields more morphemes when prompted. Online dictionaries with etymology usually do not provide this morphematic analysis. (It is also quite possible that serious linguistic literature rejects this morphological analysis as naive.)

== Authorship ==
''Old text:''

I sense that GenAI is an author or quasi-author, not the person providing the prompt. It may not be so from the copyright law standpoint, but it seems to be that way to me. GenAI is not a person, but perhaps it is a quasi-person. It is any case a very new kind of entity, not present in the ancestral(?) environment in which humans and their brains evolved; it is quite possible that we have an innate concept of person that works well with humans but not with these kinds of machines.

In cases where GenAI happens to quote a source word for word or very closely, the author is the source. See also the Wikidebate on whether GenAI engages in copyright violation.

''New text:''

The use of GenAI raises new or not so new questions on authorship. The idea that a human person who gave a two-sentence prompt (or a single word!) is somehow the author of the two-paragraph response seems absurd to me. I sometimes try to give a paragraph to GenAI and it expands it greatly; that I should be the author seems absurd. From what I understand, the author of text is the one who makes it into tangible form, with a specific formulation; the ideas themselves are not protected. This leads to some quandary in the context of lexture notes: as long as the student does not take notes word-for-word accurately, he is the author from the standpoint of the copyright law (AFAIK). Here, the author of the formulations is the GenAI, not the prompting human. Sometimes, as pointed out in the New York Times lawsuit, the author is someone else, as when GenAI is prodded/prompted to quote nearly word for word accurately from a source. But in no case is, in my view, the prompting human user an author.

But isn't GenAI a little like a human who has read ideas in literature and presented them in their own words? Except that GenAI has much better reading memory than humans? Why would then a human stating things based on literature an author? From the point of view of ideas/propositons/etc., the literature-informed human is not the author, but that is not the view of copyright law. From the point of view of the concept of plagiarism, a literature-informed human reporting only based on literature without indicating the literature is a plagiarist. Thus, lists of literature at the end of a book (e.g. the long one in Hofstadter's GEB) are there not only as a further reading but also as a anti-plagiarism exercise.

Then again, when GenAI does not quote word-for-word from its sources, is it the author of the text it outputs? I would think so. Except that copyright law does not recognize GenAI as a person and authors are persons? In the U.S. copyright law, authorship can be assigned to organizations (e.g. FSF; also work for hire is perhaps assigned to the employer corporation) and that is not really a person, certainly not a human person. It seems to me that GenAI should be construed as a quasi-person, as a person for the purpose of copyright law. That is going to require a change of law. In the Czech copyright law, there is something called &quot;moral rights&quot;, the right to be recognized as the author (this is not in the U.S. law, I think). In that sense, anyone who uses GenAI and claims the authorship of the output as if violates the Czech copyright law, except that the Czech copyright law probably also does not recognize GenAI as a person. What seems quite likely is that there arises something like a limbo, a new situation brought about by technology that was not envisioned by the drafters of the copyright law, and if it was envisioned, the problem was deferred for later.

There is a somewhat similar case of someone generating an image of the Mandelbrot set. The real author is the computer algorithm (not the computer); the human merely picks coordinates, zoom level, iteration count and color scheme. When someone uploads such an image to Commons, there would probably appear some license, implying that the uploader is the author with the right to give license. But perhaps the real author is realy the pair of the human and the computer algorithm. The system consisting of the human, the computer and the software really is like a cyborg, an entity to be analyzed as a single item/object showing authoring behavior. One may object that the computer is merely like a painter's canvas and paintbrush. But the computer is so much more; it is a machine that, when powerful enough, is capable of emulating the behavior of pretty much any system in the world, with some level of accuracy (beware of chaos). A computer is nothing like a simple tool such as a paintbrush. I would therefore maintain the idea of the cyborg as a good idea or idea worth considering for the analysis.

== Impersonation and identity theft ==
It seems to me that GenAI provides good (instrumetally good, not non-evil!) tools for scammers or agents to engage in impersonation and identity theft, using information that is available online about someone, and then providing an immitation, pretending to be someone who they are not. It seems their ability to scour(?) many pages and somehow aggregate them into a style could come in handy; for a human, it would take much more effort (but still doable).

As a test, I asked Google Gemini: &quot;Who is KYPark as a wiki user?&quot; I got a response. I then asked &quot;Can you tell me more about him and his philosophy?&quot; I got even more detail. I found the characterization quite compelling, based on my memory of KYPark from Wiktionary. Interesting.

I went ahead and I asked &quot;Who is Dan Polansky as a wiki user?&quot; I got a response that provided pretty accurate information based on my self-reports online.

Needless to say, if an agent (e.g. of a secret service) has deep interest in impersonating someone based on their online record/manifestation, they will be able to do so even without GenAI. But GenAI seems to make it so much easier for a range of nefarious actors (scammers, etc.)

See also [[IT Security/Threats/Social Engineering]], [[IT Fundamentals/2014/Security]] and [https://en.wikiversity.org/w/index.php?search=Impersonation&amp;title=Special%3ASearch&amp;go=Go search for impersonation].

== Ethical and unethical uses of GenAI ==
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One ethical (or deontic?) concern is the energy burned by the GenAI servers (the machines). If one takes that concern seriously, one must not use GenAI and that's it. But there is the idea that one cannot really by onself impact overall use and that one should not penalize oneself to no real effect. A similar consideration applies to various personal/individual approaches to environmentalism.

Another concern is that some people with apparently poor command of English (or other language) and poor command of the subject under discussion try to compensate for it by using GenAI to write for them. A problem is that they are typically not able to understand what part of the output is accurate and what isn't and there may be trouble with the organization of the material. And it is quite dubious to think that they are somehow authors of the GenAI output (are they perhaps &quot;auctors&quot; is some sense?).

The above concern pertains not only to, say, articles and non-discussion web pages but also to discussions and interactions. GenAI seems able to help produce material that is rather voluminous and irrelevant or marginally relevant to the discussed subject. GenAI cannot often compensate for a fundamental lack of understanding on part of its user.

A clear concern is with spammers, scammers, illicit fraudsters trying to get overtly unfair, especially financial, advantage. In a sense, something like their intelligence is rather augmented/amplified.

Some of the uses that I find ethical is help with a translation from a different language (but here are risks as well) and formulation, as well as idea discovery. I am uncomfoirtable using whole sentences produced by GenAI: they are not my own.

== See also ==
* [[Should Wikiversity allow editors to post content generated by LLMs?]]
* [[Wikiversity:Artificial intelligence]]
* [[Motivation and emotion/Assessment/Using generative AI]]

== Further reading ==
* {{W|Generative artificial intelligence}}, wikipedia.org
* [https://www.youtube.com/watch?v=medmEMktMlQ ChatGPT und die Mathematik] by Edmund Weitz, youtube.com (in German)
* [https://www.youtube.com/watch?v=5cYYeuwYF_0 ChatGPT und die Logik] by Edmund Weitz, youtube.com (in German)
* [https://meta.stackoverflow.com/questions/421831/temporary-policy-generative-ai-e-g-chatgpt-is-banned Policy: Generative AI (e.g., ChatGPT) is banned], meta.stackoverflow.com

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This small article by Dan Polansky looks into the acceptability of the use of the Church-Turing thesis in mathematical proofs in theoretical computer science. Some of these proofs can be characterized as a &quot;proof by Church's thesis&quot;.

The initial consideration or complaint is this. The Church-Turing thesis is not a mathematical theorem. It is an empirical hypothesis. There is a strict separation of the epistemology of mathematics and the epistemology of empirical sciences, such as physics. The universal physical laws are never certain; they are open to refutation/falsification by a later experiment. By contrast, mathematical theorems are conclusively proven to be true. To incorporate the Church-Turing thesis into a mathematical proof as if it was a lemma is to disrupt the purely mathematical character of the proof. It opens the proof to a risk of later refutation: should someone succeed to refute the Church-Turing thesis (and why should not they, given it is an empirical hypothesis), the refutation is going to impact all the putatively mathematical proofs that depend on it. Formally, this is an unacceptable state of affairs. The resulting enterprise cannot be certified as mathematical; the proofs are not math-worthy. (This is a pun on airworthiness and certification in aerospace industry; see e.g. &quot;Airworthiness Certification of Aircraft | Federal Aviation Administration&quot;&lt;ref&gt;https://www.faa.gov/aircraft/air_cert/aw_cert&lt;/ref&gt;.)

That is all fair and nice. But it is extremely impractical. Let us consider the theorem that a set that is recursively enumerable and whose complement is also recursively enumerable is thereby actually recursive (fully decidable rather than merely semidecidable). The proof is straightforward: there must be a program generating the set and a program generating the complement and all one has to do to obtain the decision procedure is to run them in parallel and soon enough, the input is going to be found either in the output of the first program or the second program. We get that the set is recursive (fully decidable). This tacitly assumes the Church-Turing thesis or something similar. Without it, one would have to proceed as follows. The set is recursively enumerable. Therefore, there exists Turing machine T1; and for the complement, there exists Turing machine T2. We will now construct Turing machine T3, including its states, transition rules, etc. It would be extremely laborious. And it is very likely to fail to illuminate anything of interest.

The initial complaint is what I raised with my teachers when I studied computer science at a university. The response to it is what I now think is quite reasonable. But the response points to the distinction between the empirical physics and the allegedly non-empirical mathematics being perhaps not as deep as one thinks, on some level. The statement that, say, theorem T1 was correctly proven by means of proof P1 has in principle certain degree of tentativeness. P1 was verified by mathematicians M1 through Mk, but they could all have been wrong. There some kind of cognitive empirical element even in mathematics. A similar point was made in Imre Lakatos in his ''Proofs and Refutations''. That said, the initially highlighted epistemic distinction between mathematics and empirical sciences is not to be abolished. Rather, one has to explain why the quasi-empirical character of mathematics does not abolish the distinction. And this story shall also be told. (End of the movie, music by Basil Poledouris playing.)

== References ==
&lt;references/&gt;

== Further reading ==
* [https://math.stackexchange.com/questions/1255803/whats-the-significance-of-the-church-turing-thesis What's the significance of the Church-Turing Thesis?], math.stackexchange.com
* [https://plato.stanford.edu/entries/church-turing/ The Church-Turing Thesis], Stanford Encyclopedia of Philosophy
* [https://www.researchgate.net/publication/320979910_Church-Turing_Thesis_in_Practice Church-Turing Thesis, in Practice] by Luca San Mauro, 2018, TU Wien

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This article by Dan Polansky looks at the philosophy of the Czech environmental philosopher Josef Šmajs. Šmajs is notable enough to have a Czech Wikipedia page and to be recognized by Gemini; moreover, multiple academic authors refer to him as per further reading.

Initial questions:
* What writings by Šmajs are available online, to serve as the basis for analysis?
* What articles about the philosophy of Šmajs are available online?
* What key concepts are introduced by Šmajs?
* What theories or doctrines are promulgated by Šmajs?

Articles are listed in the further reading. Some are in Czech, some in English.

== Initial observations ==

Šmajs introduces the key concept of ''evolutionary ontology'' (''evoluční ontologie''). I failed to figure out what he means by that. He does not seem to constrain the term evolution merely to replicator-based processes such as biological and cultural evolution; he also speaks of evolution in other contexts (example quotation to be added). One can ask whether there is some relationship to Hegelian dialectics.

Šmajs is concerned with destruction of environment by humans and with the risk of human extinction. He seems to believe that non-human biological entities should have some of the human rights.

Šmajs seems to suggest that a solution of environmental problems is to be sought more in what he calls ''společenské vědy'' (social sciences) than in physical and other natural sciences. Into ''společenské vědy'' (social sciences) he seems to include philosophy, a classification not matching the usual Anglophone one, by which philosophy is not a social science but a branch of humanities. He seems to be saying that the solution is to be found by philosophy.

Šmajs seems to use the term culture (''kultura'') to refer to totality of all currently human cultures. He posits a contrast of nature vs. culture. He seems to see culture as &quot;predatory&quot;, or at least today's culture. It is not clear whether his use of the term matches customary uses in Anglophone cultural anthropology. One sentence suggests that culture is the same thing as technosphere: &quot;Člověkem vytvářená globální kultura – planetární technosféra – se totiž osamostatňuje, vymyká se lidským záměrům a střetává se starší, svébytnější a sofistikovanější planetární biosférou.&quot;&lt;ref&gt;[https://www.blisty.cz/art/77197-filosoficky-koncept-ustavy-zeme.html Filosofický koncept Ústavy Země] by Josek Šmajs, 2015, blisty.cz&lt;/ref&gt;

== Nature vs. culture ==
Šmajs presents culture as being pitched against nature. I am not clear this is the best approach. My Popper-inspired approach is that of technosphere vs. biosphere. There are two key differences:
* It is unclear why the entity of concern should be culture rather than technology. Since, pre-technological cultures of humans did not seem to significantly impact the natural environment. Pre-technological would mean pre-fire. Even medieval cultures (and thus agricultural ones) were unable to cause the scale of destruction matching the industrial societies. Moreover, and that is perhaps not so important, a lay person will perhaps not readily understand the concept of ''culture'' that Šmajs invokes, which includes technology as it part. When Popper speaks of ''Technik als Kulturfaktor'' (or something of the sort), he does not take technology to be automatically part of culture, or else his point would trivially follow from definition. This is especially clear in Czech context; one would be surprised to find a technological museum under the head of ''Dům kultury'' (house of culture).
* It is unclear that the concept of nature--any nature--is the best pick for the conflict to be analyzed. Popper analyses technology as pitched against the ''grüne Natur'', meaning biological nature. And ''biological nature'' is the one that seems most gravely impacted by the industrial civilization. That is to say, for one thing, extraterrestrial nature (galaxies, etc.) is not impacted almost at all (one could count near-Earth space debris as extraterrestrial impact, though). And even terrestrial non-biological nature sees relatively little impact from industrial technological societies; there are quarries and reservoires, but they do not seem to achieve a scale that would mean anything like a grave destruction of landscape.

On the other hand, Šmajs does use the technosphere vs. biosphere contrast in the title &quot;Dokážeme smířit technosféru s biosférou?&quot;&lt;ref name=smirit2014&gt;[https://www.blisty.cz/art/74861-dokazeme-smirit-technosferu-s-biosferou.html Dokážeme smířit technosféru s biosférou?] by Josef Šmajs, 2014, blisty.cz&lt;/ref&gt;. Therefore, the issue raised (about nature vs. culture) applies to some of his writing but not all of it.

== Culture being predatory ==
As for the culture being predatory, it is unclear why that alone should be a bad thing: predatory relationships are widespread in biological nature. Thus, a tiger eats an antelope, but that does not make the tiger bad. Sure enough, there are problems with the technosphere in relation to biological and other nature, but it is unclear that the concept of predation is the best one to point to these problems, or even an applicable one. One can admit that the word predatory is often used pejoratively to refer to certain social interpersonal phenomena deemed harmful or unjust. But that does not seem to be the phenomenon under discussion; rather, culture or technosphere is described as predatory in relation to nature. Thus, to make a wooden chair from a cut tree is to be predatory with respect to that tree. But from an environmentalist perspective, a culture that makes wooden pieces of furniture and wooden houses, even if it is &quot;predatory&quot; with respect to the trees, does not on this account alone present an environmental problem.

== Predatory spiritual paradigm ==
Šmajs talks about ''predátorské duchovní paradigma'' (''predatory spiritual paradigm'' per Šmajs 2013&lt;ref&gt;[https://www.degruyter.com/document/doi/10.2478/s13374-013-0144-2/pdf HOW WILL THE PROMETHEAN MYTH END?] by Josef Šmajs, 2013, degruyter.com&lt;/ref&gt;). The translation of ''duchovní'' as ''spiritual'' may be imperfect; it stands in contrast to ''duševní'', ''mental''. It remains to be figured out what, if anything, is this predatory spiritual paradigm, and what makes it ''spiritual''. (As an aside, ''paradigm'' is an overused sociological buzzword originally stemming from Kuhn's classic ''Structure of Scientific Revolutions''. From what I recall, Ms. Masterman identified 21 meanings/ways in which Kuhn used the word.)

== Ontic ==
Šmajs uses the word ''ontický'', which could be rendered into English as ''ontic''. M-W defines ontic as &quot;of, relating to, or having real being&quot;.&lt;ref&gt;[https://www.merriam-webster.com/dictionary/ontic ontic], merriam-webster.com&lt;/ref&gt; I am struggling to make sense of Šmajs' sentences using the word. The Czech word ''ontický'' is absent from Czech dictionaries PSJČ and SSJČ and is absent from the website IJP. It would seem reasonable to require Šmajs to define the term (given the absence in dictionaries), but he does not seem to do so. cojeco.cz defines ''ontický'' as 'spekulativní pojem německého filozofa M. Heideggera označující vše, co náleží „jsoucnu“, na rozdíl od pojmu „ontologický“, jímž vyjadřuje vztah k „bytí“'&lt;ref&gt;[https://www.cojeco.cz/onticky ontický], cojeco.cz&lt;/ref&gt;. If Šmajs has this meaning in mind, he would do well to say to.

== Exploitation of natural forces ==
Šmajs talks of &quot;vědeckotechnické vykořisťování přírodních sil&quot; (science-technological exploitation of natural forces), e.g. here: &quot;Vysoká produktivita práce, založená na přímém vědeckotechnickém vykořisťování přírodních sil, nutně vede k nadměrné saturaci méně naléhavých abiotických potřeb lidí, tj. i k novým způsobům jejich uspokojování, podněcování a vytváření.&quot;&lt;ref name=smirit2014/&gt; To my mind, the Czech word ''vykořisťování'', which is used in Marxists philosophy in relation to capitalists and laborers, seems unduly pejorative, perhaps even more so than the English ''exploitation''. A less charged word could be ''využití''. To my mind, ''vykořisťování'' reads as if the natural forces were cast/interpreted as a person suffering from the yoke of technosphere. For instace, building a dam and a hydro powerplant would be such an exploitation. I struggle to find the &quot;poor&quot; gravitational force acting on water properly understood as a poor/unfortunate exploited person. Similarly, I struggle to interpret wind as a person exploited (''vykořisťována'') by a windmill. At least in Czech, ''vykořisťování'' sounds very anthropomorphic and negative, relating to ''kořist'' (prey or spoils).

A search for &quot;vykořisťování přírodních sil&quot; in Google finds nearly exclusively texts from Šmajs.

A search for &quot;vykořisťování přírody&quot; in Google and Google Books finds a broad range of sources, some apparently environmentalist.

A search for &quot;exploitation of natural forces&quot; finds, among others, the following quotation from Marx: &quot;This Prometheus of M. Proudhon's is a queer character, as weak in logic as in political economy. So long as Prometheus merely teaches us the division of labour, the application of machinery, the exploitation of natural forces and scientific power, multiplying the productive forces of men and giving a surplus compared with the produce of labour in isolation, this new Prometheus has the misfortune only of coming too late.&quot;&lt;ref&gt;[https://www.marxists.org/archive/marx/works/1847/poverty-philosophy/ch01c.htm The Poverty of Philosophy] by Karl Marx, marxists.org&lt;/ref&gt;

A search for &quot;exploitation of nature&quot; finds a range of sources, many of which seem to be environmentalist. The phrase does not seem positive.

A search for &quot;Ausbeutung der Natur&quot; finds a range of sources, showing the phrase to be common. German ''Ausbeutung'', in Marx, corresponds to Czech ''vykořisťování''. German ''Beute'' corresponds to Czech ''kořist''.

English ''exploit'' has, according to M-W, two senses, one neutral (&quot;to make productive use of&quot;), one negative (&quot;to make use of meanly or unfairly [...]&quot;).&lt;ref&gt;[https://www.merriam-webster.com/dictionary/exploiting exploiting], merriam-webster.com&lt;/ref&gt; This suggests that the ideological effect of English ''exploitation'' is rather different from that of Czech ''vykořisťování''. The neutral (or even positive) sense of ''exploit'' could probably be translated as ''využití'' or ''vytěžení'', and imperfective ''využívání'' and ''vytěžování''.

To get the ideological effect of Czech ''vykořisťování'' and German ''Ausbeutung'', we could consider ''outpraying'' or ''outspoiling'' (and thus ''plunder'').

We see the following candidate metaphors:
* Humans and their technological culture are beast of prey, predators (such as a tiger or wolf); nature (including mineral ores) is prey.
* Humans and their technological culture are plunderers; nature (including mineral ores) is store of goodies to be plundered.

The etymology of English ''exploit'' does not suggest anything remotely relating to ''kořist'' (prey or spoil).&lt;ref&gt;[https://www.merriam-webster.com/dictionary/exploit exploit], merriam-webster.com&lt;/ref&gt;

The theme of exploitation/''vykořisťování'' of nature is invoked in Šmajs 1982, per this: &quot;I když současné ekologické problémy souvisejí s technologií, která vznikala v období živelné kapitalistické industrializace, i když se zhoršování životního prostředí i v době vědeckotechnické revoluce dále prohlubuje ziskovými motivy exploatace přírodních zdrojů, zbrojení a válečnými přípravami imperialistických zemí — kapitalistickým vykořisťováním přírody, které je analogické vykořisťování lidské práce — socialistické společenství se plně hlásí k úkolům aktivní ochrany a cílevědomé tvorby pří
znivého životního prostředí.&quot;&lt;ref name=Š1982&gt;[https://digilib.phil.muni.cz/sites/default/files/pdf/107017.pdf Vztah přírody a společnosti jako základní ekologický problém] by Josef Šmajs, 1982&lt;/ref&gt;. Here, the capitalist exploitation of nature is claimed to bear an analogy to exploitation of human labor. Contrary to an implication made in the above by Šmajs, the socialist block was approximately as guilty (if not more?) of destruction of the environment as the capitalist block (recall not only Chernobyl but also Aral Lake).

== A Constitution for the Earth ==
Šmajs is an author of &quot;A Constitution for the Earth&quot;, linked below at earthconstitution.eu (there are other similarly-named documents online). It seems to be a rather radical document. Let us consider:
: &quot;We commit ourselves to protecting the Earth from the selfish expansion of the predation-oriented Culture. We shall enforce by any means its values, claims and rights, which are superior to both human beings and to Culture. [...] The Earth represents the highest value for both our species and for human Culture. It constitutes the oldest, broadest and most powerful creative activity, the unique planetary subjectivity. We have to defend its right to evolution, and its right to maintain a planet-wide balance between animate and inanimate systems.&quot;

It seems that the Earth is then to be construed as a person (&quot;planetary subjectivity&quot;). Like a person, it has &quot;rights&quot;. These could be defended by a guardian; let us recall that some countries are now recognizing rivers as legal persons, and similarly, the Earth could be recognized as a legal person. The rights are to be enforced &quot;by any means&quot;; that sounds like an exhortation/call to ecoterrorism (Šmajs perhaps does not mean it, but that is what he says). It could easily lead to the proposal to eliminate humankind to protect the Earth's rights (again, the enforcement is to be &quot;by any means&quot;).

On purely factual (non-normative, non-axiological) level, it is untrue that the Earth &quot;constitutes the oldest, broadest and most powerful creative activity&quot; (as for &quot;oldest&quot;); there was creative activity in the universe before the origination of the Earth.

What these Earth's rights are in practice is unclear. Does it mean that any intrusive human project would now need an approval of the appointed legal guardian? Why would the guardian approve any project? Would e.g. all dams, quarries and mines now be illegal? Could also agriculture (deforestation) become illegal?

Why the word &quot;Culture&quot; is capitalized in unclear. It is reminiscent of Pirsig's capitalization of the word &quot;Quality&quot;. It could be an insinuation that Culture is something like a god or semigod, perhaps something like Tolkien's Melkor/Morgoth, in any case a person or person-like entity. I don't really know. This capitalization seems peculiar to the English version (a translation from Czech?); the Czech version does not capitalize &quot;kultura&quot; as &quot;Kultura&quot;. It would be interesting to know who the translator into English was. At the bottom of the page, it says &quot;Copyright © 2025 Josef Šmajs | Webdesign: PRO, s.r.o.&quot;. Perhaps Šmajs translated the pages into various languages himself; perhaps his translation suppliers are not stated. If he did it himself, he would be able to translate from Czech into English, German, Russian and Slovak; that would be plausible enough, on the face of it.

As for the date of publication, it seems unclear. earthconstitution.eu does not seem to host a wiki with a revision history. Wayback Machine for https://www.earthconstitution.eu/en/proposal has only one capture (as of 2 Feb 2025), from 14 Jan 2025.&lt;ref&gt;[https://web.archive.org/web/20250000000000*/%20https://www.earthconstitution.eu/en/proposal earthconstitution.eu/en/proposal], Wayback Machine&lt;/ref&gt; However, ustavazeme.cz/cz/navrh-ustavy has a 2021 capture in WayBack Machine&lt;ref&gt;[https://web.archive.org/web/20200801000000*/https://ustavazeme.cz/cz/navrh-ustavy ustavazeme.cz/cz/navrh-ustavy], Wayback Machine&lt;/ref&gt;. Judging from cupress.cuni.cz, the original date of publication could have been 2015, with ISBN 9788089057597, publisher Pro&lt;ref&gt;[https://www.cupress.cuni.cz/ink2_ext/index.jsp?include=podrobnosti&amp;id=256971 Ústava Země. A Constitution for the Earth. Verfassung für die Erde - Šmajs Josef], Knihkupectví Karolinum&lt;/ref&gt;.

As for the license, none seems to be stated, and in particular, CC-BY-SA or a similar Creative Commons license is not stated. As a result, one cannot translate the document into other languages if wished, e.g. French or Spanish, unless one gets a permission from the author first. Moreover, when quoting the document, one has to be careful to do so in view to Fair Use or whatever similar provision exists in non-Anglophone copyright law.

Further reading:
* [https://www.earthconstitution.eu/en/proposal A Constitution For The Earth] by Josef Šmajs, earthconstitution.eu -- authorship is stated at https://www.earthconstitution.eu/en/author
* [https://earthconstitution.eu/de/vorschlag Verfassung für die Erde] by Josef Šmajs, earthconstitution.eu (in German)
* [https://earthconstitution.eu/ru/proposal Конституция Земли] by Josef Šmajs, earthconstitution.eu (in Russian)
* [https://ustavazeme.cz/cz/navrh-ustavy Ústava Země] by Josef Šmajs, ustavazeme.cz (in Czech)
* [https://ustavazeme.sk/sk/navrh-ustavy Ústava Zeme] by Josef Šmajs, ustavazeme.sk (in Slovak)
* [https://www.degruyter.com/document/doi/10.1515/humaff-2015-0028/pdf The Philosophical Conception of a Constitution for the Earth] by Josef Šmajs, 2015 -- text longer than the constitution alone, containing the constitution embedded
* [https://blisty.cz/art/77197-filosoficky-koncept-ustavy-zeme.html Filosofický koncept Ústavy Země] by Josef Šmajs, 22 April 2015 (in Czech)

== Declaration of Dependence ==
''Deklarace závislosti'' (perhaps ''A Declaration of Dependence'') seems to be a 2011 or 2012 precusor of &quot;A Constitution of the Earth&quot;.

One has to check whether the items below in the further reading are exactly the same versions of the text.

An English version/translation is available in PermaBook Wiki below. No license such as CC-BY-SA appears to be stated.

One can analyze the statements made there; this is yet to be done.

Further reading:
* [https://www.ustavazeme.cz/cz/download/deklarace_zavislosti.pdf Deklarace závislosti (dowloadable pdf)], ustavazeme.cz (in Czech)
* [http://publikacie.uke.sav.sk/sites/default/files/2011_6_320_322_smajs.pdf Deklarace závislosti], by Šmajs et al., publikacie.uke.sav.sk (in Czech); formulation participants/contributors: Antonín Bajaja, Bohuslav Binka, Petr Blahut, Etela Farkašová, Milena Fucimanová, František Houdek, Vladimír Choluj, Petr Jemenka, Ivan Klíma, Aleš Máchal, Vratislav Moudr, Gustav Rosa, Jiří Sedlák, Zuzana Škorpíková, Jan Šmarda, Gerlinda Šmausová, Marek Timko, Pavel Trpák, Emil Višňovský
* [https://permabook.brozkeff.net/doku.php?id=the_declaration_of_dependence_smajs Declaration of Dependence] by Josef Šmajs et al., uploaded to PermaBook Wiki on 21 July 2012[https://permabook.brozkeff.net/doku.php?id=the_declaration_of_dependence_smajs&amp;do=revisions],  permabook.brozkeff.net -- disclaimer: it is not clear that this is not a copyright violation; the declaration does not seem to have any license allowing free copying and translation
* [http://archiv.listy.cz/archiv.php?cislo=141&amp;clanek=011428 K podstatě evoluční ontologie] by Josef Šmajs, 2014, archiv.listy.cz -- has the declaration embedded, albeit without listing contributors/co-authors
* [https://www.degruyter.com/document/doi/10.2478/s13374-013-0144-2/pdf HOW WILL THE PROMETHEAN MYTH END?] by Josef Šmajs, 2013, degruyter.com -- contains Declaration of Dependence as an addendum

== A Lease Agreement with the Earth ==
Šmajs is the author of ''Nájemní smlouva se Zemí'', 2004 (the date follows from the statement that the document was signed/approved by ''Obec spisovatelů'' on 4 December 2004; Šmajs sometimes states 2003 as the relevent year&lt;ref&gt;https://blisty.cz/art/77197-filosoficky-koncept-ustavy-zeme.html&lt;/ref&gt;). The rendering ''The Lease Contract with the Earth'' is used in Jemelka 2010&lt;ref&gt;[https://www.ped.muni.cz/z21/knihy/2010/26/26/texty/eng/jemelka_e.pdf Bioethics and Environmental Ethics as Part of the Training of Future Civics and Social Sciences Basics Teachers] by Petr Jemelka, 2010&lt;/ref&gt;; the rendering ''A Lease Agreement with the Earth'' is used by Šmajs himself, apparently&lt;ref&gt;https://www.earthconstitution.eu/en/literature&lt;/ref&gt;. An analysis is largely pending.

Let me investigate one peculiar quotation:
: &quot;Člověk je poprvé odpovědný za svou druhovou existenci. Pochopení a přijetí této odpovědnosti však závisí na opuštění úzkých morálních, fyzikálních a technických hledisek, vyžaduje biologický a medicínský přístup, předpokládá evolučně ontologický pohled na věc.&quot;
From this, we get:
: Man is for the first time responsible for his continuing existence as a species; understanding and acceptance of this responsibility depends on [...], it assumes evolutionary-ontological perspective/point of view.
But that is implausible: it says that humans can only accept their responsibility if they accept the evolutionary ontology by Šmajs. That makes little or no sense.

Further reading:
* [http://publikacie.uke.sav.sk/sites/default/files/2005_1_047_047_smajs.pdf Nájemní smlouva se Zemí] by Josef Šmajs, apparently 2005, publikacie.uke.sav.sk
* [https://www.ustavazeme.cz/cz/download/najemni_smlouva.pdf Nájemní smlouva se Zemí (downloadable pdf)] by Josef Šmajs, indicated as 2006 (in Czech), ustavazeme.cz

== Criticism ==
Some criticism of the philosophy of Šmajs is found in Melichová and Burgan 2013, which mentions among critics the biologist A. Markoš and the environmentalist D. Storch. D. Storch seems particularly harsh:
: 'Environmentalist D. Storch (1997, 627) directly notes that he does not want “to argue with J. Šmajs, refute his opinions and draw attention to the mistakes perpetrated by him,” because “it would be possible to challenge every single word in almost every sentence and the arbitrariness in his use of some concepts (information, entropy) and even complete scientific systems must bewilder even someone with a little knowledge”. This is especially true when J. Šmajs “knowingly or unknowingly changes [the concepts] so that they confirm his (certainly well-intentioned) thesis.”'

The above seems to be from a Vesmír article by David Storch.&lt;ref&gt;[https://vesmir.cz/cz/casopis/archiv-casopisu/1997/cislo-11/ekologicka-katastrofa-co-vime-co-nevime.html Ekologická katastrofa: co víme a co nevíme] by David Storch, 5 November 1997, vesmir.cz (in Czech)&lt;/ref&gt; The reference to Markoš is to another Vesmír article&lt;ref&gt;[https://is.muni.cz/el/1441/jaro2007/Fy2MP_ENVI/um/3264959/MarkosV623-627.pdf?lang=en Cultura contra natura] by Anton Markoš, 1997 (in Czech)&lt;/ref&gt;, which seems to be a worthy read (if one knows Czech) for the specificity of the criticism. Šmajs has responded to that criticism&lt;ref&gt;[https://vesmir.cz/cz/casopis/archiv-casopisu/1998/cislo-4/cultura-contra-natura.html Cultura contra natura] by Josef Šmajs, 5 April 1998, vesmir.cz&lt;/ref&gt;.

On the other hand, Melichová and Burgan 2013 quote some assessors that lavish praise on Šmajs:
: 'For example A. Rosa, the publisher of Šmajs’ book Ohrozená kultúra (2006) [Threatened Culture], notes that of all the titles he has published this is this one he appreciates most. It deserves the Nobel Prize for its “heuristic contribution to the formulation of realistic conditions for the survival of man on Earth,” and for his “biophilic attitude contained in the very activity of every human being.” E. Višňovský (2006, 212) does not doubt that “with his sophisticated and original ontological and posthumanist concept, J. Šmajs ranks among ecophilosophers of international importance.”'

Let me note that it is E. O. Wilson of ''Sociobiology'', 1975, who is noted for biophilia; he published ''Biophilia'' in 1984.

Further reading:
* [https://www.researchgate.net/publication/272041695_Scientific_realism_and_philosophical_naturalism_in_Smajs%27_evolutionary_ontology Scientific realism and philosophical naturalism in Šmajs’ evolutionary ontology] by Inéz Melichová and Robert Burgan, 2013

== Context and originality of Šmajs' work ==
Šmajs positions his work as environmental philosophy. Environmental ethics is covered in a Stanford Encyclopedia of Philosophy (SEP) article linked below; this includes assigning intrinsic value to natural (non-human) entities such as biological species. The SEP article covers ''deep ecology'' as tracing at least to Næss 1973. The SEP article has extensive Bibliography section, which, among the older literature, features not only Næss 1973 but also e.g. Mumford 1934 and Passmore 1974. Šmajs's claim to originality and contribution could perhaps be that he is doing ''ontology'' rather than ''ethics''; on the other hand, his urgency is clearly ethical/denotic/axiological. The SEP article does not mention Šmajs. Indeed, no SEP article mentions Šmajs, as per the Google search '&quot;Šmajs&quot; site:plato.stanford.edu'. For his place in time, the oldest article by Šmajs that I found is ''K některým otázkám vztahu vědy a ideologie'', 1973&lt;ref&gt;[https://digilib2.phil.muni.cz/sites/default/files/pdf/106597.pdf K některým otázkám vztahu vědy a ideologie] by Josef Šmajs, 1973&lt;/ref&gt;&lt;ref&gt;https://digilib2.phil.muni.cz/en/node/63766&lt;/ref&gt;.

In so far as Šmajs emphasizes evolution in the broad sense of any change resulting in origination (e.g. of stars), a serious/devoted analyst should perhaps find out to what extent Šmajs is indebted to Hegel and Marx with their &quot;dialectics&quot;.

Further reading:
* [https://plato.stanford.edu/entries/ethics-environmental/ Environmental Ethics], Stanford Encyclopedia of Philosophy

== Šmajs' philosophy before 1989 ==
Šmajs's writing before 1989 (the year of the Velvet Revolution in Czechoslovakia) often references Marx and seems to accept the official philosophy/ideology of Czechoslovak socialism. Examples of statements are to be added; until then, the further reading below serves as substantiation.

Further reading:
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106597.pdf K některým otázkám vztahu vědy a ideologie] by Josef Šmajs, 1973
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106835.pdf Lejbin, Valerij Moisejevič. Psichoanaliz i filosofija neofrejdizma] by Josef Šmajs, 1981
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106838.pdf Práce a socialistický způsob života] by Josef Šmajs, 1981
* [https://digilib.phil.muni.cz/sites/default/files/pdf/107017.pdf Vztah přírody a společnosti jako základní ekologický problém] by Josef Šmajs, 1982
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106645.pdf První výsledky užitečné spolupráce] by Josef Šmajs, 1983
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106656.pdf Sociální a antropologické aspekty techniky] by Josef Šmajs, 1983
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106667.pdf Zu den Voraussetzungen und zur Methode der Kritik der bürgerlichen Konzeptionen einer ökologischen Katastrophe] by Josef Šmajs, 1983
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106497.pdf Hodnota a proměny lidské práce] by Josef Šmajs, 1984
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106947.pdf Zur Marxschen Auffassung der Beziehung zwischen der Natur und der Gesellschaft] by Josef Šmajs, 1985
* [https://digilib2.phil.muni.cz/cs/handle/11222.digilib/103866 Sociální funkce vědy] by Josef Šmajs, 1986 (a book with multiple chapters as pdfs)
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/122319.pdf Historické proměny vztahu vědy a společnosti] by Josef Šmajs, 1986
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106324.pdf Sociokulturní aspekt vědy] by Josef Šmajs, 1986
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106318.pdf Природа и общество как детерминирующие факторы свободы человека] by Josef Šmajs, 1986
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106989.pdf K problému vývoje technosféry : malé zamyšlení nad velkým tématem] by Josef Šmajs, 1988
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106682.pdf K problému humanizace přírody] by Josef Šmajs, 1989-1990 

== Academic titles ==
It is perhaps not without interest which academic titles Šmajs holds, although it is tangential to the topic of the article, which is his philosophy. To wit: Prof. PhDr. Ing. Josef Šmajs, CSc.&lt;ref&gt;[http://publikacie.uke.sav.sk/sites/default/files/2011_6_320_322_smajs.pdf Deklarace závislosti], by Šmajs et al., publikacie.uke.sav.sk (in Czech)&lt;/ref&gt;&lt;ref&gt;[https://www.muni.cz/lide/2543-josef-smajs/zivotopis prof. PhDr. Ing. Josef Šmajs, CSc. – Životopis] (Curriculum Vitae) (in Czech), muni.cz&lt;/ref&gt; The character length of this complete identification is 34; the character length of the name alone is 11; the ratio is approximatedy 3:1.

== Life ==
For this article, the life of Šmajs or curriculum vitae is a tangent. This section is here to list further reading:

Further reading:
* [https://www.muni.cz/lide/2543-josef-smajs/zivotopis prof. PhDr. Ing. Josef Šmajs, CSc. – Životopis] (Curriculum Vitae) (in Czech), muni.cz
* [https://encyklopedie.brna.cz/home-mmb/?acc=profil_osobnosti&amp;load=40483 Josef Šmajs - Profil osobnosti], encyklopedie.brna.cz
* [https://www.ustavazeme.cz/cz/autor O autorovi], ustavazeme.cz
* [https://www.phil.muni.cz/fil/scf/komplet/smajs.html Josef Šmajs], phil.muni.cz

== References ==
&lt;references /&gt;

== Further reading ==
Wikipedia:
* [[Wikipedia:cs: Josef Šmajs]]
* [[Wikipedia:cs: Evoluční ontologie]] -- an article that seems to expound Šmajs' evolutionary ontology

By Josef Šmajs in English:
* [https://books.google.com/books?id=0t5Fqh6Vmz4C Evolutionary Ontology: Reclaiming the Value of Nature by Transforming Culture], 2008, books.google.com -- preview available
* [https://permabook.brozkeff.net/doku.php?id=the_declaration_of_dependence_smajs Declaration of Dependence] by Josef Šmajs et al., uploaded to PermaBook Wiki on 21 July 2012[https://permabook.brozkeff.net/doku.php?id=the_declaration_of_dependence_smajs&amp;do=revisions],  permabook.brozkeff.net
* [https://www.degruyter.com/document/doi/10.2478/s13374-013-0144-2/pdf HOW WILL THE PROMETHEAN MYTH END?] by Josef Šmajs, 2013, degruyter.com -- contains Declaration of Dependence as an addendum
* [https://www.earthconstitution.eu/en/proposal A Constitution For The Earth] by Josef Šmajs, earthconstitution.eu -- authorship is stated at https://www.earthconstitution.eu/en/author
* [https://www.degruyter.com/document/doi/10.1515/humaff-2015-0028/pdf The Philosophical Conception of a Constitution for the Earth] by Josef Šmajs, 2015 -- text longer than the constitution alone, containing the constitution embedded
* [http://en.sciforedu.ru/system/files/articles/pdf/14smajs1-16_0.pdf On the Principle of Evolutionary Ontology] by Josef Šmajs, 2016
* [https://www.redalyc.org/journal/742/74260479008/html/ Evolutionary ontology and biofile transformation of culture] by Josef Šmajs, 2019

By Josef Šmajs in Czech:
* [https://digilib2.phil.muni.cz/sites/default/files/pdf/106597.pdf K některým otázkám vztahu vědy a ideologie] by Josef Šmajs, 1973
* [https://digilib.phil.muni.cz/sites/default/files/pdf/107017.pdf Vztah přírody a společnosti jako základní ekologický problém] by Josef Šmajs, 1982
* [https://www.pro.sk/na-stiahnutie/ohrozena_kultura.pdf Už nejsme lovci a sběrači], a Czech chapter/preface in Ohrozená kultúra by Josef Šmajs, 1995, pro.sk -- disclaimer: could be a copyright violation; on the other hand, this is only one chapter/preface from the complete book
* [https://www.ustavazeme.cz/cz/download/najemni_smlouva.pdf Nájemní smlouva se Zemí] by Josef Šmajs, 2006 (in Czech)
* [https://www.blisty.cz/authors/1453-josef-smajs Josef Šmajs], blisty.cz -- lists articles published by Josef Šmajs at Britské listy
* [http://www.sedmagenerace.cz/k-pocitacum-se-stale-rodime-jako-kromanonci K počítačům se stále rodíme jako kromaňonci] by Vít Kouřil, 2008, sedmagenerace.cz -- an interview with Josef Šmajs
* [https://digilib.phil.muni.cz/sites/default/files/pdf/127850.pdf Uspořádanost] In: Šmajs, Josef. Uvedení do evoluční ontologie : studijní text pro posluchače filosofických oborů. 1. vyd. Brno: Masarykova univerzita, 2008, pp. 72-87
* [https://is.muni.cz/do/econ/soubory/katedry/kph/3915224/BROZURA_07.pdf O smiřování kultury s přírodou] by Josef Šmajs, 2014, is.muni.cz -- parts published in 2013 as per edition/publication note
* [https://karolinum.cz/data/clanek/4616/3349_Sociologica_2_13_smajs.pdf K ONTOLOGICKÉMU POJETÍ KULTURY] by Josef Šmajs, 2013, karolinum.cz
* [https://is.muni.cz/el/1423/podzim2014/HEN626/um/Technika_KOR3.pdf Dokážeme smířit technosféru s biosférou?] by Josef Šmajs, Autumn 2014, is.muni.cz
* [https://is.muni.cz/el/1456/podzim2015/BKH_ZAFI/um/Technika_1._cast.pdf Fenomén technika] by Josef Šmajs, Autumn 2015, is.muni.cz
* [https://is.mvso.cz/el/mvso/zima2021/XESO/276544/Etika__ekonomika__priroda.pdf Etika, ekonomika, příroda] by Josef Šmajs, Bohuslav Binka, Ivo Rolný, perhaps 2021 per &quot;zima2021&quot; in the URL, is.mvso.cz
* [https://www.csfd.cz/film/1548951-valka-se-zemi/prehled/ Válka se Zemí], directed by Vladimír Kunz and Josef Šmajs, 2024, csfd.cz

About Josef Šmajs in English:
* [https://www.researchgate.net/publication/272041695_Scientific_realism_and_philosophical_naturalism_in_Smajs%27_evolutionary_ontology Scientific realism and philosophical naturalism in Šmajs’ evolutionary ontology] by Inéz Melichová and Robert Burgan, 2013
* [https://www.degruyter.com/document/doi/10.2478/s13374-013-0159-8/pdf Book review essay Evolutionary Ontology of Culture and the Issues of Business] by Zdeňka Petáková (a geologist), 2013, degruyter.com
* [https://www.degruyter.com/document/doi/10.2478/s13374-013-0146-0/html Evolutionary ontology — A somewhat sociological analysis] by Bohuslav Binka, 2013

About Josef Šmajs in Czech:
* [https://theses.cz/id/744xie/Diplomov_prce_Environmentalismus_v_eskm_filozofickm_mylen.pdf Environmentalismus v českém filozofickém myšlení 20.století (se zaměřením na vybrané osobnosti – E. Koháka, J. Šmajse)] by Kristýna Dolejšová, 2010, master's thesis, theses.cz
* [http://www.vesmir.cz/clanek/josef-smajs-ohrozena-kultura JOSEF ŠMAJS: Ohrožená kultura] by Hana Librová, 1996
* [https://is.muni.cz/th/fo8am/Diplomova_prace_Sromova_Veronika.pdf Evoluční ontologie Josefa Šmajse] by Veronika Šromová, master's thesis, is.muni.cz
* [https://kramerius.lib.cas.cz/search/nimg/IMG_FULL/uuid:7a379e7b-092c-4a18-93ce-b56d37376067 Jak oživit „zamrzlou“ evoluční ontologii] by Radim Šíp, 2014
* [https://www.researchgate.net/publication/270552398_Filozof_pred_kterym_smekam Filozof, před kterým smekám] by Zdeňka Petáková, May 2013, researchgate.net

Publication lists:
* [https://digilib2.phil.muni.cz/en/node/63766 Šmajs, Josef], digilib2.phil.muni.cz -- a list of 68 publications, mostly in Czech but also in German and Russian; the publications seem available online as scanned pdfs
* [https://www.blisty.cz/authors/1453-josef-smajs Josef Šmajs], blisty.cz -- lists articles published by Josef Šmajs at Britské listy
* [https://www.phil.muni.cz/fil/scf/komplet/smajs.html Josef Šmajs], phil.muni.cz -- has no links to publications, merely publication list

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      <comment>I have added information on the medical specialty of Phoniatrics and Pediatric Audiology and on the prevalence of infant hearing loss.</comment>
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{{CountryHeader|File:Germany (orthographic projection).svg|https://en.wikipedia.org/wiki/Germany}}

{{HTitle|General Information}} 
[https://en.wikipedia.org/wiki/Germany Germany], officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. German is the official and predominantly spoken language in Germany. Recognised native minority languages in Germany are Danish, Low German, Low Rhenish, Sorbian, Romani, North Frisian and Saterland Frisian; they are officially protected by the European Charter for Regional or Minority Languages. The most used immigrant languages are Turkish, Arabic, Kurdish, Polish, Italian, Greek, Spanish, Serbo-Croatian, Bulgarian and other Balkan languages, as well as Russian. 

{{HTitle|History of Audiology}}
The development of Audiology in Germany as a scientific discipline started in the 19&lt;sup&gt;th&lt;/sup&gt; century. An important milestone was the publication by the German physicist and physician [https://en.wikipedia.org/wiki/Hermann_von_Helmholtz Hermann von Helmholtz] entitled &quot;On the sensations of tone as a physiological basis for the theory of music&quot; in 1863. After World War II, Audiology was defined as a sub-discipline of Otorhinolaryngology. In 1949 the working group ADA („Arbeitsgemeinschaft Deutscher Audiologen“) was founded at the first conference of ENT physicians and expanded in 1973 by including Otology and Neurotology („[https://adano.hno.org Arbeitsgemeinschaft Deutschsprachiger Audiologen und Neurootologen]“). The first chairman was [https://de.wikipedia.org/wiki/Alf_Meyer_zum_Gottesberge Prof. Dr. Alf Meyer zum Gottesberge]. ADANO still exists as a working group of the German Society for Otorhinolaryngology, Head and Neck Surgery ([https://hno.org Deutsche Gesellschaft für Hals-Nasen-Ohrenheilkunde, Kopf- und Hals-Chirurgie e.V.]). In 1979, the subgroup AG-ERA („[http://ag-era.bplaced.net/wordpress/ Arbeitsgruppe Elektrische Reaktionsaudiometrie]“, working group electric response audiometry) was founded by Prof. Dr. Günter Stange in Hannover. At annual meetings of the AG-ERA the latest developments in objective audiometry are discussed. 

By way of example, several historically significant developments in German audiology may be highlighted here. In 1970, Professor Walter Kumpf, Head of the Department of Audiology at the Department of Otorhinolaryngology of the University Hospital Münster, published the first case report on spontaneous otoacoustic emissions perceived by him. Professor Harald Feldmann, Director of the University Department of Otorhinolaryngology in Münster from 1976 to 1991, discovered the masking effect of tinnitus and contributed substantially to medico-legal assessment through his work on noise-induced hearing loss and its role as an occupational disease. In 2009, universal newborn hearing screening was implemented and mandated in Germany.

In 1996, the German Society of Audiology ([https://dga-ev.com DGA, Deutsche Gesellschaft für Audiologie]) was founded in Münster as an independent interdisciplinary scientific association of experts who deal with hearing, hearing disorders, and their diagnosis, therapy, rehabilitation, and prevention. As a scientific society, the DGA promotes professional exchange, the further development of audiological standards, and networking among its members from medicine, natural sciences, engineering, education, psychology, and related disciplines. Today, the DGA has more than 600 society members. A detailed description of the development of Audiology in Germany is given in&lt;ref&gt;{{Cite journal|last=Kießling|first=Jürgen|date=2021-08-01|title=Die Entwicklung der Audiologie - von Helmholtz bis heute|url=https://www.sciencedirect.com/science/article/pii/S0939388920300933|journal=Zeitschrift für Medizinische Physik|series=Special Issue: Audiology|volume=31|issue=3|pages=238–253|doi=10.1016/j.zemedi.2020.08.003|issn=0939-3889}}&lt;/ref&gt;.

In Germany, Phoniatrics and Pediatric Audiology exists as a distinct medical specialization derived from Otorhinolaryngology. As the medical discipline of communication disorders, it integrates expertise in hearing loss in infants, children, and adolescents with knowledge of speech, language, and voice disorders. In children with hearing loss, the specialty therefore also addresses language and communication development, related disorders, and their treatment. The German Society of Phoniatrics and Pediatric Audiology ([https://dgpp.de/de/ DGPP, Deutsche Gesellschaft für Phoniatrie und Pädaudiologie]) was founded in 1983 as the scientific association of German-speaking physicians specializing in Phoniatrics and Pediatric Audiology, with Prof. Dr. med. Gerhard Kittel serving as its founding president. 

{{HTitle|Incidence and Prevalence of Hearing Loss}}
Epidemiological data on the prevalence of hearing disorders in Germany are sparse. In 2017, a study conducted in two regions in Germany found hearing impairment in approximately 16% of adults when applying the WHO criterion of 2016&lt;ref&gt;{{Cite journal|last=von Gablenz|first=Petra|last2=Hoffmann|first2=Eckehardt|last3=Holube|first3=Inga|title=Prevalence of hearing loss in Northern and Southern Germany|journal=HNO|volume=65|pages=S130-S135|doi=DOI 10.1007/s00106-016-0318-4}}&lt;/ref&gt;.  The results  are in good agreement with other European studies and show differences to US American results. A 2022 study conducted in the city of Mainz and the neighboring Mainz-Bingen district reported a prevalence of 25.5% when applying the WHO criterion of 2021 &lt;ref&gt;{{Cite journal|last=Hackenberg|first=Berit|last2=Döge|first2=Julia|last3=Lackner|first3=Karl J.|last4=Beutel|first4=Manfred E.|last5=Münzel|first5=Thomas|last6=Pfeiffer|first6=Norbert|last7=Nagler|first7=Markus|last8=Schmidtmann|first8=Irene|last9=Wild|first9=Philipp S.|date=2022-09|title=Hearing Loss and Its Burden of Disease in a Large German Cohort-Hearing Loss in Germany|url=https://pubmed.ncbi.nlm.nih.gov/34904723|journal=The Laryngoscope|volume=132|issue=9|pages=1843–1849|doi=10.1002/lary.29980|issn=1531-4995|pmid=34904723}}&lt;/ref&gt;.

In 2024 a self-report study on the prevalence and co-prevalence of the audiovestibular symptoms hearing loss, tinnitus and dizziness in the Pomerania region of Germany reported a weighted prevalence of 14.2% for hearing loss, 9.7% for tinnitus, and 13.5% for dizziness in the population of 8134 study participants. Prevalence increased with age and differed among the sexes. 28% of the study participants reported more than one symptom at once&lt;ref&gt;{{Cite journal|last=Ihler|first=Friedrich|last2=Brzoska|first2=Tina|last3=Altindal|first3=Reyhan|last4=Dziemba|first4=Oliver|last5=Völzke|first5=Henry|last6=Busch|first6=Chia-Jung|last7=Ittermann|first7=Till|date=2024-07-31|title=Prevalence and risk factors of self-reported hearing loss, tinnitus, and dizziness in a population-based sample from rural northeastern Germany|url=https://pubmed.ncbi.nlm.nih.gov/39085387|journal=Scientific Reports|volume=14|issue=1|pages=17739|doi=10.1038/s41598-024-68577-3|issn=2045-2322|pmc=11291685|pmid=39085387}}&lt;/ref&gt;.

In a population-based cohort study evaluating the outcome of the universal newborn hearing screening (UNHS) program in the German federal state of Hesse, including 17,439 screened newborns, the prevalence of unilateral and bilateral hearing loss was 2.7 per 1,000 newborns, while the prevalence of permanent bilateral hearing loss was 2.1 per 1,000. In the UNHS cohort, children with permanent hearing loss were diagnosed at a median age of 3.1 months and received treatment at a median age of 3.5 months. The corresponding ages in a non-UNHS cohort from Hesse were 17.8 and 21.0 months, respectively&lt;ref&gt;{{Cite journal|last=Neumann|first=Katrin|last2=Gross|first2=Manfred|last3=Böttcher|first3=Peter|last4=Euler|first4=Harald A.|last5=Spormann-Lagodzinski|first5=Marlies|last6=Polzer|first6=Melanie|date=2006|title=Effectiveness and Efficiency of a Universal Newborn Hearing Screening in Germany|url=https://karger.com/article/doi/10.1159/000095004|journal=Folia Phoniatrica et Logopaedica|language=en|volume=58|issue=6|pages=440–455|doi=10.1159/000095004|issn=1021-7762}}&lt;/ref&gt;. In a later study including 150,000 screened infants, the median age at diagnosis was 3.7 months and the median age at treatment initiation was 5.8 months&lt;ref&gt;Neumann K (2010) Newborn hearing screening in Germany and the State of Hesse. In: World Health Organization (ed.) Neonatal and infant hearing screening. Current issues and guiding principles for action. Outcome of a WHO Informal consultation held at WHO Head-quarters, Geneva, Switzerland, 09--10 November, 2009. (p. 19). WHO, Geneva, Switzerland, ISBN 978 92 4 159994 6&lt;/ref&gt;.

A population-based two-staged ‘screening’ and ‘follow-up’ newborn hearing screening program in North-Rhine, Germany and a hospital-based screening at a University Hospital was conducted for the 2007–2016 period. The 10-year coverage rate for these newborns was 98.7%, the referral rate after a failed two-step screening was 3.4%, and the lost-to-follow-up rate was 1% but no information on final diagnosis was provided.&lt;ref&gt;{{Cite journal|last=Thangavelu|first=Kruthika|last2=Martakis|first2=Kyriakos|last3=Feldmann|first3=Silke|last4=Roth|first4=Bernhard|last5=Herkenrath|first5=Peter|last6=Lang-Roth|first6=Ruth|date=2023-10-23|title=Universal Newborn Hearing Screening Program: 10-Year Outcome and Follow-Up from a Screening Center in Germany|url=https://www.mdpi.com/2409-515X/9/4/61|journal=International Journal of Neonatal Screening|language=en|volume=9|issue=4|pages=61|doi=10.3390/ijns9040061|issn=2409-515X|pmc=10594500|pmid=37873852}}&lt;/ref&gt; 

{{HTitle|Information About Audiology}}

=== Bachelor and Master courses in Audiology (audiologists) ===
Though the job title „Audiologist“ is not an officially protected professional title, it is usually used for people with an academic education on bachelor (B.Sc.) or master level (M.Sc.). There are two universities of applied sciences in Germany offering a bachelor program and two universities offering master courses. They are located in Oldenburg and Lübeck. In total, around 20 students finish their academic courses per year. In addition, a significant number of audiologists have primary education in physics, engineering and other related disciplines with appropriate individual training.

=== Services offered by Technical Audiologists ===
Technical audiologists work primarily in hospitals and specialized hearing clinics, where they support the diagnosis and treatment of hearing disorders under the supervision of an ENT physician. Their responsibilities include performing audiological assessments, conducting objective hearing measurements, assisting in the evaluation and follow-up of cochlear implant patients, and managing technical aspects of audiological equipment. They are also involved in the programming and technical support of cochlear implant systems, as well as patient counseling related to implant use and rehabilitation.

=== Services offered by Otolaryngologists ===
ENT doctors perform physical examination and all necessary audiometric tests for diagnosis of hearing loss. In particular, they perform subjective and objective tests in order to determine the cause and extent of hearing loss. Associated disorders such as Tinnitus, Hyperacusis and vestibular disorders are also diagnosed by ENT specialists. When no causative treatment of hearing loss is available, Hearing Aids (HAs) are prescribed. The regulatory basis for hearing aid prescription is the Guideline for assistive devices (&quot;Hilfsmittelrichtlinie&quot;). Roughly, specific audiometric criteria for puretone tresholds and speech recognition have to be fulfilled in order to justify HA prescription. A comprehensive description of the process is given in &lt;ref&gt;{{Cite journal|last=Hoppe|first=Ulrich|last2=Hesse|first2=Gerhard|title=Hearing aids: indications, technology, adaptation, and quality control|journal=GMS Current Topics in Otorhinolaryngology - Head and Neck Surgery|volume=16|doi=10.3205/cto000147. ISSN 1865-1011.}}&lt;/ref&gt;. 

=== Services offered by Phoniatricians &amp; Pediatric Audiologists ===
The scope of Phoniatrics and Pediatric Audiology encompasses the diagnosis, treatment, and research of childhood hearing loss, auditory processing disorders and other listening difficulties, developmental language and speech sound disorders, acquired communication disorders such as aphasia, as well as voice and swallowing disorders. Physicians specialized in Phoniatrics and Pediatric Audiology provide early identification of childhood hearing loss through universal newborn hearing screening, highly specialized pediatric audiological diagnostics, initiation and monitoring of hearing aid, cochlear implant, and other auditory implant provision, as well as assistive technologies, and family-centered rehabilitation for children with hearing loss. Associated conditions such as childhood tinnitus, hyperacusis, misophonia, and vestibular disorders are also diagnosed and treated by these specialists. 

The prescription of hearing aids and assistive listening devices is guided by two consensus papers &lt;ref&gt;Wiesner T, Bohnert A, Limberger A, Massinger C, Nickisch A, Fleischer K, Kruse E, Heinemann M, Schönweiler R. Konsenspapier der DGPP zur Hörgeräte-Versorgung bei Kindern, Vers. 4.0. last update 2019. &lt;nowiki&gt;https://dgpp.de/de/wp-content/files/KonsensDGPP-HG-Anpassung_bei_Kindern-Vers40.pdf&lt;/nowiki&gt;&lt;/ref&gt;&lt;ref&gt;Hohl B, Lang-Roth R, Mahlke H, Mörler W, Renzelberg G, Tiede K, Wiesner T, Zastrau Z Bogner B, Bohnert A, Flügel T, Hirschfelder A, Husstedt H, Plotz K, Matulat P, Napiontek U, Reichmuth K, Schönfeld R, Vietheer I. Interdisziplinäres Konsensuspapier zur Umfangsbestimmung von Zusatztechnik im inklusiven Schulalltag von Schüler:innen mit peripherer Hörschädigung. 2021. &lt;nowiki&gt;https://dgpp.de/de/wp-content/files/Konsensuspapier_UmfangsbestimmungZusatztechnikDrahtloseUebertragungsanlage-20220110.pdf&lt;/nowiki&gt;&lt;/ref&gt;, a clinical practice guideline&lt;ref&gt;Arbeitsgemeinschaft Deutschsprachiger Audiologen, Neurootologen und Otologen der Deutschen Gesellschaft für Hals-Nasen-Ohren-Heilkunde, Kopf- und Hals-Chirurgie. S2k-Leitlinie „Implantierbare Hörgeräte“. AWMF-Register-Nr. 017/073. 2017. &lt;nowiki&gt;https://dgpp.de/de/wp-content/files/S2k_Implantierbare-Hoergeraete_2018-06-abgelaufen.pdf&lt;/nowiki&gt;&lt;/ref&gt;, and the [https://www.g-ba.de/richtlinien/13/ Medical Aids Directive of the Federal Joint Committee]. Cochlear implant provision and rehabilitation are regulated by a separate clinical practice guideline&lt;ref&gt;DGHNO-KC-Deutsche Gesellschaft für Hals-Nasen-Ohrenheilkunde, Kopf und Hals-Chirurgie e.V. S2k-Leitlinie Cochlea-Implantat Versorgung [Internet]; AWMF-Register-Nr. 017/071; 2020. www.awmf.org/uploads/tx_szleitlinien/017-071l_S2k_Cochlea-Implantat-Versorgung-zentral-auditorische-Implantate_2020-12.pdf&lt;/ref&gt;, as are interventions for developmental language disorders in children with hearing loss&lt;ref&gt;Neumann K, Kauschke C, Fox-Boyer A, Lüke C, Sallat S, Kiese-Himmel C: Clinical practice guideline: Interventions for developmental language delay and disorders. Dtsch Arztebl Int 2024; 121: 155–62. DOI: 10.3238/arztebl.m2024.0004&lt;/ref&gt;&lt;ref&gt;Neumann K, Kauschke C, Lüke C, Fox-Boyer A, Sallat S, Bolotina A, Euler HA, Kiese-Himmel C, Leitliniengruppe. Therapie von Sprachentwicklungsstörungen. Interdisziplinäre S3-Leitlinie, Version 1.1, AWMF-Registernr. 049-015, Deutsche Gesellschaft für Phoniatrie und Pädaudiologie (DGPP) (Hrsg.), 2022; verfügbar unter &lt;nowiki&gt;https://register.awmf.org/de/leitlinien/detail/049-015&lt;/nowiki&gt;&lt;/ref&gt;.  

The specialty is inherently interdisciplinary, involving close collaboration with Otorhinolaryngology, Pediatrics, Maxillofacial Surgery, Orthodontics, Neurology, Psychology, education and special education, hearing care professionals, and speech and language therapy. These collaborations support the management of hearing, speech, language, voice, and swallowing disorders, including augmentative and alternative communication.  

=== Services offered by Hearing Aid Acousticians ===
Hearing Aid Acousticians (HAA) are non-academic craftsmen. Based on the prescription they select appropriate hearing aids and perform the HA fitting. Powers and duties are regulated by the &quot;[https://www.bgbl.de/xaver/bgbl/start.xav#/switch/tocPane?_ts=1778415605193 Hörakustikermeisterverordnung]&quot;. As demanded by §30 in the Hilfsmittelrichtlinie the success of an HA provision is confirmed by an ENT doctor at the end of the trial period. Standard health insurance covers costs for hearing aids up to about 800 € per HA including otoplastic and fitting. 

=== Services offered by Pedagogical Audiologists ===
Pedagogical Audiologists (or: Educational Audiologists) have an academic qualification in special needs education and practical experience in teaching children who are deaf or hard of hearing. They should be qualified in a training programme in accordance with the BDH and BUDIKO standards ([http://www.b-d-h.de/images/pdf/Paedagogische_Audiologie_Neuauflage_Broschuere_2020_05_11.pdf &quot;Grundsatzpapier Pädagogische Audiologie&quot;]) (2020). Pedagogical audiologists carry out hearing and speech audiometry. They analyse test results and assess hearing, speech and communication behaviour to provide advice for parents and caretakers in (pre-)school environments. 

=== Services offered by Audiometrists ===
Hearing healthcare is primarily part of ENT doctors in cabinets. Audiometry is usually done by specialized nurses or audiometrists. Audiometrists have usually an education as medical technologist („Medizinischer Technologe, MTF“).{{HTitle|Scope of Practice and Licensing}}In Germany, Austria and Switzerland, ‘audiologist’ is not a [https://www.bundestag.de/resource/blob/684720/8bc3b06008858a32d0e500882afce792/WD-8-164-19-pdf-data.pdf regulated profession] and is not a legally protected professional title. Various professional groups with differing levels of education work in the field of audiology. In Germany, there are no recognition authorities for university degrees leading to unregulated professions. Applications for jobs on the labour market must be addressed directly to the employer. The employer in question decides on suitability at their own discretion. Potential employers include, for example, hospitals, doctors’ practices, hearing aid manufacturers and implant manufacturers.

In Germany, hearing aids are fitted by hearing aid specialists in specialized shops. Such a shop must always be run by a “Meister” hearing aid specialist. “Meister” hearing aid specialist is a regulated profession that requires the successful completion of the Meister’s examination in this skilled trade (see [https://www.gesetze-im-internet.de/hwo/HwO.pdf Handwerksordnung]). The requirements for obtaining the Meister craftsman qualification are set out in the Regulations on the Meister Craftsman Examination for the Hearing Aid Dispensing Trade ([https://www.bgbl.de/xaver/bgbl/start.xav#/switch/tocPane?_ts=1778512158336 Meisterprüfungsordnung des Hörakustiker-Handwerks]). Typically, in the hearing aid dispensing trade, an apprenticeship is first completed, culminating in a journeyman’s examination. Passing the journeyman’s examination is usually a prerequisite for preparing for the Meister craftsman examination and subsequently sitting the examination. Employment in a specialist hearing aid shop is also possible without the journeyman’s certificate. In this case, the employee works under the professional supervision of a Meister craftsman. Self-employment, however, requires the acquisition of the Meister craftsman’s qualification. With regard to foreign qualifications, an equivalence assessment procedure can be initiated at the local Chamber of Crafts. Upon application, the Chamber of Crafts will assess whether the professional qualification obtained abroad is equivalent to the German master craftsman’s examination or the journeyman’s examination. The Chambers of Crafts provide advice prior to the application. The Chambers of Crafts then determine whether the qualification obtained abroad corresponds to the job profile of a German Meister hearing aid acoustician or that of a journeyman. Further training measures are also possible to address any specific gaps.

In Germany, a bachelor’s degree with a focus on audiology can currently be obtained at the Technical University of Lübeck ([https://www.th-luebeck.de/studium/studienangebot/studiengaenge/hoerakustik-bsc/uebersicht programme Hörakustik]) and Jade University of Applied Sciences in Oldenburg ([https://www.jade-hs.de/studiengang/hoertechnik-audiologie-bachelor/ Hearing Technology and Audiology programme]). Both programmes have a more technical and less clinical focus than audiology programmes abroad. They lead to the regulated higher education profession of Engineer – Hearing Technology and Audiology ([https://web.arbeitsagentur.de/berufenet/beruf/59373#ueberblick Ingenieur/in – Hörtechnik und Audiologie]).

Audiologists are included in the [https://www.make-it-in-germany.com/fileadmin/1_Rebrush_2022/a_Fachkraefte/PDF-Dateien/3_Visum_u_Aufenthalt/2024_Mangelberufe_DE.pdf list of shortage occupations in Germany] (see Group 226). In this list, audiologists are mentioned alongside speech therapists. Speech therapist (also known as a logopaedist) is a regulated profession in Germany.

In Germany, [https://www.bundesaerztekammer.de/fileadmin/user_upload/BAEK/Themen/Aus-Fort-Weiterbildung/Weiterbildung/FEWP/FA_SP-WB/20210819_20_FEWP_PhoniatriePaedaudiologie.pdf specialist training in Phoniatrics and Pediatric Audiology] typically takes five years, similar to training in Otorhinolaryngology and other medical specialties. Phoniatrics and Pediatric Audiology is the youngest recognized medical specialty in Germany. It is a combined medical and surgical discipline. Although surgery does not represent the main focus of daily clinical practice, the specialty also includes otologic procedures such as paracentesis and tympanostomy tube insertion.

In recent years, the European Academy of Phoniatrics, founded in Germany, has offered international training courses for physicians in this field. Since 2025, under the umbrella of the European Board Examination in Otorhinolaryngology – Head and Neck Surgery, the first board examinations leading to the qualification of European Phoniatrician have also been introduced. Within this medical specialization, audiology represents an important pillar.

Phoniatrics and Pediatric Audiology also maintains close links with logopedics, the discipline concerned with therapeutic interventions for disorders of language, speech, voice, hearing, and swallowing. Many phoniatric and pediatric audiology institutions in Germany are affiliated with training schools for speech-language pathologists, where students receive their theoretical and practical education in close collaboration with departments and clinics of Phoniatrics and Pediatric Audiology.{{HTitle|Professional and Regulatory Bodies}}

=== Professional organizations within Audiology in Germany are: ===
·        Deutsche Gesellschaft für Audiologie ([https://dga-ev.com/ DGA])

·        Deutsche Gesellschaft für Hals-Nasen-Ohrenheilkunde, Kopf- und Hals-Chirurgie ([https://hno.org/ DGHNO-KHC])

·        Deutsche Gesellschaft für Phoniatrie und Pädaudiologie ([https://dgpp.de/de/ DGPP])

·        Berufs- und Fachverband Hören und Kommunikation ([https://www.b-d-h.de/ BDH])

·        Europäische Union der Hörakustiker ([https://www.euha.org/ EUHA])

·        Bundesinnung der Hörakustiker ([https://www.biha.de/ biha])

·        Dachverband für Technologen/-innen und Analytiker/-innen in der Medizin Deutschland ([https://dvta.de/mtf DVTA])

·        Berufsverband der Audiologie-Assistenten ([https://www.baa-audiologie.de/ BAA]){{HTitle|Ongoing audiology research}}Audiology research is done in clinics, in technical and psychological departments as well in biological departments at universities.  Scienitifc exchange is mainly organized by the Deutsche Gesellschaft für Audiologie ([https://dga-ev.com/ DGA]) at annual conferences. The DGA comprises five working groups (&quot;Fachausschüsse&quot;) focusing on 

* Audiometry and Quality Assurance
* Hearing Aid Technology and Hearing Aid provision
* Pediatric Audiology
* Cochlear Implant Provision
* Neurotology and Vestibular System

Official publication organ of the DGA is the open access journal  [https://journals.publisso.de/de/journals/zaud/ Zeitschrift für Audiologie].

{{HTitle|Challenges, Opportunities and Notes}}Germany pioneered social health insurance in 1883 based on the social legislation of Otto von Bismarck. Today Germany's health system is strong and hearing healthcare is mainly covered by social insurance. Newborn hearings screening was established in 2009 and is completely covered by social insurance. Additionally, hearing diagnostics and therapy (including hearing aids and cochlear implants) are usually paid in total or partly by the statutory health insurance. However, several challenges remain. For example, according to the [https://www.ehima.com/sdc_download/4891/?key=q5tpwysll8pp68cia4r9mijpnpbh1i Euro Trak Germany survey in 2025], the adoption rate of hearing aids is only 47% of those with self-declared hearing loss and about 5.1% of the total population. {{HTitle|Audiology Charities}}The largest foundation for hearing research is the [https://kind-hoerstiftung.de/ KIND Hörstiftung]. According to its statutes, the KIND Hörstiftung aims to reduce the impact of hearing impairment and to foster full participation in social life of hearing impaired people. The foundation's instruments are funding of hearing research projects. Furthermore, it organizes a biennial interdisciplinary colloquium and awards a Foundation Prize for outstanding scientific work in the field of Audiology. Decisions regarding the allocation of funds are made by the Scientific Board and the Foundation Council.

There are several self-help groups for Tinnitus ([https://www.tinnitus-liga.de/ Deutsche Tinitus Liga, DTL]), hearing loss ([https://schwerhoerigen-netz.de/ Deutscher Schwerhörigenbund, DSB]) , and Cochlear Implants ([https://dcig.de/ Deutsche Cochlea Implantat Gesellschaft, DCIG]). The latter two groups combined their forces in [https://www.hoerverband.de/ Deutscher Hörverband].  {{HTitle|References}}
{{reflist}}


{{:Global Audiology/Authors-1|Ulrich Hoppe | https://de.linkedin.com/in/ulrich-hoppe-3397238b }}

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What follows are Dan Polansky's highly incomplete and relatively disorganized notes on Czech, especially Czech grammar and punctuation. Czech vocabulary is covered in dictionaries, but I may cover idiosyncratically selected vocabulary questions here. There is a hope that someone will find the notes useful as well.

== Spelling ==
Czechs seem to care very much about what they consider to be correct spelling. Czech spelling seems to correspond to a single standard, unlike British vs. U.S. vs. Canadian vs. Australian etc. Spelling can be checked in ''Pravidla českého pravopisu''.

Some forms that are commonly considered to be misspelling (even if one can argue that this is a misconception) include ''tchýně'' (vs. ''tchyně'') and ''vyjímka'' (vs. ''výjimka'').

There is a distinction between ů and ú, a result (some may say burden) of history; the pronunciation is the same. There are some heuristic rules of thumb for this aspect, but in case of doubt, one is well advised to consult a dictionary since certain exceptions seem to have been codified as correct.

There is a distinction between y and i, a result (some may say burden) of history; the pronunciation is the same. There is a set of rule for this aspect. Children seem to struggle with this aspect, and so do some adults. I seem to recall that in Russian (another Slavic language), the distinction between what Czechs call hard i (y) and soft i (i) is reflected in the pronunciation.

In general, there is a tight, nearly mechanical correspondence between pronunciation of spelling. It is rather easy to derive pronunciation from spelling. The other direction is also fairly straightforward but for ambiguities such as those mentioned above. It is fairly easy to produce phonetic spellings that are not part of the standard, e.g. ''dizajn'' and ''softvér'' (these spellings seem standard in Slovak).

Some words are taken over from English in an unchanged form as for spelling, creating exception to the rule of the spelling being phonological: design, image, banjo, smartphone, interface; these words acquire Czech pronunciation following the English one. Which words receive this treatment does not seem to be governed by any simple or fixed rule; since, by contrast, there is ''telefon'' (rather than ''telephone''), ''telegraf'', ''morfologie'', etc. Interestingly, Slovak, a closely similar language, spells e.g. ''dizajn''.

Further reading:
* {{W|Czech orthography}}, wikipedia.org

== Spelling reforms ==
Kučera and Stluka report three spelling reforms in the 19th century.&lt;ref&gt;[http://www.lrec-conf.org/proceedings/lrec2014/pdf/300_Paper.pdf Corpus of 19th-century Czech Texts: Problems and Solution] by Karel Kučera and Martin Stluka, lrec-conf.org&lt;/ref&gt;

During the 20th century, Czech underwent one or more spelling reforms. For example: ''filosofie'' --&gt; ''filozofie'', ''theorie'' --&gt; ''teorie'', ''analysovati'' --&gt; ''analyzovat'', ''president'' --&gt; ''prezident''.

== Hyphens and dashes ==
Czech uses hyphens and en dashes.

Em dash is hardly ever used in Czech.

When an en dash is used to separate a parenthetical part of a sentence, it is enclosed with spaces (which differs from the U.S. using em dash without space enclosure?)

More is currently delegated to further reading.

Further reading:
* [https://p3k.cz/odkazy/pomlcka_spojovnik.pdf Pomlčku, nebo spojovník?], p3k.cz
* [https://didacticus.cz/pomlcka-spojovnik Pomlčka versus spojovník], didacticus.cz

== Word order ==
Compared to English, Czech has a much more flexible word order. This is supported by inflection. For instance, what in English would be an object is rather often on the position of subject, e.g. ''nádobí jsem umyl'' (I washed the dishes.), although in this example, inflection does not play a role.

== Czech dictionaries ==
See [[Czech dictionaries]].

Let me mention some of the modern ones, all definition dictionaries defining Czech words using Czech words:
* PSJČ
* SSJČ
* SSČ
* ASCS
* ASSČ, in the making

== Definite and indefinite articles ==
Unlike English or German, Czech does not have definite and indefinite articles. However, some words can be pushed to serve the purpose, including ''ten'' for definite article and ''nějaký'' for indefinite article. Legal documents sometimes use the adjective ''předmětný'' in a way that resembles that of a definite article.

== Capitalization ==
In part, Czech capitalization resembles that of English:
* Sentences start with a capital letter.
* Nouns other than proper nouns are in general not capitalized, unlike in German.

However:
* For proper names, Czech generally does not use title case and only the first word is capitalized. And thus, there is ''Mnoho povyku pro nic'' (Shakespeare's Much Ado About Nothing). Of course, the word in the middle of a title can have its own rationale for capitalization, e.g. in the putative novel title ''Muž s deštníkem z Prahy''.
* For adjectives derived from proper nouns, Czech does not capitalize them. And thus, there is ''český'' (adj:Czech), ''pražský'' (attributive:Prague), ''moravský'' (adj:Moravian), etc.

== Punctuation ==
Czech seem to be using something like a syntactic comma. And thus, there is comma before ''že'', as in ''Vím, že nic nevím''. Moreover, there is a comma before ''který'' and ''jenž'' (which, that) without regard for whether they introduce a defining clause of an extra-information clause. From what I remember, this did not use to be the case; this practice was taken over either from Austria or Germany (verification pending).

Other than that, Czech punctuation resembles that of English. There is a period at the end of a sentence; there is the question mark and exclamation mark at the end of a sentence; semicolon in the middle of a sentence is much like in English, except that Czech seem to be committing comma splice quite a bit more than English. Colon seems to be used in ways similar to English.

As for quotation marks, the Czech ones are the German ones, not the English ones (verification pending).

As for brackets, the usual ones from English apply. Czech may be more inclined to insert parentheticals (like this one) into sentences; verification pending.

== Paragraph structure ==
Czechs may tend to write less well organized paragraphs, with more tangential elements, with less well logically grouped items. Anecdotal; verification pending. Other than that, a Czech paragraph is like an English paragraph. The mentioned anecdotal difference, if true, is perhaps more of a matter of culture than the language per se.

== Attributive use of nouns ==
Unlike English, Czech generally does not allow attributive use of nouns. One has to use the corresponding adjective instead. That is to say, many nouns have their corresponding adjectival version with the meaning, of or relating to. Thus, the English ''power grid'' is ''elektrická síť'', not *''elektřina síť''. (As a mnemonic, one can perhaps think of *''poweral grid'' or *''poweric grid''.)

The suffixes used to create such adjectives include ''-ní'' (e..g ''vodní''), ''-ský'' (e.g. ''pražský'') a ''-ový''. Which one is used with which noun has to be learned by heart.

== Důsledek vs. následek ==
I tend to use ''důsledek'' to refer to ''logical'' consequence and ''následek'' to refer to ''causal'' consequence. I am not sure where I have this norm from. It is not universally upheld by Czech writers.

And thus, it would be incorrect to state that ''v důsledku zranění zemřel'', but it would be fine to state that ''následkem zranění zemřel''.

== Pojem vs. termín, slovo and fráze ==
I tend to use ''pojem'' strictly as a synonym to the English ''concept'', whereas Czech writers often use ''pojem'' as a synonym of the English ''term''.  My rationale is this: we need a Czech name for the concept of ''concept'' and ''pojem'' neatly fits the bill; we do not need ''pojem'' as a reference to ''term'' since we have ''termín'' for that.

And thus, a statement like ''tento pojem má více významů'' is nonsense, in my terminology; it is the ''významy'' that are ''pojems''.

The Czech confusion may in part have to do with the German confusion concerning ''Begriff'', which sometimes refers to ''concept'' and sometimes to ''word or phrase''. Duden:Begriff 1 is concept; Duden:Begriff 2 is expression, word, marked as colloquial.&lt;ref&gt;https://www.duden.de/rechtschreibung/Begriff&lt;/ref&gt;

== Počátek vs. začátek ==
I once heard a philosophy university teacher indicate a difference between ''počátek'' and ''začátek'' that I found compelling. According to this distinction, ''počátek'' has to do with origination, unlike ''začátek''. And thus, a book's ''začátek'' are the first pages, whereas its ''počátek'' may lie somewhere quite different. I am fairly confident some authors use ''počátek'' and ''začátek'' indiscriminately as synonyms.

== Dlužno ==
I like to use the Czech word ''dlužno'' in a way that is now archaic, approximately stating a duty. Alternatives are ''radno'', ''lépe'', ''záhodno'' and ''nutno'', but, etymologically, they seem to be a worse fit. I think ''dluh'' (debt) is an excellent synecdoche for duty. The English equivalent is ''ought to'' in the deontic sense (''ought to'' is also used in epistemic sense). Czech ''dlužno'' is still in widespread use in the phrase ''dlužno dodat''. It seems unlikely that Czechs will fail to understand this use; at worst, some may be irritated by its being archaic. Some may be irritated by its surface affinity to the Russian modality dolžen or similar, given the current hatred (in part irrational) of all things Russian.

== Anglosaský vs. anglofonní ==
Czechs tend to use ''anglosaský'' in the sense of Anglophone (I think), that is, pertaining to the U.K., U.S., Canada, Australia, etc. It is perhaps a good idea to start using ''anglofonní'' instead, to avoid the habit of saying ''Anglo-Saxon'' in English, which apparently leads to some surprise in Anglophone commenters.&lt;ref&gt;https://www.reuters.com/article/business/energy/putin-says-anglo-saxon-powers-blew-up-nord-stream-pipelines-idUSS8N2Z80FZ/&lt;/ref&gt; And etymologically, avoiding ''anglosaský'' in this sense is parhaps not a bad idea; the Saxons are not at stake anyway, and nor are Angles; what about the poor Normans? On the other hand, one cannot push the etymological requirement too far: the modern ''English'' is not the language of ''Angles''; it is also the language of the former Normans but above all all European Americans including former Germans, Dutch, French, etc.

== Lze říci ==
''Lze říci'' is a Czech idiom that I plan to avoid. It would be equivalent to stating &quot;One can say that X&quot; instead of &quot;X&quot;. Since, if X can be said, say it, and be done with it. &quot;One can say that X&quot; cannot be directly refuted since it is indeed true that one can say X for all sort of wrong or implausible X.

== Náhodný vs. nahodilý ==
I tend to use ''náhodný'' for strictly random and ''nahodilý'' for something that is not guaranteed to be random but also not guaranteed to be systematic. I need to find out to what extent this is a mere idiolect of mine. There is also ''pseudonáhodný'' for pseudorandom.

== Optimálnější and nejoptimálnější ==
From a strict perspective, both forms reflect erroneous understanding of the semantics of ''optimální'' (optimal). They correspond to English &quot;more optimal&quot; (probably intended to be ''better'') and &quot;most optimal&quot; (probably intended to be ''best''). One way to meaningfully interpret &quot;most optimal&quot; is as &quot;closest to the optimum&quot;, but it is not clear why one should not simply say ''best'' instead, and in Czech, ''nejlepší''. (Actually, it is pretty clear: too many people use imporant-sounding, &quot;heavy&quot; words to sound educated/erudite, and ''optimálnější'' sounds more educated-erudite than ''lepší''.)

On a related note, ''optimální'' is not a strict synonym of ''ideální'', from what I understand; optimal means best given real-word constraints. That said, there are many contexts in which the two words can be used interchangeably.

Further reading:
* [https://www.nabla.cz/obsah/cestina/clanky/optimalni-optimalnejsi-nejoptimalnejsi-idealni-idealnejsi-nejidealnejsi.php Optimální - optimálnější - nejoptimálnější, ideální - ideálnější - nejideálnější], nabla.cz
* [https://ct24.ceskatelevize.cz/clanek/nazory/cestina-pred-kamerou-36-dobry-lepsi-nejoptimalnejsi-160625 Čeština před kamerou (36) - Dobrý, lepší, nejoptimálnější — ČT24], ceskatelevize.cz

== Pokud ==
The word ''pokud'' is often used to mean ''if''. However, the etymology seems to point to a spatial relationship involved; compare the spatial ''odkud'' and ''tudy''. This leads to a possible stylistic choice of avoiding ''pokud'' in that sense, using ''jestliže'', ''pakliže'', ''-li'' and ''v případě, že'' instead. The form ''v případě, že'' seems often used in legal documents. The form ''v případě, že'' is reminiscent of the German ''Falls''.

The stylistic choice of abandoning ''pokud'' in the sense of ''if'' can be further supported by pointing out that we need a Czech word (or phrase) corresponding to the English ''as far as'', ''to the extent'' or similar. There is a great difference between e.g. &quot;if applicable&quot; and &quot;as far as appliable&quot;. The &quot;if&quot; variants suggests that something either is applicable or it isn't, but that is generally not the case.

The English phrase ''as far as I know'' is well translated as ''pokud vím'', referring to the extent of knowledge rather than a binary/categorical presence or absence.

The German ''soweit'' should be analyzed for correspondence to ''pokud''; it could plausibly correspond. A relevant phrase is ''soweit dies möglich ist''.

== Takřka and téměř ==
My stylistic preference is to avoid ''takřka''&lt;ref&gt;https://prirucka.ujc.cas.cz/?slovo=tak%C5%99ka&lt;/ref&gt; (almost) and use ''téměř'' instead. It is driven by etymology: ''takřka'' sounds like ''takříkajíc'' (so to speak, German sozusagen), suggesting something slightly different than ''almost''. Sure enough, one cannot in general assure alignment of semantics with etymology, but one can try here and there.

== S největší pravděpodobností ==
This phrase corresponds to English ''in all probability'', but is etymologically equivalent to &quot;with the greatest probability&quot;. In my view, this vague phrase should be avoided in serious writing and reporting. It is an etymological mismatch; if there are e.g. 10 events that are similarly probable but one of them is slightly more probable, then that one happens with the greatest probability (among the considered events), but the probability is slightly above 10 percent. If what one wants to report is known with only vague degree of certainty, there are words capturing that degree, e.g. ''nejspíš''. Moreover, I think one should not use the word ''probability'' if one does not know the numerical probability and does not even have an estimate of it.

== Podle všeho ==
As if the English according to everything. According to what? Avoid in serious writing?

Seems similar to German ''allem Anschein nach'' (according to all appearances) except that the ''Anschein''/appearance is missing.

== Ztotožňovat se ==
I don't know why but I strongly dislike the idiom by which people say things like &quot;Ztotožnuji se s názorem že X&quot; to mean something like, I fully agree with the view that X, but what they say is, I identify with the view that X. Literally, that is of course nonsense. A plain way of stating the same is &quot;Souhlasím s názorem X&quot; or &quot;Zcela souhlasím s názorem X&quot;.

One reason I may dislike this idiom is that the language of identity is thereby diluted or confused, and the concept of identity is hard enough as it is.

Sure enough, it is the essence of an idiom not to be literal. And thus, the deviation from the literal meaning cannot alone be grounds for rejection.

== Zdát se vs. jevit se ==
If one wants to avoid lexicalized metaphor, one may avoid ''zdát se'' in the sense of ''seem'' in favor of ''jevit se''. It is quite possible that the legal profession often does make this stylistic choice. The core or lead literal meaning of ''zdát'' is to have a dream. Another option is ''přijít'', as in ''to mi nepřijde jako dobrý nápad'', that does not seem a good idea to me.

However, it would have to be clarified whether even the ''jevit se'' in that sense is not rather a lexicalized metaphor.

There is ''zdání klame'' but no ''jevení klame''.

== Nepříliš ==
There is an idiom: ''X je nepříliš Y'' and ''X není příliš Y'' (''příliš'' = too, excessively). I dislike the idiom, although I sometimes use it myself. I often feel the urge to say: if X is not excessively Y, then the degree of Y is perhaps about right.

== Názor and pocit ==
I tend to avoid the word ''názor'' (opinion, view) in favor or ''postoj'' (position, stance), ''odhad'' (estimate) and ''dojem'' (impression). One motivation is etymological: ''názor'', apparently from ''nazírat'', itself from ''zírat'', relating to ''nazřít'' and ''zřít'' (to see), is suggestive of objectivity, even if from a perspective. Sure enough, we cannot see a physical object/body (e.g. a cup) from all sides at once, but the use of human vision (or photography) in an epitome of objectivity. By contrast, the meaning of opinion is suggestive of subjectivity, great uncertainty, guesswork, etc. Another advantage is something like greater honesty, especially in relation to having a ''postoj'' (position, stance): there is a great difference between taking a stance and making an estimate and it is not clear it is a good idea to lump both together under one headword.

The above criticism of ''názor'' seems to apply to English ''view'' and ''point of view'' as well.

A related terminological issue is of use of ''pocit'' (feeling). I seem to recall some psychologists to propose to restrict ''pocit'' to emotions, to the exclusion of ''dojem'' (impression). This would make the form ''mám pocit že X'' incorrect/disapproved of.

== Konstatovat ==
I dislike this word and hardly ever use it myself. I am not sure what exactly it is supposed to mean (approximately, it seems to mean ''to state'') and how it is supposed to be used in contrast to ''uvést'', ''sdělit'', ''oznámit'', etc. In a more narrow usage, it could be constrained to making a &quot;dry&quot; statement of facts, but I am not sure how widepread it is. If the intended meaning is the same as ''uvést'', I do not see how a four-syllable foreign-sounding word would be preferable to two-syllable Slavic word (three-syllable in inflected forms) except among the kind of circles whose expertise consists mainly in having learned peculiar vocabulary.

== False friends ==
There are multiple false friends between Czech and English, words that sound similar but have a different meaning.

Some examples, although their value may be more for Czech speakers learning English than the other way around:
* ''eventuálně'' vs. ''eventually'' (''nakonec'')
* ''konkrétní'' (''specific'') vs. ''concrete'' (perhaps not a complete false friend, but English ''specific'' seems to be a better fit)
* ''ambulance'' vs. English ''ambulance'' (''sanitka'')
* ''aktuální'' (current) vs. ''actual'' (''skutečný'')
* ''absolvovat'' vs. ''absolve''
* ''kuchyně'' vs. ''kitchen'' (this is not wrong in one sense of ''kuchyně'', but is wrong in the sense of ''cuisine'')
* ''šéf'' (boss) vs. ''chef'' (''šéfkuchař'')
* ''kontrolovat'' vs. ''control'' (''ovládat'', ''řídit'') (wrong in the sense check or double-check of ''kontrolovat'', although ''kontrolovat'' is gaining the English sense under influence of English)
* ''gymnázium'' (a type of high school/grammar school) vs. ''gymnasium'' (''posilovna'', ''tělocvična'' or similar)

The rest is currently delegated to further reading.

Further reading:
* [[Wiktionary:cs: Příloha:Falešní přátelé v češtině a angličtině]], wiktionary.org
* [https://getintoenglish.com/learn-english-false-friends-falesni-pratele/ 7 English words Czech learners can mix up – false friends (falešní přátelé) – Get into Englishg], getintoenglish.com
* [https://is.muni.cz/th/z289m/Pavliska_diploma_thesis.pdf False Friends Between Czech and English], master's thesis, is.muni.cz
* [https://englishhacker.cz/rubrika/false-friends/ False friends], englishhacker.cz
* [https://anglictinavpohode.cz/false-friends/ False friends], anglictinavpohode.cz

== Konkrétní ==
Czech ''konkrétní'' seems to be something like a false friend of English ''concrete''. In most everyday uses, the most idiomatic translation seems to be ''specific''. In this use, ''abstraktní'' is not the opposite of ''konkrétní''; ''nekonkrétní'' and ''obecné'' is. And this shows the terminological confution here; a more &quot;natural&quot; opposite to ''obecné'' is ''zvláštní'' or ''speciální''.

One could try to figure out whether a German counterpart matches the semantics of the Czech word, which would suggest that the Czech meaning of specific stems from German.

== Eventuálně ==
Czech ''eventuálně'' seems to be something like a false friend of English ''eventually''. The Czech words seems to stem from German. Czech ''eventuálně'' does not indicate that the thing will necessarily or very likely happen in future.

== Traps for the unwarry ==
Czech features a range of traps, features that fool the unwary and require special training:
* The double negation, e.g. &quot;V krabici nic není&quot; (There isn't nothing in the box) instead of the logically correct &quot;V krabici je nic&quot; (There is nothing in the box).
* &quot;mě&quot; vs. &quot;mně&quot;, pronounced identically, with unclear rationale for existence.
* Spelling of &quot;y&quot; vs. &quot;i&quot;, pronounced identically. Children learn rules for this and lists of exceptions, called &quot;vyjmenovaná slova&quot; (enumerated/listed words).
* Spelling of &quot;ú&quot; vs. &quot;ů&quot;, an artifact of history that Slovak (a very similar language) does not have.
* &quot;Bych&quot; vs. &quot;bysem&quot; and &quot;Bychom&quot; vs. &quot;bysme&quot; or &quot;byjsme&quot;, a peculiar feature.
* Allegedly incorrect &quot;vyjímka&quot; instead of the &quot;correct&quot; &quot;výjimka&quot;.
* Allegedly incorrect &quot;tchýně&quot; instead of the &quot;correct &quot;tchyně&quot;.
* &quot;Ředitel&quot;, suggestive of &quot;ředit&quot; (dissolve), instead of the more intuitive &quot;řiditel&quot;, suggestive of &quot;řídit&quot; (drive, manage, govern).
* The Central Bohemian word variants and inflection that does not match the codified form/inflection: &quot;tejden&quot; vs. the correct/neutral &quot;týden&quot;; &quot;černej&quot; vs. &quot;černý&quot; etc. This is an artifact of history: the codification was based on the Moravian form/inflection, based on the Kralice Bible, from what I remember (Kralice is in Moravia). This is called &quot;obecná čeština&quot;, although the term also refers to other phenomena. This variant is spoken not only in Central Bohemia but also in other parts of Czechia, including Moravia. From what I remember, even the trained public broadcasters struggle to speak perfect Standard Czech, speaking a nearly Standard Czech.

It is children and foreign learners that struggle with these features most.

One could introduce a language reform to eliminate these oddities, an analogue of drying swamps, straightening out rivers and other interventions into natural orders of things. One could call it streamlining or rationalization. Such a reform would make all previously published texts archaic. Even so, multiple languages do see deep-going reforms, e.g. a complete switch to Latin script for Turkish.

Something like demotization or simplification of spelling did take place in the 20th century as part of spelling reforms. And thus, &quot;kommisse&quot; was abandonden in favor of &quot;komise&quot;, &quot;president&quot; in favor of &quot;prezident&quot;, &quot;fysika&quot; in favor of &quot;fyzika&quot;, &quot;filosofie&quot; in favor of &quot;filozofie&quot; (which remained controversial among the philosophers/pseudophilosophers), etc. This shows that where there is will, there is a way. On the other hand, removing the oddities listed above would have much more far reaching impact.

== Inflection of a proper names in an address ==
From what I recall, ''pane Nováku'' is considered correct while ''pane Novák'' is considered incorrect, substandard or colloquial.

Similarly, the correct form is not *''ve městě Praha'' but rather ''ve městě Praze''.

If one wants to use an uninflected form, one can probably use the form ''jménem X'', where X is not inflected (to be double checked). Use of uninflected forms is especially of advantage in electronic records since not all search tools know how to search for all inflected forms.

In connection to companies, there is e.g. ''ve firmě Microsoft'' but much less or almost no ''ve firmě Microsoftu''. This brings about an apparent inconsistence.

Be it as it may, the TV series title ''Uctivá poklona, pane Kohn'' does not use the form ''pane Kohne''. In the ''Pan Vrána'' comic skit, Felix Holzmann does not inflect X in ''pane X'' either, saying ''pane Vrána'', ''pane Slavík'', etc.

== Word origin or etymology ==
Czech is a Slavic language, like Polish or Russian. Naturally, many words stem from an ancestral Slavic language. However, many even basic words stem from languages or language phases ancestral to modern German, including ''barva'', ''havíř'', ''malíř'', ''rytíř'', etc.. This is likely due to long-term tight historical contact with or even dominance by Germans. Bohemia's western neighbors were German states for a long time. Moreover, Czech lands were administered in German for over 300 years before the 20th century, from what I understand (but this would not explain ''barva'' or ''rytíř''). (German also has some Slavic words, e.g. ''Grenze'' reminiscent of ''hranice'', but the Slavic-to-German imports seem far fewer.)

Of course, the modern international scientific vocabulary is from Latin and Green. Moreover, other Latin-derived vocabulary from western languages (English, French, Italian) has apparently been taken over without much effort. Indeed, it is very easy to coin Czech-sounding equivalents, e.g. *''mendaciózní'' from ''mendacious''.

A key portion of Slavic-sounding scientific vocabulary, especially from biology, is due to new coinage during the national revival movement. One person responsible for much of the coinage is Presl. The typical coining process is of ''calque'', breaking the original item down into real or putative morphemes, translating the morphemes, and joining them together to form the final product.

See also [[Word coinage during Czech National Revival]].

=== Some strange compound forms ===
One form that makes me wonder is ''[[Wikt:drahokam|drahokam]]'' (gemstone), apparently from ''drahý'' and ''kámen'' (precious stone), probably a calque from German ''[[Wikt:Edelstein|Edelstein]]''. What is not clear is how ''kámen'' became ''kam''. I think I saw some scholarly article about ''drahokam''.

A weak analogy to ''drahokam'' would be ''bolehlav''. There is also ''hlavobol'', headache, formed in a perfectly normal compounding process.

== Viz vs. vizte ==
The conventional form of the English ''see'' in Czech is ''viz''. One can sometimes see ''vizte'', a form of ''vykání'' apparently to be polite. I find it unconventional. I expect professionally written works to use ''viz'' rather than ''vizte''. (''Vizte'' is reminiscent of ''čaute'', which I find unusual; I think the Slovak counterpart is more usual and was once used by Mečiar from what I recall. Verification pending.)

The form &quot;viz.&quot; (with period at the end) is unusual and does not match etymology; &quot;viz&quot; originated as a singular imperative from &quot;vidět&quot;, an analogy to English &quot;see [...]&quot; or German &quot;siehe [...]&quot; (compare [[Wikt:en: siehe auch]]). (Germans do not seem to use the polite verb form either and use singular &quot;siehe&quot; instead.)

Example works using ''viz'' rather than ''vizte'': New Encyclopedic Dictionary of Czech, e.g. [https://www.czechency.org/slovnik/AF%C3%81ZIE AFÁZIE].

== Jednoduchý and složitý vs. snadný and obtížný ==
My stylistic preference is to use the two words in ways reflective of their etymology/morphology. I therefore draw a distinction between ''snadný úkol'' (easy task) and ''jednoduchý úkol'' (simple task). In this sense, a task can be very arduous/laborious (not easy) yet simple (consisting of simple monotonous steps). A complex task is then one that requires a complex manner of procedure.

In this vein, I disagree with the terminological choice in the name ''computational complexity'' theory, in Czech ''výpočtová složitost''. To my mind, an algorithm can be very ''simple'' yet resource-intensive, demanding on time or space; an example is bubble sort, much more simple but also generally much more resource-intensive than quick sort. By contrast, the term ''Kolmogorov complexity'' seems fine.

On a second thought, I am not sure the word ''obtížný''/difficult well captures the resource-intensiveness. ''Pracný''/laborious seems better.

Relating Latin words are ''eise'', ''difficilis'', ''simplex'' and ''complexus''.

== Jaký ==
Narrowly interpreted, ''jaký'' would be rendered as what kind of (really? what exactly does ''what kind of'' refer to? does ''kind'' really refer to qualities?). However, it is often used to mean ''what'', as in ''jaké je vaše jméno'', what is your name. Assuming the narrow constrution/interpretation, ''jaké je vaše jméno'' (to ask for a name) would be incorrect and it should be ''co je vaše jméno'', which is not usually used. One can use the narrow interpretation for Felix Holzmann-like trolling: A: Jaké je vaše jméno? B: Pěkné.

One would want to give a rule or algorithm for when to use ''jaký'' in the sense of what. None seems obvious. For instance, it is ''kdo je prezident České republiky'' (who is the president of the Czech Republic) rather than ''jaký je prezident České republiky''; the latter is valid/idiomatic Czech, but one asking for properties/qualities of the president, e.g. whether he is ''laskavý'' (kind).

SSČ has the narrow construction as sense 1&lt;ref&gt;https://prirucka.ujc.cas.cz/?slovo=jaký&lt;/ref&gt;. It indicates the ''what'' construction as ''hovorový'' (colloquial, informal), which is strange: ''jaké je vaše jméno'' is neutral Czech (I argue). ASSČ has the ''what'' construction as sense 2&lt;ref&gt;TBD&lt;/ref&gt;, &quot;uvozuje otázku týkající se výběru, vyčlenění jednotlivé věci, jevu, osoby ap. z daného souboru&quot;. I argue that ASSČ is incorrect; ''jaký'' does not refer to ''z daného souboru''. I argue that this use of ''jaký'' is equivalent to English ''what'', and is not equivalent to ''which''.

The inflection of ''jaký'' is adjectival (e.g. ''jakému'' as in ''mladému''), supporting the narrow interpretation. That is, one would expect the answer to be adjectival, referring to a quality. On the other hand, ''který'' is also inflected adjectivally, but the answers are always (or nearly always?) nominal.

== Technika vs. technologie ==
''Technika'' refers to technology (as in ''výpočetní technika'', ''Věda a technika mládeži'') and to technique (as in ''technika háčkování''). ''Technologie'' refers to technology (as in ''Fakulta informačních technologií'').

Caveat: above, I did not indicate which sense of technology is meant, as if there was only one sense.

Relating adjectives are ''technický'' and ''technologický''.

I register increased use of ''technologie'' where before there would have been ''technika''. This seems to be under influence of English, especially after the abandonment of socialism in 1989, when the teaching of Russian at schools was replaced with teaching of English and German. What is now called ''Fakulta informačních technologií'' (why the plural?) would have been called ''Fakulta informační techniky'' or even ''Fakulta výpočetní techniky''. (An aside: why Czechs adopted, perhaps from Germans and French, the term ''informatika'' for what has much more to do with computation than information and in English in ''computer science'', I often wonder.)

I am fond enouch of the older word ''technika'' (usually uncountable?) to wish to continue using it instead of the fashionable ''technologie''. Etymologically, ''technologie'' seems poorly motivated: it sounds like some academic discipline, perhaps ''the study of'' technology rather than technology itself.

The shift is likely to be also reflected in the adjectives. I would expect a shift from ''technický pokrok'' to ''technologický pokrok''. (Google Ngram Viewer does not support Czech, but it supports German.)

A similar consideration may apply to German. There too, under influence of English, one would speak e.g. of ''Internet-Technologien''. German can be analyzed using Google Ngram Viewer. Here is Informationstechnik,Informationstechnologie&lt;ref&gt;https://books.google.com/ngrams/graph?content=Informationstechnik%2CInformationstechnologie&amp;year_start=1800&amp;year_end=2019&amp;corpus=de&amp;smoothing=3&lt;/ref&gt;

Returning back to Czech, if one wants to use contemporary native-sounding Czech, one can drive the choice of ''technika'' vs. ''technologie'' by collocations with adjectives. For instance, while ''výpočetní technologie'' sees considerable use, ''výpočetní technika'' seems to produce use of more reputable/serious sources or organinations on the first page of Google search. Moreover, one can consult authority sources in the sense of library of information science, linked from Wikidata; there, ''výpočetní technika'' is the preferred term.

Links:
* https://vesmir.cz/cz/casopis/archiv-casopisu/1994/cislo-11/technologie-versus-technika.html

== Baterie vs. akumulátor ==
From what I recall, non-rechargable batteries would &quot;properly&quot; be called ''akumulátor'' rather than ''baterie''. However, many language users do not care, and call rechargeable batteries ''baterie'', perhaps under the influence of English.&lt;!-- TBD: add references or sources --&gt;

== Dynamo vs. alternátor ==
From what I recall, the item in a bicycle that ensure supply of electrical energy into a headlight (is that the term?) is informally called ''dynamo'' but would &quot;properly&quot; called ''alternátor''.&lt;!-- TBD: add references or sources --&gt;

== Ekonomie vs. ekonomika ==
Formally, ''ekonomie'' (economics) is the study of allocation of scarce resources. By contrast, there is ''národní ekonomika'' (national economy). The two words are easily confused. Part of the confusion may be that the English suffics ''-ics'' usually maps to the Czech ''-ika''. The Czech terminology is perhaps influenced by German teminology&lt;!-- TBD: check --&gt;.

== Problematika ==
It seems to me the word ''problematika'' (problem area?) can often be omitted without much loss. Consider a statement I found in beautiful slides on logic: &quot;Neformální logika studuje problematiku správné argumentace v přirozeném jazyce&quot;&lt;ref&gt;https://www.fi.muni.cz/usr/kucera/teaching/logic/log.pdf&lt;/ref&gt; I see no loss in changing that to &quot;Neformální logika studuje správnou argumentaci v přirozeném jazyce&quot;; that's how it would be phrased in English, I think. Perhaps I am missing something.

== Multi-gender expressions ==
One can sometimes find e.g. the following: &quot;Jak dlouho jste čekal/a [...]&quot; or &quot;byl/a&quot;? This did not use to be the case; Czech would have used generic masculine. The form exemplified is perhaps a result of German influence. From what I remember, some German state has indicated that the German analogue is dispreferred in official communication. Their argument was (I think) that such form does not provide for a natural or meaningful auditory reading and is sort of ungrammatical. The argument applies to Czech as well. That is, how should I read &quot;byl/a&quot;? If I read it as &quot;byla&quot;, I now get generic feminine. I could read it as &quot;byl lomeno a&quot;, but that sounds cumbersome. Also the visual typographic form looks cumbersome: one has to do it with many verbs on the page. I would think there are better ways to improve the situation/empowerment of women than such strange language games, perhaps virtue signalling.

== Připuštěno ==
I love to use the Czech sentence-initial word ''připuštěno'', sentence form &quot;Připuštěno, že X&quot;, but I suspect it is rather unusual. It is to correspond to English &quot;Admittedly, X&quot; (and perhaps &quot;Sure enough, X&quot;) and German ''Zugegeben, X'' (the forms to be verified). It is perhaps a calque from German.

An alternative that is probably rather usual is the sentence form &quot;Je pravda, že X&quot;, in the sense of &quot;I admit that X&quot;. I dislike it for its literal interpretation. Another alternative is &quot;Připouštím, že X&quot;. And there is &quot;Sice X&quot;, corresponding to German &quot;Zwar X&quot;, perhaps with slightly different semantics?

One may ask why would one want to use the passive ''připuštěno'' rather than ''připouštím''. It may be to sound objective or officially authoritative, as if the speaker were an authority, perhaps a judge. That alone may be a good reason to abandon this form. One may wonder what it says about the culture of the German form ''Zugegeben'' and the English form ''Admittedly'', none of them active.

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Czech language}}, wikipedia.org
* {{W|Category:Czech language}}, wikipedia.org
* [https://www.britannica.com/topic/Czech-language Czech language], britannica.com

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      <text bytes="9769" sha1="fb1c2hqam97bjhpse8xzrbx0l3m9vla" xml:space="preserve">{{Original research}}
This article by Dan Polansky looks at some questions concerning upper ontology. The term upper ontology is used without deep understanding; if this is a misapplication, the article should better be renamed later.

Some of the questions:
* What is an entity?
* What is a person?
* What is an artifact?
* What is a living thing?
* What is an object?

The initial draft may address only some of the questions.

==Entity==
One definition of entity could be this (M-W has other definitions):
* The root of ontology.
But that is a meta-definition. A similar meta-definition:
* A semantic node that has no hypernymic/superclass node.

Let us try something else:
* Anything (living or not) or anyone, including any referent of a word, phrase or a description, whether it exists or not, is real or imaginary/fictional, etc.

Corollary: Nile is an entity, and so is Bilbo. Numbers are entities. Geoforms are entities. Persons, animals and plants are entities. Time points and spatial points are entities and so are time regions and spatial regions.

Corollary: A mentally delineated part of an apple is an entity; since, it is referent of the description we just gave. One might object that this so-called entity only exists in the mind or by means by this description; a situation would be quite different if we used a knife to cut the apple into two halves. But an entity does not need to exist. Christian God is an entity and is omniponent, but (if you are an atheist), he does not exist.

Corollary: Words quasi-entity, pseudo-entity and non-entity should, properly taken, fail to refer. Since, there is no X such that X is not an entity.

We can formulate the matter in formal symbolic logic: For all X: entity(X). Alternatively, for all X, isInstance(X, entity); but then, it holds isInstance(entity, entity). We said that an entity may not exist. We get: Exists X, not exists(X); that seems like a contradiction, but it isn't since the first &quot;exists&quot; is a logical quantifier whereas the second one is a predicate, and then, these are two different meanings of &quot;exist&quot;. It is this confusion that may lead some sources to indicate existence as a defining characteristic of entity, which I argue it isn't. Thus, Bilbo is an entity but does not exist. Moreover, someone can tell me about a person, name the person and describe the person. I build a representation of that person in the mind as an entity. Then I realize I was lied to and no such person exists. Then I may say, person so-and-so name does not exist. In terms of domain of discourse, the entity for that person has been established and it does not exist. (This would perhaps belong rather to an article on existence, but since existence is discussed as a potential defining characteristics of entity, it is not entirely off topic.)

The concept of entity is useful in definitions when one wants to avoid premature classification or what could perhaps be called ontological commitment. Thus, when &quot;entity&quot; is used as a genus in a definition, it is doubtful that it is genus ''proximus'' (nearby one). But then, some things defined need to be defined as entities and nothing more specific; these could perhaps be called high genera or something of the sort. Thus, e.g. animal could be a high genus, at least in some naive(?) ontology.

The word thing could be used as a synonym for entity except that it is often or usually used in a more specific way; e.g. human persons would not be things.

==Object==
Object could be contrasted to entity. Mentally delineated entities, such as mentally delineated half of an apple, would not be objects. Objects would be split into abstract objects (numers, geometric shapes, etc.) and concrete objects (individual plants and animals, stones, pieces of furniture, etc.). It is not clear whether e.g. biological species would be concrete objects and why; they are much more specific/particular to the empirical world than e.g. numbers.

Wikidata seems to put object in contrast to property. Thus, a cup would be an object but its color not.

One has to clarify whether part objects are also objects, e.g. handle of a cup, a nose, the head of a nail, etc.; they seem to be.

One has to clarify whether negative objects are also objects, e.g. a cave; they seem to be.

One has to clarify whether things extended in space with weakly bound parts, e.g. heaps of stones or haystacks, are objects; they seem to be.

=== Beings as non-objects === 

Elsewhere, I have investigated a particular concept of being (so-being?), which is perhaps called elsewhere property; see [[An analysis of the concept of being]]. An example of a being is this: being a woman with blue eyes that wears a scarf. It is quite plausible that this is not an object. Grammatically, a being/property can appear as a subject in a sentence and possibly also an object. Thus, the grammatical concept of object needs to be contrasted to the ontological one. Whether this analysis is conventional I do not know. In any case, this is an impulse for distinguishing object (in ontology) from entity (which includes a being/property).

One complication is that there can be meta-properties, i.e. properties of properties (which, from an extentional/set-theoretic point of view, is trivial). And thus, in &quot;being rich is valuable&quot;, the being &quot;being valuable&quot; holds true of &quot;being rich&quot;.

As an example, a structure contrasting an object to a being:
* object: that entity over there, to which my finger is pointing (but: ambiguous)
** ''has''
*** being: being a cat
*** being: being white
*** being: being a white cat that has broken a vase
*** being: being an entity that has at least one being (tautological?)
Note: The only way to identify the object cognitively was via its beings/properties, or so it seems.

From this perspective, number as an object (an abstract one) makes sense:
* object: number 16
** ''has''
*** being: being even
*** being: being a square of an integer
An argument for the proposition that a number is in fact a being (so-being) rather than an object does not immediately come to mind.

One thing that seems to distinguish object from a being (so-being?) is that object is not said of, unlike a being.

However, an ontology consisting merely of objects and beings seems less useful or something of the sort, since there is no way to connect two objects; the only connection is between an object an a being, and then a being and a being. One could not get confused by the labels: the label &quot;being a cat&quot; apparently connects something to &quot;cat&quot;, but from the point of view of the ontology, the label is as if opaque. These beings are monadic beings, single-parameter beings. Thus, they are not relations, or are relations only in the sense that a monadic relation is also (an improper) relation (and zero-adic function is a constant). By bringing in relations, we can connect objects together:
* object: that entity over there (actually a cat)
** ''has''
*** being instance of
**** object: domestic cat (taxon)

SEP has a section that analyses the possibility that properties are not objects&lt;ref&gt;TBD&lt;/ref&gt;.

Further reading:
* [https://plato.stanford.edu/entries/object/ Object], Stanford Encyclopedia of Philosophy
*  [https://plato.stanford.edu/entries/abstract-objects/ Abstract Objects], Stanford Encyclopedia of Philosophy
* [[Wikidata:Q488383|Wikidata: object]]

==Person==
A quick sketch of a definition:
* An entity that can be a referent of ''who'' or ''someone'' (personal pronouns).

Another sketch:
* An entity with a non-trivial representative and executive agency.

For more, see [[An analysis of the concept of person]].

==Artifact==
A first attempt of a definition:
* Anything made by humans.
Some complications:
* What if the thing is made by robots (and these are made by humans)? That would also be an artifact.
* What if the entity is a result of animal husbandry, such as a domestic cow or a dog? These entities are somewhat artificial, but they would not probably come under the head of artifact.
* What if the thing is made by an animal, such as a beaver dam? Is beaver dam an artifact? Wikipedia uses the label &quot;structures built by animals&quot;.

We may complicate the matter by considering various degrees of artificiality and various degrees of being an artifact. Early flintstones could have featured minimum amount/scope of modification, and then, their being an artifact would have been borderline. One can even as if turn a found a flintstone into an artifact without a modification, by the act of careful selection via an extensive search; this matches a very deformed concept of an artifact, but maybe someone would find this convincing. This idea is perhaps inspired by Duchamp's alleged turning something into art merely by the act of choice, requiring no modification of the object ([[W:Fountain (Duchamp)]]).

We may consider a plastic chair to be more artificial than a wooden chair since the material of the latter is more natural. They seem to have the same degree of being an artifact (artifacthood), but not the same degree of artificiality. But then, perhaps the concept of artificiality vs. naturality (if it is a single concept) points to directions other than having to do with artifacts, e.g. natural vs. artificial human behavior.

==Living thing==
A first attempt of a definition:
* Anything that grows, reproduces and has a metabolism.
A subclass-based alternative:
* Any animal, plant, fungus, microorganism or virus.
Here, viruses are something of a special case/borderline case.

The subclass-based definition abandons genus-differentia and gains clarity as for scope.

==Other==
The following are yet to be covered:
* Process
* Event
* Action
* Activity
* Relation
* Agent
* Negative object? Hole?
* Quality
* State
* Property</text>
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      <text bytes="5173" sha1="5pdsgmnsn3zze1b7io4jp0pmxvhjti0" xml:space="preserve">==My relationship to Josef Šmajs==
I must have talked to Šmajs perhaps in 1995 or 1996 (I think). I must have bought a book by him back then, perhaps ''Ohrožená kultura''. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 13:49, 25 November 2024 (UTC)

== English vs. Czech ==
I realize that the language of the English Wikiversity is English, not Czech. And most texts about Šmajs and in relation to Šmajs are in Czech. But there is also something available in English, so writing an article on Šmajs in English is possible and seems worthwhile. Heavily referencing Czech texts seems better than ignoring them for being in Czech. In this time and age, the readers can also use machine translations. And people bilingual in English and Czech may find themselves in a comfortable position when dealing with the present article and the texts it references. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 18:16, 14 February 2025 (UTC)

== Culture vs. nature and technology vs. biology ==
(Perhaps to be added to the main text in some form.)

I think the culture (including technology) vs. nature is not so useful/fruitful a dichotomy as technology vs. biology/living things. Human culture without technology is harmless; cavemen making paintings on the cave walls cannot wreak havoc on the biosphere. And the main target of destruction are not e.g. geoforms but rather living things including species.

The matter is also complicated by the fact that some think culture and technology to be part of natu, and thus, the environmental threat picture does not fundamentally change if one changes the relationship of culture vs. nature from ''co''ordinate to ''sub''ordinate. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:33, 16 February 2025 (UTC)

== More items to process ==
I want to start paying attention to other things than this article for some time now. Here are some items that could still be processed:

1) The article in English from 2015 on the constitution of the Earth would perhaps be the single most as if &quot;nutritional&quot; publicly available article to analyze; it has not only the constitution but also other accompanying text.

2) DONE. The above mentioned article is linked from the middle but could perhaps also be linked from the end, given its probable value for understanding Šmajsian philosophy.

3) https://lindat.mff.cuni.cz/services/catalog/?f%5Bsubject_ssim%5D%5B%5D=evolutionary+ontology features 4 articles on Šmajs' &quot;evolutionary ontology&quot;. Some could be added as more links; some perhaps even in English.

4) I could create a section for a list of key concepts, key terms or key phrases. Candidate items: evolutionary ontology, aggressive adaptive strategy, predatory spiritual paradigm and thus spiritual paradigm, entropy, anti-entropic barrier, information, ontic, biophilia and biophilic.

5) Among the older articles, the one from 1973 (in Czech) is covered but others are not. One could perhaps put together a list of pre-1989 publications by Šmajs. That would be quite interesting: the article from 1973 has quite peculiar &quot;texture&quot;, so to speak. A list of candidate articles is at https://digilib.phil.muni.cz/sites/default/files/pdf/122318.pdf Sociální funkce vědy 1986.

6) This in particular can be added as a link: https://digilib2.phil.muni.cz/sites/default/files/pdf/106838.pdf Práce a socialistický způsob života.

7) https://digilib2.phil.muni.cz/en/node/63766 lists 68 publications by Šmajs, including some before 1989. What caught my attention was ''Zu den Voraussetzungen und zur Methode der Kritik der bürgerlichen Konzeptionen einer ökologischen Katastrophe'' from 1983, which states, from what I understand, that Westerns critics of the technological civilization are wrong to assign the environmental crisis to that civilization and that the crisis is to be assigned specifically to capitalism. This could be used in some way in the article. One thing to consider is to greatly expand the list of publications.

8) Sometimes (or often?), Šmajs is scant on referencing literature and sources of his ideas. For instance, in ''How Will the Promethean Myth End'' (see the article itself for a link), he only references his own works. As a result, the task of finding possible sources of his ideas is made more difficult.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:38, 25 February 2025 (UTC)
: Updated. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:27, 26 February 2025 (UTC)
: Updated. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:17, 4 March 2025 (UTC)
: Updated. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:31, 10 March 2025 (UTC)</text>
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Author: Dan Polansky

This article books at the concept of being, plural beings, as in being white or being a cat. An inspiration is the concept of being by Aristotle. However, what we get here may turn out to be something different.

== Initial considerations ==

In this conception, &quot;being&quot; is a countable noun. Example beings are the following:
* Being a cat.
* Being white.
* Being a brother (of at least one person).
* Being the brother of Martin.
* Being in the process of swimming.
* Being an entity that has two eyes.
* Being an entity that has at least two eyes.
* Being a cat that has broken a vase.
* Being Albert Einstein (the special relativity guy).
* Being a human called Albert Einstein.
* Being one of London, U.K., Orinoco, and Magna Carta (the referents, not the words).

Analogically, we may concieve of the concept of ''having''. This gives us the following example havings:
* Having a body.
* Having a house.
* Having a guitar.
* Having a brother.

Interestingly, purely syntactically, we may proclaim all havings to be beings. Since the following are apparently beings:
* Being an entity that has a body.
* Being an entity that has a house.

The scheme is &quot;Being an entity that has X&quot;.

We may also do it the other way around, proclaiming all beings to be havings:
* Having the characteristic of being a cat. (Having cathood.)

These beings are (putative?) entities, often taking the place of the ''subject'' in a sentence:
* Being happy is a tough assignment. (Dyer?)
* Being an entity that has a car is advantageous.
* Being in possession of an illegal drug can lead to trouble.

Unsurprisingly, they also take place of a ''predicate'':
* Being a cat in: This animal is a cat.
If we want to keep the noun form of the being, one option is to use the verb to have:
* This animal has being a cat. (Not natural, but perhaps acceptable.)
We can perhaps make it sound more natural by inserting &quot;the property of&quot;:
* The entity over there has the property of being human.

The space of all beings is very hard to overview. Beings seem to result from taking sentences and drilling a single hole (but not any drilling at any place will do).

These beings seem to be the same thing as monadic predicates. However, we may note that the beings are there regardless whether there is someone predicating, a mind. Thus, the particular individual animal's being a cat is there even if no one is looking, thinking and predicating.

It appears obvious that there are many more beings than the language can readily capture. A much more powerful mind than the human one could easily register more beings.

Some beings can be classified using Aristotelian categories, e.g. being a cat and being white. Other beings less so, e.g. being a white cat or even being a cat that has broken a vase.

The use of language brings beings forward to the mind. Let us consider:
* Being a human with XX chromosomes.
* Being a child bearer.
* Being a human with a womb.
* Being a human that wears lipstick.

The words characteristic, property, sign and pattern come to mind. Their relationship to this concept of being is yet to be investigated.

Some beings are indirect and vague:
* Being something like human but not exactly human.
* Being something that has some characteristics (beings?) of a human.

We see that some beings correspond to single words. This makes it possible to classify these beings in some ways similar to classification of words. Thus:
* Some beings correspond to nouns (e.g. cat, where the being is being a cat, or it is being an entity that has cathood).
* Some beings correspond to adjectives and certain nouns derived from them (e.g. to white and whiteness).
* Some beings correspond to verbs and certain nouns derived from them (e.g. to swim and swimming).
* Some beings pertain to the domain of biology.
* Some beings pertain to the domain of geography.
* Some beings pertain to the domain of mathematics.

But we have seen that beings can be complex and then, the above classification is impossible. Consider:
* Being a woman that wears a red scarf.
This being is multi-domain, in part biological, in part cultural.

Beings appear to be not specific to a particular language, but this is probably a matter for a debate. Thus, the following beings are the same:
* Being a cat.
* Eine Katze sein.
Since we specify beings by means of sequences of words, the question whether the beings exist independent of words and culture is at least debatable. I think they do exist independently in principle, but the matter is perhaps not entirely simple.

The concept of being is implied in certain conventional definitions in dictionaries. Thus, whiteness is:
* The quality or state of being white.
This definition explicitly classifies the being under investigation as a quality or a state. But we can omit this classification and we get:
* Being white.

Above, we mentioned the concept of having (countable). To be and to have seem somewhat central, but we can add more, e.g. feeling:
* Feeling bad.
* Feeling that this is going to be a good day.
These can again be turned into beings:
* Being in a state of feeling bad.
* Being in a state of feeling that this is going to be a good day.

And we can find some strange creatures:
* Being in the state of being. (Whatever that is supposed to mean. Does every word salad starting at &quot;being&quot; refer to a being?)

Above, we have used ambiguous specifications. Do ambiguous specifications really correspond to a single being? Thus, is being white really a being (since, in what sense of white?) It seems more plausible that a single sense in a dictionary corresponds to a single being. For a multi-word specification, we would need to disambiguate all words to get a single being. Thus, being a white cat is not a single being since in which sense of cat? On the other hand, the noun cat seems to disambiguate the adjective white.

Does every entity correspond to a being? It seems to. Since, e.g. London corresponds to this:
* Being London, the capital of the U.K.
In general:
* Being numerically identical to entity so-and-so.

But the entity is not identical to the being; London is not the same thing as being London.

We see that entities have multiple beings. Since, as for London, the following examples apply:
* Being a city.
* Being the capital of the U.K.
* Being on Thames.
* Being in England.
* Being a city that has major so-and-so.

A being can contain a large amount of information. For instance, being a person who sees photograph so-and-so. This can be further extended: being a person who has seen photograph so-and-so, photograph so-and-so, and photograph so-and-so. Here, the actual photographs are only represented via &quot;so-and-so&quot;.

Beings can be in relation of more specific or generic or neither. The following increases in specificity:
* Being an animal.
* Being a mammal.
* Being a feline.
* Being a domestic cat.
* Being a white domestic cat.
* Being a white domestic cat that has broken a vase.

Some beings have single-word names, some ending in -hood, some in -ness, some in something else. Thus:
* Being a person → personhood.
* Being white → whiteness.

Some beings can be explicitly language-specific:
* Being an entity that is the subject of the English sentence form &quot;X is a white cat&quot;.
We can translate the specification of the being into, say, German, but the quoted part cannot be translated. One might think that the above would be equivalent to being a white cat, but I am not so sure.

Some beings can be thought of as residing in the subject, but others much less so. The following seem to reside in the subject:
* Being a cat.
* Being white.
Since, inspecting the object under investigation without inspecting its environment or other objects would in principle yeild the presence of the being.

The following not so much:
* Being an entity called &quot;cat&quot;.
* Being an entity that subject so-and-so calls &quot;bavagai&quot;.
* Being an entity that is owned by person so-and-so.

Logical connectives such as and, or and not seem to be able to construct beings. Example beings depending on logical connectives:
* Being an entity that is not a cat.
* Being an entity that is a male cat, an abode or a waterfall.
There is something peculiar about the above beings; they lack something like compactness, let's say. There seems to be something absurd about it; then, any human has the being of a human or X, for any noun-specified X.

One could further consider multi-parameter beings (recalling that predicates are in general multi-parameter or perhaps &quot;polyadic&quot;):
* Being an entity that is the rightful owner of X.
The above being is not something that an entity has but rather a pair of entities has. But then, a pair is also an entity, so we may turn multi-parameter beings into the single-parameter being:
* Being a pair of entities such that the first entity is the rightful owner of the second entity.

Things can get worse, for some value of worse:
* Being an entity that satisfies formula such-and-such of the first-order logic, where the formula has one free variable.

And furthermore:
* Being an entity for which the single-parameter Python-language function such-and-such returns true (which requires coding, perhaps stringifying, the entity in some way as an input).

The art of definition and specification involves consideration of candidate beings to be incorporated into a sentence. Perhaps something like a relatively general inquiry into beings would contribute to these arts. One such inquiry or undertaking seems to be the first-order logic, but this would need to be properly articulated.

One being could be called existence, based on the usage of the verb to be in &quot;To be or not to be? That is the question.&quot; (Shakespeare, quoted from memory) or &quot;This parrot is no more!&quot; (Monty Python) But that seems to be something else. On the other hand, ''being in the state of existence'' seems to be a being. It implies a possible going over into the state of nonexistence. That interprets existence as a state in which an entity is. It implies the entity is in fact indestructible; it merely goes into the state of nonexistence. A certain analogy could be deleting a row from a database table vs. marking it via the field &quot;deleted&quot;.

The words essence and entity would be from the verb to be as well (to be verified). It would be worthwhile to clarify their relationship to beings.

Let me return to Aristotle's concept of being. I think it is Stanford Encyclopedia of Philosophy (SEP) that indicates that in Aristotle, some beings are said of and some are not. The former kind could be the concept of being I presented above. But the latter kind has to be something else: all the beings above are able to be said of. To be done: find the specific SEP article and statement.

== Beings as extensions or intensions or functions ==
I will use my naive understanding of the terminology of extension and intension; it may deviate from the established academic usage. The lead question is whether beings should be viewed as extensions (sets), intensions (formulas or procedures) or something else.

First, one may take an extensional view of beings, that is, see them as sets of entities in which they &quot;reside&quot;. I find this view uncompelling on multiple counts, in part due to Frege. And thus, being the result of adding two plus two and being the result of adding one plus three are two different beings but they reside in a single entity, the number four; extensionally, the apparent two beings would in fact be one being and that does not make any sense to me. Moreover, it would follow that all the beings that do not &quot;reside&quot; in any entity (e.g. being a positive integer that yields three when multiplied by two) are the same being. Again, that does not make sense to me. On the other hand, the extensional view (via sets) enables beings defined by infinite tables, something an intensional view may struggle with.

An intensional view looks more promising. But one has to clarify what kind of entites intensions are. Some candidate entities: formulas of first-order logic, procedures (e.g. in Python), procedures extended with a certain kind of infinite loop that completes in finite time. The procedural view looks promising except that it is less expressive than the first-order logic formula view: we would get fewer beings if we only restricted them to procedures. An objection can be that the procedural view mistakes a manner of determination whether a being resides in an entity with the being itself (like confusing detection criteria with a definition). In any case, to bring procedures closer to formulas of first-order logic, I mentioned the idea of a procedure where an infinite loop is allowed to complete, thus bringing it closer to arithmetic hierarchy. That is to say, with completing infinite loops, we can determine whether something is true for at least one positive integer and for all positive integers, and doing this in a nested way should yield the same expressive power as arithmetic hiearchy. Alright. The intensional view looks interesting but it seems less expressive than the extensional view since each intension so understood is a finite object whereas the extensions (sets) can be infinite, including not finitely specifiable.

As for the procedural view of beings, it would seem some beings must be non-procedural or there is going to be an infinite regress. Thus, there would be base beings and derived beings. The derived beings would be procedural. For instance, being a white cat would be derived from being white and being a cat; these two could either be seen as non-derived in the frame of analysis, or derived further. But that is perhaps something of a tangent.

Another way to look at it is to state that beings are functions returning a boolean value; as long as we are dealing with monadic beings, they are monadic functions. In set theory, functions are defined extensionally as certain kinds of relations, sets of ordered tuples. But there is also the intensional view of functions, which is perhaps specificationist or procedural. In any case, I readily accept that combining being by &quot;and&quot;, e.g. in being a white cat, looks like a function that combines the results of two subfunctions by means of AND operator (lambda item: isWhite(item) and isCat(item)); but I am not clear that the functional view is going to work for all beings.

== Aristotle, being, object and property ==
Perhaps the following identification could be made.

In Aristotle, we would get the following structure:
* being
** being not said of/residing in
** being said of/residing in

We could rename the structure as follows:
* entity
** object
** property

Then, beings analyzed in this article would be Aristotle's being said of/residing in or properties. I do not know enough of ontology (being-lore) and Aristotle to know positively that I am talking sense. One question is whether properties should not also being viewed as objects as long as there are meta-properties.

== Property vs. quality ==
The above deliberations and terminological proposals make it possible to distinguish a ''property'' from ''quality''. A property is nothing else but a (monadic/one-place) being we were talking about all along. And a property is in an Aristotelian category, e.g. substance or quality. A property that is in the category of quality we may call a quality. And thus, each quality is a property but not every property is a quality. Using the same terminological scheme, a property that is in the category of substance could be called a substance. And thus, each substance would be a property, but not the other way around. And thus, e.g. being a domestic cat would be in the category of substance and we could also say that it is a substance. (That is to say, we are introducing a convenience terminology &quot;X is a substance&quot; :=def= &quot;X is in the category of substance&quot;, and similarly for quality.)

Sure enough, when we allow multi-place beings (as we can by drilling multiple holes in a sentence), we also get multi-place ''properties''. Wikidata seems to make this terminological choice, by calling a two-place being a ''property''. And thus, the sentence form &quot;X is a brother of Y&quot; identifies a two-place property (which can be reduced to &quot;X is a sibling of Y&quot; and &quot;X is a male&quot;).

The plural &quot;physical qualities&quot; sees considerable use, which matches (but does not really confirm) the terminological choice as a quality as one being (in the category of quality). That the physical qualities are really qualities rather than substances is suggested by their being designated by adjectives (of course, nouns are then derived from the adjectives).

== See also ==
* [[Concept]]

== Further reading ==
* [https://plato.stanford.edu/entries/aristotle-categories/ Aristotle’s Categories], Stanford Encyclopedia of Philosophy -- uses Aristotle's concept of being
* [https://plato.stanford.edu/entries/properties/ Properties], Stanford Encyclopedia of Philosophy -- similar or same to this concept of being</text>
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    <title>User:Dan Polansky/A critical look at psychiatry</title>
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      <text bytes="41398" sha1="ezuzg42pdwt0gix8um738udnekk3ykb" xml:space="preserve">{{Original research}}
This article by Dan Polansky takes a critical look at psychiatry. That a critical look is needed is suggested by the psychiatry's portrayal in popular culture (e.g. in ''Zen and the Art of Motorcycle Maintenance'', 1974, and ''One Flew Over the Cuckoo's Nest'', 1975) as well as the well documented history of gross abuse of patients, including insulin shock therapy and lobotomy. The selection of material into this article is largely idiosyncratic; one inspiration are Peter C. Gøtzsche's books. This material is not written by a professional writer; one can perhaps benefit better from the books and further reading listed at the bottom of this article.

Key questions include the following:
* Is there anything valid about the psychiatric diagnoses?
* Is Diagnostic Statistical Manual (DSM) a result of application of the scientific method in discovery of real-world phenomena and entities?
* Is the language used to describe the symptoms of psychiatric patients a language of science? (One can recall Wittgenstein's idea to regulate language use in such a way as to make it hard to make meaningless philosophical statements.)
* Is the apparent gross violation of human rights in coercive drugging of psychiatric patients well justified?
* Is incanceration of people who have not committed a crime and are not suspected from having committed a crime well justified?
* Are psychiatrists and psychiatric nurses generally well-meaning, kind, competent and honest people?
* More generally, in case of doubt, are humans to be trusted, given their history of various kinds of misconduct?

== Critical characterization ==
A critical chracterization of psychiatry could be this:
* A field whose ethical and epistemic ineptitude and lack of compassion were demonstrated by its long-term support and administration of lobotomy and insulin shock therapy.

== Psychiatry as a medical field ==
Whether psychiatry is a medical field is debatable. There does not seem to be anything medical about the diagnostic method. What does look medical are the interventions, whether lobotomy or drugging. See also [[Is psychiatry a medical field?]].

== Making themselves look medical ==
One complaint found in the literature is this: the key objective of psychiatrists is to look medical. To do so, they must use medical ''interventions'', whether surgical or using drugs, since there is nothing medical about their ''diagnostic'' method. The key objective of the intervention is not to help patients but rather to help the psychiatrist look professional, medical and respectable.

The contention is plausible enough. The notion that a group of people systematically shows benevolence toward others is not impossible in principle, but is no more likely in general than the notion that the group is, for the most part, maximizing their own egoistic (self-centered) interests, such as power (domination), social status, wealth (supplied in part from big pharma), etc.

There is nothing rational about blindly assuming good faith. Given what we have seen in insulin shock therapy and lobotomy, it seems much more rational to avoid evidence-free assumptions, maintain an open mind, and investigate the possibility that things are astray.

== Attraction of sadistic personality types ==
One contention is that psychiatry attracts sadistic personality types. A prospective sadist, in order to meet his or her psychological needs, does well to find a profession where his or her tendencies find appropriate release. Most professions offer little opportunity of sadistic release. It should not be too hard for a prospective sadist to find out that psychiatry is a good field to enter: one can use mechanical restraints against patients, one can force drugs on patients against their will and observe them lose their ability to speak or walk or the like, one can psychologically harass them, and the patients have hardly any recourse given they are less likely to be taken seriously and that the patients usually do not have any means of objectively proving that bad things happened to them.

It seems hard to figure out another profession with so much potential for satisfaction of pathological sadistic needs.

== Psychiatry as one analytical unit ==
We may analyze psychiatry as one unit/entity or we may slice it into different phases, say pre-1950 psychiatry and post-1950 psychiatry. (It is to be clarified whether 1950 is the best year for slicing.)

The pre-1950 psychiatry is a field of unequivocal horror. The post-1950 psychiatry (post-lobotomy and post-insulin shock) perhaps less so. But did the nature of the practitioners change? Did they become different kind of people, with different epistemic and ethical compentence? If so, how? In case of doubt, one may refuse to split psychiatry into phases, and instead make the conclusion--admittedly possibly too simplistic one--that psychiatry is bad.

One attitude is to treat psychiatry as if it was one person. One could say: the person of psychiatry has shown unequivocally great epistemic, ethical and ontological deficiency. It should therefore lose the license to practice. We are not buying into any &quot;we have changed&quot; and &quot;we did not know any better&quot;. No, you have not changed, you are the same humans with too many bad tendencies.

A limitation: the year 1950 is a guess from memory. A proper procedure is to determine when lobotomy and insulin shocks ceased to be used and determine the boundary year based on that.

== Diagnostic Statistical Manual ==
According to some sources [which?], DSM is recommended against by some organizations. According to critics, DSM is not a result of science but rather of voting by commitee, which is no way to obtain scientifically valid results.

If DSM was valid, one should be able to obtain it by setting up two ot three independent committees and letting them come up with a classification scheme independently. In so far as the result would be based on (and thereby synchronized by) reality, the two independent committees should be able to arrive either at substantially same results or at least results that show some kind of reality-based correspondence. Such has not been done; instead, as long as DSM is used and distributed as a kind of Bible across the world, the result is the opposite of independence.

One critic of DSM is Ghaemi 2013&lt;ref&gt;[https://www.psychiatrictimes.com/view/why-dsm-iii-iv-and-5-are-unscientific Why DSM-III, IV, and 5 are Unscientific] by S. Nassir Ghaemi, MD, MPH, 14 Oct 14, 2013, psychiatrictimes.com&lt;/ref&gt; and Ghaemi 2023&lt;ref&gt;[https://ghaemi.substack.com/p/why-dsm-is-mostly-false Why DSM is mostly false - by Nassir Ghaemi], 20 Nov 2023, substack.com&lt;/ref&gt;. Ghaemi 2023 contains devastating criticism:
: '&quot;In addition to 14 validated diagnoses published in the RDC in 1978, a mere two years later DSM-III came out with 292 claimed diagnoses. There is no metaphysical possibility that 278 psychiatric diagnoses suddenly were discovered in two years. They were invented. This mere fact proves that DSM-III was mostly false - 95.2% false, to be exact. 278 diagnoses were made up in the final years of the process to satisfy the profession; they weren’t true, or at least proven true, and everyone knew it.
: 'By that time, most of the Washington University neo-Kraepelinian members of the task force were disgusted and dropped out of the process. One of them even committed suicide.&quot;'

Further reading:
* {{W|Diagnostic and Statistical Manual of Mental Disorders}}, wikipedia.org

== Dubious diagnoses ==
Dubious diagnostic units/entities once in use include the following:
* Homosexuality as a disorder, to be managed with drug intervention.
* Drapetomania, a label for black slaves &quot;irrationally&quot; wanting to escape slavery.

== Brain disorder ==
Multiple respected organizations describe schizophrenia as a brain disorder, for instance Johns Hopkins Medicine.&lt;ref&gt;https://www.hopkinsmedicine.org/health/conditions-and-diseases/schizophrenia&lt;/ref&gt; Critics charge this has never been demonstrated after decades of research. Conceptualizing schizophrenia as a brain disorder leads to an apparent solution: medication. Some liken psychiatric medication to insulin for diabetes, whereas critics charge this is completely wrong.

Some sources also describe bipolar disorder as a brain disroder, e.g. Ontario Shores Centre for Mental Health Sciences.&lt;ref&gt;https://www.ontarioshores.ca/bipolar-disorder&lt;/ref&gt;

It is not clear what contrast is supposed to be drawn between mental illness and brain disorder. Under physicalism, mind is an aspect of the brain, and thus, if there is something wrong with the mind, the thing is wrong with the brain. Nonetheless, one can consider a computer metaphor: software is in the hardware of the computer, but when software is wrong, it does not mean the hardware is wrong. The language of brain disorder seems to suggest there is something wrong with the hardware rather than software. If, by contrast, we would think there is something wrong with the software, e.g. beliefs and methods of validation and verification of putative knowledge, one could be inclined to try verbal interventions (cognitive therapy) and see whether one could get rid of some delusions that way.

== Mental illness ==
Psychiatry uses the term &quot;mental illness&quot;. This term implies that there is something like illness of the mind, a direct analogy of, say, an illness of the liver.

Szasz objects to this term, stating it is a mere metaphor, an inept one at that. If the analogy to the illness of the liver would be valid, it would be an illness of the relevant organ, which is the brain. He states that this leads to medicalization of the phenomenon, that is, a phenomenon that is not medical (and does not respond or responds poorly to medical treatment) is turned into an allegedly medical one.

The medicalization complaint seems plausible enough. Surely, if there is a mental illness bearing an analogy to, say, an illness of the liver, one would use a medical intervention, e.g. drugs or surgery. By contrast, if there is a problem with the mind (problem, not illness), one would expect to get good results with mental interventions, e.g. cognitive therapy. Sure enough, cognitive therapy may fail. From the point of view of an atheist, it seems unlikely that mere cognitive therapy would get most people rid of the psychotic disorder (since delusion-featuring) known as religion.

The term &quot;mental disorder&quot; is perhaps more immune to this kind of criticism.

It is quite possible that there is something like a mental symptomatology that is caused by a somatic disorder. But the somatic disorder does not need to be one of the brain; it may be e.g. one of the endocrine system.

See also [[Is there such a thing as mental illness?]]

Further reading:
* {{W|Mental illness}}, wikipedia.org
* [https://www.cambridge.org/core/journals/the-psychiatrist/article/myth-of-mental-illness-50-years-later/4B7C0377C7DF9B49E72B8B740E6B87D8 The myth of mental illness: 50 years later] by Thomas Szasz, 2 January 2018

== Chemical imbalance ==
Some sources indicate that schizophrenia and bipolar disorder are caused by chemical imbalances. Critics charge this has never been demonstrated.

== Nefarious intervention history ==
The nefarious history of psychiatric intervention is covered in the following sections on [[#Lobotomy|lobotomy]], [[#Insulin shock therapy|insulin shock therapy]] and [[#Other historical misconduct|other historical misconduct]].

== Lobotomy ==
The multiple decade long practice of lobotomy is a scandal of incompetence, malice or both. The lobotomist Walter Freeman killed many people, but it seems he was not even charged (he killed more people than many mass shooters/murderers). The case shows not only gross epistemic and ethical deficiency of psychiatry but also of its aiders and abetters, who awarded Nobel Prize for lobotomy to António Egas Moniz. The excuse of &quot;we did not know any better&quot; cannot be taken seriously. Either these people failed to realize that they know much less than they think and that given the absence of proper knowledge, the requirement &quot;do no harm&quot; would force them to avoid interventions for the fear of adverse outcomes. Or they did realize as much, but they proceeded anyway, since their objectives were primarily egoistically hedonic, seeking dominance, fame, recognition and money more than patient well-being.

Further reading:
* {{W|Lobotomy}}, wikipedia.org
* {{W|Walter Jackson Freeman II}}, wikipedia.org

== Insulin shock therapy ==
Insulin shock therapy is damned in Jones 2000.&lt;ref&gt;[http://jrsm.rsmjournals.com/cgi/reprint/93/3/147.pdf Insulin coma therapy in schizophrenia] by Jones, 2000&lt;/ref&gt; The practice resulted from epistemic and ethical failure, not of a single individual or a small group but of a relatively large network of individuals, nearly all of whom were, to use Popper's phrase, intellectually bankrupt, mutually reassuring themselves that they knew what they were doing and that it was based on &quot;science&quot; (as if the mere utterance of the word &quot;science&quot; would magically turn unfounded speculations into solid knowledge). That this could happen in 20th century, one of aircraft, submarines, modern physics and nuclear energy, beggars belief, perhaps until one recalls that this was also the century of Hitler's gas chambers and industrial extermination of Jews, and the century of the British state drugging Alan Turing for the allegged disorder of homosexuality, which is estimated to have greatly contributed to his death.

Further reading:
* {{W|Insulin shock therapy}}, wikipedia.org

== Other historical misconduct ==
Historical misconduct other than lobotomy and insuline shocks&lt;ref&gt;[https://www.madinamerica.com/2022/03/desperate-remedies/ Desperate Remedies] by Andrew Scull, 2022, madinamerica.com&lt;/ref&gt;:
* Removal of teeth and tonsils and then, stomachs, spleens, colons and uteruses.
* Injection of horse serum to produce meningitis.
* Administering barbiturates to put patients into deep sleep.
* Injection of metrazol to produce seizure.
* Administering electroconvulsive therapy (ECT) in an unhelpful way.

== Coercive treatment ==
On strict reading, the term ''coercive treatment'' (or ''forced treatment'') can be contrasted to ''involuntary treatment'': involuntary treatment could involve treatment of someone who is unconscious.

Coercive treatment with psychoactive drugs or electroconvulsive therapy (ECT) is arguably a gross violation of human rights. If there is something that is a liberal subject's own, it is the body. An intervention into that body against express will to the contrary is a gross violation. It is also in a way an attack on person or personality; the substances used are psychoactive and affect personality. If, for instance, the patient had a tendency to fight for his or her rights, the tendency is going to be quite suppressed after administration of major tranquilizers known as &quot;antipsychotics&quot;. In ECT, there is a risk of memory loss; it is as if someone hacked into a computer and erased some files.

There are organizations campaigning against coercive treatment.

World Health Organization (WHO) took a stance against coercive treatment; a link is yet to be provided.

See also [[Should coercive treatment be made illegal?]].

Further reading:
* [https://publichealth.realclearjournals.org/perspectives/2025/01/forced-treatment-in-psychiatry-is-a-crime-against-humanity/ Forced treatment in psychiatry is a crime against humanity] by Peter C. Gøtzsche, 30 Jan 2025

== Community treatment orders ==
In some countries, patients can be ordered by courts to take drugs in an outpatient (outside of the hospital) setting. This practice seems especially widespread in the U.S. And yet, the lifespan expectation shortening associated with schizophrenia is 28.5 years in the U.S., so much more than in many other countries, as per [[Life expectancy in schizophrenia]] (but: it is not clear that studies/methodologies in different countries are fully comparable).

These orders seem to be especially devious, compared to coercive inpatient medication, given their likely length.

Links:
* {{W|Outpatient commitment}}, wikipedia.org

== Electroconvulsive therapy ==
Currently delegated to further reading.

Further reading:
* [https://www.jstor.org/stable/26957011 Should we stop using electroconvulsive therapy?] by John Read et al., 2019
* [https://power2u.org/wp-content/uploads/2017/09/ECTtestimonyDanFisher.pdf Electroconvulsive Therapy (ECT) Testimony] by Daniel B. Fisher, MD, PhD, 2011, power2u.org

== Polypharmacy ==
The literature reports that psychiatric patients are often given multiple psychoactive drugs. It is unclear how the prescribing psychiatrists can possibly know the effects, given that there are no or scant clinical trials for drug combinations.

== Antipsychiatry movement ==
The concept of antipsychiatry movement focuses on people disagreeing rather than points of disagreement and criticism. A use of this concept is not a valid response to address complaints and objections. It seem at least in part to be the logical fallacy of ad hominem (you are anti psychitry, therefore what you are saying is wrong). Under this construction, any criticism of psychiatry is automatically wrong for its being criticism of psychiatry [really? any?]. That psychiatry is good becomes a tautology rather than a proposition to investigate and scrutinize.

Be it as it may, there does not seem to be e.g. any anti-heart-surgery movement. One explanation could be that the psychiatric patients are so deranged that they do not realize they were in fact helped by the well-meaning and competent psychiatrists. That does not explain the existence of too many competent naysayers who are not psychiatric patients.

== Big pharma ==
''Bad Pharma'' is a 2012/2013 book by Ben Goldacre. It documents widespread misconduct of large drug companies, including their cherry picking of studies to publish (keeping the unfavorable ones to themselves), failure to report adverse events of drugs, corrupting doctors, ghost writing, etc.

A book looking specifically at psychoactive medication and the role of big pharma in its excessive use is ''Deadly Psychiatry and Organised Denial'' by Peter C. Gøtzsche.

The notion that something is very wrong in the field of psychoactive medication and big pharma is supported by the number of related large settlements by the big pharma, as per [[Wikipedia: List of largest pharmaceutical settlements]].

The companies caught in misconduct are as follows, per [[Wikipedia: List of largest pharmaceutical settlements]] (see also [[Is psychiatry evil?]]):
* GlaxoSmithKline
* Johnson &amp; Johnso
* Abbott Laboratories
* Eli Lilly
* AstraZeneca
* Bristol-Myers Squibb

As a general and somewhat less reliable analysis, it is naive to think that the capitalist profit motive automatically leads to best patient outcomes. Under the conditions of rational profit maximization as the sole or primary objective, it is the profit that is maximized and nothing else. A solution is not to abolish the profit motive but rather to subject it to appropriate state regulation. Whether the solution is going to work well is open to doubt: just like commercial corporations, the state is a corporate entity and it may end up being &quot;in bed&quot; with the commercial corporate entities.

== First do no harm ==
A key maxim in medicine is this: first do no harm (primum non nocere). One would think that, under this principle, one would be unable to force a drug with known adverse effects on the patient against the patient's will since the requirement is not &quot;act to help&quot; but rather &quot;do no harm&quot;. There is no symmetry between a positive action (drugging) and a negative action (non-drugging). It would be worthwhile to find out how psychiatrists explain that they are in fact abiding by the duty to do no harm when administering drugs against the patient's will, if they in fact do explain it.

Somewhat related is the trolley problem. If a type of psychiatric intervention, say, helps 9 people and harms 1 person, the trolley logic says one is not allowed to sacrifice the 1 person harmed to save/help 9 people. Therefore, there would be a strong bias toward non-intervention in case of any doubt. One would have to clarify whether this is a misapplication of the trolley problem.

Links:
* {{W|Primum non nocere}}, wikipedia.org
* {{W|Trolley problem}}, wikipedia.org

== Psychiatrists lying in court ==
Gottstein 2001&lt;ref&gt;[https://gottsteinlaw.com/yoder/memo.pdf Rodney Yoder (MEMORANDUM)] by James Gottstein, 14 Dec 2001&lt;/ref&gt; states (along the lines also stated in Gottstein 2006 below): 'Dr. Torrey also quotes Psychiatrist Paul Applebaum as saying when &quot;confronted with psychotic persons who might well benefit from treatment, and who would certainly suffer without it, mental health professionals and judges alike were reluctant to comply with the law,&quot; noting that in &quot;'the dominance of the commonsense model,' the laws are sometimes simply disregarded.'

As per Gottstein 2006&lt;ref name=jg2005&gt;[http://akmhcweb.org/Articles/AKEffortsRevFeb06.pdf REPORT MULTI-FACETED G RASS-R OOTS EFFORTS TO BRING ABOUT MEANINGFUL CHANGE TO A LASKA 'S MENTAL HEALTH PROGRAM] by Jim Gottstein, 2 Aug 2005 with some updates to 3 Mar 2006, akmhcweb.org&lt;/ref&gt;: 'The Introduction mentions that Forced &quot;Treatment&quot; proceedings are essentially a sham. This is well known to those involved. Psychiatrists, with the full understanding and tacit permission of the trial judges, regularly lie in court&lt;sup&gt;71&lt;/sup&gt; to obtain involuntary commitment and forced medication orders:&quot;

As regards the above, note 71 states: &quot;This is perjury, a crime&quot;.

Gottstein goes on to quote E. Fuller Torrey&lt;ref name=jg2005/&gt;: &quot;It would probably be difficult to find any American Psychiatrist working with the mentally ill who has not, at a minimum, exaggerated the dangerousness of a mentally ill person's behavior to obtain a judicial order for commitment.&lt;sup&gt;73&lt;/sup&gt;&quot;

As regards the above, note 73 states: &quot;Torrey, E. Fuller. 1997. ''Out of the Shadows: Confronting America's Mental Illness Crisis''. New York:
John Wiley and Sons. 152.&quot;

As per Wayne Ramsay&lt;ref name=wre&gt;[http://www.wayneramsay.com/evil.htm Why Psychiatry is Evil], wayneramsay.com&lt;/ref&gt;: 'For example, in my essay Suicide: A Civil Right, I quote Paul G. Quinnett, Ph.D., a psychol­ogist, in his book about suicide saying &quot;doctors like myself will stand up in court and say something to the effect that, by reason of a mental illness, you are a danger to yourself and need treatment&quot; even when they do not believe the person so accused actually has a mental illness.'

Similar point is made in Gøtzsche 2015&lt;ref&gt;[https://archive.org/details/deadly-psychiatry-and-organised-denial_202304/page/n301/mode/1up?view=theater Deadly Psychiatry And Organised Denial] by Peter C. Gøtzsche, 2015, archive.org&lt;/ref&gt;, sourced from James Gottstein.

== Families lying or exaggerating ==
Wayne Ramsay&lt;ref name=wre/&gt; quotes Dr. Torrey as follows: &quot;Families also exaggerate their family member's symptoms to get the person committed to a hospital. In a 1989 study of 83 families in Philadelphia, 18 percent said they had lied or exaggerated to officials in order to get a relative committed. ... In fact a number of local officials with the Alliance for the Mentally Ill (AMI), a nationwide support group for families, say they privately counsel families to lie, if necessary, to get acutely ill relatives hospitalized. . . . They say they were attacked when they weren't, they say their children tried to kill themselves when they didn't... Thus, ignoring the law, exaggerating symptoms, and outright lying to get care for those who need it are important reasons the mental illness system is not even worse than it is.&quot;

== Psychiatrists lying in medical records ==
It is not clear how the patient should ever be able to prove that psychiatrists are lying in medical records, when they say e.g. that the patient was aggressive (when he was not), that he engaged in paranoid speech (when he was not), etc. In the court of law, it would be a word of nominal experts and professionals against an allegedly psychotic person suffering from delusions, hallucinations and other problems leading to harmed contact with reality.

== Comparison to organized religion ==
A comparison of psychiatry to organized religion is useful. That is not to say that psychiatry is like organized religion in all salient regards.

What could be candidate salient regards? The following ones come to mind:
* Organized religion is very rich and powerful.
* Organized religion spreads blatant falsities/implausibilities.
* The system of falsities to spread is meticuously centrally maintained (not true for all organized religions).
* The followers of organized religion accept or profess to accept the blatant falsities as true.
* Some organized religions are cruel. One can recall the Inquisition. Some religions are reported to have engaged in human sacrifice.
* Organized religion maintains apparent consensus by harsh treatment of heretics, people who disagree with the dogma.

No firm conclusion can be drawn from the above. But one thing is worth noting: humans are very gullible and humans are very willing to organize to deceive others and cause grave harm to others. And they can continue doing so over long periods of time. This is the background against which allegations against psychiatry are to be evaluated as at least plausible.

A relevant quote from Gøtzsche 2024&lt;ref name=pg2024&gt;''[https://www.scientificfreedom.dk/wp-content/uploads/2024/09/2024-Gotzsche-Is-psychiatry-a-crime.pdf Is psychiatry a crime against humanity?]'' by Peter C. Gøtzsche, 2024&lt;/ref&gt; is relevant: &quot;We [I and Klaus] met and started a fruitful research collaboration. But it had repercussions for Klaus. He was discouraged from collaborating with my research group and was warned that it would have consequences for his career. I told him that this was like religious fanatism. Jehovah’s Witnesses and Scientology treat defectors the same way, which was unheard of in an academic context but showed us a lot about where psychiatry is.&quot;

It was Thomas Szasz who compared psychiatry to the Inquisition in his book ''The Manufacture of Madness: A Comparative Study of the Inquisition and the Mental Health Movement''.

Links:
* [https://www.youtube.com/watch?v=B0m-Svt_K9A Dr. Thomas Szasz discusses his book &quot;The Manufacture of Madness&quot;], youtube.com

== Comparison to astrology ==
It seems to do little or no good arguing with astrologers that their field produces zero true knowledge. They are not convinced. It is non-astrologers, e.g. physicists and statisticians, who are able to demonstrate no correlation between heavenly phenomena and, say, the sex of the emperor's child.

Astrologers are sometimes rather sophisticated. Their methods sometimes involve science-resembling deterministic transformations of heavenly data (geometric ones), acting as an empirically seeded pseudorandom generator.

This analogy is probably fairly weak. Nonetheless, it points to the observation that unscientific fields often need field-external input to render the judgment of being unscientific. One can also recall the allegedly scientific character of Marx' economics and his historical prophecies, for which too many intelligent people fell, with enormous practical consequences.

== Ghostwriting ==
According to Gøtzsche 2024, Nemeroff and Schatzberg published a psychiatry textbook ghostwritten by GlaxoSmithKline (GSK).&lt;ref name=pg2024/&gt; The book Gøtzsche refers to seems to be ''Recognition and Treatment of Psychiatric Disorders''&lt;ref&gt;https://stanforddaily.com/2010/12/01/professor-apa-dispute-ghostwriting-allegation/&lt;/ref&gt;.

Study 329 is a famous case of ghostwriting in relation a to a psychiatric drug, Paxil/paroxetine.&lt;ref&gt;[https://davidhealy.org/329-a-study-in-what/ 329: A Study in What?] by David Healy&lt;/ref&gt; See also [[Wikipedia: Study 329]].

As per Collier 2009: '“Somewhere between 50% and 100% of articles on drugs that appear in journals are ghostwritten,” says Dr. David Healy, a psychiatrist at the University of Cardiff in Wales, United Kingdom, and a critic of the drug industry’s influence on physicians’ drug prescribing habits.'&lt;ref&gt;[https://pmc.ncbi.nlm.nih.gov/articles/PMC2761476/ Prevalence of ghostwriting spurs calls for transparency] by Roger Collier, 2009&lt;/ref&gt;

Further reading:
* {{W|Medical ghostwriter}}, wikipedia.org
* [https://www.researchgate.net/publication/261511478_Ghostwriting Ghostwriting] by Jonathan Leo and Jeffrey R. Lacasse, April 2014, researchgate.net
* [https://www.madinamerica.com/2019/12/medical-ghostwriting/ Medical Ghostwriting: When an &quot;Author&quot; Is Not Necessarily an &quot;Author&quot;] by Jonathan Leo, 2019, madinamerica.com
* [https://link.springer.com/content/pdf/10.1007/s12115-011-9455-2.pdf Why Does Academic Medicine Allow Ghostwriting?] by Jonathan Leo, Jeffrey R. Lacasse and Andrea N. Cimino, 2011

== Rosenhan experiment ==
Currently delegated to further reading.

Further reading:
* {{W|Rosenhan experiment}}, wikipedia.org

== Robert Pirsig ==
Robert Pirsig criticized psychiatry in his 1974 novel ''Zen and the Art of Motorcycle Maintenance''. He tells us that in order to get out of the psychiatric hospital, he had to learn how to tell the psychiatrists what they wanted to hear. Perhaps hyperbolically, the narrator tells his son Chris that he was not really insane. He speculates that his breakdown could have been something like a mystic experience, better handled by, say, a Zen master than a psychiatrist. Some of these things are better taken with a grain of salt. Nonetheless, the idea that holders of unchecked power proceed according to the slogan &quot;we will not let you free until you confess&quot; is plausible enough. One only has to recall e.g. Czech religious reformer Jan Huss (and other heretics), who failed to recant and was executed as a result. Pirsig uses the phrase &quot;culture of one&quot; to refer to someone whose peculiar beliefs are not part of any culture except his own.

== Dorrit Christensen ==
Dorrit Christensen is the author of the book ''Dear Luise'' recounting the troubles of her daughter in the Danish psychiatric hospital system. The troubles resulted in her daughter's death.

Links:
* [https://www.madinamerica.com/2016/03/all-for-the-best-of-the-patient/ “All for the Best of the Patient”] by Dorrit Cato Christensen, 2016, madinamerica.com

== Thomas Szasz ==
Thomas Szasz was a vocal critic of psychiatry. He has many good points but his claim that there is no such thing as mental illness is debatable; see also section [[#Mental illness|Mental illness]].

Further reading:
* {{W|Thomas Szasz}}, wikipedia.org
* [https://cdn.mises.org/3_2_1_0.pdf The Lying Truths of Psychiatry] by Thomas S. Szasz, 1979, cdn.mises.org
* [https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(12)61789-9/fulltext Thomas Szasz: rebel with a questionable cause] by Williams and Caplan, 20 October 2012
* [https://www.cambridge.org/core/journals/the-psychiatrist/article/myth-of-mental-illness-50-years-later/4B7C0377C7DF9B49E72B8B740E6B87D8 The myth of mental illness: 50 years later] by Thomas Szasz, 2 January 2018

== Peter C. Gøtzsche ==
Peter C. Gøtzsche is a vocal critic of psychiatry. He is a co-founder of Cochrane Collaboration, with skills in internal medicine and medical statistics.

Gøtzsche was expelled from the Cochrane Collaboration in 2018. He explained what happened in his 2019 book ''Death of a whistleblower and Cochrane’s moral collapse''&lt;ref&gt;[https://www.scientificfreedom.dk/books/ Books – Institute for Scientific Freedom], scientificfreedom.dk&lt;/ref&gt; and a related YouTube video&lt;ref&gt;[https://www.youtube.com/watch?v=GxTgxCr1RUU Peter C. Gøtzsche: Death of a Whistleblower and Cochrane's Moral Collapse]&lt;/ref&gt;. Several board members stepped down in protest.&lt;ref&gt;[https://www.bmj.com/content/362/bmj.k3945 Cochrane director’s expulsion results in four board members resigning], 2018, bmj.com&lt;/ref&gt;

Gøtzsche has multiple books relating to psychiatry freely available online:
* ''[https://www.scientificfreedom.dk/wp-content/uploads/2024/07/Gotzsche-Critical-Psychiatry-Textbook.pdf Critical psychiatry textbook]'' by Peter C. Gøtzsche, 2022
* ''[https://www.scientificfreedom.dk/wp-content/uploads/2024/09/2024-Gotzsche-Is-psychiatry-a-crime.pdf Is psychiatry a crime against humanity?]'' by Peter C. Gøtzsche, 2024
* [https://www.scientificfreedom.dk/wp-content/uploads/2022/07/Gotzsche-Psicofarmacos-que-matan-y-denegacion-organizada.pdf Psicofármacos que matan y denegación organizada] by Peter C. Gøtzsche, 2022 -- a Spanish translation of ''Deadly Psychiatry and Organised Denial''

Further reading:
* {{W|Peter C. Gøtzsche}}, wikipedia.org
* [https://www.scientificfreedom.dk scientificfreedom.dk]
* [https://www.madinamerica.com/author/pgotzsche/ Peter C. Gøtzsche, MD], madinamerica.com

== Scientology ==
The church (or possibly cult) of Scientology takes anti-psychiatry stances. This opens the door to a cheap smear in which people critical of psychiatry are claimed to be like the followers of Scientology.

Scientology founded The Citizens Commission on Human Rights (CCHR), together with Thomas Szasz, an organization advocating against psychiatry. Some of the videos made available online&lt;ref&gt;[https://www.cchr.org/ cchr.org]&lt;/ref&gt; by CCHR arguably give a fear-mongering impression. That does not rule out that CCHR did some decent work in advancing patient rights and preventing or reducing abuses.

Tom Cruise is a notable member of Scientology who took a well publicized anti-psychiatry stance. In 2005 (or thereabout), he stated that 'psychiatry is a “quack” field and [...] that postpartum depression cannot be treated pharmacologically'&lt;ref&gt;[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1180571/ Tom Cruise is dangerous and irresponsible] by Ushma S. Neill, 2005&lt;/ref&gt;

Links:
* {{W|Scientology}}, wikipedia.org
* {{W|Citizens Commission on Human Rights}}, wikipedia.org

== Treatment Advocacy Center ==
Treatment Advocacy Center (TAC) is a U.S. organization &quot;founded in 1998 by Dr. E. Fuller Torrey.&quot;&lt;ref&gt;[https://www.tac.org/about-tac/ About Us], Treatment Advocacy Center, tac.org&lt;/ref&gt; The organization advocates for changing laws to make it easier to psychiatrically incancerate people with serious mental illness, to &quot;help&quot; them.

Links:
* {{W|Treatment Advocacy Center}}, wikipedia.org
* [https://www.tac.org/ tac.org]

== NAMI ==
National Alliance on Mental Illness (NAMI) is a U.S.-based advocacy organization.

From what I recall, critics charge the organization is biased toward excessive incarceration or coercion.

Wikipedia Criticism section provides sourced claims about NAMI's ties to pharmaceutical companies.

NAMI was repeatedly criticized by articles on madinamerica.com&lt;ref&gt;https://www.madinamerica.com/tag/national-alliance-on-mental-illness/&lt;/ref&gt;.

Links:
* {{W|National Alliance on Mental Illness}}, wikipedia.org

== Books critical of psychiatry ==
Selected books critical of psychiatry:
* ''The Myth of Mental Illness'' by Thomas Szasz, 1974; see also many other books at [[Wikipedia: Thomas Szasz]].
* ''The Reign of Error: Psychiatry, Authority, and Law'' by Lee Coleman, 1985
* ''Talking Back to Prozac'' by Peter Breggin, 1994; see also many other books at [[Wikipedia: Peter Breggin]].
* ''Mad In America'' by Robert Whitaker, 2001; see also other books at [[Wikipedia: Robert Whitaker (author)]]
* ''Rape of the Soul'' by Ty Colbert, 2001
* ''Let Them Eat Prozac'' by David Healy, 2004; see also other books at [[Wikipedia: David Healy (psychiatrist)]]
* ''The Myth of the Chemical Cure'' by Joanna Moncrieff, 2008; see also other books at [[Wikipedia: Joanna Moncrieff]]
* ''Dear Luise'' by Dorrit Cato Christensen, 2012
* ''The Book of Woe: The DSM and the Unmaking of Psychiatry'' by Gary Greenberg, 2013
* ''Mad Science: Psychiatric Coercion, Diagnosis, and Drugs'' by Stuart A. Kirk, Tomi Gomory, David Cohen, 2013&lt;ref&gt;https://www.routledge.com/Mad-Science-Psychiatric-Coercion-Diagnosis-and-Drugs/Kirk/p/book/9781412855921&lt;/ref&gt;; see also other books at [[Wikipedia: Stuart A. Kirk]]
* ''Cracked: Why Psychiatry is Doing More Harm Than Good'' by James Davies, 2014
* ''Deadly Psychiatry and Organised Denial'' by Peter C. Gøtzsche, 2015; see also other books at [[Wikipedia: Peter C. Gøtzsche]].
* ''The Zyprexa Papers'' by James Gottstein, 2020; see also other publications at [[Wikipedia: James Gottstein]].
* ''Desperate Remedies: Psychiatry's Turbulent Quest to Cure Mental Illness'' by Andrew T. Scull, 2022; see also other publications at [[Wikipedia: Andrew Scull]].
* ''[https://www.scientificfreedom.dk/wp-content/uploads/2024/09/2024-Gotzsche-Is-psychiatry-a-crime.pdf Is psychiatry a crime against humanity?]'' by Peter C. Gøtzsche, 2024 -- available online, extensively inline referenced

There are many more books by the same authors, and these can be found listed in their Wikipedia articles. Listing them all here would perhaps make the list unpractically long. One could perhaps obtain a comprehensive list by querrying Wikidata, but the books would need to be all entered there for this to work.

Further reading:
* {{W|Category:Anti-psychiatry books}}, wikipedia.org

== Organizations critical of psychiatry ==
Organizations critical of psychiatry include the following:
* [http://www.madinamerica.com/ madinamerica.com], run by Robert Whitaker, U.S.
* [https://psychrights.org/ Law Project for Psychiatric Rights], psychrights.org
* [http://cepuk.org/ The Council for Evidence-based Psychiatry], cepuk.org, U.K.
* [https://www.scientificfreedom.dk/ Institute for Scientific Freedom], scientificfreedom.dk (Peter C. Gøtzsche)
* {{W|Citizens Commission on Human Rights}}, CCHR (linked to Scientology and Szasz)
* {{W|Critical Psychiatry Network}}, U.K.
* {{W|MindFreedom International}}, U.S.

Further reading:
* {{W|Template:Anti-psychiatry}}, wikipedia.org
* {{W|Category:Anti-psychiatry}}, wikipedia.org -- contains a mix of organizations critical of psychiatry with other topics

== Individuals critical of psychiatry ==
Some critics are mentioned above in dedicated section headings or as authors of critical books. Other ones, especially credentialled ones, are listed below:
* Dr. David Cohen&lt;ref&gt;https://www.madinamerica.com/2022/10/psychology-podcast-scientific-emptiness-psychiatry-david-cohen/&lt;/ref&gt;&lt;ref&gt;https://luskin.ucla.edu/person/david-cohen&lt;/ref&gt;, a UCLA professor of social welfare and associate dean (Cohen turns out to have a book)
* Stuart A. Kirk, &quot;a distinguished professor emeritus in Social Welfare at the Luskin School of Public Affairs, University of California, Los Angeles&quot;&lt;ref&gt;https://luskin.ucla.edu/person/stuart-a-kirk&lt;/ref&gt; (has a book)
* Josef Witt-Doerring&lt;ref&gt;https://www.madinamerica.com/2025/02/ethics-psychiatric-drug-use/&lt;/ref&gt; (has a YouTube channel); a criticism of Witt-Doerring is e.g. in Reddit (not a particularly reliable site; in the thread, a moderator deleted a comment with this: &quot;No anti-psychiatry posting - As an expansion of rule #2, no posts that are anti-psychiatry. No discussion of how psychiatry has harmed you or anyone else without published, peer-reviewed supporting evidence&quot;; so this is likely to be a pro-psychiatry echo chamber)&lt;ref&gt;https://www.reddit.com/r/Psychiatry/comments/1en1voc/about_dr_josef_witt_on_youtube_what_do_you_think/&lt;/ref&gt;; Witt-Doerring has a monetary interest with his TaperClinic
* Jaakko Seikkula, a key person in Open Dialogue&lt;ref&gt;[https://www.madinamerica.com/2025/07/is-dialogue-the-best-medicine-a-conversation-with-jaakko-seikkula/ Is Dialogue the Best Medicine? A Conversation With Jaakko Seikkula] by Robert Whitaker, 30 July 2025, madinamerica.com&lt;/ref&gt;; a quotation from Seikkula: &quot;I think that one of the responses was what we referred to at the beginning of our conversation, that there was this extreme neurobiological model that endured. There started to emerge this extremist movement of neurobiological or reductionistic ideas of schizophrenia also in Finland. [...]&quot;

Further reading:
* {{W|Category:Anti-psychiatry activists}}, wikipedia.org

== Psychiatry: An Industry of Death ==
Psychiatry: An Industry of Death is a film by CCHR and also a museum. The film seems to be executed in a yellow-journalism style, but seems not entirely without informative value.

Further reading:
* https://www.cchr.org/documentaries/psychiatry-an-industry-of-death
* {{W|de:Psychiatry: An Industry of Death}}, de.wikipedia.org (in German) -- lists people featuring in the film
* [https://www.imdb.com/title/tt1197332/ Psychiatry: An Industry of Death], imdb.com

== See also ==
* [[Is psychiatry evil?]]
* [[Do antipsychotics cause more harm than good?]]

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Controversies about psychiatry}}, wikipedia.org
* {{W|Anti-psychiatry}}, wikipedia.org
* [http://www.madinamerica.com/ madinamerica.com], madinamerica.com
* [https://psychrights.org/ Law Project for Psychiatric Rights], psychrights.org
* [http://cepuk.org/ The Council for Evidence-based Psychiatry], cepuk.org
* [https://www.scientificfreedom.dk/books/ Books], scientificfreedom.dk -- books by Peter C. Gøtzsche, multiple of which are available online

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    <title>User:Dan Polansky/One man's look at epistemology</title>
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      <comment>Atcovi moved page [[One man's look at epistemology]] to [[User:Dan Polansky/One man's look at epistemology]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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      <text bytes="34118" sha1="l4vqptqpiriyhif7cwdkb24ez0s5hs7" xml:space="preserve">{{Original research}}
This article by Dan Polansky contains various notes on epistemology, the philosophical inquiry into knowledge. A key inspiration is Karl Popper. Various observations will be sort of trivial, but one may sometimes benefit from going over platitutes.

Epistemology is to cover both any knowledge in general and scientific knowledge in particular. It therefore overlaps with philosophy of science.

Epistemology can be a worthwhile exercise. Its results can be at least in part counterintuitive. To me, the Popperian doctrine that we can never really conclusively verify scientific theories and that any genuine verification is an attempted falsification is very instructive and revealing. (Popper sometimes uses the word corroboration instead of verification to emphasize the inconclusive character.)

== Certain knowledge ==
One doctrine states that mathematics possesses certain knowledge whereas empirical sciences possess uncertain knowledge. Einstein made a point to that effect. Lakatos extended Popperian falsificationism in part to mathematics, in his ''Proofs and Refutations''. Thus, there can be certain tentativeness even in mathematics.

The uncertainty of knowledge is demonstrated by the overcoming of Newtonian mechanics with Einstein's mechanics. Newtoning mechanics seemed to be so convincing verified and final, yet it turned out to be merely approximate, failing e.g. for high velocities. (One does not need to study philosophy to note as much; study of physics suffices. One may thus claim that this result does not stem from the field of philosophy and that philosophers merely reflect on what physics would have made clear without them anyway. But it is perhaps still useful to drive the point home as forcefully as Popper did, against Marx, Freud and Adler. Popper does not state that all that e.g. Freud states is wrong; his point is that it is not scientific.)

== Everyday knowledge ==
There are countless examples of everyday knowledge for which we feel certain from direct sensory experience that we know something. Thus, we think to know that e.g. there is a domestic cat over there or that the tree over there is a fir. In addition to sensory experience, we also often rely on verbal reports (whether auditory or in writing) and call the result knowledge, but this use of the word knowledge appears rather debatable to me. Nonetheless, Wikipedia aims to collect knowledge, or so it says.

A simple heuristic scheme one can sometimes find in literature is this:
* To see --&gt; to know.
* To have heard --&gt; to believe (without necessarily knowing).
Of course, the mapping is merely heuristic; one can read something (and thus see) and merely believe what one sees and one can hear the sound of the motorcycle engine and thus know (rather than being subject to hearsay).

== Knowledge in mathematics ==
Mathematics is thought to have certain knowledge due to using conclusive proofs. But one can put this to doubt, as is suggested by Hofstadter. Since, we do not have perfect certainty (in principle) that the systems of proof that we are using are consistent, meaning contradiction free.

One can also argue as follows: human minds are mammalian brains evolved as part of natural selection. Human methods of knowing may be merely adequate for survival and reproduction (and other gene support). It may turn out that the human brain hardware contains platform-wide defects that would lead all practicing mathematicians to recognize the same kinds of proofs as conclusive which in fact were inconclusive. I find this line of argument interesting and thought-provoking but very hard to accept. I tend to side with those who claim that mathematics has certain knowledge. Or at least some mathematics; Lakatos criticism is to be taken seriously. And one can recall that Newton's and Leibniz calculus was originally in, say, somewhat provisional state, lacking the rigor that modern mathematics requires. Perhaps the picture is more complicated and varied than one would want to believe.

== Unprovable knowledge ==
Unprovable knowledge exists. If I roll a die, observe the result, remember the result, and roll the die several times again, I know the outcome bar failure of memory but I have no way of proving it to anyone. This applies to a range of situations. It seems plausible that someone may succeed in committing, say, a murder and hiding all traces or traces of having done so.

== Documented knowledge ==
Above, I noted the thought experiment with rolling a die, and then having no means of proving the outcome. I can improve my chances of proving that by taking a record of the outcome. I could then show the record in the court of law. The proof/evidence would be inconclusive since I could have cheated or make some wild mistake when taking the record. But the record is stronger evidence than memory, since human experience generally shows human memory to be all too often frail. I can use the record later not only to convince the court but also myself. Since I too know that human memory is frail, whereas sheets of paper with writing or typing do not undergo a change in which some words get changed or similar.

Textual record necessarily leads to considerable loss. Knowledge obtained through eyesight about an object is much richer than the propositional knowledge captured in sentences. This is in part addressed by photography and videorecording as well as sound recording.

== Induction ==
I believe Popper is correct in stating that induction does not work to demarcate science from non-science. Moreover, it seems to me that induction hardly ever works at all. That is to say, if we have a predicate F, no amount of affirming instances of F would alone lead us to conclusion that for all x, F x (F is true of X). This also obtains for the more narrow form where F is in fact F ==&gt; G. This is obvious in mathematics: we can have an arbitrarily large number of even numbers, but this does not lead us to conclude that all positive integers are even numbers; in this case, F is positive integer and G is even number. That is to say, we have a large set of examples meeting F and G, and thus meeting F ==&gt; G, but that does not lead us to generalize that for all x, F x ==&gt; G x. The situation is similar in sciences. Since, let us take F to be mammal and G to be domestic cat. Our seeing additional cats (examples of F and G) does not lead us to conclude that universally F ==&gt; G, that is, that all mammals are cats. Instead, we consider the existence of refuting instances (e.g. dogs) and close the case as rejected.

A meaningful investigation of a hypothesis of the form for &quot;all x, F x ==&gt; G x&quot; involves above all considering the store of all observations (in the mind or elsewhere) to check whether there are refuting instances. Additional step involves trying to find as many or varied instances of F since these are the ones that can lead to discovery of additional falsifiers, F x and not G x.

That's how it seems to me. A proper research in the literature on induction could perhaps lead me to a different conclusion or a correction of the above.

By induction I here mean induction in sciences, not mathematical induction. I constrained the concept of induction to exclude extrapolation and interpolation; it could perhaps be used more broadly to include those.

== Incompleteness of knowledge ==
Some of the Gödel's results are sometimes used to point out necessary incompleteness of mathematical knowledge. Thus, not only cannot human mind achieve all mathematical knowledge, not even machines can ever achieve it. One may trivialize the matter by pointing out that we cannot even know all the statements of the form X + Y = Z for three integers for lack of memory and such, but that is not the point.

It seems also likely that we will never have complete (empirical) scientific knowledge. At a minimum, predictive knowledge about future will be out of bounds dues to chaos or computational irreducibility. One could still hope to discover the ultimate fundamental physical laws, without being able to use them to predict everything.

== Authority and sourcing from publications ==
One often uses sourcing from publications. Interestingly enough, Popper scorns this as a method of doing science at least in one piece of writing. The theory of scientific method is not usually concerned with sourcing from publications. Einstein's famous special relativity paper does not contain much sourcing, if I remember correctly; better find the paper.

I view sourcing with a heavy dose of skepticism. Yet I cannot do without it. Things can be improved by differentiation: are we sourcing math or are we sourcing nutrition science (spinach has iron?). One can investigate various fields and their history of success and treat them accordingly, with higher skepticism as justified by the experience with the field. One can for instance suspect that math results will be more international or interculturar than history, where nations have strong interest to skew things or spin them in their favor or direction.

In mathematics classes in the high school and university, we almost never worked with &quot;reliable sources&quot;; we instead proved everything or almost everything. The teachers hardly ever invoked their authority, if at all; the authority was there of the proof, and the student had to verify the proof. Of course, this is perhaps somewhat idealized; the authority of the teacher perhaps does play a role, even in mathematics.

== Justified true belief ==
Knowledge is sometimes defined as justified true belief. That is to say, I know X if I believe it, X is true and I am justified in believing it. There is criticism of this definition/characterization. For one thing, as long as we use the word knowledge to refer to uncertain knowledge, things known to be true are not logically necessarily true (which seems like a paradox or contradiction since the word to know implies perfect certainty, but that cannot really be the case). Another criticism concerns the requirement of justification. Popper denies that knowledge is justified. But the idea of justification is plausible; in mathematics, we only know a theorem to be true if we have a proof. One could counter that axioms are not proven, to which one may respond that axioms are definitions in disguise and that theorems in ultimate analysis point to statements of the form, if axioms such-and-such are true, the following theorems are true. Yet another criticism applies to the genus of belief. As long as knowledge can be contained in a book, it does not seem to be belief. By contrast, knowledge in a mind does seem to be species of belief if one extends the concept of belief enough to include knowledge. This extension is perhaps required since otherwise, one would say that if one believes something, it implies one does not know it; and thus, knowledge and belief would be coordinate terms rather than one being subordinate to the other.

== Knowledge in plants ==
From what I remember, Popper indicates innate expectations of organism to be something like knowledge. Thus, a plant adapted to presence of sunlight via chlorophyl as if states, there is sunlight in the environment. I find this point interesting, but it perhaps stretches the concept of knowledge.

== Knowledge in animals ==
Knowledge in some animals, e.g. chimpanzees, seems plausible, including concepts. The concepts would be there, but not names for concepts.

Even simple animals can have knowledge or quasi-knowledge, including innate one in the form of innate expectations about the environemnt.

== Knowledge of historical statements ==
According to Popper, existential statements in sciences are not falsifiable and therefore not scientific. This seems rather counter-intuitive, but has some force. Thus, the statement that there is a teapot orbiting the Earth (Russell? Dawkins?) is not falsifiable/testable and does not have a scientific character.

This can be extended to historical statements. The statements of historiography would then be non-scientific. This seems strange but also not entirely so. Since, e.g. Newton's mechanics applies at all locations and all time points, so it runs the risk of being refuted in future. By contrast, the statement that the battle of Waterloo took place in year so-and-so and was between parties so-and-so does not directly run the risk of being refuted by a future event; it is not universally quantified. The textul historical record becomes an important source of (putative) knowledge, but that is not so in physics, chemistry or biology. I should perhaps learn more about the matter by studying methodology of historical and historiographic fields.

== Reason vs. experience ==
There is some kind of discussion about reason vs. experience in how we know things, relating to rationalism vs. empiricism. I cannot make much sense of it. I would argue that all or nearly all epistemic processes contain both elements of experience and reason.

Since, concerning everyday knowledge, we recieve perceptual objects in the mind, e.g. the visual perception of a cat. The visual perception appears raw in a sense, uninterpreted. But in fact, what is really uninterpreted is the retinal image; what enters the mind is merely based on that retinal image, enriched with inferred physical properties. And thus, something like reason (inference) is part of the perceptual cat, before anything like reason in narrow sense was applied.

Let us consider mirage. The raw sensory experience tells us we see something we do not see. And we use reason (informed by other experience) that what we see cannot be real. Both elements are present.

In mathematics, one could argue that it is based on reason and not experience. But I do not find that convincing. We know that our proving methods work in part from experience. That said, I fully recognize the contrast between mathematical knowledge and empirical knowledge.

We know very little by reason or critical thinking alone. Never direct your eyes to the sky and never engage in careful observation. Instead, lock yourself in an ivory tower and have a computer to do large-scale speculative simulations and analysis. You may find out about e.g. mathematical fractals or the road to chaos, but never about the stars. No amount of analysis can compensate for missing observation and experiment and for the missing observational and experimental instrumentation.

== Instrumentation ==
Large portions of science do not get very far without instrumentation, including telescopes, microscopes, measuring devices but also computers (computing and information storage and retrieval devices). These instruments enhance our getting to know, or make it possible in the first place.

== Revisionism and scientific revolutions ==
Inspired by Kuhn and Popper. In general, scientific knowledge does not grow merely by extension/expansion but also by modification. It is in general not cumulative in this sense. One cannot hope to establish a method so good that it will only lead to statements in no need of revision. In a geographic analogy, one could naively think of science as map maping where one only fills in the white blanks and never has to redraw any parts of the map. History of science shows that redrawing is necessary once in a while. But the cumulative character is far from absent. The filling of periodic table was probably not a process of continual scientific revolution; once the concept of chemical element was well established, the process of finding additional chemical elements was probably relatively cumulative. (But I would need to check relevant literature to learn more and be sure I know what I am talking about.)

Kuhn makes the point that a certain degree of resistance to refutation and sticking to theories that appear to be refuted by observation does not need to be a bad or unscientific thing. The apparent refuting observation may later turn out not to have been refuting after all. On the other hand, the contrast between religious dogma and scientific successive modification of tentative knowledge is real, and one characteristic of good science is that it does not stick to refuted theory beyond what is reasonable (for some value of reasonable).

== Proof and evidence ==
As part of inquiry into knowledge, one can include inquiry into what serves as proof and evidence, in relation to the ''justified'' part of the characterization of knowledge. This concerns not only science but also courts of law. Courts accept witness evidence although it is logically very inconclusive.

Mathematics provides one idea for what a proof is. This idea does not seem to directly carry over to other fields.

In the field of software, automatic test suite run against the software is a form of proof or evidence that the software meets the requirements/works as required. Educational examination provides something like a proof or evidence that the student has learned the matter. Industrial testing is another case.

In another section, I supported Popperian falsificationism as a standard. There, one does not prove things; one tries to refute them. How, then, can one substantiate corroboration (attempted falsification) of a hypothesis? For instance by submitting documentary or data evidence indicating what attepts at refutation were attempted, what observations and experiments and with what results. That is the first idea; a better elaboration would be preferable.

Further reading:
* [https://www.britannica.com/topic/evidence-law evidence], britannica.com
* [https://www.britannica.com/topic/proof-logic proof], britannica.com

== Certificates ==
Certificates seem to be something like evidence or proof. They can perhaps be thought of as written testimonies of the entity issuing the certificate. Educational diplomas are one class of certificates, it seems. Identity documents are a related concept.

Certificates are subject to the risk of forgery. This is one source of their being less than fully conclusive as evidence. Even so, one may say: I know that his name is so-and-so since he showed me his identity card. This is one piece of evidence supporting a weakened use of the verb to know. The utility of certificates depends in part on our willingness to run the risk of being deceived by them. Indeed, if authorities and other organizations did not see any addition of certitute resulting from their use, they would not use them. Obtaining a forged document requires additional effort and expenditure compared to merely making an untrue statement.

Further reading:
* {{W|Identity document forgery}}, wikipedia.org

== Procedural knowledge ==
Apart from declarative knowledge (e.g. knowing there is a cat over there), there is also procedural knowledge or know-how. Procedural knowledge can have a non-propositional form; thus, one may know how to dance jive without being able to give verbal instructions. Even human ability to walk can be seen as a procedural knowledge. Tigers can be thought of knowing how to run, thus having procedural knowledge. Alternatively, one could distinguish knowledge from skil and consider ability to dance jive to be skill, not knowledge.

Some procedural knowledge does have a propositional form, form of sentences.

== Innate knowledge ==
Some knowledge is innate, given by the genes. Knowledge-acquisition aparatus (e.g. eyes and the visual cortext) is innate. Knowledge being innate does not make it necessarily accurate. Thus, it seems likely that the innate geometry in human vision and understanding of space is approximately Euclidean; the human environment under which it evolved seems unlikely to contain anything to give stimulus to evolution of Einstenian geometry (which is needed in GPS).

These considerations can lead to deep skepticism. One may think that human knowledge acquisition faculties are only good enough for survival and reproduction (and other support of the genes) and that they may fail miserably when used outside of their bounds. Part of this skepticism is perhaps healthy. One can launch a defense: how do you know that humans originated by evolution by natural selection? If the human faculties are so frail, you should not be so certain. And then you should not be so certain about your skepticism either. It is an entersting twist, pointing to certain apparent circularity in attempts to reason about knowledge with the use of Darwinism. Since, one needed an initial knowledge theory to learn about evolution by natural selection, but the results can then impinge on the knowledge theory itself. I sense this is not a grave defect, but I acknowledge the line of reasoning as not without merit.

== Knowledge of word meaning ==
The knowledge of word meaning is an interesting problem. In order to formulate an observation in language, one needs to have knowledge of word meaning. But word meanings are not trivially objectively observable entities, unlike e.g. cats or rivers. The knowledge of word meaning does not need to be explicitly represented in words; thus, one may be able to use language productively without being able to give plausible definitions.

Lexicography seems to posit that word meaning can be extracted from quotations of use. But this seems to be far from trivially obvious. It seems one has to insert a lot of conceptual interpretive analysis to extract the word meaning.

Knowledge of word meaning cannot be innate since words are not innate. But some general concepts could be innate rather than obtained from experience. A child could be trying to map the words heard to the naive observational ontology (or entitology?) given by the senses, especially sight, and then refine the ontology based on the language use. It seems doubtful that the child's naive observational ontology would contain the nodes of mammal or feline, but it could well contain animal and cat. The node of animal could be innate; cat perhaps not. These questions would need to be seriously investiated.

== Cybernetics ==
One could use the ideas from cybernetics to investigate knowledge. Thus, one could set up two abstract systems, one trying to learn about the other and try to figure out what that learning would consist in. In relation to that, I seem to remember that Ashby indicates that being a model is given by isomorphism or homomorphism.

== Scientific models ==
The concept of a scientific model seems to point to the idea that elements of scientific knowledge are rather imperfect representations of reality. Both Newtonian and Eistenian mechanics can be seen as models. But also Ptolemaic astronomy can be seen as a model, one that has been made increasingly observationally adequate by subsequent modifications during its use.

A visual analogy for the concept of scientific model can be a toy model of a car. The toy model bears some resemblance to the real thing, but key aspects are missing. To what extent this analogy is apt would need to be clarified.

Further reading:
* [https://plato.stanford.edu/entries/models-science/ Models in Science], Stanford Encyclopedia of Philosophy

== Counting and calculation ==
Counting and calculation are both epistemic processes.

Counting is additional to seeing. Thus, one can see e.g. many cows, but to know exactly one many, one has to count, unless the cows are only few.

Calculation with numbers can answer arithmetic questions. Some indicate this results in no true additional knowledge, which makes sense from the perspective of empirical knowledge, but sounds strange anyway.

Logical derivation using logical calculus is an analogue to calculation with numbers. In any case, it is a mechanical manipulation of symbolic encodings.

Calculation is a key part of computed tomography and magnetic resonance imaging. Without calculation, the medical doctor would not be able to see much. Revisiting the argument sometimes made that calculation adds no true knowledge, that is all nice and perhaps superficially plausible, but here calculation makes a difference between seeing something (on the display or other visual representation) and seeing nothing at all.

Humans are rather bad at calculation, too ready to make calculation errors. This can be addressed by verification. One may do the same calculation multiple times. One may let another person do the same calculation independently (the person doing the first calculation may have a blinder that will lead to the same error when he tries to make a 2nd calculation). And one may calculate the inverse function, e.g. first do long division, and then multiply the result back. There seems to be a host of various other partial plausibility checks, depending on what one calculates.

== Measurement ==
Measurement is an epistemic process. Like counting, it yields a quantitative characterization of something.

There seems to be the field of metrology concerned with this subject.

Measurement adds information beyond mere visual inspection. Thus, there is a difference e.g. between estimating the length of a table from looking at it and measuring the length using meter.

== Knowledge of the knowing agent and apparatus ==
Something like metaknowledge can contribute to epistemology, knowledge of the knowing agent and apparatus. Thus, one may empirically study limitations of human cognition, limitations of measuring instruments and measuring procedures, etc.

One could object that part of such inquiry is no longer philosophical but rather psychological. Nonetheless, I am wary of strictly separating philosophy from psychology. Perhaps someone can execute such a separation well enough; let them then present what they have done and how and let us see whether the result is satisfactory.

== Epistemology vs. history of knowledge ==
One could want to separate epistemology from history of knowledge and history of science. One could want to prohibit input from the latter to the former; the former would be purely philosophical. I can see the attraction of doing so from something like architecture of inquiry standpoint, but I do not think it a good idea. For instance, one can hardly fail to observe the impact of Einsteinian special relativity on the philosophy of scientific knowledge. The history of human theories about the world is very instructive, revealing incredible fallibility and openness to wrong suggestion.

One can say: I am fallible. My analyses of knowledge are tentative. Their being philosophical is not a good thing per se. If findings of special sciences can shed some light on the questions being asked, so much better. Thus, it is e.g. all fine to use Darwinian thinking to speculate about quasi-knowledge embedded in plants.

== Failed epistemic methods ==
It is instructive to consider not only what is likely to work well but also what has demonstrably failed. Torture is one thing that does not necessarily make one say truth. There are other absurd methods that were sometimes used in history, to be added later.

== Epistemology of philosophy ==
If philosophy contains a key non-empirical element, one can wonder whether there is a separate epistemology of philosophy, different from epistemology of empirical sciences.

For philosophy, one can use something like proposals and refutations, arguments and counter-arguments. The basis for making them is not constrained, but it usually contains both empirical and deliberative element. It is understood that the proposals are too likely to be wrong too often. It is also understood that running the proposals through the acid test of counter-arguments does not establish anything like certainty or validity. The results do not resemble science with its marked progress, e.g. from before the concept of chemical element to the concept and discovery of the individual chemical elements.

Be it as it may, the human brain has this remarkable capacity of coming up with ideas formulated as sentences, without knowing whether they are true or right. The brain seems to use some fantasy or inventive method: figure out something half-plausible and say it. And then, see whether we can refute or effectively criticize the thing said. This is hardly satisfactory. We should have something better.

== Reviewing ==
Reviewing is a powerful method for reducing mistakes. A review can take place when there is something to be reviewed, e.g. a document such as a draft of a scientific article. One can review one's own writing, but bringing in other people generally makes a remarkable difference. There may be a subliminal block or resistance to seriously and earnestly looking for mistakes in one's own creation; other people may be more openly adversary (and pointing out mistakes is adversary in principle). Moreover, other people may happen to see things from a different perspective. And they may be more experienced and know better.

== Evolutionary epistemology ==
The phrase evolutionary epistemology could refer to epistemology informed by biological evolution, e.g. one emphasizing the evolutionary origin of organs that play a key role in knowledge acquisition, including eyes and the brain. Or it could refer to epistemology that sees scientific theories are objects undergoing evolution somewhat similar to biological evolution. It seems to refer to both, as per SEP.

Further reading:
* [https://plato.stanford.edu/entries/epistemology-evolutionary/ Evolutionary Epistemology], Stanford Encyclopedia of Philosophy

== Artificial intelligence ==
One would expect artificial intelligence to be able to produce something like knowledge from observation. Sufficiently capable artificial (general) intelligence should be able to use e.g. camera to produce observational reports in natural language. One would naturally ask whether the machine really knows anything or merely imitates knowledge or pretends to know. Study of design of an AGI machine would seem to be a contribution to study of knowledge processes. One would be forced to technically clarify issues instead of waffling about them. One would be forced to discover sets of technically formulated principles, rules and algorithms. Alas, one thing one would discover would be artificial neural networks, which can be trained, but from which it seems hard to extract anything like human-intelligible sets of rules or principles.

Machines can produce mathematical knowledge without having anything like human-like subjective knowledge states. Thus, machines can do arithmetic calculations. Moreover, machines can do computer algebra, including derivation. There are theorem provers. That is to say, whenever the knowledge production (reliable production of true statements) can be supported by a reasonably small set of mechanical rules, it can be done by a machine.

One may look at a human as a gigantic lumbering (biological) robot (to use Dawkins phrasing) and wonder whether the human intelligence and cognition is after all also a collection of mechanical rules embedded in neural and endocrinal anatomical structures. Many of these rules would be heuristic, rules of thumb.

Recalling the section on instrumention, current production of human knowledge is an effect of biotechnosphere, of a combination of humans (bio-) and machines (techno-). For instance, astronomy uses telescopes as well as computers.

== Knowledge about knowledge sources ==
Knowledge about knowledge sources/providers is key for distinguishing reliable from unreliable sources and thus reducing chance that one ends up in error.

For instance, one may have good experience with a particular geographic map publisher, having learned first-hand that their maps match the terrain visited. One may then say: I know there is a bridge over the river at that location since a map published by a reliable publisher indicates as much. Alternatively, there may be an indirection: one may not have first-hand experience with the map publisher but one may know a reliable assessor of publishers, and the reliable assessor may indicate the publisher is reliable.

He who trusts unreliable sources and makes reports based on them is himself unreliable. Thus, one may feel to have a duty to only trust sources for which one may have good reason to believe they are reliable. And if not because of duty, one may dislike being considered unreliable.

In an ideal world, one would simply divide sources into reliable and unreliable, trust the reliable ones and be done with it. Unfortunately, there hardly exist any perfectly reliable sources completely free from mistakes. One may know about a source that it contains remarkable number of mistakes but continue using the source anyway for lack of better alternatives, mentally marking the information as having an increased uncertainty. Moreover, one may differentiate what kind of statements are more likely to contain mistakes in the source class, e.g. mainstream media. For instance, when mainstream media report that so-and-so was elected a president, that is perhaps much more reliable than when they report that scientists found such-and-such.

One can increase confidence by considering multiple independent sources instead of only a single source. However, true independence may be hard to come by. Even so, consulting multiple sources is often a meaningful exercise that reveals how the sources differ.

== Positive knowledge ==
The phrase ''positive knowledge'' by implication differentiates the concept from ''knowledge''. The adjective ''positive'' seems to refer to some kind of positivism; it could be Comte's positivism (verify) or logical positivism of Wiennese circle.

One could argue that &quot;there is a cat on the street&quot; is positive knowledge, something like &quot;protocol&quot; observational statement/basic statement, whereas &quot;the world behaves according to Einstein's general relativity&quot; is not positive knowledge. I need to look into this deeper.

== See also ==
* [[Epistemology]]

== Further reading ==
* {{W|Epistemology}}, wikipedia.org
* [https://www.britannica.com/topic/epistemology epistemology], britannica.com
* [https://plato.stanford.edu/entries/epistemology/ Epistemology], plato.stanford.edu

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This article by Dan Polansky looks at the concept of value. One inspiration is a note by Mandelbrot in his ''The (mis)behavior of Markets'' to the effect that the concept of value is mysterious, elusive or something of the sort. Another inspiration is the concept of Quality by Robert Pirsig, which Pirsig wants to leave undefined, but is somehow relating to goodness or value. I suspect that the resulting analysis is going to be weak and confusing. Perhaps Mandelbrot is right: the concept is elusive.

Let me start with an initial take at a definition of value:
* The degree to which someone is unwilling to part with something.

The something one may want to part with can be an object but also a state of affairs or being. The concept of being used here is perhaps somewhat untraditional, so let me elucidate a bit. Someone who lives is London has ''being an entity living in London'' or ''being a London inhabitant''. If they move from London to, say, Edinburgh, they part with ''being a London inhabitant'' or with London-inhabitanthood. One may be unwilling to leave London, that is to say, to part with being a London inhabitant. And that degree of unwillingness is identical to the (subjective) value of that being. Havings are species of beings; that is, having is car is being such that one has a car. in this way, we may reduce all partings to parting with beings. Thus, instead of parting with a car, one parts with being one who has a car. This seems strangely technical, but it seems to have a theoretical or analytical significance or advantage. For one thing, one may part with an object only in part; for instance, a real estate owner renting the real estate does not part with being the rightful owner but does part with being the rightful user of the real estate. This all seems perhaps rather counter-intuitive and I hope to develop these ideas further in more detail later. Be it as it may, it is still meaningful to talk about the value of an object (a car, a golden piece, etc.) as a shortcut for the value of ''having'' the object (more technically, being the rightful owner of the object or other form of having).

The definition is doubly subjective. For one thing, the value of insulin for someone with diabetes will be different from its value to someone without. But additionally, someone with diabetes may happen to be in an unsound state of mind and be eager to part with insulin despite its obvious utility.

The definition seems to fail to differentiate value from an ''estimate'' of value. Since, appreciation of something is limited by its knowledge. If I have a box with unknown content, the value of the box depends on the value of the unknown content. Learning about the content would change my unwillingness to part with the box (and the content), but it seems strange that the value would change only based on change in knowledge of the valuing person.

The definition is made in terms of parting rather than acquisition. Whether it is the best option is unclear. At least, there are some things one does not acquire, e.g. hands. And for them, the relevant change is parting. Moreover, refusal to part generally does not require expenditure of attention, unlike a decision to acquire.

== Use value vs. exchange value ==
The unwillingness to part may be driven by use value or by exchange value. Thus, someone with diabetes has use for insulin. By contrast, someone without diabetes does not has use for it, but can sell insulin or offer it to someone as a favor. Both cases match the doubly subjective definition of value, and this split seems to be meaningful.

The use of the word ''use'' in the name of the concept may lead to some confusion. One may argue as such: gold is ''useful'' as a means of exchange, and therefore, gold has ''use value''. And thus, exchange value is a species of use value; to exchange something for something else is to make one particular use of it. I propose to reject this reasoning and exclude exchange from ''use'', retaining use value and exchange value as contrast terms rather than subordinate terms.

One may futher ponder whether ''use'' can be contrasted to ''beauty''. Things that are ''useful'' are sometimes contrasted to those that are merely ''beutiful''. Thus, a beautiful painting would have no ''use'' value since one does not ''use'' it, merely looks at it. However, for the purpose of this conceptual distinction, deriving pleasure or changed cognitive state from looking at a beautiful picture would probably count as ''use'', indicative of ''use value''. Put differently, one may think of use value as that kind of value that remains when one ignores exchange value. This concern also has to do with the word ''utility'', which I would think would mean something like ''usefulness'', but in Millian utilitarianism and modern economics seems to be something slightly different. Like in the previous paragraph, we see that we need to carefully consider what concepts we are trying to indicate by means of partially misnaming concept names instead of relying on a naive or common-sense meaning of the words used in the analysis.

----

In the remainder of this section, let me look at the historical literature.

This distinction is recognized by Smith&lt;ref&gt;[[Wikisource: The Wealth of Nations/Book I/Chapter 4]]&lt;/ref&gt;: &quot;The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of some particular object, and sometimes the power of purchasing other goods which the possession of that object conveys. The one maybe called &quot;value in use,&quot; the other, &quot;value in exchange.&quot; The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water; but it will purchase scarce anything; scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any value in use: but a very great quantity of other goods may frequently be had in exchange for it.&quot;

This distinction is recognized by Malthus 1823&lt;ref&gt;[[Wikisource: The measure of value stated and illustrated]]&lt;/ref&gt;: &quot;It is generally allowed that the word value, in common language, has two different meanings; one, value in use, the other, value in exchange; the first expressing merely the usefulness of an object in supplying the most important wants of mankind, without reference to its power of commanding other objects in exchange; and the second expressing the power of commanding other objects in exchange, without reference to its usefulness in supplying the most important wants of mankind. [...] It is obviously value in the last sense, not the first, with which the science of Political Economy is mainly concerned.&quot;

This distinction is also recognized by The New International Encyclopædia&lt;ref&gt;[[Wikisource: The New International Encyclopædia/Value (political economy)]]&lt;/ref&gt;: &quot;VALUE (OF. value, value, fem. sg. of p.p. of valoir, from Lat. valere, to be strong, able). In political economy, a word that is most commonly used to designate the power of a commodity to command other commodities in exchange. The term is applied, however, to several other conceptions. The potential capacity of an object to meet human needs is sometimes called value — ‘value in use,’ in the terminology of the classical economists. In modern scientific economics, the term ‘utility’ has for the most part supplanted this use of the word value. Another meaning which the term value conveys is the significance of an object to an individual as the indispensable condition of a certain satisfaction. Value in this sense of the term is frequently called ‘subjective value,’ to distinguish it from ‘objective’ or ‘exchange’ value (the first conception noted above). Subjective value is of two kinds, ‘subjective use value,’ where the importance of an object is gauged by the direct satisfaction to be obtained through its consumption, and ‘subjective exchange value,’ where the importance of an object is gauged by the satisfaction it will yield indirectly, through exchange.&quot;

Further reading:
* {{W|Use value}}, wikipedia.org -- for some reason, largely devoted to Marx

== Exchange value ==
Above, I think to have established a meaningful distinction between use value and exchange value.

What is the exchange value? One could think it is the price, that is, the exchange rate with respect to the currency. There are problems with this proposal:
* In barter, there is no currency, but there is exchange value.
* The proposal would make it impossible to track the value of currency in time, making the phrase &quot;devaluation of currency&quot; meaningless. Since, a given currency's value expressed in itself is constant (not changing in time).
* In a situation where multiple currencies with variable exchange rates are available, the proposal fails to identify one standard of value.
* Different prices obtain in different places even within the same relatively small country such as Switzerland.

A solution is to relate the exchange value not to, say, the nominal dollar but to &quot;real&quot; (inflation-adjusted) dollar. A problem with that is that inflation is always with respect to some basket of goods, commodities and services, so there is no single inflation-adjusted dollar. But the problem is not entirely fatal; picking a basket is somewhat arbitrary but far from completely so.

A currency-independent concept of exchange value can be obtained by linking the assessed item to a basket of goods, commodities and services directly. This works also for barter or currency-free situation. As above, there does not seem to be a single correct basket, so this does not give us a single standard of exchange value either.

== Value vs. goodness ==
Goodness and value are two distinct concepts. A good knife may lose its value because of reduced demand on knifes, which may result from availability of cheap substitutes on the market. But the knife does not become any less good (in the sense of e.g. rust resistant, maintaining sharpness for long, etc.). Value has something to do with supply and demand. If the example of knife seems too contrived, one may think of factory machines that lose value as a result for loss of demand on the kind of product they are used to make or as a result of arrival of new technology requiring new machines.

One can nonetheless perhaps connect value to goodness as follows. The value of the knife is given by the degree of goodness of having the knife. Here, goodness of the knife is distinguished from the goodness of ''having'' (a good) knife. With changing market conditions, the goodness of the knife does not change, but the goodness of having the knife does change. One may object that this departs from the doubly subjective definition by an implied objectivity of the word good. This would need to be clarified. For one thing, the idea that the goodness of having insulin at disposal differs between a person with diabetes and one without is plausible enough; so far so good.

== Value vs. price ==
A thing or state of affairs does not need to be for sale to have value. For instance, having healthy organs is of value in a country that does not allow people to sell their body parts for money. Moreover, having the purchased food at home rather than in the grocery store is of additional value since this is where one wants to have the food. This is an example of not only having the food but also having it in the right place being of value.

In some contexts, the value does seem to match the price. It is so at least linguistically: one talks about the value of the stock rising. And in so far as one mostly holds stock for the exchange value, the value is given by the price, although there is also the dividend income.

One also talks of good value for the money. This could refer to something like use value. However, it could also return to a future selling price, future exchange value. Thus, a tradesman who has no intent to use the things he trades in may consider to have gained good value for the money, or bought cheaply (or so I think; quotations of this kind of use would solidify the point).

== Objective value ==
I would like to come up with something like objective value or intersubjective value. Alas, there is some difficulty.

One difficulty is something like inversion of value in transactions. Thus, when I buy e.g. bread for money, I indicate that the bread has more value to me than the money I give up. But for the seller, the relation has to be the opposite: the money must be of more value than the bread.

Nonetheless, something like objective value in market context makes sense. Thus, I may have a certain degree of unwillingness to part with money in the given market conditions. That unwillingness does not seem to be purely subjective: whatever I want to acquire, I will need money for that, so I naturally do not freely want to part with the money without gaining something in exchange. And this applies to other people as well. Sure enough, the unwillingness to part with a specific amount of money is different between a rich person and a poor person.

Be it as it may, one may reason as follows. There is more objective value in food, clothing and shelter since everyone needs those. There is less objective value in luxury items or various pieces of art whose trading resembles trading of bitcoin in certain ways.

Let us consider: did the tulips during the noted speculative bubble have objective value? They seemed to since they had exchange value. That is to say, a holder of a tulip could exchange it for something of value and in fact something of high value during the peak of the fever. This is strange. This kind of concept of objective value does not seem to be anything like underlying value, whatever that would be. But excluding exchange value from the concept of value does not seem reasonable. A puzzle.

== Personal value ==
Things can have nostalgic or other psychologically subjective or personal value. Someone may grow fond of old items and be unwilling to part with them as a result, regardless of availability of cheap new replacement items on the market. Someone may appreciate old letters from a friend or a romantic partner, and these same letters will have almost no value for anyone else.

== Marginalism ==
Marginalism features the interesting idea of additional items having increasingly less value. Thus, additional items of food have increasingly less use value; when one is satiated, one cannot appreciate the additional food items so much.

== Objective value 2 ==
An attempt at objective value:
* The degree to which something contributes to the continuing existence of the value assignor.
This is very generic. The value assignor can be a human, an animal or a robot; perhaps even a plant. There is an element of objectivity: if someone who has diabetes does not appreciate insulin, he is objectively wrong about its value.

How this concept is going to interact with exchange value is unclear. It should probably involve it as part: money has this kind of value--indirectly--for its ability to purchase things of direct value, e.g. food or drinking water.

In a biological context, one may replace the objective of the continuing existence of the value assignor with the success of the genes of the value assignor. How this would translate into the case of robots would need to be figured out.

In this conception of value, there is no room for subjective preferences. It seems to be a very cold, as if Spartan concept.

We may modify the definition to be not in relation to continuing existence but to something like power or ability. Since, without modification, someone who is very rich does not gain much in terms of survival ability by earning additional huge sums of money, but it is implausible that these additional sums are of almost no value.

== Things having value ==
At first thought, one may think that what is of value are objects, e.g. a loaf of bread or a silver coin. But it turns out that what is of value are beings (including havings), states of affairs. Even to speak of bread as having value seems to be a shorcut for saying that ''having bread'' is of value rather than e.g. its existence. And then, it is of more value to have the bread where one needs it rather than merely owning it; one spends effort to gain having the bread in the paltry.

Other beings and havings of value include having hands, having both kidneys, having good friends and associates, having a good reputation, having an educational certificate, having skills even if uncertified, etc. Sometimes it is ''not'' having something that is of value, e.g. in a game mentioned by László Mérő in which one of the truck drivers throws away the steering wheel and thereby wins the game (detail to be added).

Also of value may be negative objects, such as holes, lacks of fullness, etc. Thus, having pantry not completely full may be of value, or else one has no place for adding more items. Thus, getting rid of unnecessary items may be of value.

For workers, being subjected to state-enacted work safety regulations may be of value; it improves their negotiation power. Here, the reduction of freedom of contract is of value.

For some of the poorest people, being in a country such as the U.K. that has NHS (state-funded single-payer healthcare) may be of value.

== Negative value ==
Some things can have negative value. Thus, one would prefer to get rid of them or even pay someone to get rid of them. Household waste is a case in point. Having dirt on the kitchen is another. Being ill is a being that usually has negative value.

Thus, not only is there willingness rather than unwilingness to part; there is also willingness to part with something additional that one would not want to part with otherwise, e.g. with the time required to take the household waste bin to a shared waste container.

Having items with low use and exchange value that take up valuable space may have negative value. For someone else with more than enough space, having the items can have positive use or exchange value. (Maybe there is a mistake here; I need to work out an example.)

== Labor theory of value ==
This theory states that things have value to the degree of the amount of labor necessary to produce or acquire them. I find this theory wrong. It disregards the demand part: someone having spent a lot of labor in creating a useless thing does not automatically make the thing valuable. Furthermore, it disregards scarcity-driven value of natural resources. Sure enough, human labor is one key scarce resource affecting prices, resource most people have at disposal. But I see no reason why scarcity of other scarce resources should not affect prices or that it should not be reflected in the concept of value.

Another objection is that labor by an unskilled person is generally not necessarily as valuable as labor by skilled person. One could try to account for this by considering the skill to be a result of past labor, effort spent in acquiring the skill. But acquiring the innate talent, a capital asset, does not seem to be a result of labor; it is not acquired at all, it seems.

Further reading:
* {{W|Labor theory of value}}, wikipedia.org

== The value of art ==
One may think the value of art has something to do with immediate utility or quasi-utility, which, in the case of paintings, would consist in production of pleasing aesthetic response as a result of looking at the painting. Alas, that does not match art prices. There seems to be some strange speculative element in art prices. A key property of art items is that they are not so easy to copy or copying is prohibited. The items share this property with money. There is a scarcity of talented painters or there is a scarcity of positive critical appraisals for paintings by respected critics. What kind of game is really going on I do not know. Some people apparently take pleasure in destroying property to demonstrate wealth. Why, then, would one not want to demonstrate wealth by buying arguably overpriced fundamentally useless items? Look how wealthy I am, I can afford to spend this incredible amount of money for something of no apparent utility, at least as narrowly understood. Conspicuous consumption is the keyword.

IEP takes a different view of the value of art.

Further reading:
* [https://iep.utm.edu/value-of-art/ Value of Art], Internet Encyclopedia of Philosophy

== The plural values ==
The plural ''values'' seems to refer to a different concept. Remains to be investigated.

== Economic value ==
The term ''economic value'' sees some use. Intuitively, I would think that this concept can be split into use value and exchange value, no less than the doubly subjective concept of value. Since, having a machine useful for manufacturing has use value revealed in the manufacturing use as well as exchange value upon a sale to someone else who wants to use it for manufacturing. And both would seem to be economic value, as opposed to e.g. personal value, artistic value or cultural value. The term intuitively does not seem equivalent to the doubly subjective concept of value; especially personal value (resulting e.g. from an emotional attachment) would not be economic value.

Further reading:
* [https://dictionary.cambridge.org/dictionary/english/economic-value economic value], dictionary.cambridge.org
* {{W|Value (economics)}}, wikipedia.org

== References ==
&lt;references /&gt;

== Further reading ==
* [[Wikisource: The measure of value stated and illustrated]] by Malthus
* [[Wikisource: 1911 Encyclopædia Britannica/Value]]
* [[Wikisource: The New International Encyclopædia/Value (political economy)]]
* [https://plato.stanford.edu/entries/value-theory/ Value Theory], Stanford Encyclopedia of Philosophy -- despite the word &quot;value&quot;, this seems to be about something else</text>
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This article by Dan Polansky looks at logic, the study of correct inference. It is in part idiosyncratic.

Let me open the discussion by asking why anyone would want to study correct inference, correct conclusion drawing, that is, production of correct/true statements from correct/true statements. Are we not all born with ability to draw conclusions from premises? Can express articulation of principles of correct inference really bring us forward in any way?

My tentative answer is yes, studying correct inference is of value. Above all, our experience shows that humans are too frail, too ready to make errors in inference/conclusion drawing. Given this fact, it does not yet follow that logic is going to help. Whether logic is going to help is an empirical question in the field of human psychology; it cannot be answered purely logically. It could turn out that people who learn logic (especially formal logic) do not really improve in ability to draw correct conclusions.

One kind of logic taught is propositional logic. Here one learns to interpret logical connectives (and, or, implication, not) as truth-value/boolean functions. Thus, one can think of them as algebraic operators defines by means of truth-value tables. The idea is of logic as algebra. One can ask whether this brings us any further. It does. For instance, in natural language, or is sometimes implied to mean exclusive or. By defining the logical or by means of a table, one removes all ambiguity. One says: in logic, when we say or, this is what we mean. Another important idea is to interpret sentences as propositions that have truth value, true or false. That assumes the law of the excluded middle: a sentence has to be either true or false (whatever our knowledge of it). It is not obvious that sentences in natural language generally can be unambiguously interpreted in that way. Proposition logic requires us to try to think of unambiguous sentences that have truth value; if a sentence is ambiguous, it cannot be immediately fed as an input into propositional logic. Another thing of note is the table-based implication. It is defined as follows: A ==&gt; B =def= not A or B. One sometimes reads &quot;==&gt;&quot; as implies or from which follows, but that does not really make sense. The idea that from an untrue statement any true statement follows seems suspect. Thus, the idea that e.g. from the grass being always yellow it follows that all cars are green does not make sense. In case of doubt, one is well reminded that &quot;==&gt;&quot; is defined by the truth table, which is equivalent to not A or B.

The real powerhorse is the first-order predicate logic. It seems to be based on the 19th century work of Frege. Here, one adds variables and existential and universal quantifiers as well as predicate symbols and function symbols. The variable refers to entities in the universe of discourse, that is, entity one can talk about given the particular language of concern. A language of concern is a set of predicate and function symbols together with their arities; semantics is not involved. The &quot;first-order&quot; part in the name refers to the quantification being only over items in the universe of discourse and not over sets of such items.

Natural language is sometimes said to be not logical. That is misleading. In fact, language cannot violate the laws of logic. What is often meant by it is that language contains a lot of peculiarities, deviations from pattern-based expectations. For instance, one could think that &quot;here&quot; and &quot;where&quot; would be pronounced is a similar way, but that is not so. More importantly, there are semantic peculiarities, in which the semantics deviates from the pattern-based expectation. None of this violates the canons of logic. One simply has to learn that instead of making pattern-based guesses/estimates, one has to get more serious about word and phrase meaning, examining the meaning of each indivudal item in case of doubt regardless of the suggestiveness of the morphology or etymology.

We may also mention Aristotle. He pointed out that we can sometimes reliably produce true sentences from true sentences. Thus, we can in fact discover some purely mechanical rules. A classic example is this: Socrates is a human; all humans are mortal ==&gt; Socrates is mortal. This reminds us of the predicate logic, but the Aristotelian logic is much less powerful. I will not delve more into this here since I find it mainly of historical interest; if one is serious about logic, one should go for the first-order predicate logic.

Strangely enough, arithmetic calculation can be seen as a species of logic in that it is in the business of mechanically producing true sentences from true sentences. For instance, from noting that soldiers are in a rectangular formation of 6 rows and 8 columns, we may reliably conclude that there are 48 soliders. One may then perhaps ask whether the whole of mathematics is a branch of logic. Whatever the case, there is a traditional separation of logic from mathematics.

One concern about application of logic is that in order to produce true sentences from true sentences, we need to have some true sentences to start with, obtained without use of logic. That is true enough; these can be observational report sentences. One can charge that the observational report sentences are uncertain, and therefore, also the strictly logical conclusions are uncertain. That may be true in principle, but does not really seem practically relevant. For instance, we think to know reliably that Socrates is a human and that all humans are mortal; and then, we feel comfortable about drawing the conclusion that Socrates is mortal. That said, the GIGO problem (garbage in, garbage out) is in general a real one as for mechanical/algorithmic sentence production. There are too many sentences that we do not know reliably enough and yet we want to draw correct conclusions. Importantly, the mechanical conclusion drawing is of great value as part of falsificationism: if an uncertain sentence has a necessary logical consequence known to be untrue, the sentence cannot be true. Rejection of mechanical deductive inference as a principle would seem to prevent falsificationism from operating.

One idea brought forward by the first-order predicate logic is that mechanical rules work well when all symbols are unambigous. The mechanisms of this logic do not have any way to disambiguate by context; all occurrences of a symbol (predicate, function or variable) are taken to mean the same thing. One suggestion is then that human mind is helped when sentences deliberated about have reduced ambiguity; something like the logical engines in the background mind can start to work much better. However, this is an empirical hypothesis and would need a proper examination.

A related idea is something that I call export of semantic items on the syntactic surface. Formal symbolic logic can only operate on what has been expressly stated using syntactic means as part of a sentence. Human deliberation about sentences often does not work like that; practical conclusion drawing often involves incorporation of unstated assumptions. Symbolic logic can inspire us to state additional assumption to make purely mechanical inference and argument verification work.

One interesting application of predicate logic is having the pronoun ''nothing'' disappear by translating sentences into their logical form. Thus, the sentence &quot;there is nothing in the box&quot; can be rendered as &quot;for each macroscopic object, it holds that it is not in the box&quot;. This points to natural language syntactically constructing apparent objects that are in fact not there, as part of something like syntactic sugar, here the putative referent of the word ''nothing'' that is allegedly contained in the box. The syntactic sugar is nice to have; it is much nicer to say &quot;there is nothing in the box&quot; or respond to the question &quot;what is in the box&quot; with &quot;nothing&quot; than use the more complex phrasing used above. And then, one can suspect that inquiries into the so-called ''nothingness'' end up to be nonsense (or maybe not?).

There are various specialized formal symbolic logics, e.g. modal and temporal logics. In modal logics, the formal operators are interrelated in the same way as existential and universal quantifiers: &lt;&gt; =def= not [] not. Wikipedia article on modal logics has a lattice structure of different axiomatic modal logics. One can ask which of these logics is the true valid one and why. This remains something of a puzzle. More is currently for further reading.

Apart from formal symbolic logic, there is also a thing called informal logic. It investiages e.g. logical fallacies, a classic being ad hominem. It does seem to have the capacity to reduce the rate of certain kind of wrong arguments, but to what extent it really does is again an empirical question.

There is also something called argumentation theory. One would think it could be part of logic. I would need to have a closer look at it to see what it does. As a first note, it appears clear that the ''support'' relation (a statement supporting another statement) is usually not necessary one of strict deductive inference. Something else must be going on, but what it is exactly I would need to figure out. One part of argumentation is something I would call argument and counter-argument, on nested level. It is reminiscent of Popper's conjectures and refutations and Lakatos' proofs and refutations, but it can be something somewhat different. One idea is that in order to critically investigate a statement, one must allow even relatively weak counter-arguments into the discussion (but not completely irrelevant). And then one may criticize the counter-arguments as well, leading to a nested argument structure. Wikidebates in Wikiversity are a great example of this structure.

There is something called inductive logic. From what I remember, Popper says something to the effect that there is no such thing as inductive logic since logic is the study of correct inference and inductive inferences are not correct. I would like to look more into the matter, paying more attention to defenders of induction (Carnap?) I also need to clarify whether I want to treat of induction here or in the epistemology article.

The relation of logic to epistemology should be clarified. Logic could be seen as part of epistemology; since, if someone asks me how do I know that Socrates is mortal, I can answer: I know it by applying mechanical rules of logical inference, taking reliably known facts as an input.

Mathematical symbolic formal logic can be contrasted to logic used in mathematics by mathematicians. There is a certain degree of informality in mathematical proofs, even when they invoke existential and universal quantifiers. Mathematical logic sets up axioms and proofs (which it sometimes calls derivations) as formally mathematically concieved/defined entities, subject to rigorous mathematical analysis. And thus, mathematical logic is metamatematics (matematics about tools used by mathematics) as well as metafield (field about tools used by various fields of inquiry). Let us recall that mathematics was not in a very bad state before the arrival of Fregean logic in the 19th century. Mathematicians succeeded in doing mathematics at least since the Ancient Greek Euclid, noted for the axiomatic system of Euclidean geometry. It would seem that mathematicians must have informally known something like first-order predicate logic all along. Which really is the case I do not know; this would require a thorough and serious look into the history of mathematics. One could argue that Newton and Leibniz did not practice the modern mathematical rigor with their early versions of calculus and that therefore something could have changed with the arrival of mathematical logic, especially with Cantor's set theory. One would do well to investiage the possible impact of Frege on Cantor.

One may wonder what value can there be in mathematical first-order logic. Since, in order to execute the study, one needs to assume something like informal logic anyway. Thus, to prove theorems that are part of mathematical logic, one needs something like informal logic. We already know how informal logic works before we even started, so why the fuzz? What's the point of this bureaucratic exercise, investigating something that was clear before we even started? Not so fast. For one thing, it is on the basis of the mathematical formal symbolic logic that we can get such results as Gödel's incompleteness theorems. Without formalizing logic in this way to be studied as an object, it is unclear how these could be oobtained. Moreover, first-order logic opens itself directly to computer support, such as in theorem provers.

There are multi-valued mathematical logics, including fuzzy logic. Thus, instead of a predicate either being true or false about its subject or subjects, the truth value can have degrees. In fuzzy logic, the truth value (also interpreted as degree of memebership in a fuzzy set) is a real number in [0, 1]. One then has to figure out how to calculate logical connectives and, or, implication and not, and multiple proposals are given. Fuzzy logic has applications in devices such as photographic cameras.

There is what is known as intuitionist logic. (One should not read too much into the name &quot;intuitionist&quot;, I think. The intent does not seem to be to abandon formal rigor in favor of something like Poincaré's mathematical intution.) It is weaker than the classical logic (such as the classical first-order logic): it makes fewer inferences possible. There seems to be the idea of ''constructive'' involved. I know almost nothing about it; further reading can be in SEP and WP.

One can sometimes read that logic is a normative field. I find that doubtful. Logic does not tell anyone how he ''ought'' to think or whether he has anything like a duty to think in a particular way. Logic says: if you want to avoid producing untrue statements from true statements, here is how to go about it. A society can in fact require people to adhere to canons of logic, but that is not because logic says it should. Similarly, bridge engineering studies parameters of bridges and manner of bridge building that lead to low likelihood of the bridge failing. Bridge engineering does not tell anyone that they have a duty to build good bridges. Thus, bridge engineering is not a normative field. And nor is logic. I do not find the idea of logic being normative entirely wrong, in part since indeed, if e.g. a judge openly violates canons of logic or sound reasoning, there is likely to be a complaint that he broke his duty. It is just that the putative duty to engage in correct reasoning can be separated from study of correct reasoning.

Logic is sometimes contrasted to psychology of reasoning. Popper argues these are different fields or domains and I find that convincing. On one hand, people often do feel the force of logic as if it was innate (and perhaps it is in some sense). On the other hand, people in fact often do reason in incorrect or brutally heuristic ways; logic does not recognize that reasoning as valid only because it is or seems natural. Thus, logic does not seem to be part of psychology. It is this contrast that may lead people to say that logic is normative. But perhaps it is more debatable than seems to me.

== Further reading ==
* {{W|Logic}}, wikipedia.org
* [https://plato.stanford.edu/entries/logic-classical/ Classical Logic], Stanford Encyclopedia of Philosophy -- features first-order predicate logic
* [https://plato.stanford.edu/search/searcher.py?query=logic Search for &quot;logic&quot;] in Stanford Encyclopedia of Philosophy -- shows there are many articles on the subject
* [https://www.fi.muni.cz/usr/kucera/teaching/logic/log.pdf Matematická logika] by Antonín Kučera (in Czech)

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This article by Dan Polansky looks at certain questions concerning philosophy. Some questions are for specialized articles, e.g. logic and epistemology.

I love philosophy. I am horrified and offended by the amount of writing called philosophy that to my mind are pseudophilosophy at best and pure nonsense at worst. And then, I feel philosophy needs a defense; the people who think that philosophy is a load of nonsense appear all too reasonable, given their bad experience. As an approximation, it is above all the Anglophone world that has decent philosophers. They do not necessarily get everything right (or I do not necessarily agree with all that they say), but fundamentally, they talk a lot of sense. Let us mention David Hume, John Locke, J.S.Mill and Bertrand Russell. The British even claim ownership to Popper, arguably more of an Austrian philosopher. The German and French worlds are mixed blessings. To state that German is the language dominated by pseudophilosophers would perhaps be unfair; what, if not a philosopher, is Frege, considered to be one of the greatest logicians ever? And even if one claims that Frege's work on logic is in fact mathematics, one can recall Frege's ''Sinn und Bedeutung''. Popper and Carnap are decent German-language philosophers; some could count Kant in the bag. French is the language of Derrida and other postmodern impostors. But Descartes is fine. Let me add some praise to the two great ancients, Plato and Aristotle; a lot of what they say is obviously untrue or unconvicing, especially from the modern perspective, but their way of going about doing philosophy is worth noting. They were pioneers and got a lot of things wrong.

Let us consider some questions that belong to the field of philosophy today no less than in the ancient times (some part of what used to be called philosophy is now sciences):
* What is there? What entities whose existence is implied by language in fact are not there?
* What are the ultimate constituents of matter? Perhaps indestructible atoms moving in the Euclidean void?
* What is knowledge and how do we know things? How can we avoid wrongly thinking something that is not true?
* What distinguishes science from non-science? Is there such a thing as the scientific method?
* Is induction a valid form of inference? Is there such a thing as premature generalization?
* How do proper nouns refer to their referents? By means of a description or by means of rigid designation?
* What is value and how do you define it? Is there something like value? Is anything worthwhile?
* What is good and what is not good? What is excellence and quality? How can one reliably detect quality (if it exists) and distinguish it from mere surface appearances and first impressions?
* How do definitions work? Can we really capture natural language semantics in definitions? Are definitions worth anything or are they just a passtime or certain kind of addicts?
* Shall we enforce the right of freedom of speech, to what extent and why?
* What is beauty? How do we know something is beautiful? Is it all subjective, in the eye of the beholder? Is it culturally relative? Is there some universal core of the concept beauty that works across different cultures?

A human hardly gets to do anything without answering at least some of these questions in some at least preliminary or naive way. Thus, as to what is worthwhile, a child could answer that it is pleasure/fun and go enjoying himself in the playground. What remains to be clarified is whether people benefit from a more rigorous inquiry that is philosophy, for some value of ''benefit'' of course.

A related question is what is philosophy, which includes a search for definition. In one sense, this metaphilosophical question is unnecessary. Philosophy is the inquiry into the kinds of questions that are being addressed by the books that we find in the philosophy rubric in the library. Conceptually, this answer is unsatisfactory, but it can be granted that to do philosophy, one does not need to clarify technical scoping questions of where exactly is the boundary between philosophy and, say, sciences and other humanities. (And then, is philosophy really properly part of humanities?) Another answer is that philosophy is the kind of inquiry exemplified by the questions above. Yet another is that philosophy is the union of ethics, metaphysics, epistemology, logic and aesthetics and leave it open what it is that binds these fields together. Yet another answer is that philosophy is the inquiry into the kind of (relatively general) questions that are not covered by mathematics, sciences, engineering and other humanities. Yet another is that typical for philosophy is the search for definitions, detection criteria, demarcation criteria, conceptual analysis, tentative general principles, arguments and counter-arguments. Let me add that parts of what is now physics used to be called natural philosophy. What philosophy is not is love of wisdom. That is etymology, not semantics. It points to the desire of Socrates to take opposition to Ancient Greek sophists. Socrates would say: I do not inquire into wisdom to earn money; I inquire for the love of wisdom and the inquiry. The resulting name is something of an etymological trainwreck showing the traces of the origin; most other fields are called ''-logy'', ''-nomy'' or ''-ics''. The name philosophy would improve if we would call it ''sophology'' or ''sophics'', but the name philosophy is traditional and we can stick to it. (Then again, a physicist may do physics for the love of it and not for profit, as I suspect many do, but the concept of love does not appear in the name ''physics''.)

One charge is that philosophy features two kinds of statements: platitudes and absurdities. I see the appeal of the argument, but to me it's wrong. To me, Popper's falsificationism (previously called hypothetico-deductive method, I think), Kripke's rigid designation and Kuhn's structure of scientific revolutions are some examples of source of statements that I feel I would not have figured out myself and that I find enriching. Even Wiennese logical positivism seems to be a valuable contribution; without it, Popper would perhaps not find a good reason to present his falsificationism.

Philosophy can do a great harm. Marx's philosophising pseudoeconomics and his philosophy of the social revolution that will necessarily come caused untold suffering. Nietszche's philosophy could have contributed to Hitler, together with a misapplication of Darwinian theory of evolution by natural selection. The only remedy I see against bad philosophy is good counter-philosophy. It is Mill who argues in a compelling way for extensive freedom of speech. Instead of censoring Marx and burning all his books, we should use e.g. Popper as a line of defense (and other critics, of course).

The charge that philosophy is mostly nonsense can be in part traced to Wittgenstein (a philosopher, hah). According to Wittgenstein, the task of philosophy would be something like careful analysis of proper language use to help prevent abuses of language that lead to bad philosophy, that is, most philosophy. A contrast to this is Popper, who says that he is not interested in analysis of language but of genuine philosophical problems, which according to Popper exist. Let us recall the poker incident between Wittgenstein and Popper, by which Popper was trying to show that inquiry into proper or good behavior does not need to be meaningless gibberish. Let us consider Democritos. His atomistic proposal was not empirical but rather speculative and its detail does not match modern physics (not only the physical &quot;atoms&quot; are not Democritean atoms, but nor are the putative quarks like Democritean atoms). Popper further argues that a certain ancient philosopher proposed the shape of the Earth to be possibly one of drum, using philosophical argument counter to experience. A step toward a drum is a step toward a sphere (or more accurately, rotational ellipsoid) and a step away from flat Earth resting on tortoise or something. These cases are not abuse of language, and therefore cannot be eliminated by careful analysis of language. They should not be eliminated in any other way either; philosophical theories or speculations are often forerunners of scientific theories.

It may turn out that philosophy is mostly passtime. That is, it may turn out that the philosophical analysis has low utility, scarce practical applications. Then, if one adopts the philosophical stance of egoistic hedonism and if one finds joy in these kinds of analysis, one may say: maybe so. But, then, at least the carbon footprint of philosophy is better than that of, say, hedonic car driving, motor racing or acrobatic flying. And then, one may say: without philosophy, there would not be Monty Python's philosopher sketch, with philosophers playing soccer. See, philosophers are good for something, after all. (Enough with this jocularity! Who is this disruptive derogator of philosophy? Sieze him!) Let us get serious again. It may turn out that large portions of pure mathematics are not much more practically useful than philosophy. But then, perhaps they are philosophy in some sense.

Let me make my bias clear, although it should be obvious by now. I am predominantly interested in Western philosophy and in its latest and most modern versions. Thus, one who wants to learn e.g. physics does not need to study ancient physics; one can study the latest physics even if one does not start with relativity and quantum mechanics, but this is to start with the easier, more accessible applications, not to proceed historically. I find the historical method of teaching philosophy suspect, while perhaps not entirely without merit. I am interested in validity or strength of ideas, concepts, arguments and counter-arguments, and much less in their historical development. Thus, I prefer 20th century philosophers and, say, Stanford Encyclopedia of Philosophy online over reading ancient texts. I also strongly prefer engaging in original deliberation, even if it turns out to be wrong. I prefer to read something that makes some sense to reading something of which I cannot make any sense. I avoid wasting my time on the latter, which may result in some loss, but that's life. To add an item against the historical method, I learned logic without recourse to Aristotle and I do not feel I lost much if anything at all. Considering Aristotle is interesting, but it does not seem to be especially valuable as far as the subject matter of logic goes.

One of the greatest and most notable currently living Anglophone philosophers is, in my estimate, Richard Dawkins. He is noted as a biologist and would perhaps deny to be a philosopher, but to my mind, there is a strong philosophical (or at least analytical as opposed to empirical in the style of physics) element in what he does, e.g. in ''The Selfish Gene''.

== See also ==
* [[Is philosophy any good?]]
* [[Is postmodernism a pseudo-philosophy?]]
* [[One man's look at epistemology]]
* [[One man's look at logic]]
* [[An analysis of value]]
* [[An analysis of identity]]

== Further reading ==
* {{W|Philosophy}}, wikipedia.org
* [https://www.britannica.com/topic/philosophy philosophy], britannica.com

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      <text bytes="1716" sha1="tl0c3vey7u7kpl7b7fd53y8qf61kag6" xml:space="preserve">== Some evaluative remarks ==
On one hand, I find the article too confusing. On the other hand, I am quite happy with the doubly subjective definition of value as unwillingness to part with the entity (including beings) valued. This definition seems to make it clear that use value and exchange value are indeed something like narrower concepts belonging to a broader concept of value, or if not belonging then at least both being pointed toward by that concept, rather than sharing the name &quot;value&quot; by a historical accident. [[:W:de:Gebrauchswert]] seems to disagree with me: &quot;Gebrauchswert und Tauschwert sind keine Erscheinungsformen derselben logischen Kategorie „Wert“, sondern selbständige Kategorien und erklären ganz verschiedene Sachverhalte.&quot; On the other hand, I am not sure what is meant by ''Erscheinungsform''. I hesitate to talk about value as ''phenomenon'', perhaps in part since I am not sure what I mean by ''phenomenon'' anyway.

The sections on objective value are rather unsatisfactory. It seems to be the best I am currently capable of, but let us see. Perhaps there is no such thing as objective value, but there seems to be something like partially desubjectivized value. The proposal to treat value as survival value (survival would be in an extended sense that includes gene copying) would make it objective, but is would be a huge departure from common usage. This proposal does not in any way incorporate whimsical subjectivity, e.g. intersubjective fashions. But then, maybe that is what we wanted from this kind of concept? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:23, 13 December 2024 (UTC)</text>
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      <text bytes="549" sha1="7gxbc5rt4eolawt38x59qvcekhf035f" xml:space="preserve">== Outline to cover ==
* Knowledge
** Concepts and classes and natural kinds
*** Under induction?
** Black swan
*** Under induction?
*** White by definition?
*** Species?
*** Swan-shaped?
*** Not only induction?
** Rare events, probabiliies
*** Arbitrarily rare events vs. knowledge
*** Roll a die many times; all 6 is a very rare event
**** Can I claim I ''know'' all 6 will not be the outcome?
--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:44, 6 January 2025 (UTC)</text>
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|&lt;div style=&quot;font-size:200%;border:none;margin: 0;padding:.1em;color:#000&quot;&gt;'''International Communication Law Learning Project'''&lt;/div&gt;&lt;div style=&quot;top:+0.2em;font-size:150%&quot;&gt;part of the [[School:Law|'''School of Law''']]&lt;/div&gt;
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{{SearchWithPrefix}}'''[[Help:Resources by subject|Subject classification]]''': this is a [[Portal:Law|law learning projects]] resource.

'''Class''': International Communication Law

'''Professor''': Juan Carlos Riofrio
[[File:International Communication Law.png|thumb|300x300px]]Welcome to the '''International Communication Law''' Learning Project, part of the [[School:Law|School of Law]]. This learning project aspires to establish the highest standards in the field of international communication law by fostering a comparative analysis of legal systems across different countries. By examining and contrasting the regulations, principles, and practices governing communication in diverse jurisdictions, the project aims to identify best practices and promote a deeper understanding of global legal standards.

The ultimate goal of this project is to equip legal professionals with the knowledge necessary to navigate the complexities of cross-border communication, ensuring compliance with diverse legal systems while upholding fundamental principles of fairness and accuracy.

== 2025 ==

[[Armenian Legal System]]

[https://w.wiki/F6Yy France's Legal System]

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[[Canadian Communications Law|Canadian Legal System]]

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[[United Kingdom Legal System]]

[[Puerto Rico's Legal System]]

[[German Legal System]]

[[Russian Legal System]]

[[Jamaican Legal System]]

[[Brazilian Legal System]]

[[Communications Law in Austria]]

[[Republic of Ireland Legal System]]

[[Australia's Legal System]]

== 2026 ==
[[Communications Law in Malta]]

[https://w.wiki/Hc5V The Kingdom of Morocco]  

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This article by Dan Polansky analyzes the concept of river. One might think that everyone knows what a river is, but I have found something analytically interesting here. Perhaps someone will find these deliberations useful as well.

First of all, we may distinguish river from a stream, and rivulet. But that does not seem to lead to really interesting questions. It merely distinguishes different sizes of channeled (natural?) water streams.

Is river a stream of water? In particular, is riverbed part of river? It could be. One could see river as a compound object consisting of a river stream and the riverbed. This would distinguish river from a stream of water flowing out from a faucet. What about a stream of water flowing through a half-open pipe, one that results from splitting a pipe in half along the long axis? That would be more like this compound object of river.

Then, a river individual is a stream of water flowing through a riverbed, one that has an origin and an end. The existence of tributaries complicates the matter. Are the tributaries part of the river? Apparently not, especially small ones. But what if two similarly large rivers merge into one larger stream? Is the merging point an origin of a new river? One may decide to conventionally claim one of the two merging rivers to be the same river as the outflowing merged river. But is it really the same river? There does not seem to be a fit answer.

To address the above quandary about merging rivers, we could identify the river with the river basin. Thus, all tributaries would be part of the river. Sure enough, this is not a conventional way of doing things on the maps, but why not? For one thing, the statement &quot;he lives near a river&quot; would lose its meaning; nearly everyone lives in some river basin so nearly everyone would live near a river (not even near it). There would be no river banks, unless one would consider the boundaries of the basin to be some kind of banks, which is uncustomary. And this concept of a river would probably deviate from a use in all human languages.

There is another way out of the above quandary. It is an observation that if we make a conventional arbitrary choice about which of the incoming rivers is the outgoing river, we can create a language custom that can be very productive. If all speakers understand the name of the river to refer to the part after the merge and a chosen part above the merge, they speak the same language (that uses a proper name) and can make statements understood to be true. But the question remains: is this arbitrarily designated or delineated entity really a river? If we want to nitpick, we can classify it as river-or-river-sequence, or the like.

We can ask what parts does a river consist of, if any. It does not consist of molecules of water; water is inflowing and outflowing from any fixed segment of the river or even the complete river. And yet, it would seem odd to identify a river only with the riverbed. And a dried up river is arguably no longer a river, making &quot;dried up&quot; an alienans.

The definition that sees a river as a compound of a water stream and riverbed does not match language dictionaries; they see river as a water stream. Britannica does emphasize that a river is channeled.&lt;ref&gt;[https://www.britannica.com/science/river river], britannica.com&lt;/ref&gt;. However, riverbed is perhaps not the only channel for a river.

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|River}}, wikipedia.org

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This article by Dan Polansky looks at psychological differences between men and women.

Some research questions:
* Are there measuable psychological differences between men and women, such as cognitive, affective, executive and other behavioral?
* If so, do they exist cross-culturally?
* If so, are they caused by culture, by biology (being innate) or both?
* If by both, what are the extents? Like, is it 50%-50% between cultural and innate/biological?
* What are examples of such differences?

Some of these questions are controversial and seem not settled. It will be therefore useful to report not matter-of-factly but rather in the form of &quot;Source X says Y&quot;. That is, in this kind of subject, relativization by source of the claim seems useful/proper/important.

The linked English Wikipedia article seems quite decent and has 132 inline references. The German Wikipedia article has 126 references. An advantage of Wikipedia articles is that different parties may try to control them and fail to do so. This may result in a degree of neutrality that many other sources will fail to have. One can read the discussion pages and see what issues with the articles were raised and what sources and claims were debated. A review of the revision history can reveal which statements were removed or modified by various parties.

For the purpose of this analysis, the words ''men'' and ''women'' refer to sexes, not self-identified genders. Although practically, this should not make all that much difference in the statistical results, given the very strong correlation between sex and gender. The choice of ''men'' and ''women'' is perhaps a bit unfortunate since it excludes children. After all, there can be differences between boys and girls. This is to be clarified. The title could possibly be changed from &quot;men and women&quot; to &quot;male sex and female sex in humans&quot;; we have to add &quot;in humans&quot; since other animals also have sexes.

What follows is a start, to be expanded. It is probably one-sided, with sources indicating significant innate differences dominant. To get a view from both sides of the debate, one can consider e.g. the 2005 debate between Steven Pinker and Elizabeth Spelke.

== Controversy ==
The matter seems to rise high passions. Per Pinker 2005&lt;ref name=Pinker2005&gt;[https://newrepublic.com/article/68044/sex-ed Sex Ed] by Steven Pinker, 2005, newrepublic.com&lt;/ref&gt;:
: 'Yet to hear the reaction to Harvard President Lawrence Summers's remarks at a conference on gender imbalances in science, in which he raised the possibility of innate sex differences, one might guess that he had proposed exactly that. Nancy Hopkins, the eminent MIT biologist and advocate for women in science, stormed out of the room to avoid, she said, passing out from shock. An engineering dean called his remarks &quot;an intellectual tsunami,&quot; and, with equal tastelessness, a Boston Globe columnist compared him to people who utter racial epithets or wear swastikas. Alumnae threatened to withhold donations, and the National Organization of Women called for his resignation. Summers was raked in a letter signed by more than 100 Harvard faculty members and shamed into issuing serial apologies.'

== Jarrett 2016 ==
One useful source is an article by Christian Jarrett from 2016 from BBC. An advantage of it is that it looks at various pieces of research for us. Moreover, BBC seems unlikely to be biased to the U.S. conservative political view, so if the findings do not meet the left-wing ideological position, a charge of bias is prevented or reduced.

Further reading:
* [https://www.bbc.com/future/article/20161011-do-men-and-women-really-have-different-personalities Do men and women really have different personalities?] by Christian Jarrett, 12 October 2016, bbc.com

== Popular books ==
Some popular books on the subject are the following. One needs to use them with care/caution since they usually do not constitute peer-reviewed science or academic work.

* ''Men Are from Mars, Women Are from Venus'' by John Gray, 1992. A critical reception is in the Wikipedia article for the book.
* ''Why Men Don't Listen and Women Can't Read Maps'' by Allan Pease and Barbara Pease, 1999.
* ''The Essential Difference: The Truth About the Male and Female Brain'' by Simon Baron-Cohen, 2003.

It would be worthwhile to find serious reviews of these books and link them from here.

Further reading:
* {{W|Men Are from Mars, Women Are from Venus}}, wikipedia.org

== Michael Kimmel ==
As per {{W|Men Are from Mars, Women Are from Venus}}, wikipedia.org:

'Michael Kimmel, a professor of sociology at Stony Brook University, makes the assertion that men and women are not fundamentally different, contrary to what Gray suggests in his book. In Kimmel's 2008 lecture at Middlebury College in Vermont, titled &quot;Venus, Mars, or Planet Earth? Women and Men in a New Millennium&quot;, Kimmel contends that the perceived differences between men and women are ultimately a social construction, and that socially and politically, men and women want the same things.&lt;ref&gt;{{YouTube|U-rpbihTvlY|Mars, Venus, or Planet Earth? Women &amp; Men in a New Millennium}}&lt;/ref&gt;'

== Jordan Peterson ==
Jordan Peterson is a Canadian clinical psychologist. Some relevant statements by him:

&quot;Here’s a paper, for example, indicating that more gender-equal countries produce comparatively fewer women in the STEM fields. Here’s another, showing that at least some of the much-vaunted gender gap in pay, which is caused by many factors, can be attributed to male/female personality differences and not to simple discrimination.&quot;

My estimate is that the above is controversial. It would be good to find an attempted rebuttal.

Further reading:
* [https://www.jordanbpeterson.com/political-correctness/the-gender-scandal-part-one-scandinavia-and-part-two-canada/ The Gender Scandal: Part One (Scandinavia) and Part Two (Canada)], 7 Dec 2018, jordanbpeterson.com

== James Damore ==
James Damore is a former Google engineer fired for airing views concerning biological basis for differences in employment rates between sexes that Google considered to violate the code of conduct. This generated extensive response from various parties via media, one notable example being philosopher Peter Singer. And thus, one can get an idea of how polarized the discussion landscape is and who supports what. As per Wikipedia: 

'James Damore wrote the memo after a Google diversity program he attended solicited feedback. The memo was written on a flight to China. Calling the culture at Google an &quot;ideological echo chamber&quot;, the memo states that, whereas discrimination exists, it is extreme to ascribe all disparities to oppression, and it is authoritarian to try to correct disparities through reverse discrimination. Instead, the memo argues that male to female disparities can be partly explained by biological differences. Alluding to the work of Simon Baron-Cohen, Damore said that those differences include women generally having a stronger interest in people rather than things, and tending to be more social, artistic, and prone to neuroticism (a higher-order personality trait). Damore's memorandum also suggests ways to adapt the tech workplace to those differences to increase women's representation and comfort, without resorting to discrimination.'

Further reading:
* {{W|Google's Ideological Echo Chamber}}, wikipedia.org

== Steven Pinker ==
Steven Pinker is an evolutionary psychologist who took a stance on the differences between men and women back in 2005. He seems to have been controversial.

A 2005 excerpt to give an idea of his position:
: 'I'll quote from one of them, a book called Sex Differences in Cognitive Ability by Diane Halpern. She is a respected psychologist, recently elected as president of the American Psychological Association, and someone with no theoretical axe to grind. She does not subscribe to any particular theory, and has been a critic, for example, of evolutionary psychology. And here what she wrote in the preface to her book:
:: &quot;At the time I started writing this book it seemed clear to me that any between sex differences in thinking abilities were due to socialization practices, artifacts, and mistakes in the research. After reviewing a pile of journal articles that stood several feet high, and numerous books and book chapters that dwarfed the stack of journal articles, I changed my mind. The literature on sex differences in cognitive abilities is filled with inconsistent findings, contradictory theories, and emotional claims that are unsupported by the research. Yet despite all the noise in the data, clear and consistent messages could be heard. There are real and in some cases sizable sex differences with respect to some cognitive abilities. Socialization practices are undoubtedly important, but there is also good evidence that biological sex differences play a role in establishing and maintaining cognitive sex differences, a conclusion I wasn't prepared to make when I began reviewing the relevant literature.&quot;
: 'This captures my assessment perfectly.'

Steven Pinker is not mentioned in Wikipedia's Sex differences in psychology article as of 7 Jan 2025.

Steven Pinker's book ''The Blank Slate'' (2002) is where Pinker possibly exposes evidence for his sex-difference-related views; to be verified.

A 2005 debate between Steven Pinker and Elizabeth Spelke seems to be a worthy read. Subjectively, I have a very good impression of that debate. It follows that two experts who study the available literature have reached very different conclusions. One may wonder whether a lay person can have a better success in evaluating the relevant literature. It is quite possible that a lay person would apply their personal experience and biases as filters on the liteature to follow or give weight to.

Further reading:
* [https://www.edge.org/3rd_culture/debate05/debate05_index.html Edge: THE SCIENCE OF GENDER AND SCIENCE PINKER VS. SPELKE A DEBATE], 5.16.2005, edge.org -- a debate between Steven Pinker and Elizabeth Spelke; Pinker says there are significant innate differences in aptitutes and motives whereas which Spelke seems to deny
* [https://www.youtube.com/watch?v=-Hb3oe7-PJ8 Steven Pinker &amp; Elizabeth Spelke | The Science of Gender &amp; Science | Mind Brain Behavior Discussion], 2013, youtube.com -- a video of the debate that is transcribed at the link above
* [https://newrepublic.com/article/68044/sex-ed Sex Ed] by Steven Pinker, 2005, newrepublic.com
* {{W|Steven Pinker}}, wikipedia.org
* {{W|The Blank Slate}}, wikipedia.org

== Consequences ==
An error about the chief causes of differences in the direction of underestimation of biological causes can have undesirable practical consequences, as per Pinker 2005&lt;ref name=Pinker2005/&gt;, starting at &quot;Nor is a better understanding of the causes of gender disparities inconsequential.&quot;

An error about the chief causes of differences in the direction of overestimation of biological causes has clear undesirable practical consequences. It can turn out that in a male-dominated society, males are going to seek excuses to continue maintaining an unjust dominance (in so far as such exists, which I would guess still does to some extent) and to oppose rules and policies that could improve the situation.

== Applications ==
Some applications of the analysis and the questions:

1) If there are significant psychological differences between men and women, this opens us a potential for great mutual enrichment resulting from certain complementarity. For instance, if a man hardly ever talks to women, he may be greatly enriched by changing this pattern, and vice versa, that is, if a woman hardly ever talks to men.

2) If the biological causes of the differences are minimal and if there is a great disparity between employment distribution and salaries, interventions to rectify the matter are so much more meaningful (they are meaningful even if there are biological causes, to some extent).

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Sex differences in psychology}}, wikipedia.org</text>
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      <comment>Atcovi moved page [[One man's look at software version numbering and naming]] to [[User:Dan Polansky/One man's look at software version numbering and naming]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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This article by Dan Polansky intends to look at software version numbering and naming, to complement the linked Wikipedia article. It intends to contain descriptions/observations, with view to application: designing and choosing a scheme.

Conflicting requirements on version numbering and naming clash and result in considerable chaos, lack of unity. Example of conflicting requirements:
* Software versions of the same product should use a single numbering and naming scheme.
* Software version identifications of the same product should have some charm, avoiding boredom.
* When the software version identification consists of multiple separated parts, there should be some meaning to these parts, e.g. major version and minor version.

== Microsoft Windows ==
One case illustrating the lack of unity/consistency is Microsoft Windows. Let us consider some of the versions (mostly from memory, to be double checked):
* Windows 1.01&lt;ref&gt;https://en.wikipedia.org/wiki/File:Windows1.0.png&lt;/ref&gt;
* Windows 3.0
* Windows 3.1
* Windows 3.11
* Windows NT 3.1&lt;ref&gt;[[:File:VirtualBox_Windows_NT_3.10.511.1_08_12_2024_20_00_45.png]]&lt;/ref&gt;&lt;ref&gt;[[Wikidata: Q748319]]&lt;/ref&gt;
* Windows NT 3.5
* Windows NT 4.0
* Windows 95 (Windows 9x branch)
* Windows 98 (Windows 9x branch)
* Windows 2000 (NT branch)
* Windows Me (Windows 9x branch)
* Windows 2003 (NT branch)
* Windows XP (NT branch)
* Windows Vista (NT branch)
* Windows 7 (NT branch)
* Windows 8 (NT branch)
* Windows 10 (NT branch)
* Windows 11 (NT branch)

We see multiple numbering/naming schemes:
* Use of a two-part number (1.0, 3.0, 3.1)
* Use of a single-part numnber (7, 8, 10, 11)
* Use of a year (95, 98, 2000, 2003)
* Use of an acronym (NT, XP)
* Use of a single-word name

Some oddities or things worth mentioning:
* There is the same scheme of using a year referring to different platforms, the non-NT platform (95, 98) and the NT platform (2000, 2003). From the version number, one could think that Windows 2000 is an iteration of Windows 98, but that is not so.
* 7 stands out apart from Vista although it can be seen as a relatively minor iteration of Vista; the big break was between XP and Vista.
* 3.11 seems to be a strange follow-up on 3.1 until one realizes that 3.1 is something like 3.10 (zero appended, but without additional dot).

Further reading:
* {{W|List of Microsoft Windows versions}}, wikipedia.org

== Microsoft Office ==
In Microsoft Office version labeling we see some of the patterns seen in Windows.

Further reading:
* {{W|History of Microsoft Office}}, wikipedia.org

== Mac OS X ==
Mac OS X (meanwhile rebranded to macOS) has numbered versioning accompanied by names. I seem to recall the version numbers are deemphasized in the marketing materials, but this needs verification.

In Max OS X itself, &quot;X&quot; stood for 10, hinting at being an iteration of Mac OS 9. But it was no such iteration. On the other hand, the form &quot;X&quot; can be interpreted as suggestive of a break from previous Mac OS versions.

Further reading:
* {{W|macOS#Release history}}, wikipedia.org
* {{W|MacOS version history#Releases}}, wikipedia.org
* {{W|Classic Mac OS}}, wikipedia.org

== Ubuntu ==
Ubuntu (a GNU/Linux distribution) accompanies version numbers with codenames, perhaps as mnemonic.

Examples:
* Ubuntu 24.04 LTS: Noble Numbat
* Ubuntu 24.10: Oracular Oriole
* Ubuntu 25.04: Plucky Puffin

Further reading:
* [https://wiki.ubuntu.com/Releases Releases], wiki.ubuntu.com
* [https://betawiki.net/wiki/Ubuntu Ubuntu], betawiki.net

== Emacs and XEmacs ==
The case of Emacs and XEmacs illustrates naming/branding of forks. If Emacs was a brand name of a commercial corporation, one could imagine the corporation suing the fork supplier for using the brand name Emacs in the name XEmacs, competing for the same market. By contrast, OpenOffice and LibreOffice stand fartehr apart in their names. (XEmacs was previously called Lucid Emacs).

One could think that forking does not have that much to do with versioning. However, I find it sufficiently reasonable/compelling to view versions of the fork as versions of the ancestral code that both the fork and the main continuation share.

Further reading:
* [https://www.gnu.org/software/emacs/history.html GNU Emacs Release History], gnu.org

== Java ==
Java is interesting for having switched from 1.X numbering scheme to X numbering scheme, dropping the leading 1. Thus, e.g. Java 8 is what would have been Java 1.8. Careful verification pending.

Further reading:
* {{W|Java version history}}, wikipedia.org

== Perl ==
Perl is interesting in that what was originally called Perl 6 was eventually considered so different from Perl 5 as to deserve a new name; Raku was picked.

Further reading:
* {{W|Raku}}, wikipedia.org

== Firefox ==
Early on, Firefox used a major-minor version number scheme; for instance:
* Firefox 1.5
* Firefox 2
* Firefox 3
* Firefox 3.5
* Firefox 3.6
* Firefox 4
Then, it switched to a single-number rapid release scheme. As per Wikipedia: &quot;In March 2011, Mozilla presented plans to switch to a faster 16-week development cycle, similar to Google Chrome.&quot; The idea would be to push/nudge all users to be at the latest version. A rationale could have been that this will avoid people using versions with known vulnerabilities. Double check needed.

Further reading:
* {{W|Firefox version history}}, wikipedia.org
* {{W|Firefox early version history}}, wikipedia.org

== GCC and EGCS ==
EGCS was a fork of GCC, GNU C Compiler, which later became GNU Compiler Collection. EGCS was later either merged into GCC or it became GCC by act of renaming.

As per gnu.org, &quot;The first compiler version released after the reunification was GCC version 2.95.&quot;&lt;ref&gt;[https://gcc.gnu.org/wiki/History History], gcc.gnu.org&lt;/ref&gt;

Relevant release numbers showing the interplay between GCC and EGCS release numbers, as per gcc.gnu.org:&lt;ref&gt;[https://gcc.gnu.org/releases.html GCC Releases], gcc.gnu.org&lt;/ref&gt;
{|
|-
| GCC 2.95 ||	July 31, 1999
|-
| EGCS 1.1.2 ||	March 15, 1999
|-
| EGCS 1.1.1 ||	December 1, 1998
|-
| EGCS 1.1 ||	September 3, 1998
|-
| EGCS 1.0.3 ||	May 15, 1998
|-
| EGCS 1.0.2 ||	March 16, 1998
|-
| gcc 2.8.1 ||	March 2, 1998
|-
| gcc 2.8.0 ||	January 7, 1998
|-
| EGCS 1.0.1 ||	January 6, 1998
|-
| EGCS 1.0 ||	December 3, 1997
|-
| 2.7.2.3 ||	August 22, 1997
|}

The meaning of 95 in 2.95 is unclear: one would expect 2.9.x.

Further reading:
* {{W|GNU Compiler Collection#EGCS Fork}}, wikipedia.org

== TeX ==
TeX's version numbering scheme is an outlier/peculiarity: the version numbers are ever longer decimal expansions of pi, and thus, 3.1, 3.14, 3.141, 3.1415, etc. This has come as far as 3.141592653.&lt;ref&gt;[https://tex.stackexchange.com/questions/581118/whats-new-in-tex-version-3-141592653 What's new in TeX, version 3.141592653?], tex.stackexchange.com&lt;/ref&gt; From what I recall, one idea behind this scheme was that ever expanding feature set or changes of software are not necessarily a good thing and that a software package should convert to something definite within its niche; needs verification. I find this idea of software converging/stabilizing attractive; the playful numbering scheme, not so much, or at least I would not recommend its emulation.

== HTML ==
HTML is not a software package but is related to it and is subject to versioning.

HTML versions include:
* HTML 3.2&lt;ref&gt;https://www.w3.org/TR/2018/SPSD-html32-20180315/&lt;/ref&gt;
* HTML 4.0&lt;ref&gt;https://www.w3.org/TR/1998/REC-html40-19980424/&lt;/ref&gt;
* HTML 4.01&lt;ref&gt;https://www.w3.org/TR/html401/&lt;/ref&gt;
* HTML 5.1
* HTML 5.2

Further reading:
* {{W|HTML#HTML version timeline}}, wikipedia.org

== C++ ==
C++ is not a software package, but just like them, it is subject to versioning.

C++ versions include (and are based on year):
* C++98&lt;ref&gt;https://www.wikidata.org/wiki/Q764453&lt;/ref&gt;
* C++03
* C++11
* C++14
* C++17
* C++20
* C++23

Further reading:
* {{W|C++}}, wikipedia.org

== Alpha, Beta, Release Candidate ==
Some [which?] software projects use alpha, beta and release candidate labels to indicate pre-release versions.

LibreOffice uses the label ''release candidate''.&lt;ref&gt;https://www.libreoffice.org/download/pre-releases/&lt;/ref&gt;

OpenOffice uses the label ''beta''.&lt;ref&gt;https://www.openoffice.org/development/releases/dev_index.html&lt;/ref&gt;

Microsoft Windows 1.0 used the labels ''alpha''&lt;ref&gt;https://betawiki.net/wiki/Windows_1.0_Alpha_Release&lt;/ref&gt; and ''beta''&lt;ref&gt;[[:Commons: Category:Microsoft Windows 1.0 Beta Release]]&lt;/ref&gt;. Some Windows versions used the label ''release candidate''.&lt;ref&gt;https://blogs.windows.com/windowsexperience/tag/release-candidate/&lt;/ref&gt; Microsoft used label ''release candidate'' for some versions of .NET&lt;ref&gt;https://devblogs.microsoft.com/dotnet/dotnet-9-rc-2/&lt;/ref&gt; and SQL Server&lt;ref&gt;https://techcommunity.microsoft.com/blog/sqlserver/sql-server-2022-release-candidate-1-is-now-available/3641091&lt;/ref&gt;.

Further reading:
* {{W|Software release life cycle}}, wikipedia.org
* [https://stackoverflow.com/questions/40067469/what-is-the-difference-between-alpha-and-beta-release What is the difference between alpha and beta release?], stackoverflow.com

== Semantic versioning ==
Semantic versioning is multi-part numbering scheme, covered in the Wikipedia article. The first idea is to use numbering scheme MAJOR_VERSION_NUMBER.MINOR_VERSION_NUMBER, e.g. Windows 3.1. Further components can be added, e.g. build number; up to four components are sometimes used. Minor versions are less breaking in some sense than major versions. There is a technically specified concept of semantic versioning linked from Wikipedia.

== References ==
&lt;references /&gt;

== Further reading ==
* {{W|Software versioning}}, wikipedia.org
* {{W|Fork (software development)}}, wikipedia.org
* [https://stackoverflow.com/questions/1889615/version-numbering-basics Version numbering basics?], stackoverflow.com

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      <comment>Atcovi moved page [[One man's look at zuclopenthixol acetate]] to [[User:Dan Polansky/One man's look at zuclopenthixol acetate]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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This article by Dan Polansky looks at zuclopenthixol acetate, a variant[terminology?] of zuclopenthixol and apparently a particularly potent and dangerous injectable chemical substance used in psychiatric drug interventions. This variant of zuclopenthixol has no dedicated Wikipedia article; only zuclopenthixol does, which refers to three variants per Wikipedia, with different potency.

This substance was administered to Jindřich Jašík, a Czech author of the book ''Journey out of Schizophrenia'', 2019, in which he describes his experience with Czech psychiatric system as well as his approach toward self-treating his condition. The result of administration to Jašík was that he could not walk and talk; the administering personnel had to stop it before he reached the full dose  (see a quotation at [[#The case of Jindřich Jašík|The case of Jindřich Jašík]]). One can expect this kind of outcome in a substance that is particularly potent/dangerous.

The above leads to research questions for this article:
* Is zuclopenthixol acetate very potent? To be done.
* Is zuclopenthixol acetate dangerous? Answered below in affirmative.
* What is the potency relationship between zuclopenthixol acetate and other zuclopenthixol formulations? To be done.
* Are there guidlelines online on administering zuclopenthixol acetate, especially such ones as suggest caution? Answered below; more can be done.
* What reports of adverse effects from zuclopenthixol acetate are available online? To be done.

== Brand names ==

Brand names of zuclopenthixol acetate are as follows:
* Clopixol Acuphase (no hyphen), apparently used in English-speaking countries including the U.K.&lt;ref name=NHSSCOT&gt;[https://rightdecisions.scot.nhs.uk/media/1887/mhs-33-use-of-zuclopenthixol-acetate-clopixol-acuphase-guidelines.pdf Use of Zuclopenthixol Acetate (Clopixol Acuphase)], rightdecisions.scot.nhs.uk -- Date approved: 20/2/2023&lt;/ref&gt;, Australia&lt;ref name=west-aust&gt;[https://www.wacountry.health.wa.gov.au/~/media/WACHS/Documents/About-us/Policies/Specialised-Medication---Zuclopenthixol-Acetate---Clopixol-Acuphase-Guideline.pdf?thn=0 Specialised Medication – Zuclopenthixol Acetate - Clopixol Acuphase® Guideline], wacountry.health.wa.gov.au&lt;/ref&gt; and South Africa&lt;ref name=LB-SA&gt;[https://www.lundbeck.com/content/dam/lundbeck-com/africa/south-africa/products/product-pi/Clopixol%20Acuphase%20Injection%2050%20mg-ml.pdf PROFESSIONAL INFORMATION/PACKAGE INSERT CLOPIXOL ACUPHASE® INJECTION], South Africa, lundbeck.com&lt;/ref&gt; (but not the U.S., apparently)
* Clopixol-Acuphase (with a hyphen): used in a leaflet for Canada&lt;ref name=leaflet-canada/&gt;
* Cisordinol-Acutard (with a hyphen): apparently used in non-English-speaking countries, with a hyphen, e.g. in Norway&lt;ref&gt;https://www.felleskatalogen.no/medisin/cisordinol-acutard-lundbeck-547522&lt;/ref&gt;, Czechia&lt;ref&gt;https://www.lundbeck.com/content/dam/lundbeck-com/europe/czech-republic/spc/cisordinol/SPC_Cisordinol_Acutard.pdf&lt;/ref&gt;, Denmark&lt;ref&gt;https://pro.medicin.dk/medicin/praeparater/1100&lt;/ref&gt;, Finland&lt;ref&gt;https://laakeinfo.fi/Medicine.aspx?sl=3385&lt;/ref&gt;, Sweden&lt;ref&gt;https://www.fass.se/LIF/product?userType=0&amp;nplId=19870918000038&amp;docType=30&lt;/ref&gt;, Latvia&lt;ref&gt;https://dati.zva.gov.lv/zalu-registrs/en/info/07-0122&lt;/ref&gt;, etc.
* Cisordinol Acutard (no hyphen) is apparently used in Island&lt;ref&gt;https://www.lyfja.is/lyfjabokin/lyf/CisordinolAcutard&lt;/ref&gt; and Austria&lt;ref&gt;https://info-patient.at/cisordinol-acutard-50-mg-ampullen-104020/beipackzettel&lt;/ref&gt;.

== Availability ==
The leaflets in section [[#Brand names|Brand names]] are suggestive of availability in the respective countries.

No form of zuclopenthixol seems to be available in the U.S.&lt;ref&gt;[https://www.ncbi.nlm.nih.gov/books/NBK501768/ Zuclopenthixol - Drugs and Lactation Database (LactMed®) - NCBI Bookshelf], nih.gov&lt;/ref&gt;&lt;ref&gt;[https://www.mentalhealth.com/library/zuclopenthixol-uses-dosage-side-effects Zuclopenthixol - Uses, dosage, and side effects] by Dr. Jenni Jacobsen, Ph.D., last updated: 10 November 2023, mentalhealth.com&lt;/ref&gt;

== Producer ==
One producer is Lundbeck.&lt;ref name=LB-SA/&gt; To be found whether there are other producers. Wikipedia states that &quot;Zuclopenthixol was introduced by Lundbeck in 1978&quot;, which is not specifically in reference to the acetate variant.

Lundbeck was criticized by Peter C. Gøtzsche&lt;ref&gt;[https://www.scientificfreedom.dk/wp-content/uploads/2024/09/2024-Gotzsche-Is-psychiatry-a-crime.pdf Is psychiatry a crime against humanity?] by Peter C. Gøtzsche, 2024&lt;/ref&gt;.

== Required caution ==
An increased required caution follows from the following, a direct quotation from NHS Greater Glasgow and Glyde Guideline&lt;ref name=NHSSCOT/&gt;:

&quot;Key Points
* Zuclopenthixol acetate (Clopixol Acuphase®) is NOT quick acting and should NOT be prescribed if immediate sedation is required. It is a potentially toxic and hazardous drug, which has the potential to be used inappropriately. There is little published data to support its use in psychiatric emergencies.
* The advice and authorisation of a consultant psychiatrist must be obtained before zuclopenthixol acetate is prescribed.
* Zuclopenthixol must never be given to anyone who has not previously received treatment with a first generation antipsychotic.&quot;

DrugBank cautions&lt;ref name=drugbank/&gt;:
: &quot;However, the use of zuclopenthixol acetate in psychiatric emergencies as an alternative to standard treatments (haloperidol, clotiapine, etc.) should be cautioned, since well executed and documented trials of zuclopenthixol acetate for this use have yet to be conducted. Zuclopenthixol acetate is not intended for long-term use.&quot;

== Risk of confusion ==
Risk of confusion of zuclopenthixol acetate with the zuclopenthixol decanoate (depot injection, LAI) is indicated in the further reading below.

Further reading:
* [https://www.england.nhs.uk/wp-content/uploads/2018/01/B0203_How-we-acted-on-patient-safety-issues-you-reported-Report_.pdf How we acted on patient safety issues you reported], england.nhs.uk
* [https://www.wacountry.health.wa.gov.au/~/media/WACHS/Documents/About-us/Policies/Specialised-Medication---Zuclopenthixol-Acetate---Clopixol-Acuphase-Guideline.pdf?thn=0 Specialised Medication – Zuclopenthixol Acetate - Clopixol Acuphase® Guideline], wacountry.health.wa.gov.au

== Toxicity ==
Potential toxicity is asserted by NHS Greater Glasgow and Glyde Guideline&lt;ref name=NHSSCOT/&gt; and PsychDB&lt;ref name=psychdb-za/&gt;.

== Misuse ==
According to psychdb.com: &quot;Clopixol-Acuphase is widely misused, and in reality, can be a potentially toxic medication with poor evidence to support its use. However, it should be considered as a last line of effective short-term chemical restraint.&quot;&lt;ref name=psychdb-za&gt;https://www.psychdb.com/meds/antipsychotics/first-gen-typical/4-zuclopenthixol&lt;/ref&gt;. PsychDB &quot;is made and run by a Canadian psychiatrist with an interest in medical education.&quot;&lt;ref&gt;https://www.psychdb.com/about/home&lt;/ref&gt; The name of the Canadian psychiatrist is not provided, it seems. It is unclear that PsychDB is a reliable source.

== Dosage ==
As per U.K. leaflet&lt;ref&gt;[https://www.medicines.org.uk/emc/files/pil.993.pdf Package leaflet: Information for the patient Clopixol-Acuphase® 50 mg/ml solution for injection zuclopenthixol acetate], U.K., medicines.org.uk&lt;/ref&gt;, zuclopenthixol acetate is given to adults via intramuscular injections, at a usual dose of 50-150 mg, given repeatedly if necessary after 2-3 days; the total amount given in the treatment course shall be no more than 400 mg, in no more than 4 injections. This matches multiple other leaflets from the further reading. In case of doubt, better read the leaflet for full, non-rephrased information.

We can compare the above dosage to other zuclopenthixol variants:
* For zuclopenthixol &quot;vanilla&quot; tablets, &quot;[t]he usual therapeutic range is 20 mg to 60 mg daily. Daily dosage higher than 100 mg is not recommended.&quot;&lt;ref name=leaflet-canada&gt;[https://www.lundbeck.com/content/dam/lundbeck-com/americas/canada/products/files/clopixol_product_monograph_english.pdf PRODUCT MONOGRAPH CLOPIXOL CLOPIXOL-ACUPHASE CLOPIXOL® DEPOT], Canada, lundbeck.com&lt;/ref&gt;
* For zuclopenthixol decanoate/Clopixol Depot, &quot;[t]he usual maintenance dose is 150-300 mg intramuscularly, every 2-4 weeks. Some patients may require higher or lower doses, or shorter intervals between doses.&quot;&lt;ref name=leaflet-canada/&gt;

Let us do a comparison. If we reckon with 100 mg of zuclopenthixol acetate given every 2nd day up to the maximum dosage 400 mg, we get 50 mg per day during 8 days. If, by contrast, we reckon with 300 mg of zuclopenthixol decanoate every 2 weeks (14 days), we get 21 mg per day. However, it could well be that the intent was to pair 150 mg of decanoate with every 2 weeks and 300 mg every 4 weeks, which would yield 11 mg per day, and thus, the ratio of 4.5 of acetate dosage to decanoate dosage; but the potency per 1 mg may differ between the two. This requires a more careful look and analysis.

== The case of Jindřich Jašík ==
From the medical record of Jindřich Jašík, in relation to zuclopenthixol acetate/Cisordinol Acutard (the original is in Czech):
: &quot;Medication included risperidol and clonazepam, but the patient did not take the pills and his condition worsened on the third day of hospitalization. Therefore, it was necessary to proceed to the injection of Cisordinol Acutard in combination with levomepromazine - the latter was then administered orally as well. The patient was calmer on this medication and more willing to cooperate, but showed signs of EPS syndrome. The dose of levomepromazine was thus reduced, no further injection of Cisordinol Acutard was administered. Instead, the patient was treated with olanzapine (20 mg pro die); temporary administration of Akineton. [...]&quot;&lt;ref&gt;[https://books.google.com/books?id=Rz_2EAAAQBAJ&amp;pg=PT12 Journey out of Schizophrenia] by Jindřich Jašík, 2019, books.google.com&lt;/ref&gt;
The above seems untrue: it was not ''necessary'' to use this drug. The conditions required by NHS Greater Glasgow and Glyde Guideline for administration of zuclopenthixol acetate were not met above (see [[#Required caution|Required caution]]).

Jindřich Jašík's description of the effects of the medication, from a video, in Czech:&lt;ref&gt;[https://www.youtube.com/watch?v=2uNL_WFj57s__at CZ HOVORY ZE ZEMĚ - Cesta ze schizofrenie - Jindřich Jašík], at about 30 minute&lt;/ref&gt;
: &quot;Pak jsem šel na injekci a po tý injekci si několik dní jako nepamatuju [...] já jsem pak nebyl schopnej chodit, mluvit, když jsem se měl najíst tak jsem se tak třebal že jsem nebyl schopnej do sebe [...] zápis od doktorů že pacient po medikaci klidnější, spolupráce zlepšená, avšak dostavily se symptomy EPS. [...] Ale já musím říct že mi to pomohlo. [...] Není to úplně černobílý.&quot;
Translated from Czech into English:
: &quot;Then they gave me injection and I do not recall several days after the injection [...] I was then unable to walk, talk; when I had to eat, I was unable to put into myself [...; food?] record from the doctors that the patient is calmer after the medication, cooperation improved, but there are extrapyramidal symptoms&quot; [...] But I have to say it helped. [...] It is not entirely black and white.&quot;
The injection must have been one of zuclopenthixol acetate, to match the above quoted medical record.

A reservation: The above described response to medication is to a combination of Cisordinol Acutard and levomepromazine, not Cisordinol Acutard alone.

See also [[A review of Jindřich Jašík's Journey out of Schizophrenia]].

== Adverse event reports ==
I do not know of an online database reporting adverse events of psychiatric drugs. This section will therefore be very unsatisfactory and anecdotal.

Reported adverse events:
* In Jindřich Jašík; see [[#The case of Jindřich Jašík|The case of Jindřich Jašík]].
* An anonymous report about zuclopenthixol ''decanoate'' now available on the talk page of the English Wikipedia: [[W: Talk:Zuclopenthixol]], 203.59.200.161, 29 June 2007 (UTC), [https://en.wikipedia.org/w/index.php?title=Zuclopenthixol&amp;diff=141411618&amp;oldid=141407756 diff comparison]. However, this is not  directly applicable since it is about ''decanoate''.
* Second anonymous report on the talk page of the English Wikipedia: [[W: Talk:Zuclopenthixol]], 185.69.145.23. It is not clear in that report which variant it refers to.

Another source of reports can be obtained by searching &quot;zuclopenthixol&quot; and &quot;Clopixol&quot; in site:madinamerica.com via Google. The search does find some stories but none specifically on the acetate variant.

== Adverse effects ==
Adverse effects (also known as side effects) are provided in the leaflets in the further reading.

== Chemical formula ==
The chemical formula of zuclopenthixol acetate alongside the other zuclopenthixol variants, per PubChem:
* zuclopenthixol&lt;ref&gt;[https://pubchem.ncbi.nlm.nih.gov/compound/5311507 Zuclopenthixol], PubChem&lt;/ref&gt;: C₂₂H₂₅ClN₂OS
* zuclopenthixol dihydrochloride&lt;ref&gt;[https://pubchem.ncbi.nlm.nih.gov/compound/Zuclopenthixol-dihydrochloride Zuclopenthixol Hydrochloride], PubChem&lt;/ref&gt;: C₂₂H₂₇Cl₃N₂OS (tablet)
* zuclopenthixol decanoate&lt;ref&gt;[https://pubchem.ncbi.nlm.nih.gov/compound/Zuclopenthixol-Decanoate Zuclopenthixol Decanoate], PubChem&lt;/ref&gt;: C₃₂H₄₃ClN₂O₂S (depot injection, LAI)
* zuclopenthixol acetate&lt;ref&gt;[https://pubchem.ncbi.nlm.nih.gov/compound/Zuclopenthixol-Acetate Zuclopenthixol Acetate], PubChem&lt;/ref&gt;: C₂₄H₂₇ClN₂O₂S (relatively short-acting injection)
To be determined: find out whether &quot;zuclopenthixol&quot; alone sometimes or per default refers to zuclopenthixol dihydrochloride.

== Classification ==
Zuclopenthixol is ranked as typical antipsychotic/first-generation antipsychotic&lt;ref name=drugbank&gt;[https://go.drugbank.com/drugs/DB01624 Zuclopenthixol: Uses, Interactions, Mechanism of Action], drugbank.com&lt;/ref&gt;. Presumably, zuclopenthixol acetate is so ranked as well. Synonyms for antipsychotics include neuroleptics and major tranquilizers.

== References ==
&lt;references /&gt;

== Further reading ==
Wikipedia et al.:
* {{W|Zuclopenthixol}}, wikipedia.org
* [[Wikidata:Q27256348|zuclopenthixol acetate]], wikidata.org
* [https://mdwiki.org/wiki/Zuclopenthixol Zuclopenthixol], mdwiki.org -- a fork/separately developed copy

Guidelines:
* [https://rightdecisions.scot.nhs.uk/media/1887/mhs-33-use-of-zuclopenthixol-acetate-clopixol-acuphase-guidelines.pdf Use of Zuclopenthixol Acetate (Clopixol Acuphase)], rightdecisions.scot.nhs.uk -- Date approved: 20/2/2023
* [https://www.wacountry.health.wa.gov.au/~/media/WACHS/Documents/About-us/Policies/Specialised-Medication---Zuclopenthixol-Acetate---Clopixol-Acuphase-Guideline.pdf?thn=0 Specialised Medication – Zuclopenthixol Acetate - Clopixol Acuphase® Guideline], wacountry.health.wa.gov.au -- Current from: 30 June 2023
* [https://www.tewv.nhs.uk/wp-content/uploads/2021/11/Clopixol-Acuphase-Guidelines-for-the-safe-use-of.pdf Guidelines for the Safe Use of Clopixol Acuphase® (zuclopenthixol acetate)], Tees, Esk and Wear Valleys NHS, tewv.nhs.uk -- Date of Approval: 22nd September 2022
* [https://www.oxfordhealthformulary.nhs.uk/docs/Acuphase%20Guidelines%202014_Final.pdf?UNLID=6611601162016313174026 Guidelines for the use of Zuclopenthixol Acetate (Clopixol Acuphase®) injection], Oxford Health NHS Foundation Trust, oxfordhealthformulary.nhs.uk -- DATE OF APPROVAL: 8th July 2014

Lundbeck leaflets at lundbeck.com:
* [https://www.lundbeck.com/content/dam/lundbeck-com/africa/south-africa/products/product-pi/Clopixol%20Acuphase%20Injection%2050%20mg-ml.pdf PROFESSIONAL INFORMATION/PACKAGE INSERT CLOPIXOL ACUPHASE® INJECTION], South Africa, lundbeck.com
* [https://www.lundbeck.com/content/dam/lundbeck-com/americas/canada/products/files/clopixol_product_monograph_english.pdf PRODUCT MONOGRAPH CLOPIXOL CLOPIXOL-ACUPHASE CLOPIXOL® DEPOT], Canada, lundbeck.com
* [https://www.lundbeck.com/content/dam/lundbeck-com/europe/czech-republic/spc/cisordinol/SPC_Cisordinol_Acutard.pdf Cisordinol-Acutard SOUHRN ÚDAJŮ O PŘÍPRAVKU], lundbeck.com (in Czech)
* [https://www.lundbeck.com/content/dam/lundbeck-com/europe/poland/pdfs/20200713%20PL%20Clopixol%20Acuphase%20%20solution%20for%20injection%2050%20mg%20per%20ml%20PIL%20.pdf Ulotka dołączona do opakowania: informacja dla użytkownika Clopixol Acuphase, 50 mg/ml, roztwór do wstrzykiwań], lundbeck.com (in Polish)
* [https://www.lundbeck.com/content/dam/lundbeck-com/europe/netherlands/smpc---pil/cisordinol/Cisordinol%20Acutard%2050%20mg%20per%20ml%20SmPC%202020-03.pdf Cisordinol-Acutard 50 mg/ml injectievloeistof], lundbeck.com (in Dutch)
* [https://www.lundbeck.com/content/dam/lundbeck-com/americas/chile/productos/imagenes-y-pdfs/Cisordinol%20Acutard_CL.pdf CISORDINOL Acutard Solución Inyectable 50 mg/ml], lundbeck.com (in Spanish)

Leaflets other than at lundbeck.com:
* [https://www.medicines.org.uk/emc/files/pil.993.pdf Package leaflet: Information for the patient Clopixol-Acuphase® 50 mg/ml solution for injection zuclopenthixol acetate], U.K., medicines.org.uk
* [https://www.medsafe.govt.nz/consumers/cmi/c/clopixol.pdf Clopixol Tablets 10 mg Clopixol Acuphase Injection 50 mg/mL Clopixol Depot Injection 200 mg/mL], New Zealand, medsafe.govt.nz
* [https://rss.medsinfo.com.au/lu/pi.cfm?product=lupclopi AUSTRALIAN PRODUCT INFORMATION CLOPIXOL (ZUCLOPENTHIXOL HYDROCHLORIDE) FILM-COATED TABLETS CLOPIXOL ACUPHASE (ZUCLOPENTHIXOL ACETATE) INJECTION CLOPIXOL DEPOT (ZUCLOPENTHIXOL DECANOATE) INJECTION], Australia, medsinfo.com.au
* [https://verification.fda.gov.ph/files/DR-XY15245_PI_01.pdf Zuclopenthixol acetate Clopixol-Acuphase® 50mg/ml solution for injection], verification.fda.gov.ph -- some leaflet for Philippines

Other:
* [https://pharmaceutical-journal.com/article/letters/risk-of-medication-errors-with-zuclopenthixol Risk of medication errors with zuclopenthixol], 13 July 2021, pharmaceutical-journal.com
* [https://knowledgehub.health.gov.za/system/files/elibdownloads/2022-03/Zuclopenthixol%20acetate%20for%20acute%20psychosis%20in%20adults_PHC-Adult%20Review_6June2017.pdf Zuclopenthixol acetate for acute psychosis in adult  PHC-Adult Review], 6 June 2017, knowledgehub.health.gov.za
* [https://journals.sagepub.com/doi/10.1177/10398562231154311?icid=int.sj-abstract.similar-articles.1 Quality improvement through audit: Zuclopenthixol acetate prescribing, monitoring and patient outcomes in a regional health service], journals.sagepub.com
* [https://mentalhealth.bmj.com/content/1/2/56 Review: zuclopenthixol is not more effective than other neuroleptic drugs in the acute treatment of schizophrenia] by McNulty et al.
* [https://pubmed.ncbi.nlm.nih.gov/10796549/ Zuclopenthixol acetate in the treatment of acute schizophrenia and similar serious mental illnesses] by Fenton et al., 2000
* [https://pubmed.ncbi.nlm.nih.gov/11686965/ Zuclopenthixol acetate in the treatment of acute schizophrenia and similar serious mental illnesses] by Fenton et al., 2001
* [https://pubmed.ncbi.nlm.nih.gov/15266432/ Zuclopenthixol acetate for acute schizophrenia and similar serious mental illnesses] by Gibson et al., 2004
* [https://pubmed.ncbi.nlm.nih.gov/22513898/ Zuclopenthixol acetate for acute schizophrenia and similar serious mental illnesses] by Jayakody et al., 2012</text>
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    <title>User:Dan Polansky/One man's look at schizophrenia</title>
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      <comment>Atcovi moved page [[One man's look at schizophrenia]] to [[User:Dan Polansky/One man's look at schizophrenia]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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      <text bytes="16662" sha1="cjuw56glkww0i4d48c5wszz7dxw0aq6" xml:space="preserve">{{Original research}}
This article by Dan Polansky looks at what is called schizophrenia and what was originally called dementia praecox. It is in part overlapping and in part complementary to Wikipedia. The look is going to be critical, aiming to question things.

== Existence ==
The existence of the nosological entity of schizophrenia is less well established than one might think. It follows from Goel 2011.&lt;ref name=Goel&gt;[https://pmc.ncbi.nlm.nih.gov/articles/PMC4925361/ Does Schizophrenia Exist?] by DS Goel, 2011&lt;/ref&gt;

== Differential diagnosis ==
Schizophrenia, an entity that one might as well call ''major psychotic disorder'' since the etymology of ''schizophrenia'' has almost no bearing on the referent, needs to be distinguished from other psychotic disorders, especially the bipolar disorder. Bipolar is mentioned as potentially confounding or overlapping in Goel 2011.&lt;ref name=Goel/&gt; There is also the nosological unit of ''schizoaffective disorder'', which combines symptoms of schizophrenia and affective disorders (mania, depression, bipolar, etc.)

== Symptoms ==
A bulleted structure:
* Positive symptoms
** Hallucinations (visual&lt;ref name=nhs/&gt;, auditory&lt;ref name=nhs/&gt;, olfactory&lt;ref name=nhs/&gt;, etc.)&lt;ref name=mayo/&gt;&lt;ref name=merck-prof/&gt;
** Delusions&lt;ref name=mayo/&gt;&lt;ref name=merck-prof/&gt;
* Negative symptoms
** Cognitive decline&lt;ref name=merck-prof/&gt;
*** Memory down&lt;ref name=merck-prof/&gt;
*** Attention down&lt;ref name=merck-prof/&gt;
** Executive decline&lt;ref name=merck-prof&gt;[https://www.merckmanuals.com/professional/psychiatric-disorders/schizophrenia-and-related-disorders/introduction-to-schizophrenia-and-related-disorders Introduction to Schizophrenia and Related Disorders - Psychiatric Disorders], Merck Manual Professional Edition (Merck manufactures at least one schizophrenia drug)&lt;/ref&gt;
*** Bad personal hygiene&lt;ref name=nhs&gt;[https://www.nhs.uk/mental-health/conditions/schizophrenia/symptoms/ Symptoms - Schizophrenia], NHS&lt;/ref&gt;
*** Difficulty making decisions&lt;ref name=webmd-sym&gt;[https://www.webmd.com/schizophrenia/schizophrenia-symptoms Schizophrenia Symptoms: Positive and Negative Symptoms], webmd.com&lt;/ref&gt;
*** Poor planning/goal-setting?
** Reduced interest in social interaction&lt;ref name=nhs/&gt;
** Disorganized thinking&lt;ref name=mayo&gt;[https://www.mayoclinic.org/diseases-conditions/schizophrenia/symptoms-causes/syc-20354443 Schizophrenia - Symptoms and causes], Mayo Clinic&lt;/ref&gt;
** Emotional blunting/blunt affect&lt;ref&gt;[https://pmc.ncbi.nlm.nih.gov/articles/PMC4452733/ Instruments Measuring Blunted Affect in Schizophrenia: A Systematic Review]&lt;/ref&gt;&lt;ref&gt;[https://www.webmd.com/mental-health/flat-affect Flat Affect in Schizophrenia, Depression, Autism, &amp; More], webmd.com&lt;/ref&gt;&lt;ref name=nhs/&gt;&lt;!-- per &quot;emotionless and flat&quot; --&gt;

Merck manual considers executive decline to be a species of cognitive decline&lt;ref name=merck-prof/&gt;. The reason I list cognitive on the same level as executive is that the former is intuitively difficulty ''thinking'' (and getting to know) while the latter is difficulty ''doing''. On the other hand, it may be true that the difficulty doing has to do with difficulty thining, making decision, memory, attention, etc.

Delusion is one class of symptoms that deserve a note. Following the definitions in the sources, most people on the planet are delusional in so far as they believe in the existence of God or gods. Even one who believes in, say, Christian God has to accept that while he is right, the other believers are delusional. Moreover, religious people sometimes report to talk to God, which would fit under the head of auditory hallucinations (hearing voices). One would think religious people are in permanent psychosis. The reason why they are not so diagnosed is probably that ''culturally accepted'' delusions do not count as delusions for diagnostic purposes.

== Treatment ==
Treatment options as a bulleted outline:
* Antipsychotics&lt;ref name=nhs-treat&gt;[https://www.nhs.uk/mental-health/conditions/schizophrenia/treatment/ Treatment - Schizophrenia], NHS&lt;/ref&gt;
* CBT&lt;ref name=nhs-treat/&gt;
* Family therapy&lt;ref name=nhs-treat/&gt;
* Arts therapy&lt;ref name=nhs-treat/&gt;

== Notable bearers ==
An arbitrary pick from Wikipedia (characterizations in part based on Wikipedia):
* Robert M. Pirsig – American writer and philosopher, whose &quot;bestseller Zen and the Art of Motorcycle Maintenance was the biggest-selling philosophy book ever&quot; per Guardian&lt;ref&gt;[https://www.theguardian.com/books/2006/nov/19/fiction The interview: Robert Pirsig], 19 Nov 2006, theguardian.com&lt;/ref&gt;
* John Nash – American economist, mathematician and Nobel Prize winner in Economic Sciences
* Eduard Einstein – a son of the physicist Albert Einstein, the quintessential genius noted for his relativistic and counter-intuitive mechanics

The physicist Isaac Newton of the Newtonian mechanics and calculus fame is reported by some sources to have developed psychosis (a key symptom of schizophrenia) at some point in life.&lt;ref&gt;[https://psychiatryonline.org/doi/pdf/10.1176/appi.ajp.157.3.444 Chronic Late-Onset Schizophrenia-Like Psychosis That Remitted: Revisiting Newton’s Psychosis?]&lt;/ref&gt;

The American novelist and poet Jack Kerouac&lt;ref&gt;[https://www.britannica.com/biography/Jack-Kerouac Jack Kerouac], britannica.com&lt;/ref&gt; was diagnosed with dementia praecox (schizophrenia)&lt;ref&gt;[https://www.archives.gov/publications/prologue/2011/fall/kerouac.html Hit the Road, Jack!] by Miriam Kleiman, 2011, archives.gov&lt;/ref&gt;.

The Austrian logician Kurt Gödel, considered to be one of the greatest logicians ever, is not known to have had schizophrenia. Nonetheless, he sufferred from paranoia: &quot;As Gödel aged, he grew more and more paranoid and eventually became convinced that he was being poisoned. He refused to eat unless his wife tasted his food first. When she became ill and had to be hospitalized for an extended period of time, Gödel essentially stopped eating and starved to death.&quot;&lt;ref&gt;[https://www.britannica.com/biography/Kurt-Godel Kurt Gödel], britannica.com&lt;/ref&gt; Paranoia is one symptom of schizophrenia or of certain kind of schizophrenia.

An arbitrary pick from Wikipedia for bipolar disorder, which can be confused with schizophrenia (characterizations based on Wikipedia):
* Stephen Fry – actor, comedian, and writer
* Mel Gibson – actor and director
* Ernest Hemingway – American journalist, won the Pulitzer Prize (1953) and the Nobel Prize in Literature (1954) for his novel The Old Man and the Sea
* Emil Post – American mathematician and logician

Georg Cantor, the German mathematician who founded the set theory in the 19th century&lt;ref&gt;[https://www.britannica.com/biography/Georg-Ferdinand-Ludwig-Philipp-Cantor Georg Cantor], britannica.com&lt;/ref&gt;, is reported by some sources to have had a bipolar disorder; {{W|Georg Cantor}} (Wikipedia) traces the bipolar statement to Dauben 2004&lt;ref&gt;http://acmsonline.org/home2/wp-content/uploads/2016/05/Dauben-Cantor.pdf&lt;/ref&gt;, which quotes the psychiatrist Karl Pollitt as stating: &quot;As a young assistant I treated a prominent professor of mathematics [Georg Cantor] who had to be admitted to the clinic because of the recurrence of a cyclic manic-depression.&quot;

Ludwig Boltzmann, the Austrian physicist and philosopher noted for statistical mechanics, is reported to possibly have had the bipolar disorder.&lt;ref&gt;[https://www.worldscientific.com/doi/10.1142/9789814759786_0005 Chapter 5: An Unsolved Mystery] in A Bouquet of Numbers and Other Scientific Offerings, worldscientific.com&lt;/ref&gt;

Further reading:
* {{W|List of people with schizophrenia}}, wikipedia.org
* {{W|List of people with bipolar disorder}}, wikipedia.org -- of interest, since schizophrenia seems easily confused/confounded with bipolar disorder

== Classification ==
One source tracking classification is Wikidata. Classification (also includes bipolar) follows.

Questions:
* Into which broader categories is schizophrenia classified?
* How far is schizophrenia in the categorizaztion/classification tree from bipolar disorder?

In ICD-11 ID (Foundation)&lt;ref&gt;[https://icd.who.int/browse/2024-01/mms/en#613065957 ICD-11 for Mortality and Morbidity Statistics], icd.who.int&lt;/ref&gt;:
* 06 Mental, behavioural or neurodevelopmental disorders
** Schizophrenia or other primary psychotic disorders
*** 6A20 Schizophrenia
** Mood disorders
*** Bipolar or related disorders

As for serious mental illness (SMI), U.S. National Institute of Mental Health (NIMH) defines it as follows: &quot;Serious mental illness (SMI) is defined as a mental, behavioral, or emotional disorder resulting in serious functional impairment, which substantially interferes with or limits one or more major life activities. The burden of mental illnesses is particularly concentrated among those who experience disability due to SMI.&quot;&lt;ref&gt;[https://www.nimh.nih.gov/health/statistics/mental-illness Mental Illness], National Institute of Mental Health (NIMH)&lt;/ref&gt; Schizophrenia is one of SMIs&lt;ref&gt;[https://www.samhsa.gov/mental-health/serious-mental-illness/managing-life Managing Life with Serious Mental Illness], samhsa.gov&lt;/ref&gt;. The label &quot;serious mental disorder&quot; is sometimes seen in literature; it remains to be clarified whether this is intended to be a synonym of &quot;serious mental illness&quot; (one would think so).

DSM-5: Schizophrenia is classified as &quot;Schizophrenia Spectrum and Other Psychotic Disorders&quot;; bipolar is classified as &quot;Bipolar and Related Disorders&quot;.&lt;ref&gt;[https://www.psychiatry.org/File%20Library/Psychiatrists/Practice/DSM/APA_DSM-5-Contents.pdf DSM-5 Table of Contents], psychiatry.org&lt;/ref&gt;

Further reading:
* [[Wikidata:Q41112|Wikidata: schizophrenia]]
* {{W|Serious mental illness}}, wikipedia.org

== Risk of violence ==
The following is about the risk that someone diagnosed with schizophrenia commits violence, especially whether the risk is greater than with the baseline general population. (For instance, is it possible that Pr(Murder|Schizo) &gt;&gt; Pr (Murder)?) Such people being subject to violence is a separate question.

As per ox.ac.uk (University of Oxford) 2022, &quot;Researchers at Oxford University’s Department of Psychiatry have found that people with schizophrenia and related disorders are at higher-than-average risk of perpetrating violence, but that the overall risk remains low (less than 1 in 20 in women, and less than 1 in 4 for men over a 35-year period for violent arrests and crimes).&quot;&lt;ref&gt;[https://www.ox.ac.uk/news/2022-01-19-review-highlights-risk-factors-associated-violence-schizophrenia Review highlights risk factors associated with violence in schizophrenia], 19 Jan 2022, ox.ac.uk&lt;/ref&gt;

As per Norton 2009 in Reuters, &quot;People with schizophrenia are responsible for a disproportionate number of homicides; while they account for about 0.5 percent of the world's population, they are estimated to commit 6.5 percent of homicides worldwide, according to Dr. Olav Nielssen of the University of Sydney in Australia, the lead researcher on the new study.&quot;&lt;ref name=Norton2009&gt;[https://www.reuters.com/article/us-schizophrenia-strangers-idUSTRE59K4J620091021/ People with schizophrenia rarely kill strangers] by Amy Norton, 2009, Reuters&lt;/ref&gt; As a potential for improvement, it would be preferable to directly quote and reference Niels's study.

Fazel et al. 2009 indicate that &quot;Persons with schizophrenia are thought to be at increased risk of committing violent crime 4 to 6 times the level of general population individuals without this disorder. However, risk estimates vary substantially across studies, and considerable uncertainty exists as to what mediates this elevated risk.&quot;&lt;ref&gt;[https://pubmed.ncbi.nlm.nih.gov/19454640/ Schizophrenia, substance abuse, and violent crime] by Fazel et al., 2009&lt;/ref&gt;

News from Karolinska Institutet 2009 interprets Fazer et al. 2009 as indicating that it is not schizophrenia alone but rather schizophrenia in conjunction with substance abuse that leads to increased rate of violence.&lt;ref&gt;[https://news.ki.se/schizophrenia-does-not-increase-risk-of-violent-crime Schizophrenia does not increase risk of violent crime], 11 July 2009, news.ki.se&lt;/ref&gt; Their wording: &quot;A new study from the Swedish medical university Karolinska Institutet and the University of Oxford finds that the severe mental disorder schizophrenia only marginally increases the risk of committing violent crime. Rather, the overrepresentation of individuals with schizophrenia in violent crime is almost entirely attributable to concurrent substance abuse.&quot;

Per vic.gov.au, when the violence occurs, it more often occurs toward family members and frieds and less often toward strangers&lt;ref&gt;[https://www.betterhealth.vic.gov.au/health/conditionsandtreatments/mental-illness-and-violence Mental illness and violence], betterhealth.vic.gov.au&lt;/ref&gt;. The link to family members as targets is also given by Norton 2009 in Reuters.&lt;ref name=Norton2009/&gt;

Sapolsky, in 2011, some time after 38:30 into a video says that schizophrenics are less violent that non-schizophrenics.&lt;ref&gt;[https://www.youtube.com/watch?v=nEnklxGAmak 24. Schizophrenia] by Stanford, 2011, youtube.com&lt;/ref&gt; That contradicts the above quotations.

See also [[Schizophrenia, Criminality, and its Portrayal in the Media]].

Further reading:
* [https://livingwithschizophreniauk.org/information-sheets/schizophrenia-and-dangerous-behaviour/ Schizophrenia and Dangerous Behaviour], livingwithschizophreniauk.org
* [https://www.cambridge.org/core/journals/the-british-journal-of-psychiatry/article/violence-and-schizophrenia-examining-the-evidence/BEC530F212F98C0400D3D32CB2710BA9 Violence and schizophrenia: Examining the evidence] by Walsh, Buchanan and Fahy, 2 Jan 2018, cambridge.org
* [https://www.evidence-based-psychiatric-care.org/wp-content/uploads/2015/02/03_Nielssen.pdf Preventing violence in schizophrenia] by Olav Nielssen, 2015
* [https://www.academia.edu/5651538/The_relationship_between_rates_of_homicide_by_those_with_schizophrenia_and_the_overall_homicide_rate_a_systematic_review_and_meta_analysis The relationship between rates of homicide by those with schizophrenia and the overall homicide rate; a systematic review and meta-analysis] by Matthew Large et al.
* [https://pmc.ncbi.nlm.nih.gov/articles/PMC3160236/ Violence and Schizophrenia] by Wehring and Carpenter, 2011
* {{W|Schizophrenia#Violence}}, wikipedia.org

== Use of alcohol ==
NHS indicates caution about the use of alcohol with schizophrenia, although stoping short of stating that alcohol must be avoided at all cost.&lt;ref&gt;[https://www.nhs.uk/mental-health/conditions/schizophrenia/living-with/ Living with - Schizophrenia], nhs.uk&lt;/ref&gt;

Mayo Clinic is stringent with its &quot;Don't use alcohol or drugs.&quot;&lt;ref&gt;[https://www.mayoclinic.org/diseases-conditions/schizophrenia/diagnosis-treatment/drc-20354449 Schizophrenia - Diagnosis and treatment], mayoclinic.org&lt;/ref&gt;

WebMD has a cautionary tone, including &quot;It’s best not to drink alcohol at all if you’re on antipsychotic medications.&quot;&lt;ref&gt;[https://www.webmd.com/schizophrenia/features/alcohol-schizophrenia-meds Can I Drink Alcohol While Taking Schizophrenia Medications?], webmd.com&lt;/ref&gt; However, that does not tell us anything about when not being on medications.

== See also ==
* [[Bipolar disorder and psychosis]]
* [[Do antipsychotics cause more harm than good?]]
* [[Studies by Martin Harrow on treatment of schizophrenia]]
* [[A review of Jindřich Jašík's Journey out of Schizophrenia]]

== References ==
&lt;references /&gt;

== Further reading ==
* {{W|Schizophrenia}}, wikipedia.org
* [https://mdwiki.org/wiki/Schizophrenia Schizophrenia], mdwiki.org
* [https://www.britannica.com/science/schizophrenia schizophrenia], britannica.com
* [https://www.merckmanuals.com/professional/psychiatric-disorders/schizophrenia-and-related-disorders/introduction-to-schizophrenia-and-related-disorders Introduction to Schizophrenia and Related Disorders - Psychiatric Disorders], Merck Manual Professional Edition (Merck manufactures at least one schizophrenia drug)
* [https://www.mayoclinic.org/diseases-conditions/schizophrenia/symptoms-causes/syc-20354443 Schizophrenia - Symptoms and causes], Mayo Clinic
* [https://www.webmd.com/schizophrenia/mental-health-schizophrenia Schizophrenia: Definition, Symptoms, Causes, Diagnosis, Treatment], webmd.com
* [https://www.merckmanuals.com/professional/psychiatric-disorders/schizophrenia-and-related-disorders/schizophrenia Schizophrenia], Merck Manual Professional Edition
* [https://www.rcpsych.ac.uk/mental-health/mental-illnesses-and-mental-health-problems/schizophrenia Schizophrenia], Royal College of Psychiatrist, rcpsych.ac.uk

[[Category:Schizophrenia]]</text>
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    <title>Book Reviews/A review of Jindřich Jašík's Journey out of Schizophrenia</title>
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This short article by Dan Polansky is a cursory critical review of the book by Jindřich Jašík ''Journey out of Schizophrenia'', 2019. The book was published in Czech and English; the Czech original title is ''Cesta ze schizofrenie''. A preview of the English publication is available in Google Books. My estimate is that the book is much better available for purchase to Czech readers than English readers, so it may turn out this review will be more useful for them. Nonetheless, some of the topics and points made here may be interesting for international audience.

Good things and problematic things:

1) (Problematic) The book has the word ''schizophrenia'' in the title, but the author reports on the first pages that it is not clear that he has schizophrenia and that he had some symptoms of bipolar disorder.&lt;ref&gt;The author states: &quot;However, I don't really think the specific diagnosis matters, as this book may be beneficial to people with various psychiatric diagnoses. Before I was diagnosed with paranoid schizophrenia, not only had I suffered from all kinds of schizophrenia and schizoaffective disorders, but also from a bipolar disorder, a spiritual crisis and most likely from many other disorders I'm not even aware of.&quot;&lt;/ref&gt; It may turn out that the author has a condition that different psychiatrists would rank as bipolar disorder (in which psychosis is often present per [[Bipolar disorder and psychosis]]) or at least psychoaffective disorder. And then, it may turn out that the author has a relatively mild form of serious mental illness (SMI) with a psychotic component (hallucinations, delusions) and an affective component (mania, hypomania, depression), which could explain why his drug-free autotherapy works well for him while it may not work so well for people with a more serious form of SMI, with different composition of elementary signs (halluciations, delusions, disorganized thinking, executive dysfunction, manic or hypomanic phases, depressive phases, etc.) This is a crucial point for the readers who would like to use Jašík's method to self-treat their condition that someone has diagnosed as schizophrenia. Much more important than whether the SMI belongs to the arguably non-existent (arbitrarily carved out) entities &quot;schizophrenia&quot; (formerly &quot;dementia praecox&quot;) and &quot;bipolar disorder&quot; (formerly &quot;maniodepressive psychosis&quot;) is whether the SMI is ''mild'' and whether it has components that can respond to cognitive psychotherapy, e.g. delusions (for the purpose of psychiatric diagnosis, blatantly wrong beliefs that are not culturally accepted).

2) (Problematic) The book has no list of used literature and no inline references. This presents a room for improvement since the book makes multiple statements that the author must have learned from literature rather than experience and deliberation, but we do not know which literature. For instance: &quot;After decades of research, no schizophrenic gene has been found, nor has the dopamine hypothesis been proved.&quot; On the other hand, the reader can take these statements and try to verify them for themselves, so they are not without value.

3) (Problematic) Expanding on the above, there seems to be no or very little acknowledgement of the serious people who did serious publishing work critical of psychiatry, e.g. Whitaker, Moncrieff and Gøtzsche. On the other hand, the reader can find out about these using the Internet.

4) (Good) I find the authentic report of Jašík's experience valuable. This is reporting things he positively knows (his own experience) rather than speculations.

5) (Good) I find the copy of Jašík's medical report valuable. It presents evidence against Czech psychiatry. It reveals part of the problematic language and problematic thinking on part of psychiatrists, as well as the suspect polypharmacy (using a coctail of drugs). And thus: &quot;Therapy: Risperdal, Zolpidem, Rivotril, Nozinan, Cisordinol Acutar, Akineton, Zyprexa Velotab, Risperdal Consta, regime therapy, supportive psychotherapy.&quot;&lt;ref&gt;[https://books.google.com/books?id=Rz_2EAAAQBAJ Journey out of Schizophrenia], books.google.com&lt;/ref&gt;

6) (Good) I find Jašík's description of his self-treatment method worthwhile at least as a look into someone's mind.

7) (Good) There are many interesting points, e.g. &quot;After decades of research, no schizophrenic gene has been found, nor has the dopamine hypothesis been proved.&quot; (It would be even better if they were properly referenced, as mentioned above.)

Verdict: the book seems to be a worthwhile read if one applies the appropriate caution.

== See also ==
* [[A critical look at psychiatry]]

== Notes and references ==
&lt;references /&gt;

== Further reading ==
* [https://www.databazeknih.cz/knihy/cesta-ze-schizofrenie-400170 Cesta ze schizofrenie - Jindřich Jašík], Databáze knih -- has small Czech reviews
* [https://www.martinus.cz/1140459-cesta-ze-schizofrenie/kniha Cesta ze schizofrenie - Jindřich Jašík], Martinus -- has small Slovak reviews
* [https://www.youtube.com/watch?v=2uNL_WFj57s HOVORY ZE ZEMĚ - Cesta ze schizofrenie - Jindřich Jašík], youtube.com -- a video interview with Jašík narrating some of the points from the book, in Czech
* [https://www.youtube.com/watch?v=RWNW3wqIds4 Studio 27 - Jindřich Jašík - Cesta ze schizofrenie], youtube.com -- another video interview
* [https://cpk-front.mzk.cz:10001/Record/nkp.NKC01-003062134?sid=482114 Cesta ze schizofrenie], cpk-front.mzk.cz -- a library catalog record for the Czech edition</text>
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      <text bytes="586" sha1="obm43smz3vdycfomswubbeagaabf04h" xml:space="preserve">== Encyclopedic significance ==
The book seems to be not significant for a Wikipedia article, but I have no experience with WP significance discussions. Since Wikiversity does not seem to have any significance requirements, I took the liberty to create the article. The book is interesting, and unsurprisingly, I find my comments on it interesting as well. The book has a Wikidata item created not by me: [[Wikidata: Q122031402]]. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:23, 13 February 2025 (UTC)</text>
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This article by Dan Polansky looks at personal environmentalism (or individual or individualistic environmentalism), by which I mean choice of action by an ordinary citizen on a personal level toward the protection of the environment and nature. It is written from a European perspective, that is, of one living in a rather rich, technologically developed country; and thus, e.g. avoiding flying to a vacation is discussed, a concern that poor people in Africa do not have.

It seems to me that personal (or individual), as opposed to political, environmentalism is largely in vain, with low chance of making sizable impact. It seems unlikely to me that personal environmentally protective choices are going to spread through population by means of immitation; most people seem too reckless, uncaring or unconcerned for that. Moreover, in a societal setup adapted to harmful practices, a small number of individuals trying to engage in different practices lead to them incurring much larger inconvenience than would otherwise be the case. For instance, in a country with well developed and dense network of public transportation, it is much easier to use it and avoid driving a personal car, but this is usually a result of political action, not personal/individual action. Even so, one may want to do what one can to limit one's harmful impact for symbolic reasons (whether this is rational and in what sense is another matter).

Some of the things one can do for the environment on personal level, often for symbolic value only:
* Population measures
** Kill oneself. This will relieve the environment of one human burden. This action seems unwise since it can do almost nothing to address environmental issues: if adopted as a policy of environmentally conscientious citizens, it would eliminate being conscientious from the pool and all that would remain would be reckless people. That cannot be desirable.
** Kill multiple other people. This will relieve the environment of multiple items of human burden. This action seems unwise since, apart from being unethical, it will paint those who want to protect the environment as dangerous terrorists. This action was chosen by Ted Kaczynski/Unabomber, who engaged in bombing campaign in relation to spread of new technology.
** Go childless. This will relieve the environment of the burden of the humans that would be born. It seems not sustainable and somewhat problematic: it leads to the putative gene of being considerate being eliminated from the gene pool. (It is not necessarily genetic or solely genetic, though; this is the first idea.)
** Reduce the number of children one has. More children means more burden on the environment.
* Reduced consumption
** Avoid buying bottled water.
** Avoid buying bottled beverages other than water.
** Avoid buying foods imported from afar.
** Avoid buying foods with a high ratio of packaging mass to food mass.
** Avoid buying needless items bought just for pleasure, perhaps pieces of art.
** Avoid buying musical instruments; use your voice instead for pleasure from music.
** Do not dye your hair.
* Other
** Have selected consumer items repaired rather than buying new despite the increased effort and inconvenience.
** Avoid flying to a vacation.
** Avoid long distance driving a car to a vacation.
** Avoid hobbies that harm the environment, e.g. motor racing, car driving for fun, flying for fun, etc.
** Sort waste to support recycling.

For contrast to personal/individual environmentalism, let us consider how political action looks like:
* Introducing or increasing environmental taxes on fossil fuels and other items that economists call externalities.
* Introducing environmental subsidies.
* Prohibition of classes of toxic substances.
* Other prohibitions in cases where one can expect them to work better than environmental taxes.

Let me expand on why government regulation is required or preferable. We have to do with a form of prisoner's dilemma. If a lone company decides to implement processes less harmful to the environment, it can be expected in general to incur additional costs, and unless it can successfully pass these additional costs on the consumers or other buyers, it will be less competitive. By contrast, when the burden of implementing the less harmful processes is imposed on all market actors, none of them is made less competitive (roughly speaking; a more careful analysis could show that e.g. larger actors have it easier to accomodate environmental requirements). One could object that the environmentally friendly company could market its products as environmentally friendly, that will attract environment-conscious consumers and that will compensate for the incurred additional cost; without sound empirical substantiation, I find it unconvincing.

A related question is whether it is contradictory for a climate politician to fly a private jet. It does not seem to be contradictory since individual actions have hardly ever the impact/scale of a political action. Views apparently differ on this.

A somewhat related (and somewhat tangential) question is whether, in environmental issues, the free market usually or always solves these issues better than government regulation. It can be admitted that the price mechanism does to some extent lead e.g. to introduction of less energy-wasteful technology since the result is paying less for the energy inputs. But I do not see how free markets would generally solve these issues, nor do I see it as somehow obvious; this would require careful, specific analysis, informed by empirical detail and historical experience, I think. Nor, on a tangent, do I see how free markets make government regulation of medicines unnecessary. (Passing this paragraph to Google Gemini produces much more impressive and compelling text.) That is not to deny: there is such a thing as bad government regulation and government and regulatory roles all too often attract incompetent people who have not seen a paying customer in their life and who have no idea how to serve but rather want to rule and govern.

== Further reading ==
* {{W|Individual action on climate change}}, wikipedia.org
* [https://www.sierraclub.org/sierra/yes-actually-individual-responsibility-essential-solving-climate-crisis Yes, Actually, Individual Responsibility Is Essential to Solving the Climate Crisis], sierraclub.org
* [https://news.climate.columbia.edu/2021/05/10/the-role-of-individual-responsibility-in-the-transition-to-environmental-sustainability/ The Role of Individual Responsibility in the Transition to Environmental Sustainability – State of the Planet] by Steven Cohen, 2021, news.climate.columbia.edu
* [https://www.theguardian.com/commentisfree/2019/jul/10/individuals-climate-crisis-government-planet-priority Individuals can’t solve the climate crisis. Governments need to step up] by Anders Levermann (head of complexity science at the Potsdam Institute for Climate Research in Germany), 10 July 2019, theguardian.com</text>
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This article by Dan Polansky looks at the art of writing. It could also be called a look at rhetoric and composition, following the model of the name of a book in Wikibooks. Some ideas are from a slender book by Gary Provost.

One could think that writing on the art of writing should better come from an accomplished and competent writer. Maybe so. Be it as it may, the objectives of instructions on the art of writing include turning bad writers into half-decent ones or better. It may be true that excellent writers do not need any principles and rules of thumb. But may also be that excellent writers figure out rules of thumb themselves. And that I find plausible enough.

Some ideas from Gary Provost, from memory so perhaps some elements are mine:
* Get yourself some reference works, including a dictionary, an encyclopedia and Roget's thesaurus (word finder).
* Writing is an auditory art. Sentences should also sound good. You can test your sentences by reading them out loud.
* A small physical exercise can make you more ready to write. (Perhaps more blood gets into the brain?)
* Revising is key. Hardly anyone can do an excellent writing job without heavy revising. It was perhaps Hemingway who was known to rewrite his drafts an incredible number of times.
* Vary sentence length. Too many too long sentences tire the reader. Too many too short sentences bore the reader.
There are many more of them. The book by Gary Provost seems to be a popular and worthwhile read.

Some ideas from memory, some mine, some from or inspired by various sources:
* Written sentences are composed of discrete items that are words, phrases, collocations, idioms and such. Unless one is a genius, one can greatly benefit from repeatedly reading documentation of these building blocks, including dictiony definitions.
* Apart from revising, one can use the techniques of engineering review, which includes accumulation of stated issues/defects with the text. This method is more bureaucratic: one not only corrects issues one finds but one also formulates descriptions of these issues.
* Apart from revising, one can also start anew, as if restart the writing. During the writing, the short-term memory structures of the mind change, in support of the written text. In an incrementally revised text, there is something like burden of history. By starting anew (without destroying the old version), one can get free from that burden of history.
* Outlining is a traditional technique used by professionals in writing. I find it valuable, although I often write without outlining. The present writeup is written without outlining, and perhaps it shows.
* Checklisting is similar to outlining but is different in principle. The idea is to list items to be covered in any old order and then make sure they are covered, possibly rejecting some of them. Something like this is mentioned in Pirsig's ZMM, when Pirsig helps Chris write a letter to mother.
* Similar to the above items is Pirsig's idea from his philosophical novel Lila to use catalogue cards as some kind of information system into which to write ideas in a random-access manner. It seems like a neat idea.
* Terminology clarification is one dedicated activity. It includes figuring out what terms to use to refer to concepts, out of multiple candidates.
* One of the few stylistic advices that I got from Czechs is to rotate synonyms, avoiding using the same word or phrase again and again. While the advice is perhaps not complely bad for all circumstances, I find it rather pitiable. For engineering writing, I find it completely inappropriate: to the contrary, the same concept should always be referred to using the same name. As a reader of a technical document, I don't care about anyone's professed richness of vocabulary.
* I must have read a Czech writing guide state something to the effect that if writing comes bad or difficult to you, you should better give up since you probably do not have enough talent. I find this so-called advice pitiable or outright despicable. The only way to produce a half-decent writer from a bad writer is practice. I would echo Pirsig here, paraphrasing: so you want to know how to become a great writer? Just make yourself perfect by practice and then write naturally. Sure enough, where there is no talent, practice does not help. But then again, I see nothing wrong per se in one trying to become a half-decent writer by practice.
* Cut needless words. Make every word tell. This must be from Strunk and White.
* Sometimes I find myself too wordy. When I make a pause and take the time and effort, I can often find a much shorter way without any information loss. This requires discipline and sometimes I do not have it, being in a hurry.
* The quality/excellence requirements do differ between textual artifact types, novels and short stories on one hand and technical documentation on the other. In technical documentation, it is much less important that it reads well or is interesting; it has to be accurate, have good reader usability, etc. Yet different are probably requirements on clerical writing, e.g. filling request forms.
* Good writing was not turned into a fully algorithmic process for humans, unlike e.g. correct decimal multiplication.
* Taste and style does play a role. Thus, there is certain relativity in the word ''good'' as applied to good fiction writing. As a result, a reviewer may raise issues that are not in reference to objective badness but rather merely issues of deviation from the reviewer's preferred style. That said, there are some objectively given classes of defects in writing, and not only petty trivialities as spelling and grammar.
* From information value perspective, bad writing is better than no writing. And thus, sometimes the reader would do well to thank the author for trying to express valuable ideas rather than avoiding the task for the fear of being a bad writer.

Books that I have read or have in my library that pertain to writing:
* ''100 Ways to Improve Your Writing'' by Gary Provost, 1972
* ''Good Style: Writing for science and technology'' by John Kirkman, 1992, 2005
* ''Writing in Style: a guide to good English'' by Richard Palmer, 1993, 2002
* ''Zen and the Art of Motorcycle Maintenance'' by Robert Pirsig, 1974
* ''Lila'' by Robert Pirsig, 1991
* ''The Elements of Style'' by Strunk and White

== See also ==
* [[One man's look at English]]

== Further reading ==
* [[Wikibooks: Rhetoric and Composition]], wikibooks.org

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Author: Dan Polansky

This article looks at wikis, including Wikipedia. The material is going to be idiosyncratically selected and organized.

== General notes==
Wikis are pure genius: The use of plain text enables some of the best diff determination/calculation available. The plain text is reasonably human legible, which is much less true of e.g. LaTeX markup. At the same time, the preview and the final form is good-looking HTML. The inline referencing facility is very convenient, as is templating and even Lua programming. Editors can prepare their page changes offline using a plain text editor of their choice. Editors can easily produce some wiki content programmatically, e.g. a wiki table from some data source.

Not all wikis use the same governance model as Wikipedias and their ilk. For instance, Czech medical doctors and medical students operate a wiki called WikiSkripta&lt;ref&gt;[https://www.wikiskripta.eu/w/Home WikiSkripta], wikiskripta.eu&lt;/ref&gt;, in which not everyone can edit (I think) and some editors appear to be more important than the others. And that does not need to be a bad thing; it is not the MediaWiki technology that enforces particular governance model. Of course, there is the failed fork Citizendium with its failed governance model.

Revision histories of wiki pages are typically public. This provides excellent transparency for the readers. However, embarassing mistakes by the wiki contributors are available for inspection, which is perhaps somewhat problematic.

== Angophone vs. Czech wiki culture ==
Let me note some differences I observed:
* In Czech wiki projects, editors are often asked on their talk page to use preview function and avoid saving many intermediate revisions. I don't recall seeing this in an Anglophone project, though it may exist; if it does, it is not widespread.
* In Czech wiki projects, editors are often asked on their talk page to provide an edit summary for each edit. Unless I am mistaken, editors who repeatedly refuse to comply are blocked for a short time. I have seen nothing of the sort in the English Wiktionary or the English Wikiversity; as for the English Wikipedia, I am rather inactive.
* In Czech wiki projects, people often address each other ''kolego'' and ''kolega'' (colleague), which reminds me of ''soudruhu'' (Comrade). In the Anglophone wikis, I did not notice any similar term of address.
* In Anglophone wikis, use of vulgarities by administrators is relatively common; it is unacceptable in the Czech Wikipedia.

== MediaWiki ==
MediaWiki is the wiki engine/wiki software running Wikipedia, the most popular wiki on the planet by far. It has the following selected features, common with many other wiki engines:
* Pages are editable as plain text that uses a mark up with decent user legibility.
* The editing interface provides a preview function and a diff function to the last saved revision.
* Revision histories of pages are available, keeping time stamp and the user of the revision/edit.
* Images can be used, including PNG and SVG.
* Inline references can be marked up using &lt;nowiki&gt;&lt;ref&gt;...&lt;/ref&gt;&lt;/nowiki&gt; syntax and a list of them is auto-generated using &lt;nowiki&gt;&lt;references /&gt;&lt;/nowiki&gt; syntax. This is provided by a plug-in/add-in/extension&lt;ref&gt;https://www.mediawiki.org/wiki/Extension:Cite&lt;/ref&gt;.
* The plain text markup is rendered as a neat HTML, with headings, italics, boldface, lists, tables, etc.
* The table of contents is generated automatically from the heading markup.
* Pages are put into categories, one page in multiple categories in general. The categories form a directed acyclic graph, I think (a category can be in multiple categories).
* Templating is available. The templates can have parameter.
* Modules programmed in Lua can be made, usually called from a template. This did not use to be the case.
* A set of pages can be exported to XML, either the latest revisions only or with full revision history (Special:Export.)

Links:
* [[Wikibooks: MediaWiki User Guide]]

== Websites using MediaWiki ==
Idiosyncratically selected other websites using MediaWiki (Wikipedia sister projects such as Wikiversity are not listed):
{| class=wikitable
|-
| Website || Link || License || Description/Note
|-
| {{W|Fandom (website)|Fandom}} || D/C&lt;ref&gt;Link blocked by an editing filter.&lt;/ref&gt; || ? || Formerly Wikicities and Wikia, a for-profit wiki farm hosting wikis on popular subjects/areas founded in part by Wikipedia's Jimmy Wales/Jimbo Wales.
|-
| {{W|Rosetta Code}} || [https://rosettacode.org/wiki/Rosetta_Code Link] || GFDL || Programming solutions for tasks in very many programming languages, including relatively obscure ones.
|-
| C++ Reference || [https://cppreference.com/ Link] || ? || A comprehensive reference for the C++ language.
|-
| New World Encyclopedia || [https://www.newworldencyclopedia.org Link] || CC-BY-SA || An encyclopedia whose many articles started as a fork of Wikipedia.
|-
| {{W|Citizendium}} || [https://www.citizendium.org/ Link] || CC-BY-SA&lt;ref&gt;They state that some content is also available by CC-BY-SA-NC; unclear&lt;/ref&gt;  || An unsuccessful fork of Wikipedia started by Wikipedia co-founder Larry Sanger. I think they required people to use real names and prove their identity and credentials.
|-
| {{W|Conservapedia}} || [https://www.conservapedia.com Link] || Unclear&lt;ref&gt;per {{W|Conservapedia#Licensing of content}}&lt;/ref&gt; || An encyclopedia with a politically conservative twist/bias.
|-
| {{W|RationalWiki}} || [https://rationalwiki.org/ Link] || CC BY-SA || A wiki self-styled as being opposed to the irrationality of religion, etc.
|-
| Miraheze || [https://miraheze.org/ Link] || ? || A free/gratis wiki hosting platform.
|-
| MDWiki || [https://mdwiki.org/wiki/Main_Page Link] || CC-BY-SA || A medical wiki where Doc James/James Heilman of the Rorschach test image release fame is active.
|-
| Free Software Directory || [https://directory.fsf.org/wiki/Main_Page Link ] || GFDL || A directory of free-as-in-freedom software run by Stallman's Free Software Foundation.
|-
| The Document Foundation's wiki || [https://wiki.documentfoundation.org/Main_Page Link] || CC-BY-SA || A wiki relating somehow to LibreOffice.
|-
| ArchWiki || [https://wiki.archlinux.org/title/Main_page Link] || GFDL || A wiki for Arch Linux.
|-
| WikiSkripta || [https://www.wikiskripta.eu/w/Home Link] || CC-BY || A medical reference in Czech.
|-
| Sociologická encyklopedie || [https://encyklopedie.soc.cas.cz/ Link] || ? || An official, professionaly made encyclopedia by a Czech research institution.
|}

Further reading:
* {{W|MediaWiki#Sites using MediaWiki}}, wikipedia.org
* {{W|Category:MediaWiki websites}}, wikipedia.org -- about 100 wikis, which seems to be a fraction of the actual use; the below MediaWiki lists are much more comprehensive
* [[MediaWikiWiki: Sites using MediaWiki]] -- only points to language-specific pages
* [[MediaWikiWiki: Sites using MediaWiki/en]] -- about 370 wikis as of 18 Nov 2025
* [[MediaWikiWiki: Sites using MediaWiki/fr]]
* [[MediaWikiWiki: Sites using MediaWiki/de]]
* [[MediaWikiWiki: Sites using MediaWiki/es]]
* {{W|Category:MediaWiki websites}}, wikipedia.org

== Licensing ==
Wikipedia and Wikiversity are currently licensed under CC-BY-SA 4.0, a strong copyleft license, another famous instance being Stallman's GNU GPL used by the GNU project and Linux. From what I recall, Wikipedia started using Stallman's GFDL, but switched to CC-BY-SA; Stallman even made some change to GFDL to make this possible, I think. One of the objectives was to simplify the requirements on attribution, I think (to be researched).

For other licensing examples, see [[#Websites using MediaWiki]].

== Wiki development vs. free software development ==
While wikis share the idea of copyleft license with free software development, the development models are quite unlike. In software, there is often a benevolent dictator (for Python, it used to be Guido van Rossum) or in any case people with different power levels. It is not possible for a newcomer to a software project to insist to get write/commit rights to the repository and start throwing &quot;assume good faith&quot; and &quot;don't bite the newbies&quot; at the project maintainers. To the contrary, it was Linus Torvalds of Linux fame who responded to a somewhat rude newcomer with rather strong (and unwelcoming) language criticising the C++ language and by implication the newcomer&lt;ref&gt;https://harmful.cat-v.org/software/c++/linus&lt;/ref&gt;. This suggests great disparity between software making and wiki making.

Software has to work. It has to compile and show various non-trivial functional characteristics. By contrast, paper (or electronic paper) is patient with words put on it to form sentences in natural language for humans to read, as they say.

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|Wiki}}, wikipedia.org
* [https://www.britannica.com/topic/wiki wiki], britannica.com

[[Category:Wiki]]</text>
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  <page>
    <title>User talk:Dan Polansky/A human as multiple persons</title>
    <ns>3</ns>
    <id>318904</id>
    <revision>
      <id>2810234</id>
      <parentid>2760864</parentid>
      <timestamp>2026-05-18T20:27:22Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:A human as multiple persons]] to [[User talk:Dan Polansky/A human as multiple persons]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2760864</origin>
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      <text bytes="926" sha1="72hi0tolxk9uewczj76rt1i5dssr2s2" xml:space="preserve">== inner self ==
Some sources talk of &quot;inner self&quot;; M-W has a definition. The phrase is suggestive of multiple selves. I should perhaps do a research in literature and add something to the article. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:59, 23 February 2025 (UTC)

== More notes ==
1) There is a broader topic: the psychological structure of a human (not of scientific revolutions). An advantage would be that the question whether the analyzed components are person-like could be less acutely dealt with. For instance, if a person has something like a mind and a heart by definition, then it is not clear that mind is again person like, i.e. that mind has mind-mind and mind-heart. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:06, 15 October 2025 (UTC)</text>
      <sha1>72hi0tolxk9uewczj76rt1i5dssr2s2</sha1>
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  <page>
    <title>User talk:Dan Polansky/What is ethics</title>
    <ns>3</ns>
    <id>318910</id>
    <revision>
      <id>2810208</id>
      <parentid>2702357</parentid>
      <timestamp>2026-05-18T20:04:50Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:What is ethics]] to [[User talk:Dan Polansky/What is ethics]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2702357</origin>
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      <format>text/x-wiki</format>
      <text bytes="831" sha1="e1flb8g4mhhilodoo1kq24vl3o0pxik" xml:space="preserve">== Inquiry into norms ==
Perhaps ethics, or some kind of ethics, would be inquiry into norms, or ''normatics''. It would be inquiry into correct norms or perhaps best norms, but not in customary norms. Needs a closer look.

One complication is that also logic is sometimes considered to be normative.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:36, 24 February 2025 (UTC)

== Inquiry into custom ==
I should perhaps create a dedicated section for &quot;Inquiry into custom&quot; and note it would follow from etymology. It would perhaps lead to a better structure. An idea: anthropology, not ethics. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:29, 24 February 2025 (UTC)</text>
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  <page>
    <title>User talk:Dan Polansky/A critical look at psychiatry</title>
    <ns>3</ns>
    <id>319006</id>
    <revision>
      <id>2810180</id>
      <parentid>2741730</parentid>
      <timestamp>2026-05-18T19:51:35Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:A critical look at psychiatry]] to [[User talk:Dan Polansky/A critical look at psychiatry]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2741730</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1166" sha1="irriturumdbk4kbiipvw100kszrfp41" xml:space="preserve">== Gaslighting in psychiatry ==
An old Wikipedia article version has a section on gaslighting in psychiatry:

https://en.wikipedia.org/w/index.php?title=Gaslighting&amp;oldid=1247077324#In_psychiatry_and_psychology, 22 September 2024

To wit: &quot;Barton and Whitehead described three case reports of gaslighting with the goal of securing a person's involuntary commitment to a psychiatric hospital, motivated by a desire to get rid of relatives or obtain financial gain: [...]&quot;

Perhaps an even older version of the article has even more on the subject.

The above can probably be used in this article. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:52, 26 February 2025 (UTC)

== Foucault's Madness and Civilization ==
While Wikipedia's {{W|Madness and Civilization}} ranks the 1961 book as belonging to anti-psychiatry, I cannot confirm this from reading the Wikipedia article. I would need to find a good source supporting the thesis. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:15, 31 August 2025 (UTC)</text>
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  <page>
    <title>User talk:Dan Polansky/Czech national identity</title>
    <ns>3</ns>
    <id>319077</id>
    <revision>
      <id>2810222</id>
      <parentid>2703246</parentid>
      <timestamp>2026-05-18T20:15:30Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:Czech national identity]] to [[User talk:Dan Polansky/Czech national identity]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2703246</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="680" sha1="0no2opbmj4l5kyqur1uazn1d2ji2jp9" xml:space="preserve">== How to pick the famous Czechs ==
I am not clear about this. Requiring an article in Britannica online is a neat trick, but does not do all the selection.

One can ask GenAI and hope the result is not going to be too skewed. I asked Gemini &quot;What are some of the most famous Czechs?&quot; and obtained an interesting if short list, with nice characterizations. I then asked &quot;What are 50 most famous Czechs?&quot; and got impressive output.

There is {{W|List of Czechs}} in Wikipedia; that one is too long to give a concise picture.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:43, 28 February 2025 (UTC)</text>
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  <page>
    <title>User talk:Dan Polansky/One man's look at philosophy</title>
    <ns>3</ns>
    <id>319078</id>
    <revision>
      <id>2810192</id>
      <parentid>2703254</parentid>
      <timestamp>2026-05-18T19:54:23Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:One man's look at philosophy]] to [[User talk:Dan Polansky/One man's look at philosophy]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2703254</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1480" sha1="d37spv5op6hqkpvmctxpwkriucu9br4" xml:space="preserve">== Demarcation ==
It seems to me that especially psychology is a field against which philosophy needs to be demarcated. Thus, one can try to distinguish the philosophy of knowledge and psychology of knowledge. To what extent this will be successful is not so clear.

To wit, is Russell's ''The Analysis of Mind'' a work solely in philosophy or also in psychology?

The distinction between philosophy and psychology is well applied to study of inference: correct inference vs. actual (and often incorrect) inference. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:22, 28 February 2025 (UTC)

== Classification ==
Philosophy is sometimes or often ranked as one of the humanities. I find it a bit problematic, while not completely wrong. Thus, I do not see what e.g. Democritean atomism has to do with humanities or humans. One could perhaps object that Democritean atomism was actually physics. Maybe so. Even so, one can ask whether natural philosophy or philosophy of nature are thereby contradictions in terms. 

I tend to think that philosophy defies these kinds of classification. It has more to do with mathematics than anything else by its apparent unviersality. However, most of philosophy cannot reasonably be ranked as formal science. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:26, 28 February 2025 (UTC)</text>
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  <page>
    <title>User:Dan Polansky/One man's look at email confidentiality</title>
    <ns>2</ns>
    <id>319174</id>
    <revision>
      <id>2810172</id>
      <parentid>2703800</parentid>
      <timestamp>2026-05-18T19:49:07Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[One man's look at email confidentiality]] to [[User:Dan Polansky/One man's look at email confidentiality]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2703800</origin>
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      <text bytes="5102" sha1="fu5i7bu61khg9qkbffzjbneui0csgfn" xml:space="preserve">{{Original research}}
This article by Dan Polansky looks at email confidentiality. Initial questions:
* Under what circumstances is email content confidential?
* Is there a legal requirement to maintain email confidentiality?
* Is there a moral requirement to maintain email confidentiality?
* Is the fact that an email with title so-and-so was received from person so-and-so confidential?
* Is the fact that some email was received from person so-and-so confidential?
* Does confidentiality, when it applies, protect every single sentence? (Probably yes?)

== Introductory considerations ==

If an email is expressly marked as confidential, e.g. in the email header or footer, it is obvious that it is itended as confidential (but it is not obvious that this alone makes the confidentiality legaly binding). The fact that some emails are expressly marked as confidential suggests that emails are not automatically considered confidential (but this is a mere ''suggestion''; the fact that some people place a copyright notice on text does not mean that published text in a tangible form without that notice is not protected by copyright).

An email sent or received as part of employment is subject to a possible contractual requirement of confidentiality. Such an email does not even need to be marked as confidential to be prohibited from divulging outside of the employer organization (or outside of a broader scope, as specified in the employment contract).

A receiver of an email would seem advised to generally treat email content as confidential, by avoiding devulging the content (since it is not clear that it isn't confidential) and in case of a need to divulge, consult a lawyer?

The other way around, the sender has to consider the risk that the content will be divulged anyway. In this sense, sending an email is something of a pre-publication of a statement. It seems likely that a court can order divulging of the content of an email that was marked as confidential.

It is not clear whether the sender of the email holds copyright in its text; he would seem to if sending the email would be considered to be publishing. But sending an email does not really seem to be publishing proper.

== Wiki context ==
Publishing content of emails sent via the wiki interface is dealt with in the further reading. As per {{W|Wikipedia:Emailing users#Reposting emails publicly}}:
: &quot;There is no formal consensus by the community regarding the act of reposting private off-wiki correspondence onto public Wikipedia locations, or the restriction or prohibition of the exercise thereof. However, it is often considered to be an unacceptable action for legal reasons. Unlike edits and posts to Wikipedia's web pages, emails that are sent through the email facility are not automatically &quot;freely&quot; licensed by the sender, and therefore, reposting the messages or correspondence to a public Wikipedia location would suggest or imply to any and all readers that the text is freely licensed for reuse and republication by its author, which is generally not the case.
: &quot;Users who feel that they are allowed to repost text from an email or other off-wiki source, or that doing so is necessary or the right to do so given a certain situation, discussion, report, or event, are advised to take extreme caution, and to consult with other trusted and experienced users before doing so, in order to ensure that the act will not accidentally create a problem for themselves, or create a negative perception or result in negative consequences. This might involve consulting, or asking the sender if they will allow the email to be quoted under Wikipedia's license in a post on Wikipedia's discussion pages. Note that this only applies to reposting on Wikipedia and its sister projects – other forms of quoting which do not involve risk of copyright breach (such as forwarding the text to an administrator for advice, or quoting words or brief phrases in a way that constitutes Fair Use) are generally unaffected by this concern.&quot;

In {{W|Wikipedia talk:Emailing users#email privacy}}, user Herostratus opined the following:
: &quot;[...] For one thing, the default rule in this world is that gentlemen don't publicize private correspondence without permission. (Exceptions might be made in some special rare cases, but in those cases its usually better to involve the authorities instead.) [...]&quot;
It seems plausible enough (as for ''gentlemen''), but is it accurate and how universal is it (what exceptions apply)?

== Further reading ==
* {{W|Email disclaimer}}, wikipedia.org
* {{W|Wikipedia:Harassment#Private correspondence}}, wikipedia.org
* {{W|Wikipedia:Private correspondence}}, wikipedia.org
** {{W|Wikipedia:Harassment#Private correspondence}}, wikipedia.org
** {{W|Wikipedia:Harassment#Posting of personal information}}, wikipedia.org
** {{W|Wikipedia:Emailing users#Reposting emails publicly}}, wikipedia.org
** {{W|Wikipedia talk:Emailing users#email privacy}}, 2012, wikipedia.org
* {{W|cs: Wikipedie:Žádost o komentář/Vynášení soukromé komunikace}}, wikipedia.org (in Czech)

[[Category:Email]]</text>
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  <page>
    <title>User talk:Dan Polansky/One man's look at zuclopenthixol acetate</title>
    <ns>3</ns>
    <id>319401</id>
    <revision>
      <id>2810187</id>
      <parentid>2708139</parentid>
      <timestamp>2026-05-18T19:53:04Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>Atcovi moved page [[Talk:One man's look at zuclopenthixol acetate]] to [[User talk:Dan Polansky/One man's look at zuclopenthixol acetate]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
      <origin>2708139</origin>
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      <text bytes="1164" sha1="l4selrx86d4qj6p61x18gcbhw7vdqqh" xml:space="preserve">== Items to process ==
1) DONE. Risk of confusion with the decanoate variant: per https://www.england.nhs.uk/wp-content/uploads/2018/01/B0203_How-we-acted-on-patient-safety-issues-you-reported-Report_.pdf and per https://www.wacountry.health.wa.gov.au/~/media/WACHS/Documents/About-us/Policies/Specialised-Medication---Zuclopenthixol-Acetate---Clopixol-Acuphase-Guideline.pdf?thn=0. To be added.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:25, 10 March 2025 (UTC)
: Updated. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:06, 22 March 2025 (UTC)

== Semidepot injection ==
I have found no use of this putative term; semi-depot injection does not fare any better. The Czech variant ''Semidepotní injekce'' finds two hits&lt;ref&gt;https://medicinapropraxi.cz/pdfs/med/2012/09/07.pdf&lt;/ref&gt;, one of which wants me to confirm that I work in healthcare. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:29, 22 March 2025 (UTC)</text>
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    <title>User:Tommy Kronkvist</title>
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      <comment>User statistics.</comment>
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      <text bytes="2645" sha1="g7otfe5k8qzq0amlphbfbov5wh2j7o6" xml:space="preserve">&lt;div style=&quot;margin: 0 0 1em 0;&quot;&gt;{{userpage}}&lt;/div&gt;
{{Userboxtop|toptext=Babel:}}
{{#babel:sv|en-4|de-2|la-1}}
{{Userboxbottom}}
[[File:Sorbus torminalis Trunk and canopy.jpg|thumb|310px|The intracanopy of a Wild Service Tree, i.e. &lt;small&gt;''Torminalis glaberrima'' (Gand.) Sennikov &amp; Kurtto, ''Memoranda Soc. Fauna Fl. Fenn.'' 93: 32 (2017).&lt;/small&gt;]]&lt;br /&gt;
 
Most of my wiki contributions are made to [[:species:Main Page|Wikispecies]] where I'm an administrator, bureaucrat and interface admin,&lt;small&gt;&lt;sup&gt;[https://species.wikimedia.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Tommy_Kronkvist (verify)]&lt;/sup&gt;&lt;/small&gt; to the Swedish Wikimedia Chapter [[WMSE:|Wikimedia Sverige]] (WMSE) where I'm an administrator,&lt;small&gt;&lt;sup&gt;(&lt;span class=&quot;plainlinks&quot;&gt;[https://se.wikimedia.org/w/index.php?title=Special:Användare&amp;limit=1&amp;username=Tommy_Kronkvist verify]&lt;/span&gt;)&lt;/sup&gt;&lt;/small&gt; and as administrator and interface administrator at the Swedish version of [[wikivoyage:sv:Huvudsida|Wikivoyage]].&lt;small&gt;&lt;sup&gt;(&lt;span class=&quot;plainlinks&quot;&gt;[https://sv.wikivoyage.org/w/index.php?title=Special:ListUsers&amp;limit=1&amp;username=Tommy_Kronkvist verify]&lt;/span&gt;)&lt;/sup&gt;&lt;/small&gt;

So far (May 18, 2026), I've made just over 392,600 edits to 153 of the Wikimedia sister projects&amp;nbsp;– the majority of them to Wikispecies and Wikidata. My global account information for all of Wikimedia can be found [[meta:Special:CentralAuth/Tommy Kronkvist|here]].

Swedish is my mother tongue&amp;nbsp;– even though I was born in Finland&amp;nbsp;– but I feel comfortable speaking and writing English and to some extent in German as well. Odd as it may seem, unfortunately I can't speak any Finnish even though I went to school there for a few years prior to moving to Sweden (see [[w:Swedish-speaking population of Finland|Swedish-speaking population of Finland]] in Wikipedia). I've lived all over Sweden but nowadays reside in Uppsala, the fourth biggest city and former capital of Sweden.

I'm only the fourth generation named &quot;Kronkvist&quot;. My family name consists of two parts: ''kron'' – a short form of the Swedish word ''krona'' meaning 'crown', as in coronation crown or tree crown – and ''kvist'', meaning 'bough' or 'twig'. Hence the name ''Kronkvist'' refers to a twig in the canopy of a forest. I'm the fourth generation of Kronkvist's. Prior to that our family name was ''Mattus'': an oeconym meaning &quot;Matthew's Farm&quot;, dating back to at least 1637.
{{Clear}}
{{User committed identity|a6edd6d2fdbf82621f0cda4e5525c71f8da9b5dfd308242c3c63365e998c32c5406b75448380903265a5403edffd1a0435b61ac943f3c65870db9250f8b884a9|SHA-512|background=#e0e8ff|border=e0e8ff}}</text>
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  <page>
    <title>User:Dan Polansky/Transgender-related politics in Czechia</title>
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      <id>2810171</id>
      <parentid>2717000</parentid>
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        <username>Atcovi</username>
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      <comment>Atcovi moved page [[Transgender-related politics in Czechia]] to [[User:Dan Polansky/Transgender-related politics in Czechia]] without leaving a redirect: banned user + personal, unstructured, exploratory essays should be under userspace</comment>
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This article by Dan Polansky intends to investigate the transgender-related politics in Czechia/the Czech Republic, a small landlocked country in Central Europe, bordering on Germany, Austria, Poland and Slovakia (which borders on Orbán's Hungary), post-socialist, having about 10 000 000 inhabitants.

Initial questions:
* What support and opposition do transgender ideas (called by the opposition gender ideology) receive in Czechia from major political parties?
* What are the political positions of some major political figures in Czechia?
* What political entities (parties, politicians) use the phrase ''genderová ideologie'', ''transgenderová ideologie'', ''LGBT ideologie'' or similar?

== Political parties ==

In Czechia, the support and opposition of transgenderism/gender ideology by political parties is as follows:
* Socdem/ČSSD - a hint of support&lt;ref&gt;https://www.instagram.com/misasocdem/p/C7EmW5GsV5c/&lt;/ref&gt;; they seem to support Istanbul Convention&lt;ref&gt;[https://eu.socdem.cz/akt-aktuality/odpor-vuci-istanbulske-umluve-je-projevem-prazdnoty-takzvanych-konzervativcu/ Odpor vůči Istanbulské úmluvě je projevem prázdnoty takzvaných konzervativců] by Daniela Ostrá, 26 January 2024, socdem.cz (in Czech)&lt;/ref&gt;; search for &quot;transgender&quot; in site:socdem.cz did not find anything; in 2024 article, Daniela Ostrá, a member of Socdem, refers to the concept of gender in an accepting way and criticizes the opposition to the Istanbul Convention&lt;ref&gt;https://eu.socdem.cz/akt-aktuality/odpor-vuci-istanbulske-umluve-je-projevem-prazdnoty-takzvanych-konzervativcu/&lt;/ref&gt;.
* Greens - support&lt;ref&gt;https://www.zeleni.cz/lgbt/&lt;/ref&gt;
* Pirates - support&lt;ref&gt;https://www.pirati.cz/jak-pirati-pracuji/trans-lide-jste-krasni-k-spontanni-vyzve-piratky-gregorove-se-za-jediny-den-pripojilo-na-2000-lidi/&lt;/ref&gt;
* The right-wing Okamura's SPD - oppose&lt;ref&gt;https://www.spd.cz/nepodporeni-lgbt-ideologie/&lt;/ref&gt;&lt;ref&gt;https://www.spd.cz/odmitame-fialovou-vladou-vedenou-propagandu-lgbt-a-gender-na-skolach/&lt;/ref&gt;
* Nationalistic-conservative Trikolora - oppose&lt;ref&gt;https://volimtrikoloru.cz/komentare/stanovisko-trikolory-k-jednani-o-ratifikaci-istanbulske-umluvy/&lt;/ref&gt;&lt;ref&gt;https://volimtrikoloru.cz/clanky/obeti-tohoto-rezimu-zacina-byt-docela-dlouha-rada-kritizuje-predsedkyne-trikolory-zuzana-majerova/&lt;/ref&gt;
* Babiš's ANO - apparently oppose&lt;ref&gt;[https://www.facebook.com/watch/?v=297741249530219 Transgender lekce pro děti od šílenců v Německu] by Andrej Babiš, 1 Sep 2023, facebook.com&lt;/ref&gt;; however, a Google search for 'site:nobudelip.cz transgender' did not find anything.
* ODS - apparently oppose&lt;ref&gt;[https://www.ods.cz/clanek/20471-gender-vyhodite-dvermi-vrati-se-oknem Gender vyhodíte dveřmi, vrátí se oknem] by Jitka Chalánková, 19 January 2021, ods.cz&lt;/ref&gt;&lt;ref&gt;[https://www.ods.cz/clanek/17384-xtv-cz-genderova-ideologie-je-nebezpecna-vaclav-klaus-ml-si-neuvedomuje-sve-chyby-jde-proti-kolegum XTV.cz: Genderová ideologie je nebezpečná. Václav Klaus ml. si neuvědomuje své chyby, jde proti kolegům], 22 March 2019, ods.cz&lt;/ref&gt;
* STAN - unclear; they celebrated a decision of Constitutional Court to drop requirement of sterilization before sex change in identity documents was possible (or something of the sort)&lt;ref&gt;https://www.facebook.com/starostove/posts/lidsk%C3%A1-pr%C3%A1va-zv%C3%ADt%C4%9Bzila-%C3%BAstavn%C3%AD-soud-zru%C5%A1il-povinn%C3%A9-sterilizace-transgender-osob-/871054291731375/&lt;/ref&gt;, which is suggestive of support; Google web search for 'site:starostove.cz transgender' did not find anything
* Christian KDU-ČSL - apparently oppose&lt;ref name=czlobby&gt;https://czlobby.cz/stret-o-genderovou-ideologii-se-odklada-kontroverzni-smlouva-pocka-nez-pelikan-zmeni-zakony/&lt;/ref&gt;
* Conservative TOP 09 - apparently oppose&lt;ref name=czlobby/&gt;; on the other hand, they use the term LGBT (with T) without reservation&lt;ref&gt;https://www.top09.cz/files/soubory/toplife-c-12-evropu-uz-umime_2137.pdf&lt;/ref&gt;

The state of support and opposition to transgenderism can perhaps be tracked in the political debates about Istanbul Convention.

Believing polls for 2025 election, Greens, Socdem and Trikolora are unlikely to get into parliament and Pirates are likely to get a small number of seats.

On a related note, the right of center ODS seems to be agains same-sex marriage&lt;ref&gt;https://www.ods.cz/clanek/23082-pro-a-proti-cro-plus&lt;/ref&gt;.

== Political personalities ==

People from the Václav Klaus' Institute are opposed&lt;ref&gt;https://media.klaus.cz/files/news-plus-03-2019.pdf&lt;/ref&gt;; Václav Klaus is a former president, a free market champion, and a former member of ODS.

Miloš Zeman, a former Czech president and left-wing (Socdem under the former name ČSSD) politician, opposes transgenderism&lt;ref&gt;[https://www.bbc.com/news/world-europe-57635373 Milos Zeman: Czech president calls transgender people 'disgusting'], 28 June 2021, bbc.com&lt;/ref&gt;

As for Petr Pavel, the current (2025) Czech president, his positions seem transgenderism-friendly in principle&lt;ref&gt;https://www.echo24.cz/a/HEVvy/zpravy-domov-pavel-kritizuje-fiala-brusel-cesko-se-melo-pripojit-zaloba-madarsko-kvuli-lgbt&lt;/ref&gt;, but I could not find an explicit statement.

== Views of the general population ==

Views of Czechs can be glimpsed at a sport.cz article discussion&lt;ref&gt;https://www.sport.cz/diskuze/ostatni-odmitla-bojovat-s-transgender-souperkou-tak-sermirku-diskvalifikovali-5209277&lt;/ref&gt;, but that cannot replace a serious sociological polling. Similarly for an idnes.cz article&lt;ref&gt;https://www.idnes.cz/onadnes/vztahy/leyna-bloom-modelka-trans.A210322_081615_ona-vztahy_job/diskuse/1&lt;/ref&gt;. One would have to find out whether these discussion participants are unrepresentative of the general population in these regards.

== The Istanbul Convention ==
In January 2024, the Czechia senate rejected a ratification of the Instanbul Convention, which Czechia previously signed (but not ratified); the miss was by two votes&lt;ref&gt;https://www.reuters.com/world/europe/czech-senate-fails-ratify-european-treaty-violence-against-women-2024-01-25/&lt;/ref&gt;. Arguments against seem to include objections to the use of the word ''gender'' (or its Czech equivalent)&lt;ref name=nov1&gt;https://www.novinky.cz/clanek/domaci-senat-neschvalil-umluvu-40458478&lt;/ref&gt;; Michael Canov from STAN did raise the use of the term gender as the concern&lt;ref&gt;https://www.facebook.com/watch/?v=919865429657145&lt;/ref&gt;.

The Czech text of the convention is available online&lt;ref&gt;[https://rm.coe.int/1680462471 Úmluva Rady Evropy o prevenci a potírání násilí vůči ženám a domácího násilí], Rada Evropy, Istanbul, 11.V.2011&lt;/ref&gt;. It features e.g. this: 'pod pojmem “gender” se rozumí společensky ustavená role, chování, aktivity a atributy, jež daná společnost považuje za náležité pro ženy a muže'; the term &quot;gender&quot; is defined as socially established role, behavior, activities and attributes, which a given society considers appropriate for women and men (this is not checked to match the English version of the treaty but rather is a translation from Czech to English). It may be this definition, and the extensive use of the word ''genderový'' pointing to that definition that could have lead to opposition from more conservative parties.

The Czech text states: &quot;The official languages of the Council of Europe are English and French ( Article 12 of the Statute of the Council of Europe). Only the treaties published by the Secretary General of the Council of Europe, each in a separate booklet of the &quot;European Treaty Series&quot; (ETS) continued since 2004 by the &quot;Council of Europe Treaty Series&quot; (CETS), are deemed authentic. The translation presented here is for
information only&quot;. One would think that it is the English or French text that Czechia would be ratifying, not the Czech one. Peculiar.

According to novinky.cz (not generally realiable but let us hope they got this right), opposition to the Istanbul Convention included ODS, KDU-ČSL, ANO and SPD; the support for ratification was coming from TOP 09, STAN and Pirates.&lt;ref&gt;https://www.novinky.cz/clanek/domaci-istanbulskou-umluvu-cupuji-ods-i-opozice-40445185&lt;/ref&gt; However, part of TOP 09 eventually opposed the ratification&lt;ref name=nov1/&gt;.

Senator Zdeněk Hraba, formerly for STAN, later as independent (''nestraník'') for ODS, opposed The Instanbul Convention for its use of the langugage of gender&lt;ref&gt;[https://www.youtube.com/watch?v=aboYOnYZgBM Duel: Istanbulská úmluva je trojský kůň genderové ideologie, říká Hraba. Je neškodná, oponuje Šípová], DVTV, youtube.com&lt;/ref&gt;&lt;ref&gt;https://medium.seznam.cz/clanek/zdenek-hraba-umluva-ktera-si-na-boj-proti-nasili-jen-hraje-to-je-istanbul-41862&lt;/ref&gt;.

== Miscellaneous ==

Hungary, another post-socialist country in Central or Central-Eastern Europe, seems to be in a different league as for opposition to transgenderism, as per [[Wikipedia: LGBTQ rights in Hungary]].

In 2024, the Czech Constitutional Court removed the requirement of physical sex change (surgery, including castration?) before a legal recognition of a sex change&lt;ref&gt;https://www.reuters.com/world/europe/czech-court-removes-surgery-requirement-gender-transition-2024-05-07/&lt;/ref&gt;&lt;ref&gt;https://www.usoud.cz/aktualne/chirurgicky-zakrok-vcetne-sterilizace-jako-podminka-uredni-zmeny-pohlavi-neobstal-pred-ustavnim-soudem&lt;/ref&gt;. The court's communication uses the Czech word ''pohlaví'' (sex) rather than ''gender''. What is terminologically going on here is hard to tell. It seems that it is going to be possible to change one's ''pohlaví'' (sex) based on self-identification. The decision requires the legislators to take a legislative action, which has not yet (14 April 2025) been taken. In Czechia, the supermajority for changing (including clarifying) the constitution is 60%&lt;ref&gt;https://www.psp.cz/sqw/hp.sqw?k=308&lt;/ref&gt;; we will see whether this decision is going to prompt an attempt to change the constitution by parties opposing this kind of legislation (sex and gender related changes were made to the Hungarian constitution).

== References ==
&lt;references/&gt;

== Further reading ==
* {{W|LGBTQ rights in the Czech Republic}}, wikipedia.org
* {{W|Recognition of same-sex unions in Europe}}, wikipedia.org
* {{W|Recognition of same-sex unions in the Czech Republic}}, wikipedia.org
* [[W:cs:Úmluva Rady Evropy o prevenci a potírání násilí vůči ženám a domácího násilí#Proces přijímání v České_republice]], wikipedia.org
* {{W|Istanbul Convention#Czech Republic}}, wikipedia.org
* {{W|2021 Czech parliamentary election}}, wikipedia.org
* {{W|2025 Czech parliamentary election}}, wikipedia.org
* [https://jsmetransparent.cz/ Transparent], jsmetransparent.cz -- a trans support group
* [https://www.youtube.com/watch?v=fj4zhnGqhz0 Komediograf - Muž Ondatra], youtube.com -- a Czech television skit about a man who wants to be a muskrat, which possibly hints at transgender (it talks about regular intake of muskrat hormones)

[[Category:Transgender]]
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This article by Dan Polansky looks at language (human natural language), containing somewhat idiosyncratic notes, observations and deliberations on the subject.

I see language above all as a tool of thought (and deliberation), not of communication. It is in fact a tool of both and which of the two uses is primary and in what sense of primary is debatable. The idea that the primary function of language is as a tool of thought is found in literature; from memory, I think Chomsky has this idea. Whether language originated by the pull created by its use in communication within a tribe of early humans or their ancestors is a separate matter: in biological evolution, a feature evolved for one purpose can then be reused for different purposes.

Functions of language were treated of by Bühler as mentioned by Popper; from what I remember, there were five functions. Popper mentiones argumentative function of language as a separate function, different from descriptive (I think).

If we see language as a tool of thought, a tool of inference and getting to know, then our mastery of the tool would seem to be a contribution to correct inference, desired by anyone interested in correct inference. And who of us wants to be fooled/deceived, by other people or by one's own erroneous thinking by means of language?

The Sapir–Whorf hypothesis hypothesis states, by my understanding, that the language we have at our disposal limits and shapes what we are able to think. I find this rather compelling. However, language is extensible; we can create new words to capture newly discovered entities and phenomena. Scientists are coining new terms all the time. To wit, most names of chemical elements are a relatively recent creation. A reservation: perhaps my understanding of what this hypothesis is about is wrong. I would like to do more reading on it.

The diagnostic/epistemic value of language is hinted at by Robert Pirsig. His exhortation to write thing down during diagnosis as part of motorcycle maintenance is to write words down, not to sketch drawnings. His description of the formal scientific methods emphasized careful record keeping, by means of natural language. Sure enough, these things written down have the benefit to be easily communicable. But that is added value, not the essense of their use during the diagnostic process.

The above initial considerations hint at a key source of my interest in language: as a tool of thought, including argument and counterargument. This leads to interest in semantics and certain parts of philosophy. It does not lead to interest in phonology and inflection; I could not care less. These, to my mind, are not serious linguistic fields and concerns. By contrast, I find etymology supremely interesting, but why that is requires an explanation especially given the etymological fallacy principle which points out that etymology does not necessarily drive semantics.

The simplification of English (from Old English to Middle English and Modern English), resulting in dropping of gender and large parts of inflection, are, from my perspective, getting rid of burdensome unnecessary parts and keeping what really matters. We could have much worse language than English as lingua franca/the one world language; Latin has much more complex inflection. That English is written in pronunciation-relating letters rather than e.g. Chinese characters/ideographs is an additional bonus. What one can perhaps complain about in English is the hybrid character, by which it features two systems of morphology or quasi-morphology: the English one and the Latin-based/Romance one. By quasi-morphology I mean e.g. the breakdown of ''inscription'' into ''in-'', ''scrib-'' and ''-(t)ion''. Another complaint is that too many English verbs have too many senses. As a bonus, with English we get access to excellent philosophy that originated in English; to my mind, no language can compete with English as a carrier of excellent philosophy, not French and not German, two likely prime competitors; only Latin could perhaps be claimed to outperform English, being the former lingua franca of philosophy. But these are asides. There does not seem anything special about French and German that should prevent them from being carriers/vehicles for good philosophy, and they are carriers/vehicles for some excellent philosophy.

One question that I used to ask is whether language works. Since, especially in philosophy, there is a suspicion that it does not. A first-impression answer is a resounding yes. The ability of language to aid humans in their various objectives, including their massive biological expansion, is remarkable. It is in philosophy where doubt arises as more plausible. Perhaps language is good in talking about men, women, children, rivers, mountains, valleys, stars, planets, gold, silver, food crops, medicines, buildings, roads, bridges, manufacturing processes, etc., but it is perhaps not so good in talking about Aristotelian substances, qualities, ethics,  etc. My impression is that language can be made to serve philosophical enterprise rather well, if one is careful enough in using this tool. That too many bunglers have misused this tool is no automatic indictment of the tool. As Kuhn says in a different context, it is a poor carpenter who blames his tools.

One could want to design an unambiguous language, or at least one with very good correspondence between words and concepts/word meanings. Artificial languages have been designed, e.g. Esperanto, but I do not know whether unambiguity was a design objective and whether it was achieved to some extent (I could find out with a bit of effort). The language of OmegaWiki defined meanings and WordNet synsets would be an unambiguous one (OmegaWiki is currently down), but WordNet synsets are not single words so this is impractical. Wikidata Q-numbers provide an unambiguous language, but we do not want to talk in q-numbers (as a partial example, &quot;I saw a Q487975 over there&quot;, oh, right).

Language is sometimes said to be not logical. This is misleading; language cannot violate the canons of logic. What this points to is that pattern-based expectations often fail as a result of language being more irregular than it could be if one made appropriate changes to it. For instance, &quot;here&quot; and &quot;where&quot; are not pronounced similarly. For another case, many words are not morphological sum of parts, so semantics derived from morphology turns out to be incorrect. English past participles are often formed regularly (and thus, &quot;logically&quot;), e.g. &quot;shined&quot;, but not &quot;swam&quot;. Most natural language probably show odd irregularities that an analogue of straightening out rivers could remove; I know this to be the case in English, German and Czech. This points to natural language being something like a natural object, despite apparently being a product of a mind; it is not a result of careful systematic engineering aiming at optimization of specified objectives/criteria.

On prescriptivism and descriptivism. Above all, descriptivism does not state that anything goes. A Martian observer could note that language users readily recognize possible variations on the commonly used language as not part of the language; in general, language users do not need a manual or a grammar book to aid in this recognition (small children can do it). Rather, descriptivism points out that there are too many clowns/bozos/frauds peddling invented norms that do not match general usage patterns. However, not all things looking like prescriptivism are bad. Specifications of stylistic preferences shape language and there is nothing wrong with it. But they are not language science but rather something like language engineering. An example of stylistic preference in contrast to prescriptivism is &quot;I find X preferable for reason R&quot; as opposed to &quot;X is incorrect&quot;. And a similar descriptivist statement is &quot;Many language users find X preferable and claim Y (an altenative to X) to be incorrect but Y is widely used by competent and reputable language users&quot;. Since we have river engineering, why not language engineering?

== See also ==
* [[An analysis of truth]]
* [[One man's look at proper names]]

== Further reading ==
* {{W|Language}}, wikipedia.org
* {{W|Sapir–Whorf hypothesis}}, , wikipedia.org 
* {{W|Karl Bühler}}, wikipedia.org
* {{W|Karl Popper}}, wikipedia.org
* {{W|Robert Pirsig}}, wikipedia.org
* {{W|Zen and the Art of Motorcycle Maintenance}}, wikipedia.org

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This article by Dan Polansky takes a cursory look at LibreOffice (a cousin of OpenOffice), especially evaluative look. It is minimal and idiosyncratically organized.

LibreOffice is a 2010-fork of OpenOffice, which is a result of open sourcing StarOffice in 2000&lt;ref&gt;[https://www.openoffice.org/about_us/milestones.html OpenOffice.org History and Milestones], openoffice.org&lt;/ref&gt;. StarOffice was a proprietary office suite that Wikipedia says originated in 1985 as StarWriter by Star Division, a German software company.&lt;!-- TBD: better source than Wikipedia --&gt;

== Initial questions and observations ==

Some questions:
* Can LibreOffice compete with Microsoft Office in the market?
* Is the ease of use of LibreOffice as good as the one of Microsoft Office?
* Is LibreOffice as powerful/feature-rich as Microsoft Office?
* Which organizations adopted LibreOffice as their office platform?
* What are the download statistics for LibreOffice?
* Is LibreOffice using some cross-platform graphical toolkit (its own toolkit)? If so, can that toolkit contribute to slowness? (Not answered.)
* Where can one find a decent collections of example macros for LibreOffice Basic (or whatever else the Basic dialect is called)? (Not answered.)

Some observations/estimates/guesses/opinion:
* As of 2025, 25 years after LibreOffice/OpenOffice became FOSS as a result of open sourcing StarOffice, LibreOffice does not seem to see adoption and success anywhere close to Linux, the spectacular success.
* LibreOffice does not seem to support Microsoft's VBA (Visual Basic for Applications, used for scripting and programming). This makes it generally incompatible with Microsoft Office. VBA is an extremely powerful feature, making Microsoft Office a programming platform. From my experience, it is especially Excel VBA that is the killer; Word VBA and Powerpoint VBA less so. Perhaps the Access VBA is also rather useful; I have no experience with that. I vaguely remember (and would have to verify) that one of SAP's major products used Excel with VBA as a frontend, as if Excel with VBA was a web browser/presentation layer.
* A personal anecdote/case: recently in 2025, I created a new docx document (the modern MS Office Word format) in LibreOffice, with some tables. I tried to open it in Microsoft Office on a different computer and it failed to open. I opened the document in an old version of LibreOffice on that computer, and it did open, but the order of columns was changed. To ensure proper opening in other people's environments, I converted the document to pdf. If this experience is all too typical, this would explain why LibreOffice sees rather little adoption.
* It is great to have LibreOffice (and OpenOffice) available; it is a meaningful project. But at this stage of quality achieved, it seems unlikely it will achieve anything like Linux success in the forseeable future. LibreOffice seems to be no threat to Microsoft Office quasi-monopoly.
** A personal anecdote/case: I recall that when I was working at SAP in Germany (2001-2006), colleagues from product management received some Microsoft Office documents that failed to open in Microsoft Office. They succeeded opening these documents in what was then probably OpenOffice (of which LibreOffice is a fork). This substantiates LibreOffice's value as a backup solution.
* LibreOffice can perhaps achieve the best success on the native document format rather than Microsoft's ones.
* LibreOffice's unique differentiator appears to be in its providing an office suite for Linux, at least a half-usable one. Microsoft desktop Office does not support Linux&lt;ref&gt;[https://answers.microsoft.com/en-us/msoffice/forum/all/office-365-on-linux-is-possible/cd82052c-574a-4053-bfb8-32aac8098883 Office 365 on linux is possible ? - Microsoft Community], answers.microsoft.com&lt;/ref&gt;

== Adoption ==
LibreOffice's own &quot;who uses LibreOffice&quot; lists government entities (a fairly small number of them) but no business entities (except indirectly by reference to Czech companies)&lt;ref&gt;[https://www.libreoffice.org/discover/who-uses-libreoffice/ Who uses LibreOffice?], LibreOffice&lt;/ref&gt;. The following users are listed:
* France: MIMO, France's inter-ministerial working group on free software
* France: a list of users merely linked to&lt;ref&gt;[https://comptoir-du-libre.org/en/softwares/usersSoftware/33 Users of LibreOffice], comptoir-du-libre.org -- perhaps users from France&lt;/ref&gt;
* Spain: The administration of the Spanish autonomous region of Valenci
* Italy: Italy's Ministry of Defence
* Taiwan: Taiwan's Ministry of Finance
* Brazil: Brazil's UNESP - Universidade Estadual Paulista
* Czechia: multiple companies, schools and other organisations without being listed at that page, but are listed at cs.libreoffice.org&lt;ref&gt;[https://cs.libreoffice.org/discover/who-uses-libreoffice/odpovedi-na-dotaznik/ Odpovědi na dotazník | LibreOffice], cs.libreoffice.org (in Czech) -- self-reports by organizations in Czechi that they use LibreOffice&lt;/ref&gt;

As per Computer World 2025: '“We estimate around 200 million [LibreOffice] users, but [...] we respect users’ privacy and don’t track them, so we can’t say for sure,” said Mike Saunders, an open-source advocate and a deputy to the board of directors at The Document Foundation.'&lt;ref&gt;[https://www.computerworld.com/article/3840480/libreoffice-downloads-on-the-rise-as-users-look-to-avoid-subscription-costs.html LibreOffice downloads on the rise as users look to avoid subscription costs – Computerworld] by Agam Shah, 6 Mar 2025, computerworld.com&lt;/ref&gt; As long as no substantiation/breakdown of that estimate is available, this information should be taken with a caution. The figure of 200 million was also quoted in a comment from 15 Oct 2020 by Mike Saunders&lt;ref&gt;https://blog.documentfoundation.org/blog/2020/10/12/open-letter-to-apache-openoffice/&lt;/ref&gt;&lt;!-- TBD: merge the ref? --&gt; as well as a 25 Sep 2018 article&lt;ref&gt;https://opensource.com/article/18/9/libreoffice-history&lt;/ref&gt;.

As for Germany, Schleswig-Holstein seemed to had been switching to LibreOffice in 2024&lt;ref&gt;[https://www.zdnet.com/article/german-state-ditches-microsoft-for-linux-and-libreoffice/ German state ditches Microsoft for Linux and LibreOffice], 4 April 2024, zdnet.com&lt;/ref&gt;.

Munich seems to have planned to adopt Linux + LibreOffice, but eventually cancelle the project.

The rest is delegated to further reading.

Further reading:
* {{W|LibreOffice#Users and deployments}}, wikipedia.org
* [https://www.libreoffice.org/discover/who-uses-libreoffice/ Who uses LibreOffice?], LibreOffice
* [https://wiki.documentfoundation.org/LibreOffice_Migrations LibreOffice Migrations], wiki.documentfoundation.org
* [https://theirstack.com/en/technology/libreoffice/de List of companies that use LibreOffice in Germany (40)],  TheirStack.com

== Download statistics ==
Some kind of download statistics is available from documentfoundation.org&lt;ref&gt;[https://stats.documentfoundation.org/downloads#week,version LibreOffice Download Metrics], stats.documentfoundation.org&lt;/ref&gt;. The form is one of a chart with numbers/figures available on a mouseover. However, it seems hard to determine the total number of downloads per release/version, which would be a vital statistic. One could perhaps write a Python script to parse the source of the web page and calculate that statistic.

By contrast, OpenOffice statistics is available from SourceForge on a per version/release basis&lt;ref&gt;https://sourceforge.net/projects/openofficeorg.mirror/files/stats/timeline&lt;/ref&gt;. For instance, one can query the statistics for version 4.1.15 and note over 25,600,000 downloads as of 28 Sep 2025&lt;ref&gt;[https://sourceforge.net/projects/openofficeorg.mirror/files/4.1.15/binaries/stats/timeline?dates=2023-02-03%20to%202025-09-28 Apache OpenOffice Download Statistics: 4.1.15/binaries], sourceforge.net&lt;/ref&gt;.

Some numbers are presented in [[Wikipedia:LibreOffice#Users and deployments]]. It states that &quot;From 2011 to 2018, the estimated number of LibreOffice users grew from 25 million to 200 million&quot; and points to [[:File:LibreOffice weekly downloads.svg]] chart. And then, &quot;For comparison, Microsoft Office had an estimated 1.2 billion users in 2018.&quot; I find the 200 000 000 figure hard to believe; the numbers do not come from an independent organization critically (aiming to find error) analyzing the estimates. In 2012, Rob Weir (a software engineer who helped establish the OpenOffice project at Apache) cast doubt of LibreOffice work with statistics&lt;ref&gt;[https://www.robweir.com/blog/2012/10/libreoffices-dubious-claims-part-i-downloads.html LibreOffice’s Dubious Claims: Part I, Download Counts] by Rob Weir, 2012&lt;/ref&gt;. Of course, he will have a vested interest to be critical and is not necessarily unbiased either. Moreover, whether his 2012 criticism still applies to 2025 is a question. One thing is certain: there is no obvious way to get the total number of downloads for a given release, for LibreOffice.

== Example macros for Basic ==
Examples macros for LibreOffice Basic [term?] can be found in the links below. (Macros can also be written in Python and other languages, but Basic is most suggestive of similarity to Microsoft VBA for applications. On the other hand, LibreOffice Basic is not compatible with Microsoft VBA anyway&lt;ref&gt;https://wiki.documentfoundation.org/Documentation/BASIC_Guide&lt;/ref&gt;)

Subjective impression: the macros found in the links below suggest the way one uses Basic to write macros for LibreOffice is cumbersome (the API is cumbersome). An implied requirement of compatibility and continuity with old LibreOffice versions (and file format, as long as they are stored in the document files?) suggests the cumbersomeness is not going to be removed or addressed any time soon.

Links:
* [https://wiki.documentfoundation.org/Macros/Calc Macros/Calc], wiki.documentfoundation.org
* [https://wiki.documentfoundation.org/Category:Macros Category:Macros], wiki.documentfoundation.org
* [https://wiki.documentfoundation.org/Macros/Calc/ba001 Copy content cell from Spreadsheet to other], wiki.documentfoundation.org

== File format ==
As of 2025, the primary supported file format is the OpenDocument Format (ODF) (a zipped xml?). This is not the historical file format of StarOffice (a proprietary suite from which OpenOffice was created).

There is some support for reading and writing the newer Microsoft Office file format, but there is no VBA compatibility and a report I placed above suggests the support is far from perfect also in other regards.

The ODF file format is perhaps best suitable for files to be used in open collaborative environments such as wikis, including Wikipedia and Wikiversity. Since, not every user is on Windows and not every Windows user has a Microsoft Office license (and there are macOS users). But almost anyone can be asked to install LibreOffice for free and edit the file using it. This presents unique value of LibreOffice. (Admittedly, LibreOffice can also read and write Microsoft formats, but probably less reliably.)

An extensive table of supported file formats is in Wikipedia.

Support for legacy binary forat SDW, SDC etc.: User Etc Etera indicated in a comment from 25 Sep 2018 that LibreOffice at some point stopped support for its previous [binary?] document format, SDW, SDC, etc. (the comment indicates OpenOffice did the same later)&lt;ref&gt;https://opensource.com/article/18/9/libreoffice-history&lt;/ref&gt;. The comment matches release notes for version 4.0&lt;ref&gt;https://wiki.documentfoundation.org/ReleaseNotes/4.0&lt;/ref&gt; (release 4.0 seems to have been released in 2013). Wikipedia indicates the support was added back in release 5.3, but that seems to have been no full reversal of the removal but rather from the scratch implementation of a new filter, with unclear match to the old functionality; namely: &quot;StarOffice binary files (.sdc, .sda and .sdw) can again be imported, via libstaroffice (Laurent Alonso) [...] This filter is written from scratch and it is at an early development stage. So it should be able to convert simple files but it could (and probably will) fail badly on more complex ones.&quot;&lt;ref&gt;https://wiki.documentfoundation.org/ReleaseNotes/5.3&lt;/ref&gt;. The project of the filter indicates that &quot;actually it is only at the early stages&quot;&lt;ref&gt;https://github.com/fosnola/libstaroffice/wiki&lt;/ref&gt;.

Links:
* {{W|LibreOffice#Supported file formats}}, wikipedia.org

== LibreOffice vs. OpenOffice ==
The two projects, LibreOffice and Apache OpenOffice, can be seen as direct competitors, stemming from a shared codebase. My superficial impression:
* Apache OpenOffice provides a stable package that sees relatively few changes. Some may prefer it in part for that reason. As of 28 Sep 2025, the latest release is Apache OpenOffice 4.1.15 from 22 Dec 2023&lt;ref&gt;https://www.openoffice.org/&lt;/ref&gt;.
* LibreOffice sees quite a lot of changes and many more substantial releases. This also increase chances that something will get broken. As of 28 Sep 2025, the latest stable release is LibreOffice 25.8 from a date I cannot quickly determine; its release note wiki page was created on 9 Dec. 2024&lt;ref&gt;https://wiki.documentfoundation.org/WikiAction/history/ReleaseNotes/25.8&lt;/ref&gt;, which was probably earlier than the actual release?

libreoffice.org provides a superficially compelling comparison table suggestive of LibreOffice being preferable (no suprise here, coming from libreoffice.org, but the table seems fine)&lt;ref&gt;[https://www.libreoffice.org/discover/libreoffice-vs-openoffice/ LibreOffice vs OpenOffice], libreoffice.org&lt;/ref&gt;. Let me single out that, allegedly, LibreOffice can export to Microsoft's formats for .xlsx, etc. (which they probably incorrectly identify as &quot;Microsoft Office OOXML formats&quot;) while OpenOffice cannot.

Further reading:
* [https://www.linux-magazine.com/Online/Features/LibreOffice-vs-OpenOffice LibreOffice vs OpenOffice], date unclear but the oldest archive.org version&lt;ref&gt;https://web.archive.org/web/20220209181218/https://www.linux-magazine.com/Online/Features/LibreOffice-vs-OpenOffice&lt;/ref&gt; is from 9 Feb 2022, linux-magazine.com
* [https://blog.documentfoundation.org/blog/2020/10/12/open-letter-to-apache-openoffice/ Open Letter to Apache OpenOffice] by Mike Saunders, 12 Oct 2020, blog.documentfoundation.org

== Miscellaneous ==
As a marginal note, let us recall other schisms and forks: GNU Emacs vs. XEmacs, GCC vs. EGCS, FreeMind vs. Freeplane, and MySQL vs. MariaDB.

== Alternatives ==
Alternatives include {{W|Microsoft Office}}, {{W|OnlyOffice}} and {{W|Gnumeric}} (and the cousin {{W|Apache OpenOffice}}). For online storage in the cloud, there are Google Docs.

Charts to be exported to SVG can be created using Python's matplotlib library; code for it can be generated using GenAI (if one is programming shy). SVG (vector graphics) editing software include {{W|Inkscape}}.

== References ==
&lt;references /&gt;

== Further reading ==
* {{W|LibreOffice}}, wikipedia.org
* [[Commons: Category:Created with LibreOffice]], commons.wikimedia.org
* [https://www.libreoffice.org/ libreoffice.org], libreoffice.org
* [https://www.dedoimedo.com/computers/libreoffice-adoption.html The biggest blocker to LibreOffice adoption? LibreOffice.], 30 September 2023, dedoimedo.com
* [https://news.ycombinator.com/item?id=31634704 Ask HN: Has anyone successfully used LibreOffice for their business?], Hacker News</text>
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      <text bytes="1908" sha1="lukrtzwx40bkkm9fgkldbntpbuwa4ta" xml:space="preserve">== How many beings are there ==
(I am posting it here since I do not want to worry about the integration into the main article. I also do not need to worry all that much about going on a tangent.)

I have noted that beings are something like monadic predicates or correspond to monadic predicates. Monadic predicates can be looked at intensionally or extensionally. An intensional look could be via a computer program/algorithm or more broadly via a formula of first-order-logic, perhaps a formula of Peano arithmetic. In the extensional look, a being is (or corresponds to) a set of all entities of which the being is predicated/said of rather than denied.

The extensional look tells us that the answer about how many beings there are probably does not have a reasonable answer. For a start, we may ask how many beings there are of positive integers. Being an even number is an example applicable being. In this domain, the count of beings is the count of sets of positive integers. The sets of positive integers are more plentiful than the positive integers.

And then, we can move away from the domain of positive integers to the domain of sets of positive integers. The beings applicable to the latter domain are again extensionally given as sets, here sets of sets of positive integers. These are even more plentiful. (This all follows from the set theory tought in introductory courses at various universities.)

And then, since every set can be interpreted as an extension of a being (or property?), there would be as many beings as there are sets. But I suspect that the question how many sets there are does not have an answer (sure enough, we have to pick a particular set theory to technically investigate the question), e.g. Zermelo–Fraenkel.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:04, 3 May 2025 (UTC)</text>
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This article by Dan Polansky looks at the ethics and legality of using an ad blocker in a web browser. The key questions are:
: Is using an ad blocker in a web browser unethical?
: Is using an ad blocker in a web browser illegal?
One could think it is unethical. The web sites serving ads derive revenue from ads. One can argue that he who uses an ad blocker makes use of a valuable information artifacts without paying the analogue of price that the supplier of the artifact requests to be paid, which is exposure to ads. This may have the consequence that it becomes economically unfeasible for the supplier to provide the artifacts. But even if it does not become unfeasible, the one using an ad blocker would be something like a free rider, not quasi-paying for something for which others are quasi-paying (assuming only a fraction of users use ad blockers). Moreover, for a content provider, an alternative to going out of business is to place the content behind a paywall; it is the free riders who would then contribute to everyone else's becoming unable to quasi-pay with one's attention for content, having to pay with money.

One who has the above ethical concern yet does not want to give up on using an ad blocker entirely can proceed in a differentiated manner. One option is to explicitly block ads only on the web sites whose ads are particularly intrusive. One would argue that intrusive ads are unethical and that blocking someone else's unethical conduct is not unethical. However, one could counter that even with intrusive ads, the web site operator is not forcing anyone to use the web site and that the user is free to accept or reject the implied contract/agreement by which the operator offers the content under the condition that intrusive ads are served.

One could even argue that using ad blockers is illegal (a copyright violation), in the U.S. at least. Since, in order to view a web page, one has to make a ''copy'' of it in a web browser. One can do so, but only under the license provided by the web page provider. The license is usually ''implied'': it is implied that the web page provider gives license to viewers to make such a copy in a web browser or else the provider would not serve the page in the first place. But it is similarly implied that the license in an ad-serving web site requires the ads to be served.

There is some debate about whether web site's blocking ad blockers (preventing full load when an ad blocker is detected) is illegal, a different question, going in the other direction.

Technically minded users do not need to use ad blockers to achieve the same effect, though. One can use a site-specific CSS to hide selected elements from web pages. On the other hand, it is much more work, needed on a per site basis. Be it as it may, the ethical and legal questions are the same: is it ethical? Is it illegal, a copyright violation by violating the implied license?

The rest is currently delegated to further reading.

Key concepts/entities: ads, unintrusive ads, intrusive ads, ethics, duty, honor, revenue, quasi-payment, free rider, attention, economic feasibility, availability, paywall.

== Further reading ==
* {{W|Ad blocker}}, wikipedia.org
* [https://www.quora.com/Are-ad-blockers-ethical-1 Are ad blockers ethical?], quora.com
* [https://www.prindleinstitute.org/2018/08/the-moral-question-of-ad-blocking/ The Moral Question of Ad-Blocking], prindleinstitute.org
* [https://blogs.cornell.edu/info2040/2017/10/19/the-ethicality-of-ad-blocking/ The Ethicality of Ad Blocking], blogs.cornell.edu
* [https://blog.practicalethics.ox.ac.uk/2015/10/why-its-ok-to-block-ads/ Why It’s OK to Block Ads] by James Williams, 16 October 2015, blog.practicalethics.ox.ac.uk -- links to four other sources at the beginning
* [https://adage.com/article/digitalnext/ad-blocking-unnecessary-internet-apocalypse/300470/ Ad Blocking: The Unnecessary Internet Apocalypse], adage.com
* [https://blog.getadmiral.com/is-adblocking-illegal Is Adblock Illegal?], blog.getadmiral.com</text>
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This article by Dan Polansky is to contain various notes on economics, idiosyncratically organized. One hope is that someone is going to find them useful as well.

I have read Economics textbook by Samuelson and Nordhaus many years ago, so some notes based on memory can be based on that book.

== Scientific character ==
One key question is whether economics is a science, quasi-science or pseudoscience. Economics seems likely to fall short of the scientific standards applied to such physical theory as Newton's mechanics and Einstein's special relativity.

Some economics reads like philosophy applied to economic questions.

Whatever the case, my impression is that economics features a lot of interesting and compelling ideas. We cannot do without dealing with economic questions; we have to find a way of at least tentatively answering them, one way or the other.

== Some items to cover ==
* Allocation of scarce resources
* Sunk cost; Concorde
* Economic rationality of humans and its constrains
* Competing concerns and interests; limits of economic output
* Supply and demand curves in microeconomics
* Supply and demand curves in macroeconomics; aggregate demand, price level, GPD or GNP as an intersection of aggregate curves
* Maynard Keyness vs. Milton Freeman; fiscal vs. monetary policy; Keynessian multiplier
* Money, gold-backed money, fiat money, store of value, inflation, causes of inflation
* Money supply, various monetary aggregates (or whatever they are called)
* Kenneth Arrow; the game theory and its application to economics
* Comparative advantage
* Globalization vs. autarchy, tariffs, trade wars, World Trade Organization
* Capital, investment, return on investment, interest, the time value of money (net present value)
* Accounting, ledger, etc.
* Assert prices including share prices, their development in time, fractal scaling
* Efficient market hypothesis, option pricing, Black-Sholes formula (see also Mandelbrot)
* Monopoly, quasi-monopoly, oligopoly
* Etc.

== Inflation ==
Inflation is the change of price levels. To be calculated/determined, inflation has to be referred to a particular basked of goods/items. Thus, there is e.g. a change of consumer prices vs. a change of building material prices. When media report inflation, they usually report in relation to some kind of consumer basket since that is what the population at large is likely to be most interested in.

The chief cause of inflation seems to be expansion of money supply; Milton Friedman thinks so. There are other factors (e.g. artifically created scarcity of petroleum), but these have hardly ever caused anything like the insane&lt;!--TBD: better wording--&gt; inflation levels caused by money supply increase, at least in the 20th and 21th century. The adverse effects of runaway inflation are such that one can ask whether the flood-like printing money seen in hyperinflation is somehow caused by a disruptive operation of secret agencies of hostile countries (perhaps not); the irrationality of such an action seems to defy understanding.

Inflation that fiat money is exposed to is one of the chief causes of demand for gold, part of the demand for real estate and cryptoassets (sometimes called cryptocurrencies).

Inflation seems to bring about a redistribution of wealth from creditors to debitors, for debt relations denominated in the inflated currency. Thus, beneficiaries of central-bank-caused inflation include the excessively spending state but also entrepreneurs taking debt.

The current international view seems to be that mild inflation (say, 2%) is good for economic growth and should be aimed at. Intuitively, one may think that money owners spend on investment as a hedge to inflation, and therefore, inflation nudges them to engage in investment or in consumption. From what I recall, there is a debate on this; some economists would defend absence of inflation or changing periods of mild inflation and mild deflation as preferable. Be it as it may, the central banks in general seem to be failing to meet their 2% targets, so something seems very astray.

== Externalities ==
The concept of externalities is key to environmental economics, but has also other applications. An externality is something like cost or harm that does not enter into accounting as cost item and that the producer of the externality does not pay for. For instance, a chemical plant can release harmful substances into water without having to compensate anyone; and the harmful substances can have tangible consequences, e.g. reduction of fish one can fish (I made this example up; better source one from serious literature).

One brand of environmental economics argues that instead of outright prohibiting certain activities or effects of them, it is advisable to tax them.

(Reservations: above, I mixed up externality with ''negative'' externality; there are also ''positive'' externalities.)

Further reading:
* {{W|Externality}}, wikipedia.org
* [https://www.britannica.com/topic/externality-economics externality], britannica.com -- topic finding multiple articles
* [https://www.britannica.com/topic/negative-externality negative externality], britannica.com

== Further reading ==
* {{W|Economics}}, wikipedia.org
* https://open.umn.edu/opentextbooks/subjects/economics</text>
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This article by Dan Polansky looks at relativism.

In my view, there are reasonable and unreasonable forms of relativism (as opposed to absolutism?). One could perhaps call the reasonable forms moderate and the unreasonable radical or extreme, but whether that is a good plan would need an investigation.

Let me start with cultural relativism. Language is part of culture. And what to call what is ''relative to a particular language''. Thus, as for the question &quot;what shall we call that object over there?&quot;, the English answer is, say, ''tree'', whereas the German answer is ''Baum''. But which is correct? That question does not make sense; within the English lexical convention, ''tree'' is correct, and within the German lexical convention, ''Baum'' is correct. That seems very reasonable. Let us move further to banking, to interest calculation, specifically to ''day count convention''. Different countries use different day count conventions. But which is correct? They all work reasonably well and neither is really &quot;correct&quot;. One might thus conclude that in interest calculation, anything goes. But nothing could be farther from truth. Here, multiple conventions are workable and make sense, but they are just a tiny fraction of the space of all possible conventions. The same is true of natural language: all natural languages need to have words short enough to neatly fit into a human mind. And thus, all natural languages are just a tiny portion of the space of all possible languages, not only because of the total quantity (which is a trivial point) but because any actually used language needs to meet nontrivial functional requirements relating to human psychology on one hand and the world being described on the other hand.

The good thing about cultural relativism is that it teaches one not to confuse one's conventions for the only correct way of doing things. It leads to ''pluralism''. But pluralism is not anything-goes-ism.

The (arguably) bad thing about cultural relativism or certains forms of it is that it denies the objective validity of morals. Thus, each set of morals is relative to a particular culture (or cultures), and none is better or more correct than the other. Even if this would somehow be theoretically true, it is eminently impractical. No society can possibly tolerate any cultural practice. For instance, countries that codify marriage as monogamous in law are disinclined to tolerate polygamous marriages. Most western countries do not tolerate people walking on the streets naked even if this practice would be likely tolerated in a different culture. Most western countries will not tolerate intentional killing of people who fall away from a certain religion, regardless of the standard cultural practice of that religion. It follows that religious tolerance is in practice extremely constrained and has to be that way.

But there is even a good thing about cultural relativism in the field of analysis of value and norm. It can teach one to state value assumptions and derive value statements from there. One is reminded that the value assumptions that seem obvious to one are not universally accepted across the world. In serious analysis, being explicit about assumptions or foundational starting points is likely often useful.

Another item possibly worth mentioning are geometries. In mathematics, there is no one true geometry; there is the Euclidean geometry, hyperbolic geometries etc. Some are likely to point to that fact as a proof that there is no absolute truth and everything is relative to the speaker. That is not so. As a mathematical theory, a geometry's theorems indeed depend on the axioms. As a physical theory, a geometry has worse or better fit to the physical world (in Newtonian mechanics, the Euclidean geometry was thought to accurately fit the world). Moreover, an axiomatic theory still has to have some features to be a geometry at all rather than e.g. an arithmetic theory. No, it is not true that anything goes, that all is relative and that truth, reality and value are somehow &quot;constructed by discourse&quot;, whatever that is supposed to mean.

A relativist can further point to logics: there is not only the classical logic but also, say, the intuitionist logic, weaker than the classical one. The relativist can then claim that all mathematical proofs executed using the classical logic do not establish the absolute truth of the theorems since that truth is relative to the logical framework employed. Thus, not only are the axioms of geometry assumptions but there are also meta-assumptions, assumptions about how one works with assumptions and derives conclusions from them. All statement and belief rest on unproven assumptions, including meta-assumptions. Therefore, anyone is in fact free to believe anything they want, based on different assumptions. And thus, the requirement of freedom from contradiction is a mere assumption. I am not sure how to respond to this brand of rubbish (pardon my informal language), in part since there is some truth to it. That is, there is some absolute truth to it.

Indeed, any half-reasonable discussion has to start with assumptions, including meta-assumptions. For a start, one assumption is that the discussing parties are going to take effort to communicate in a way that is understandable, ideally using a shared language. It will not do when one party starts using a language that the other party does not know (and has no other way of deciphering, e.g. GenAI or online translation). Any attempt at reasoning together and finding common ground requires a minimum good will. And when even the minimum good will is missing, one has to reach for the gun (when the stakes are high; sometimes it suffices to walk away/disengage), use the force of law (and thus have the state reach for the gun), etc.

Another way of putting some of the points is that there being irreducibles, ultimates, etc. does not automatically make those items untrue, etc. Thus, it is quite possible that some axioms are true (of something), even though by definition, axioms cannot be reduced (or are not being reduced in that framework) to other statements by means of a proof. (As per Popper, theorems/proven statements are reduced to axioms/unproven statements by means of proof, and defined terms are reduced to undefined terms by means of a definition. The former reduction is as for being known to be true, the latter reduction is as for semantics.) A related concept seems to be infinite regress.

== See also ==
* [[Street Epistemology#Relativism]]

== Further reading ==
* {{W|Relativism}}, wikipedia.org
* {{W|Infinite regress}}, wikipedia.org
* [[S:Catholic Encyclopedia (1913)/Relativism]], wikisource.org</text>
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This article by Dan Polansky looks at metaphor.

== Introductory considerations ==

I consider metaphor to be a dangerous means of argumentation and analysis. I made the relevant points in the Wikidebate [[Are metaphors a good thing?]]. One salient example: if the 9/11 attack on the U.S. is a metaphorical war (rather than merely a terror attack), and if one forgets the word &quot;metaphorical&quot;, then raq War/The Second Gulf War is a war responding to war, which does not sound entirely unreasonable. As another example, if Jews are rats, their extermination would seem like a good idea.

Metaphor is perhaps not the only dangerous figure of speech. Other candidates include synecdoche, personification and hyperbole. Nonetheless, metaphor seems particularly dangerous to me.

Metaphor is to be distinguished from simile by means of the syntactic form. The most canonical syntactic form for metaphor is &quot;X is Y&quot;, whereas the one for simile is &quot;X is like Y&quot;. Jakub Mácha thinks that metaphory is assymetical whereas simile is symmetrical; I am not so sure of that. Nonetheless, &quot;X is Y&quot; is not the only form of metaphor. One striking difference between live metaphor and simile that the former can turned into a dead metaphor (lexicalized, ossified, etc.) by repeated use while the latter cannot since the alienation is signaled there by ''like'' or ''as''; that makes me think that simile is less dangerous but also less useful in enriching language.

One could think that each metaphorical use is literally untrue. But that is not so, especially for those of the form &quot;X is not Y&quot;, e.g. &quot;no man is an island&quot;. (This point is made by Mácha.)

Metaphor finds a rich use in poetry. Whether harm ensues is not so clear.

Metaphor is a linguistic phenomenon, but the concept can be extended to visual representation e.g. on posters. Thus, Jews can be depicted as rats on a propaganda poster, and the statement &quot;Jews are rats&quot; is then implied in the image.

Mácha mentions Thomas Hobbes and John Locke as critics of use of metaphor&lt;ref name=macha&gt;[https://philpapers.org/archive/MCHATD.pdf Analytische Theorien der Metapher], Untersuchungen zum Konzept der metaphorischen Bedeutung by Jakub Mácha, 2009, a doctoral thesis (in German)&lt;/ref&gt;. He quotes Locke as stating: &quot;Eloquence, like the fair sex, has too prevailing beauties in it to suffer itself ever to be spoken against.&quot;, going on to quoting Paul de Man who criticized the passage as a particularly eloquent criticism of eloquence. I do not see this criticism as damning; indeed, my favorite way of criticizing metaphor is by stating that it is the mother of nonsense and uncle of deception or the like. Pirsig makes a similar point as Paul de Man: he accuses Plato of charging the sophists with using rhetorical means of persuasion while using them himself. (I need to add detail.)

An extended metaphor is multiple metaphoric uses pointing to the same comparison, from what I remember. An example is to be added.

== Thomas Hobbes ==
Hobbes seems to have been critical of the use of metaphor. For now, see the further reading:

Further reading:
* [https://www.researchgate.net/profile/Andreas-Musolff/publication/237452637_Metaphor_as_Deception_Thomas_Hobbes_and_political_metaphor/links/54cf67c30cf298d656636ca8/Metaphor-as-Deception-Thomas-Hobbes-and-political-metaphor.pdf Metaphor as “Deception”: Thomas Hobbes and political metaphor] by Andreas Musolff, University of Durham
* [https://etheses.lse.ac.uk/1204/ Hobbes, metaphor and political thought.] by James Willson-Quayle, 1991

== Lexicalized metaphor ==
Lexicalized metaphor, usually known as dead metaphor and contrasted to live metaphor, is one that became part of the meaning of the word and is usually tracked in a dictionary as a sense. Users of lexicalized metaphors do not need to be fully aware of the metaphorical origin. (Metonymy is another common source of new senses originating as solification/ossification of a figure of speech.)

== Language as a store of metaphors ==
I got this idea from Mácha (&quot;Grabmäler toter Metaphern trägt man in ein Wörterbuch ein&quot;, perhaps one enters the tombs of dead metaphors in a dictionary), but it is pretty obvious.

Senses that arose from metaphorical extensions of other senses point to metaphors that were once live and can be actually live in a different langauge.

Etymology is another pointer to metaphor, when taken to point to quasi-senses or pseudo-senses given by the items in the etymology.

As a result, one who want to browse a disorganized catalogue of metaphors only needs to consult a definition and etymological dictionary.

In so far as a metaphor can be interpreted as a small theory (or hint at a theory) about part of the world, to be explored and perhaps turned into a literal form, different languages provide their users (including children) with different theoretical outlook. This sounds perhaps a bit crazy, but may make more sense than the surface suggests. That is not to say that the conscious of the child would necessarily be involved; it could well be unconscious. Not only would the Berne's priests be as if programming children; the language would. Could this be possible?

== See also ==
* [[Are metaphors a good thing?]]

== References ==
&lt;references /&gt;

== Further reading ==
* {{W|Metaphor}}, wikipedia.org
* [https://www.britannica.com/art/metaphor Metaphor], britannica.com
* [https://publications-prairial.fr/elad-silda/index.php?id=884&amp;lang=en?id=884&amp;lang=en#tocto3n1 What Makes Metaphors Manipulative Tools?] by Denis Jamet and Adeline Terry
* [https://www.garretthardinsociety.org/articles/art_living_on_a_lifeboat.html Living on a Lifeboat] by Garrett Hardin, 1974, garretthardinsociety.org -- some mentions of the value of metaphor
* [https://vitrina96.ru/en/ventilation/nominativnaya-metafora-metafora-tipy-metafory-nominativnaya-kognitivnaya-obraznaya-funkcii-metafo/ nominative metaphor. Metaphor. Types of metaphor (nominative, cognitive, figurative). Functions of metaphor in speech. The use of metaphor in the media. Place of language metaphor], vitrina96.ru
* [https://philpapers.org/archive/MCHATD.pdf Analytische Theorien der Metapher], Untersuchungen zum Konzept der metaphorischen Bedeutung by Jakub Mácha, 2009, a doctoral thesis (in German)</text>
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      <text bytes="4072" sha1="6hpf1c2badask4u2nxqqlmtjbut7gmn" xml:space="preserve">{{Original research}}
This article by Dan Polansky looks at direct democracy and referendum. In a ''representative'' democracy, voters choose between persons and parties. In a referendum (item belonging to ''direct'' democracy), voters choose to accept or reject a policy change proposal. The persons and parties run on vague policy proposals stated in manifestos, but these are not binding contracts between the parties and the voters. At the end of the day, the party or the politician can do something else than what the manifesto says, or do something that the manifesto did not envision. And thus, no party had Covid lockdown in a manifesto.

Switzerland is a country that implements the idea of direct democracy. The country is peaceful, educated and rich. One would have to look whether there are some outcomes that some would find highly problematic.

I find direct democracy to be a good idea. Arguments against include that it is vulnerable to populism or the like and that people are not good at assessing policies. But if people are not good at assessing policies, then I do not see what makes them qualified to assess party manifestos, policy bundles. In representative democracy, parties are running on policy items, not just on personal characteristics of the politicians.

The transgender politics is perhaps a good item in support of direct democracy, even from the point of view of some Democratic voters in the U.S. Since, the transgender politics can be driving some Democrat voters to Trump, while the same voters could otherwise vote for Harris. In the system of policy item bundles (representative democracy with parties representing the bundles), the voters are faced with irresoluble dilemmas.

Quorum. 50% of eligible is too much; 10% of eligible could be okay. Or those who supported must make at least 10% of the eligible voters, which could in some sense be equivalent to 20% of the eligible voters except that the temptation to oppose by abstinence is curbed. I seem to remember that a Slovak referendum failed since the 50% threshold was not reached. I find the 50% threshold absurdly high. Too high a threshold opens the option of speculative non-participation on part of the opposers. Once the quorum is only calculated from supports (as I just proposed), the incentive for opposers to refrain from participation disappears.

The problem of voters being forced to choose from predefined policy bundles can be likened to grocery shopping and to customizing software. As an analogy, the party system is similar to a shopper having to pick one of, say, three grocery item baskets to buy. Shoppers do not like that. They want to put together their own shopping basket. In software, end users like to customize their experience. In business software, the corporate users have extensive customizing at their disposal rather than having to choose between, say, three customizing presets. This can be generalized to all sorts of choice people make in life.

Parties advocating for direct democracies are listed at [[Wikipedia: List of direct democracy parties]]. However, the article features no inline references and clicking on the various linked party articles do not universally substantiate the list membership either.

The referendum system does not prevent parties from taking positions on the proposed policy change, hosting debates, producing detailed reports in support or opposition, etc. A voter who wants to delegate decision making to a particular political party has the option, by finding out the position of that party. On the other hand, one can suspect that the less qualified or more unwise voters would fail to realize their own limitations, and would want to make their own uninformed decision and vote accordingly.

== Further reading ==
* {{W|Direct democracy}}, wikipedia.org
* [https://www.britannica.com/topic/direct-democracy direct democracy], britannica.com
* [https://www.aboutswitzerland.eda.admin.ch/en/direct-democracy Direct Democracy], aboutswitzerland.eda.admin.ch

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      <text bytes="715" sha1="ttzfe1czcmdgevzd2yqjute43jfik8a" xml:space="preserve">== Invalid Slovak referendum ==
Per this:
* [https://www.irozhlas.cz/zpravy-svet/slovensko-referendum-neplatne-volebni-ucast-caputova_2301220645_har Na Slovensku proběhlo referendum o předčasných volbách, je ale neplatné. Nepřišel dostatek voličů], 22 January 2023, irozhlas.cz

The participation rate was 27.25 %, which in my view should have been enough to make the referendum valid. However, the threshold for validity was 50% of the eligible voters per the article above.

Further reading:
* {{W|2023 Slovak constitutional referendum}}, wikipedia.org
--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:56, 15 May 2025 (UTC)</text>
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This article by Dan Polansky looks at what is or what could be extropianism.
== Introductory analysis ==

One access point to a potential definition is etymology. We note the term is extropian + -ism. And extropian is extropy + -ian. And extropy is apparently ex- + entropy with en- removed. This leads to the following candidate definition:
* A philosophy or approach emphasizing moving out (ex-) of (or away from) entropy.

Another access point is via the organization called Extropy Institute and the associated Extropy magazine. If people from that institute coined the word extropy and perhaps even extropian and extropianism, their view of what it is would deserve special attention or consideration. This leads to the following candidate definition of extropianism:
* A philosophy or approach championed by the Extropy magazine and the Extropy Institute.
The above definition/topic is more closely examined in the following section.

== Extropianism of Extropy magazine and the Extropy Institute ==
Extropy magazine was launched in 1988 while the Extropy Institute 2 or 3 years later. Max More/Max O'Connor was a key driver of both (together with Tom W. Bell, who seems to have played a somewhat lesser role?). Therefore, the analyzed entity approximates the extropian philosophy of Max More.

What philosophy is championed by the Extropy magazine and the Extropy Institute? We can get an idea from the first issue of the Extropy magazine&lt;ref&gt;https://github.com/Extropians/Extropy&lt;/ref&gt;, Fall 1988, available online.

=== Extropy magazine ===
Extropy magazine is a major source for what is Max More's extropianism, together with extropy.org of Extropy Institute. The source uses the words &quot;extropy&quot;, &quot;extropian&quot; and &quot;extropianism&quot;. It is available from github, archive.org and other places. 

The first issue appeared in 1988. Issue 17 appeared in second half of 1996 per GitHub; this was perhaps the last issue or the last offline issue (unless the GitHub repo is incomplete). Extropy.org states: &quot;Extropy: The Journal of Transhumanist Thought from 1989 to late 1996 in high-gloss print and distributed at major bookstores.&quot;&lt;ref&gt;https://web.archive.org/web/20100618114155/http://www.extropy.org/publications.htm&lt;/ref&gt;

Issues subtitles:
* Vaccine for Future Shock, issue 1-5 (or more?)
* The Journal of Transhumanist Thought, issue 7-? (including #14&lt;ref&gt;https://github.com/Extropians/Extropy/blob/master/Extropy-14_FirstQuarter-1995.pdf&lt;/ref&gt;)
* Journal of Transhumanist Solutions (see below)

Topics covered are identified in various issues. Issue 14 has the following (quoted word for word):
* Transhumanism and futurist philosophy
* Life extension, immortalism and cryonics
* Smart drugs (nootropics) and intelligence increase technologies
* Machine intelligence, personality uploading, and Artificial life
* Nanocomputers and nanotechnology
* Memetics (ideas as viruses)
* Experimental free communities in space, on the oceans, and within computer networks
* Effective thinking and information filtering
* Self-transformative psychology
* Spontaneous orders (free markets, neural networks, evolutionary processes, etc)
* Digital economy (privacy technologies, digital money and electronic markets)
* Rational, market-based environmentalism
* Probing the ultimate limits of physics

As for whether it is a magazine or a journal, Max More uses the phrase &quot;Extropy magazine&quot; here: &quot;We founded Extropy magazine in the late 1980s, and later the Institute, while still graduate students in philosophy and could not plausibly be called rich by Anglo-American standards.&quot;&lt;ref&gt;https://www.theregister.com/2003/09/18/extropian_cofounder_locks_horns/&lt;/ref&gt;.

As per extropy.org: &quot; Then, in November 1997, it [the magazine] moved to the Web as Extropy Online, where it continued to publish articles for three years. After a year of dormancy, it returned to the Web in February 2002 as its current form, Extropy: Journal of Transhumanist Solutions.&quot;&lt;ref&gt;https://web.archive.org/web/20131106011118/http://www.extropy.org/extropyonline.htm&lt;/ref&gt;

Links:
* {{W|Extropianism}}, wikipedia.org
* https://github.com/Extropians/Extropy, e.g. https://github.com/Extropians/Extropy/blob/master/Extropy-01.pdf; has issue 1-17; https://github.com/Extropians/Extropy/blob/master/Extropy-14_FirstQuarter-1995.pdf is an example of a pdf with OCR
* https://archive.org/details/extropy-01/, https://archive.org/details/extropy-02/ (nothing seems available for direct view), https://archive.org/details/extropy-03/, etc.
* https://www.resistance.money/research/extropy/Extropy-01.pdf; tweaking the URL yields other issues

=== Future forecasts ===
One can get an idea of what future events extropians are discussing or even looking forward to from future forecast published in one issue of Extropy magazine. The forecast was reposted into a mailing list much later:
* https://lists.extropy.org/pipermail/extropy-chat/2003-December/001657.html
The forecasters were Benford, Eric Drexler, Miller, Szabo, Bridge, FM-2030, and Max More.

Events forecast include indefinite biological lifespans, uploaded minds and big fraction of economy off earth. Apparently, these people are serious; there are no signs that this is humor.

The Extropy magazine issue is #15, 1995:
* https://raw.githubusercontent.com/Extropians/Extropy/master/ext15.pdf

=== The extropian principles ===
&lt;!-- TBD: integrate the two paras; they are artifacts of history --&gt;
One set of ideas of what extropy is about is presented in ''Principles of Extropy'' by Max More (born Max T. O'Connor)&lt;ref&gt;https://web.archive.org/web/20131015142449/http://extropy.org/principles.htm&lt;/ref&gt;, a former chairman of Extropy Institute. This version of the text, V 3.11, does not contain the word ''entropy'', does not indicate etymology and does not present anything that I would recognize as a definition proper of ''extropianism'' or ''extropy''. Instead, it contains principles such as the following one:
* &quot;Extropy means fueling action with positive expectations – individuals and organizations being tirelessly proactive. Adopting a rational, action-based optimism or &quot;proaction&quot;, in place of both blind faith and stagnant pessimism.&quot;
What this has to do with moving out of or away from entropy is unclear. An older version of the text, 3.1, features the following definition&lt;ref&gt;http://web.archive.org/web/20030919194923/http://extropy.org/principles.htm&lt;/ref&gt;:
* &quot;Extropy —  The extent of a living or organizational system’s intelligence, functional order, vitality, and capacity and drive for improvement&quot;.

One capture of the ideas of extropianism is the document ''Extropian Principles'' (version 2.5) and other versions of it. Extropian Principles 2.5 seems to be an early version of what became ''Principles of Extropy''; one can find ''The Extropian Principles 2.5'' indicated as from July 1993, (c) 1993 Max More, President, Extropy Institute&lt;ref&gt;https://www.aleph.se/Trans/Cultural/Philosophy/princip.html&lt;/ref&gt;. One can further find ''The Extropian Principles, v. 3.0'' indicated to be a transhumanist declaration, (c) 1998 Max More, President, Extropy Institute, more@extropy.org or max@maxmore.com&lt;ref&gt;https://www.mrob.com/pub/religion/extro_prin.html&lt;/ref&gt;. There is also ''The Extropian Principles'', V. 2.6, ©1995 Max More, Ph.D.&lt;ref&gt;https://www.alamut.com/subj/ideologies/manifestos/extropian_principles.html&lt;/ref&gt;, using the definition &quot;extropy: a measure of intelligence, information, energy, vitality, experience, diversity, opportunity, and growth.&quot;

=== Extropianism vs. transhumanism ===

A connection of extropy or extropianism to transhumanism is as follows. The Extropy magazine is designated in some sources as &quot;journal of transhumanist thought&quot;. Moreover, ''The Extropian Principles 2.5'' state that &quot;Extropianism is a transhumanist philosophy: Like humanism, transhumanism values reason and humanity and sees no grounds for belief in unknowable, supernatural forces externally controlling our destiny, but goes further in urging us to push beyond the merely human stage of evolution.&quot; Furthermore, extropianism is mentioned as part of transhumanism in an article called ''A Philosophical History of Transhumanism''&lt;ref&gt;https://philosophynow.org/issues/160/A_Philosophical_History_of_Transhumanism&lt;/ref&gt;. More stated: &quot;Although the Principles of Extropy define a specific form of transhumanism, that document is both the first comprehensive and explicit statement of transhumanism and embodies several crucial elements shared by all extant forms of transhumanism.&quot;&lt;ref&gt;[https://media.johnwiley.com.au/product_data/excerpt/10/11183343/1118334310-109.pdf The Philosophy of Transhumanism] by Max More&lt;/ref&gt;

== The Extropist Manifesto ==

There exists something called ''The Extropist Manifesto'', with unclear author and provenience&lt;ref&gt;https://extropism.tumblr.com/post/393563122/the-extropist-manifesto&lt;/ref&gt;. Its anti-property item positions it as part of communism, going in a direction very different from More's philosophy and his apparent love of libertarianism and free markets. One can learn more in a 5 December 2015 revision of the Wikipedia article&lt;ref&gt;https://en.wikipedia.org/w/index.php?title=Extropianism&amp;oldid=693820976&lt;/ref&gt;.

== Kevin Kelly ==
Kevin Kelly sometimes uses the word &quot;exotropy&quot;, slightly different from &quot;extropy&quot;&lt;ref&gt;https://www.theguardian.com/technology/2010/oct/24/my-bright-idea-kevin-kelly&lt;/ref&gt;&lt;ref&gt;https://kk.org/thetechnium/infinite-order/&lt;/ref&gt;

At the same time, he has one analysis using the word &quot;extropy&quot;&lt;ref&gt;[https://kk.org/thetechnium/extropy/ The Technium: Extropy] by Kevin Kelly, kk.org&lt;/ref&gt;.

Whether Kevin Helly is an extropian in the Max More's sense is unclear. He would need to support at least indefinite lifespan, mind uploading and an expansion into the universe (space colonization).

== Workshop ==
This page is supported by [[One man's look at extropianism/Workshop]], featuring a lot of supporting material not yet incorporated.

== References ==
&lt;references /&gt;

== Further reading ==
* {{W|Extropianism}}, wikipedia.org
* [https://en.wikipedia.org/w/index.php?title=Extropianism&amp;oldid=693820976 Extropianism], revision 5 December 2015, wikipedia.org
* [https://kk.org/thetechnium/extropy/ The Technium: Extropy] by Kevin Kelly, kk.org
* http://web.archive.org/web/20160104221308/https://www.wired.com/1994/10/extropians/
* https://www.britannica.com/topic/transhumanism -- apparently the only mention of &quot;extropy&quot; in Britannica; also mentions &quot;extropianism&quot;
* [https://julesevans.medium.com/how-did-transhumanism-become-the-religion-of-the-super-rich-d670a410b01a How did transhumanism become the religion of the super-rich?] by Jules Evans, 28 Oct 2022, medium.com -- uses the words extropy, extropian and extropianism and mentions some notable extropians and members of the extropian mailing list
* [https://mason.gmu.edu/~rhanson/press/UKObserver-3-26-95.htm The Tomorrow People], March 26 1995 UK Observer Cover Story, mason.gmu.edu
* [https://bitcoinmagazine.com/culture/how-extropian-quest-for-digital-cash-secured-our-trips-to-the-stars How The Extropian Quest For Digital Cash Secured Our Trips To The Stars], 2020, bitcoinmagazine.com&lt;!--TBD: author--&gt;</text>
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      <text bytes="43958" sha1="rssod8gokfbi9fysdsbma3ezqiqs7fn" xml:space="preserve">This page by Dan Polansky, tentatively named &quot;workshop&quot;, is to support the main article.

==Timeline==
(Possibly to be moved to the mainspace.)
* 1988: the first issue of the Extropy magazine was published, &quot;co-edited by Tom W. Bell and Max T. O'Connor,&quot;&lt;ref&gt;https://github.com/Extropians/Extropy/blob/master/Extropy-01_Introductory-fall-1988.pdf&lt;/ref&gt;
* 1990: the Extropy Institute was founded by Max More and Tom Bell&lt;ref name=closeann&gt;https://web.archive.org/web/20110225075011/http://www.extropy.org/future.htm&lt;/ref&gt;. A different page from extropy.org states 1991 as the founding date&lt;ref&gt;https://web.archive.org/web/20100618121452/http://www.extropy.org/events.htm&lt;/ref&gt; Even 1988 is mentioned in extropy.org&lt;ref&gt;3.1 What is Extropy Institute (&quot;ExI&quot;)? Extropy Institute (&quot;ExI&quot;) is 501(c)3 not-for-profit educational organization. It is the original international transhumanist organization founded in 1988 to incubate positive futures.&lt;/ref&gt;
* 1993: ''The Extropian Principles 2.5'' by Max More was published.
* 2005: Pein 2016 states:&lt;ref name=pein2016&gt;[https://thebaffler.com/salvos/everybody-freeze-pein Everybody Freeze!] by Corey Pein, 2016, thebaffler.com&lt;/ref&gt;'In 2005, More filed for personal bankruptcy protection. The court filings listed $110,000 in unsecured debts, including a combined $32,000 for two Extropy Institute credit cards. In 2006, More, having left California for Austin, Texas, closed the Extropy Institute for good, announcing that “its mission was essentially completed.” The transhuman revolution occurred at the end of the Bush era, it seems, without anyone much noticing.' Reservation: I cannot find any independent confirmation of the bankrupty protection.
* 2006: the Extropy Institute was announced to be closed&lt;ref name=closeann/&gt;.

Links:
* http://web.archive.org/web/20100618120009/http://www.extropy.org/history.htm

==Issues/todos==
1) The para starting with &quot;An early mention of extropy, extropian and extropianism is in a 1994 Wired [...]&quot; is misleading; 1994 is not the earlies use of extropy since Extropy Magazine started in 1988. Moreover, some sources indicate Diane Duane used the word ''extropy'' much earlier.

2) It should be figured out whether extropianism can be defined as the philosophy of Max More, or perhaps Max More and Tom Bell. They seem to be responsible for all so far identified articulations of that philosophy. We could then get rid of &quot;A philosophy or approach championed by the Extropy Institute&quot;.

3 The &quot;Transhumanist FAQ&quot; from extropy.org is perhaps worth analysis. It contains some dubious statements, e.g. that an effort to replace humans with non-humat posthumans is somehow an effort to improve human condition. Or there is e.g. '“Extropy” is not meant as a real entity or force, but only as a metaphor representing all that contributes to our flourishing.' so in the end, all the talk about extropy is just about &quot;our flourishing&quot;, presumably implying &quot;human flourishing&quot;, but really intending a broader concept since it includes posthuman flourishing.

== More links ==
(Some could be added to the mainspace.)
* https://archive.org/details/extropy-01/, https://archive.org/details/extropy-02/ (nothing seems available for direct view), https://archive.org/details/extropy-03/, etc. (The magazine/journal is also in GitHub.)
* https://nickbostrom.com/papers/a-history-of-transhumanist-thought/ -- mentions extropianism
* https://philosophynow.org/issues/160/A_Philosophical_History_of_Transhumanism -- mentions extropianism
* [https://digital.library.unt.edu/ark:/67531/metadc1505282/m2/1/high_res_d/ROSS-DISSERTATION-2019.pdf TRANSHUMANISM: AN ONTOLOGY OF THE WORLD’S MOST DANGEROUS IDEA] by Benjamin D. Ross, a doctoral thesis/dissertation, 2019

== Analytical plan ==
I started writing the article without an analytical plan (plan of analysis) and it probably shows in its being disorganized.

Some items that could contribute toward such a plan
* Extropianism
** Extropianism as per etymology
** Extropianism as per (primary?) texts using the word
*** Extropianism as per the Extropy magazine
**** As per issue 1
**** Etc.
*** Extropianism as per the Principles of Extropy
**** As per first version
**** Etc.
*** Extropianism as per the Extropy magazine and Extropy.org (seems promising)
** Secondary (uninvoled or less involved) sources about extropianism
** Extropianism as per texts by a particular person
*** Extropianism as per Max O'Connor/More (seems to be a promising approach)
*** Extropianism as per Tom Bell

The different items can lead to different results, which is trivial e.g. for etymology, but perhaps less trivial as for the different versions of the Principles of Extropy. My reading of the different versions of the Principles of Extropy suggest that the differences are quite significant.

A proper original research exercise would be to create something like a spreadsheet with items to be analyzed and the the results of analysis. Then, the results would be aggregated/summarized in some way.

== Quotations of the word extropianism ==
We can try something like a lexicographical approach toward the word. Some quotations are in https://www.oed.com/dictionary/extropianism_n?tl=true, which I have discovered when searching for &quot;will carry people past the limits of the human body&quot;, which I found in Google Books.

* [https://archive.org/details/extropy-05/page/4/mode/1up?q=extropianism&amp;view=theater EXTROPY #5], 1990, archive.org
*: &quot;If all of this extropianism leaves you hungering for more, turn to “Extropian Resources,&quot; where Max and I list a number of organizations and publications that fight entropy in one way or another.&quot;
* [https://archive.org/details/extropy-06/page/4/mode/1up?view=theater&amp;q=extropianism EXTROPY #6], 1990, archive.org
*: '“Extropy&quot; - the process of increasing intelligence, information, usable energy, life, experience, and growth. &quot;Extropianism&quot; - the philosophy that seeks t promote these goals. The Extropian Principles are: (1) Boundless Expansion; (2) Dynamic Optimism; (3) Self-Transformation; (4) Intelligent Technology.'
*: &quot;The Society for Venturism is a philosophical organization dedicated to promoting the ideas and values of cryonics and physical immortality. I regard it as a subset of extropianism.&quot;
* [https://archive.org/details/extropy-13/Extropy-13/page/n1/mode/1up?view=theater EXTROPY #13], 1994, archive.org
*: &quot;TRANSHUMANISM — Philosophies of life (such as Extropianism) that seek the continuation and acceleration of the evolution of intelligent life beyond its currently human form and human limitations by means of science and technology, guided by life-promoting principles and values, while rejecting dogma and religion. [See Extropy #6]&quot;
* [http://web.archive.org/web/20160104221308/https://www.wired.com/1994/10/extropians/ Meet the Extropians], 1994, wired.com at archive.org
*: &lt;p&gt;&quot;For all its gonzo metaphysics, the fact is that Extropianism is a carefully worked out philosophical movement, one whose rituals, symbolism, and mind-set are rooted in a deep and rich body of principles. The basic idea is to fight entropy – the natural tendency of things to run down, degenerate, and die out – with its polar opposite, &quot;extropy.&quot;&lt;/p&gt;&lt;p&gt;Extropy, according to the official Extropian Principles (version 2.5), is &quot;a measure of intelligence, information, energy, vitality, experience, diversity, opportunity, and capacity for growth.&quot; Extropianism, then, is &quot;the philosophy that seeks to increase extropy.&lt;/p&gt;&lt;p&gt;The principles themselves are five in number: Boundless Expansion, Self-Transformation, Dynamic Optimism, Intelligent Technology, and Spontaneous Order. They make up the handy Extropian acronym: BEST DO IT SO!&quot;&lt;/p&gt;
* [https://web.archive.org/web/20150527070625/http://www.nytimes.com/1997/09/28/magazine/technology-makes-us-optimistic-they-want-to-live.html?pagewanted=3 Technology Makes Us Optimistic; They Want To Live], 1997, nytimes.com at archive.org
*: &quot;The buffs certainly don't buy that. My last stop in California is with Dr. Max More and his wife, Natasha Vita More, who live in a perky white-walled apartment in Marina Del Rey. ''More'' is a name they adopted in keeping with a futuristic philosophy that guides their lives. It's called Extropianism -- as in, ''away from entropy'' -- and its 3,000 or so adherents long for a day when technology, in various ways, will carry people past the limits of the human body. [...] That's a novel way of looking at it -- death as a bad life-style option -- but it's no joke to the Mores.&quot;
* [https://www.theguardian.com/theobserver/2000/dec/31/life1.lifemagazine1 Alas, mankind, we knew him...], 2000, theguardian.com/theobserver (OED identifies this as Observer)
*: &quot;Unsurprisingly, this set of circumstances supports a healthy fringe of cultish pseudo-philosophies, with names like Transhumanism and Extropianism, which welcome the prospect of biological and neurological augmentation. They also await the coming of 'singularity', or the 'techno rapture', which is expected to happen when the super-intelligent computers we create acquire the capacity to design their successors, at which stage, it is believed, the cycles of Moore's Law will move from human to machine timescales.&quot;
* [https://web.archive.org/web/20150911045217/https://www.britannica.com/topic/transhumanism Transhumanism], 2015, britannica.com at archive.org
*: &quot;The movement has evolved since its beginnings as a loose association of groups dedicated to “extropianism” (a philosophy devoted to the transcendence of human limits). Transhumanism is principally divided between adherents of two visions of post-humanity—one in which technological and genetic improvements have created a distinct species of radically enhanced humans and the other in which greater-than-human machine intelligence emerges.&quot;

== Quotations of the word extropian ==
Unlike ''extropianism'', ''extropian'' appears already in the first issue of Extropy magazine.
* [https://archive.org/details/extropy-01/page/9/mode/1up EXTROPY No. 1.], Fall 1988, archive.org
*: &quot;Extropians are already special people, in that they reject the common entropic perspective and have the insight and courage to choose the perspectives-expanding extropian paradigm. It is intended that articles in this area will reinforce our ability to live in accordance with this unlimited model of reality and self. If you are already an extropian you can become an übermensch!&quot;

== Relation to Hans Moravec's Mind Children ==
The 2nd issue of EXTROPY (https://github.com/Extropians/Extropy/blob/master/Extropy-02_Winter-Jan-1989.pdf) features an enthusiatic review by Max O'Connor/Max More of the book [[Mind Children]]. A blurb (is that the word?) at the right says:
: &quot;We can leave our weak, vulnerable, stupid bodies and brains for something enormously superior&quot;.
At the end of the view, it says:
: &quot;Moravec's Mind Children will take its place alongside other recent extropian and scientific classics such as Eric Drexler's Engines of Creation, Freeman Dyson's Disturbing the Universe, and Infinite In All Directions, and Robert Ettinger's The Prospect of Immortality. I can't recommend this book highly enough. Anyone who shares the perspectives that we present in Extropy will find it a rich source of wonderful ideas, and even the ones that you have come across before will acquire new life.&quot;
The first para of the interview is this:
: &quot;This is a book that every extropian not only should read but would enjoy immensely. It is packed with fantastic, imaginative, wild ideas which are almost all solidly based in real science. The ideas in the book revolve around the coming massive boost in intelligence resulting from advanced artificial intelligence (AI) and an upbeat, optimistic view of our future. It is impossible to do justice to all the invigorating ideas and style of presentation here but I will try to convey some impression of the treasures to be found in the book.&quot;
It follows that Max O'Connor/More (at least at that time) found the prospect of postbiological future without any real biological humans &quot;optimistic&quot; (there could be still human uploads, or emulated humans, in human-like robots). One may also note the use of &quot;our future&quot; in &quot;optimistic view of our future&quot;; since, what is &quot;our&quot; supposed to mean? If &quot;our&quot; means &quot;our human's&quot;, then the &quot;optimistic&quot; (good-envisioning) future for humans is human extinction, at least biological humans. It would seem to follow that it is ''good'' for ''humans'' to go extict.

== What are extropians and what they think ==
I think this question is difficult to answer, depending on how one approaches the matter. To find out what extropians think, one needs to find who they are. If one defines an extropian as someone who (completely) subscribes to a set of principles published in a document so-and-so, the question reduces to what the document as if thinks, and the question becomes manageable. By contrast, if an extropian is someone who says &quot;I am an extropian&quot;, someone who appears on a particular list of extropians or someone who is on a mailing list of the Extropy Institute, the thinking of extropians becomes much more of chaotic/scattered/diversity-showing object.

It therefore seems to me that the question of what extropians think is better replaced with the question of what is extropianism as per document so-and-so, unless one wants to do sociological research by means of interviewing extropians from a particular list or something of the sort.

Some sources of individual extropians:
* Editors of Extropy magazine: Max More and Tom Bell
* Contributors to Extropy magazine
** The several people who made future forcasts in an issue of Extropy magazine: Benford, Drexler, Miller, Szabo, Bridge, FM-2030, Max More&lt;ref&gt;https://lists.extropy.org/pipermail/extropy-chat/2003-December/001657.html&lt;/ref&gt;
* The list of directors of the Extropy Institute, changing in time
* The designers of Primo whole body prosthetic: &quot;The collaborative scientific team that designed Primo includes Max More, Marvin Minsky, Robert Freitas, Michael Rose, Greg Fahy, Ralph Merkle, Alexander Sasha Chislenko, Roy Walford, Gregory Benford, Robin Hanson, Vernor Vinge, and Hans Moravec.&quot;&lt;ref&gt;https://www.thekurzweillibrary.com/essay-a-concept-for-future-body-design&lt;/ref&gt;.
* People who spoke at Extro conferences. Max More says of himself: &quot;Chaired and organized five Extro conferences (1994-2001) whose speakers included scientists, social theorists, and artists, such as Raymond Kurzweil, Marvin Minsky, Cynthia Kenyon, Calvin Harley, Eric Drexler, Roy Walford, Kevin Kelly, Bart Kosko, Natasha Vita-More, Hans Moravec, and Michael Rothschild.&quot;&lt;ref&gt;https://web.archive.org/web/20030808171852/http://www.maxmore.com/bio.htm&lt;/ref&gt;

== Relation to mind uploading ==
In [[#Relation to Hans Moravec's Mind Children]], we see Max More (an editor of Extropy magazine) being enthusiastic about Moravec's Mind Children, which celebrates mind uploding.

Extropy magazine, issue 11, has the following:
* [https://archive.org/details/extropy-11/Extropy-11/page/5/mode/1up?view=theater Uploading: Transferring Consciousness from Mind to Computer] by Ralph C. Merkle, Summer/Fall 1993, archive.org

Extropy magazine, issue 10, has an article by Moravec referring to something like mind uploading:
* [https://archive.org/details/extropy-10/Extropy-10/page/6/mode/1up?view=theater Pings in Cyberspace] by Hans Moravec, Winter/Spring 1993, archive.org
*: Bit by bit our brain is replaced by electronic equivalents, which workat least as well, leaving our personality and thoughts clearer than — ever. Eventually everything has been replaced by manufactured parts. No vestige of our original body remains, but our thoughts and awareness continue. We willcall this process, and otherapproaches with thesame end result, the downloading of a human mind into a machine. 

Extropy magazine, issue 15, has a table of future forecasts that features mind uploading as one event to forecast:
* [https://archive.org/details/extropy-15/Extropy-15/page/6/mode/1up?view=theater https://archive.org/details/extropy-15/Extropy-15/page/9/mode/1up?view=theater]

Links:
* https://www.researchgate.net/publication/226871090_Cyborgs_uploading_and_immortality_-_Some_serious_concerns

== Postbiologism ==
This is relating [[#Relation to mind uploading]]. In TechnoCalyps, Max More states: &quot;Posthuman I think will be postbiological. [...] We will gradually integrate more technology into our bodies. [...] So eventually we will replace our brain cells with essentially computerized parts; it will be much more efficient, much more powerful.&quot;&lt;ref&gt;https://www.youtube.com/watch?t=1608&amp;v=7MXQSbjBL7Q TechnoCalyps Part I TransHuman&lt;/ref&gt;. (A champion of postbiologism is Hans Moravec in his [[Mind Children]].)

In extropy.org's Transhumanist FAQ, it says&lt;ref&gt;https://web.archive.org/web/20110718075135/http://www.extropy.org/faq.htm&lt;/ref&gt;: &quot;The new sexual landscapes will bring about different types of sexuality, different types of genders. In the future, we may still want to perform the traditional types of sex, or we may want to participate in the reconstituted and reconfigured gender roles and sexuality that will radically change us. We may do away with our bodily nerves, but keep some sensations, the ones for pleasure of perhaps some for pain to remind us not to do something. Yet, eventually we will begin to shuttle more and more parts of ourselves as we become post-biological.&quot;

== Chief extropian ==
The analysis would be simplified if we identified the chief extropian. Let's say this would be Max More/O'Connor. Then, we would not be looking at extropianism but rather at &quot;Max More's extropianism&quot; or &quot;Extropianism as per Max More&quot;.

Max More is indeed one candidate for the title of chief extropian; he is one of the two editors of Extropy magazine. Moreover, he is the author of The Principles of Extropy/Extropian Principles.

Tom W. Bell is another candidate: he was one of the two editors of Extropy magazine, and he coined the word extropy.

== Tom W. Bell ==
Tom W. Bell is one of the two candidates for the title chief extropian (&quot;co-edited by Tom W. Bell and Max T. O'Connor,&quot;&lt;ref&gt;https://github.com/Extropians/Extropy/blob/master/Extropy-01_Introductory-fall-1988.pdf&lt;/ref&gt;), so it makes sense to have a closer look at him:
* There is an article [[W:sk:Tom Bell]], identifying him also as 'Thomas „Tom“ W. Bell' and 'T.O. Morrow'. For some reason, I got a little doubt whether the identification of the person linked from the external links with the extropian is correct; maybe it is.
** Links:
*** http://www.tomwbell.com/ (does not load, unlike http://www.tomwbell.com/BellCV.pdf)
*** http://www.cato.org/people/tom-bell
*** http://www.chapman.edu/our-faculty/thomas-bell (no longer works, but found here: https://web.archive.org/web/20240419180433/http://www.chapman.edu/our-faculty/thomas-bell)
* As for &quot;T.O.Morrow&quot; moniker, https://www.extropy.org/future.htm states &quot;Coined by Prof. Tom Bell (T.O. Morrow) in 1988.&quot;, probably in relation to the word &quot;extropy&quot;.
* Further relevant links:
** https://hpluspedia.org/wiki/Tom_Bell
** https://web.archive.org/web/20020309035652/http://members.aol.com/t0morrow/T0Mpage.html
*** This reveals moniker &quot;T.0. Morrow&quot; with zero rather than O.; the form &quot;T.0. Morrow&quot; is also at extropy.org&lt;ref&gt;https://web.archive.org/web/20131106011118/http://www.extropy.org/extropyonline.htm&lt;/ref&gt;
*** It says &quot;Coined &quot;extropy&quot; (as in &quot;Extropianism&quot;) in January 1988.&quot;
** The T. O. Morrow (with spaces) moniker is in https://www.newscientist.com/article/mg23431191-800-exploring-the-hidden-politics-of-the-quest-to-live-forever/
** The &quot;Tom Morrow&quot; appears in Extropy magazine #14 and seem to refer to him.

Under which name does Extropy magazine present Tom Bell: &quot;Tom W. Bell&quot;, per first issue of the magazine.

Which &quot;Thomas W. Bell&quot; is it? It could be [[Wikidata:Q17115573]], linking e.g. to https://id.loc.gov/authorities/names/n98064978.html.

Where is he in Google Books?
* Possibly: https://books.google.com/books/about/Your_Next_Government.html?id=w-w0DwAAQBAJ&amp;source=kp_author_description&amp;redir_esc=y
*: &quot;Tom W. Bell earned his J.D. from the University of Chicago in 1993, then practiced law in Silicon Valley and Washington, DC before serving as a policy director at the Cato Institute. In 1998, he joined the faculty of Chapman University, Fowler School of Law, where he teaches all of the first-year common law courses and electives in high-tech and intellectual property law. Bell's prior publications include Intellectual Privilege: Copyright, Common Law, and the Common Good (2014). Through Archimediate LLC, Bell advises companies developing special economic zones on the design, installation, and support of legal systems.&quot;

Some Tom W. Bell is here: http://www.tomwbell.com/BellCV.pdf, Chapman University School of Law, &quot;Scholar, legal consultant, and practicing attorney.&quot; Role mentioned: &quot;Cato Institute: Director of Telecommunications and Technology Studies&quot;. No mention of &quot;extropy&quot;.

Tom Bell of Cato is here: https://www.cato.org/people/tom-bell. There is a photo. &quot;a professor at Chapman University. He is an expert in technology, intellectual property, and telecommunications law.&quot;

extropy.org:
* https://www.extropy.org/directors.htm - mentioned as Honorary Advisor (photo fails to load)
** Has a photo here: https://web.archive.org/web/20100618112954/https://www.extropy.org/directors.htm
** And that seems to be the same person as in the photo as here: https://www.cato.org/people/tom-bell
*** As here as well: https://www.cato-unbound.org/contributors/tom-w-bell/

His article Privately Produced Law, Winter/Spring 1991: https://archive.org/details/extropy-07/page/12/mode/1up?view=theater

Another quasi-home page: https://www.libertarianism.org/people/tom-w-bell. It links to three videos.

== Max More ==
Max More/O'Connor is a candidate key extropian; &quot;He served as President of Extropy Institute from 1992 until 2003, and became Chairman in 2003.&quot;&lt;ref&gt;https://web.archive.org/web/20030929154855/http://maxmore.com/&lt;/ref&gt;. To simplify the analysis, instead of asking what do extropians think, we may ask what does Max More think. Links help:
* https://web.archive.org/web/20031004165123/http://maxmore.com/writing.htm
* https://maxmore.substack.com/, entitled Extropic Thoughts | Max More | Substack -- still available, no need to hit archive.org

== Natasha Vita-More ==
Natasha Vita-More served as president of Extropy Institute, from what I recall (she is listed among directors, I think). Her birth name seems to be Nancie Clark per multiple sources&lt;ref&gt;https://web.archive.org/web/20010620084329/www.natasha.cc/laweekly.htm&lt;/ref&gt;&lt;ref&gt;https://www.degruyterbrill.com/document/doi/10.1515/9783839450598-014/html?lang=de&lt;/ref&gt;&lt;ref&gt;https://hpluspedia.org/index.php?title=Natasha_Vita-More&lt;/ref&gt;&lt;ref&gt;https://www.humanityplus.org/transhumanist-faq&lt;/ref&gt;.

She is perhaps less of a candidate for a chief extropian.

Links:
* {{W|Natasha Vita-More}}, wikipedia.org
* https://en.wikipedia.org/w/index.php?title=Natasha_Vita-More&amp;oldid=561551368#Papers, an older revision featuring Papers section
* [https://web.archive.org/web/20180612142702/http://www.natasha.cc/cv.pdf natasha.cc/cv.pdf], version 2012, archive.org
* [https://cryonics.miraheze.org/wiki/Natasha_Vita-More Natasha Vita-More], cryonics.miraheze.org (a wiki)
* [https://www.forbes.com/sites/calumchace/2023/02/01/pioneering-transhumanism-a-conversation-with-natasha-vita-more/ Pioneering Transhumanism: a conversation with Natasha Vita-More], 2023, forbes.com -- reinforces notability; relates an interesting experiment with nematodes (kind of worms) concerning cryonics

== Eliezer Yudkowsky ==
Yudkowsky is interesting at least for his pro-extinctionist ideas&lt;ref&gt;[https://web.archive.org/web/20030814012950/http://www.extropy.org/ideas/journal/previous/1998/10-01a.html A Critical Discussion of Vinge's Singularity Concept: Thirteen Comments], October 1998, extropy.org at archive.org&lt;/ref&gt;, which he seems to have later renounced&lt;ref&gt;https://julesevans.medium.com/how-did-transhumanism-become-the-religion-of-the-super-rich-d670a410b01a&lt;/ref&gt;. Whether he can be considered an extropian is not so clear, but he seems to have been on the extropian mailing list.

A pro-extictionist quotation:
: &quot;I must warn my reader that my first allegiance is to the Singularity, not humanity. I don't know what the Singularity will do with us. I don't know whether Singularities upgrade mortal races, or disassemble us for spare atoms. While possible, I will balance the interests of mortality and Singularity. But if it comes down to Us or Them, I'm with Them. You have been warned.&quot;

== Eric Drexler ==
Per WP, Eric Drexler was on the extropian mailing list. He features as a forecaster of future in Extropy #15, 1995 (the forcasters are Gregory Benford, Stephen Bridge, Eric Drexler, FM-2030, Mark Miller, Max More, Nick Szabo):
* https://raw.githubusercontent.com/Extropians/Extropy/master/ext15.pdf
Drexler forecasts uploaded minds to happen in 2006-2021 and big fraction of economy out of solar system to happen in 2011-2026. (The table of future forecasts from that Extropy issue gives a good impression of what kind of events these people envision or even are looking forward to happening.)

Drexler is especially noted for his 1986 book ''Engines of Creation'', whose full text is available online&lt;ref&gt;https://web.archive.org/web/20060105213124/http://www.foresight.org/EOC/&lt;/ref&gt;.

Links:
* {{W|Eric Drexler}}
* {{W|Engines of Creation}}

== Libertarianism ==
Extropianism is indicated to be libertarian by https://www.britannica.com/topic/transhumanism.

== TechnoCalyps ==
[[Wikipedia: TechnoCalyps]] is a film featuring interviews with people identified as transhumanist. We can compare the list of interviewed people with Extropy institute directors (https://web.archive.org/web/20100618112954/https://www.extropy.org/directors.htm).

From memory, items common to the two lists (positively checked agains the list above, from memory against the film):
* {{W|Max More}}
* {{W|Natasha Vita-More}}
* {{W|Marvin Minsky}}
* {{W|Gregory Stock}}
* {{W|Ray Kurzweil}}

Wikipedia: TechnoCalyps has a list of cast, but some of them are not transhumanists. It seems to me (from memory) that the five people above all fit the label transhumanist reasonably well; by contrast, among the cast there is {{W|Kirkpatrick Sale}} who is rather a neo-Luddite.

== Cryonics ==
Extropians seem to be fans of cryonics. Max More had some role in {{W|Alcor Life Extension Foundation}}. I seem to remember some talk about cryonics in Extropy magazine.

Links:
* [https://thebaffler.com/salvos/everybody-freeze-pein Everybody Freeze!] by Corey Pein, 2016, thebaffler.com
*: (A slightly unrelated quote, but related to extropianism) &quot;But More was much more than an effective publicist who found himself in the right place at the right time. He was the vanguard leader of a peculiar hyper-libertarian, anti-government, techno-utopian ideology that came to dominate Silicon Valley as the computer industry cast itself as the panacea for all the world’s problems.&quot;

== Characterizations of extropianism ==
Candidate adjectival characterizations, to be researched:
* Transhumanist
* Superhumanist
* Techno-optimistic
* Techno-futuristic
* Techno-utopian
* Technophillic/technophile
* Postbiological or pro-postbiology
* Pro-extinctionist
* Anti-environmentalist
* Atheist
* Libertarian
* Pro-capitalist/pro-market
Whether they all apply and to what extent needs a proper analysis/substantiation.

== Singularity ==
I recall one article contrasting extropianism with singularitanism. However, at least the discussion of technological singularity is rather part of extropianism. Since Vinge's article on singularity is from 1993, it would not have been there in 1988, the first issue in Extropy magazine. On the other hand, it was in the 2nd issue (I think) that Max More was enthusiastic about Mind Children, which is somewhat singularitarian without using the label or concept of singularity.

Some sources and indications:
* [https://web.archive.org/web/20030814012950/http://www.extropy.org/ideas/journal/previous/1998/10-01a.html A Critical Discussion of Vinge's Singularity Concept: Thirteen Comments], October 1998, extropy.org at archive.org -- comments by Max More and others (Eliezer S. Yudkowsky presents some pro-extictionist ideas)
* [https://web.archive.org/web/20020308052054/http://www.kurzweilai.net/meme/frame.html?main=/articles/art0408.html Max More and Ray Kurzweil on the Singularity], 26 Febr 2002[https://web.archive.org/web/20031004165123/http://maxmore.com/writing.htm], kurzweilai.net at archive.org

== The Principles of Extropy ==
The Extropian Principles/The Principles of Extropy is a document by Max More. Working hypothesis: &quot;The Extropian Principles&quot; and &quot;The Principles of Extropy&quot; are the same evolving document.
* [https://www.aleph.se/Trans/Cultural/Philosophy/princip.html The Extropian Principles 2.5] by Max More, 1993, aleph.se -- I recall this was also published in Extropy magazine
* [https://web.archive.org/web/20031005110304/http://maxmore.com/extprn26.htm THE EXTROPIAN PRINCIPLES V. 2.6] by Max More, 1995, maxmore.com at archive.org
* [https://web.archive.org/web/19991008222337/http://www.maxmore.com/extprn3.htm THE EXTROPIAN PRINCIPLES Version 3.0], A Transhumanist Declaration, by Max More, 1998, maxmore.com at archive.org
* [https://web.archive.org/web/20031002105702/http://www.extropy.org/principles.htm Principles of Extropy Version 3.11] by Max More, 2003, extropy.org at archive.org

== Space colonization ==
1) &quot;Boundless expansion&quot;, into the universe, must be in version 2.5 of the Extropian Principles. Later versions of the document radically changed this item (detail to be provided later).

2) In issue 2 of Extropy Magazine (I think), Max More speaks enthusiastically about [[Mind Children]], which features space colonization.

A reservation: this is not necessarily space colonization ''by humans'', that is, members of the biological homo sapiens species.

== Immortalism ==
Something like immortalism seems to be a key objective of extropianism, or at least by Max More. It is not necessarily literal immortalism but rather extreme longevitist: making sure human lifespan spans perhaps 1000 years or more (rather than ca. 100) for those who opt for it. Max More presents similar ideas even in 2023&lt;ref&gt;https://maxmore.substack.com/p/letter-to-mother-nature-amendments by Max More, 2023&lt;/ref&gt;:
: &quot;Amendment No.1: We will no longer tolerate the tyranny of aging and death. Through genetic alterations, cellular manipulations, synthetic organs, and any necessary means, we will endow ourselves with enduring vitality and remove our expiration date. We will each decide for ourselves how long we shall live.&quot;
A logical consequence of the last statement is literally indefinite life span (including 1E20 years if one so chooses), which seems to be physical nonsense unless one engages in some of the arguably wild/crazy idea from Moravec's [[Mind Children]], such as exponentially accelerating time (the phrasing is perhaps lacking) enabling subjective experience of indefinite time.

For some values of longevity, [[#Space colonization]] will seem to be a necessity, to escape the expanding Sun making the Earth uninhabitable. Unless, that is, the extropians/transhumanists will have technologies to upload themselves into a Sun-embedded computer or some such wild idea.

As per extropy.org's Transhumanis FAQ&lt;ref&gt;https://web.archive.org/web/20110718075135/http://www.extropy.org/faq.htm&lt;/ref&gt;: 'Transhumanist Arts was founded in 1982 by Natasha Vita-More (f/k/a/ Nancie Clark) and introduced as an &quot;art theory&quot; (originally, &quot;TransArt&quot;). The &quot;Transhumanist Arts Statement&quot; written to established a poetic doctrine of transhumanist expression: &quot;Transhumanist Arts represent the aesthetic and creative culture of transhumanity…Our aesthetics and expressions are merging with science and technology in designing increased sensory experience…Transhumanist Artists want to extend life and overcome death…[...]' And further from the FAQ: &quot;For the first time in history, transhumans as artists want to live indefinitely, want to live in space, want to augment our intelligence, want to grow more desirable, brighter, more creative.&quot;

== Cornucopianism ==
Max More seems to be a cornucopian&lt;ref&gt;[https://maxmore.substack.com/p/limits-of-limits-to-growth Limits of Limits to Growth - by Max More], 2024, maxmore.substack.com&lt;/ref&gt;:
: &quot;Resources never “run out”. As Julian Simon argued in The Ultimate Resource [Simon, 1998], human ingenuity creates new resources as required from the raw materials of the universe. We will never run out of copper because its price will increase as it becomes scarcer, stimulating the discovery of more deposits, more recycling, new methods that use less of it, and better substitutes.&quot;

However, the above is not from the prime time of Extropy magazine and the Extropy Institute/extropy.org, 1998-2006.

== Cryonics ==
Extropians seem to be fans of cryonics. Max More had some role in {{W|Alcor Life Extension Foundation}}. I seem to remember some talk about cryonics in Extropy magazine.

Links:	
* [https://thebaffler.com/salvos/everybody-freeze-pein Everybody Freeze!] by Corey Pein, 2016, thebaffler.com
*: (A slightly unrelated quote, but related to extropianism) &quot;But More was much more than an effective publicist who found himself in the right place at the right time. He was the vanguard leader of a peculiar hyper-libertarian, anti-government, techno-utopian ideology that came to dominate Silicon Valley as the computer industry cast itself as the panacea for all the world’s problems.&quot;

== Everybody Freeze! ==
Link:
* [https://thebaffler.com/salvos/everybody-freeze-pein Everybody Freeze!] by Corey Pein, 2016, thebaffler.com

Everybody Freeze! is a fascinating article whose title fails to clarify that it presents Max More's extropianism and people around it in fascinating detail. One problem is that it has no line references.

== Extropy magazine ==
Extropy magazine is a major source for what is Max More's extropianism, together with extropy.org of Extropy Institute. The source uses the words &quot;extropy&quot;, &quot;extropian&quot; and &quot;extropianism&quot;. It is available from github, archive.org and other places.

Something like a summary of previous issues is available somewhere at the end of some issues.

The first issue appeared in 1988. Issue 17 appeared in second half of 1996 per GitHub; this was perhaps the last issue or the last offline issue (unless the GitHub repo is incomplete). Extropy.org states: &quot;Extropy: The Journal of Transhumanist Thought from 1989 to late 1996 in high-gloss print and distributed at major bookstores.&quot;&lt;ref&gt;https://web.archive.org/web/20100618114155/http://www.extropy.org/publications.htm&lt;/ref&gt;

Issues subtitles:
* Vaccine for Future Shock, issue 1-5 (or more?)
* The Journal of Transhumanist Thought, issue 7-? (including #14&lt;ref&gt;https://github.com/Extropians/Extropy/blob/master/Extropy-14_FirstQuarter-1995.pdf&lt;/ref&gt;)
* Journal of Transhumanist Solutions (see below)

Topics covered are identified in various issues. Issue 14 has the following (quoted word for word):
* Transhumanism and futurist philosophy
* Life extension, immortalism and cryonics
* Smart drugs (nootropics) and intelligence increase technologies
* Machine intelligence, personality uploading, and Artificial life
* Nanocomputers and nanotechnology
* Memetics (ideas as viruses)
* Experimental free communities in space, on the oceans, and within computer networks
* Effective thinking and information filtering
* Self-transformative psychology
* Spontaneous orders (free markets, neural networks, evolutionary processes, etc)
* Digital economy (privacy technologies, digital money and electronic markets)
* Rational, market-based environmentalism
* Probing the ultimate limits of physics

As for whether it is a magazine or a journal, Max More uses the phrase &quot;Extropy magazine&quot; here: &quot;We founded Extropy magazine in the late 1980s, and later the Institute, while still graduate students in philosophy and could not plausibly be called rich by Anglo-American standards.&quot;&lt;ref&gt;https://www.theregister.com/2003/09/18/extropian_cofounder_locks_horns/&lt;/ref&gt;.

As per extropy.org: &quot; Then, in November 1997, it [the magazine] moved to the Web as Extropy Online, where it continued to publish articles for three years. After a year of dormancy, it returned to the Web in February 2002 as its current form, Extropy: Journal of Transhumanist Solutions.&quot;&lt;ref&gt;https://web.archive.org/web/20131106011118/http://www.extropy.org/extropyonline.htm&lt;/ref&gt;

Links:
* {{W|Extropianism}}, wikipedia.org
* https://github.com/Extropians/Extropy, e.g. https://github.com/Extropians/Extropy/blob/master/Extropy-01.pdf; has issue 1-17; https://github.com/Extropians/Extropy/blob/master/Extropy-14_FirstQuarter-1995.pdf is an example of a pdf with OCR
* https://archive.org/details/extropy-01/, https://archive.org/details/extropy-02/ (nothing seems available for direct view), https://archive.org/details/extropy-03/, etc.
* https://www.resistance.money/research/extropy/Extropy-01.pdf; tweaking the URL yields other issues

== Extropy.org ==
Extropy.org is a website of the (now-defunct?) Extropy Institute. The website is still available as of Sep 2025, but some pages are only be available in archive.org, including https://extropy.org/principles.htm and https://extropy.org/history.htm and http://www.extropy.org/faq.htm.

Subpages (links often to archive.org):
* The list of directors is covered in https://www.extropy.org/directors.htm, with images not loading; archive helps: https://web.archive.org/web/20100618112954/https://www.extropy.org/directors.htm.
* Extro conferences are covered in https://www.extropy.org/events.htm, with images not loading; archive helps: https://web.archive.org/web/20100618121452/http://www.extropy.org/events.htm.
* A list of publications with images loding is in https://web.archive.org/web/20100618114155/http://www.extropy.org/publications.htm. It prominently features this: &quot;Extropy: The Journal of Transhumanist Thought from 1989 to late 1996 in high-gloss print and distributed at major bookstores.&quot;
* Principles of extropy are here: https://web.archive.org/web/20100618114647/http://www.extropy.org/principles.htm. Different historical versions in part yield different versions of the principles.
* Mailing lists are linked from here: https://web.archive.org/web/20100618112553/http://www.extropy.org/emaillists.htm.
* TBD:History
* FAQ (called &quot;Transhumanist FAQ&quot;): https://web.archive.org/web/20110718075135/http://www.extropy.org/faq.htm

Links:
* http://www.extropy.org
* https://web.archive.org/web/20100618114451/http://www.extropy.org/About.htm

== Extropianism and life ==
Life appears as an element in some definitions of extropy. Other word that appears is vitalism, relating to Latin ''vita''. Natasha Vita-More is perhaps named after Latin vita, but that is just a guess.

It was Schrödinger who characterized life as entity that feeds on negative entropy. In that sense, one who wants more extropy simply wants more life. But life is not the only element in the definitions of extropy by Max More. Moreover, the definition of life as that which feeds on negative entropy was criticized by Popper as per [[Technology as a threat or promise for life and its forms]]. Traditional definitions of life (entity featuring growth, metabolism, reproduction, etc.) includes biological entities but excludes assembled android hosting a Moravecian upload. Those who are happy to exist in an android as Moravecian uploads either want to go beyond life, consider a broader concept of life than the traditional one or something of the sort.

== Workshop ==
I am considering moving this talk page to something like [[One man's look at extropianism/Workshop]]. The material does not need signatures. It is intended to support the main material, but it not really talk or discussion. On one hand, this slight abuse of a talk page seem tolerable. On the other hand, it seems increasingly impractical, especially since restructuring and major changes would require changing all the signatures. Moreover, should someone want to start a discussion, it would be intermixed with the supporting material, perhaps far from ideal. Whether the name &quot;workshop&quot; is good I am not sure; other candidates are &quot;Supporting material&quot; and &quot;Appendix&quot;. I never saw anything like that in Wikipedia, only perhaps in arbitrarion committee cases, but not for mainspace articles. And that is strange: surely, to write a good article collaboratively, something like supporting material should possibly be available somewhere? (The same problem applies to [[Technology as a threat or promise for life and its forms]], but the scale is much smaller]].) --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:59, 13 September 2025 (UTC)

== Transhumanist FAQ ==
The title &quot;Transhumanist FAQ&quot; somewhat ambiguously (but for the definite article?) refers to at least three documents:
* Extropy.org's Transhumanist FAQ, https://web.archive.org/web/20040401172610/http://www.extropy.org/faq.htm. As for the authors, it states: '8.2 Who created the FAQ?  Members of Extropy Institute have provided information for the FAQ. Special thanks goes to Dr. Max More, Greg Burch, Natasha Vita-More, Harvey Newstrom, Riley Jones, Prof. Tom Bell, Christine Peterson, Dr. Eric Drexler, Prof. Marvin Minsky, Dave Krieger, E. Shaun Russell, Ziana Astralos, Anand and [many others to be included here.]'
* The Transhumanist FAQ by Nick Bostrom, https://nickbostrom.com/views/transhumanist.pdf; the link currently points to Version 2.1 (2003). Apparently the same as https://web.archive.org/web/20040602145152/http://transhumanism.org/resources/FAQv21.pdf.
* The Transhumanist FAQ https://whatistranshumanism.org/. While the title says &quot;What is Transhumanism?&quot;, down the document, it says &quot;The Transhumanist FAQ was developed in 1998 and authored into a formal FAQ in 1999 through the inspirational work of transhumanists, including Alexander Chislenko, Max More, Anders Sandberg, Natasha Vita-More, James Hughes, and Nick Bostrom.&quot; And then, as a heading od sort, &quot;Transhumanist FAQ – version 3.0&quot;.

A comparison would perhaps be in order, as well as checking historical versions. Bostrom references extropianism and Max More. And Extropy.org/Max more references &quot;World Transhumanist Association&quot;, but no explicitly &quot;Bostrom&quot;.

A question: was Bostrom associated in any way with Extropy magazine and the Extropy Institute? Is his brand of &quot;transhumanism&quot; some kind of competition, taking the non-trademarked term &quot;transhumanism&quot; from Extropy magazine and applying it is somewhat differently?

One possible connection is that Bostrom relates to what became Humanity+, in which a key role was taken by Natasha Vita-More.

As an aside, what about this putative parody based on [[Wikipedia: Transhumanism]]: 'Transchimpism is a philosophical and intellectual movement that advocates the enhancement of the chimp condition by developing and making widely available new and future technologies that can greatly enhance longevity, cognition, and well-being [of the chimps, even if it results in homo sapiens sapiens].' Of course, humans evolved from a common ancestors with chimps rather than from chimps, but you get the idea. The &quot;future technology&quot; could include guided genetic modification of the chimps to accelerate the evolution of chimps (or pre-chimps) into humans (creationists seem to believe something like that happened anyway).

As a 2nd order aside, I gave the above paragraph to Gemini and it responded as if it understood it.

== References ==
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    <title>User talk:Dan Polansky/One man's look at proper names</title>
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      <text bytes="1195" sha1="irqkto53x9bm108pty2g072c780nqgx" xml:space="preserve">== Issues ==
1) In section &quot;Distinguishing proper names from common nouns&quot;, countable and uncountable common nouns are not well enough separated, resulting in inaccurate statements. Since, an uncountable word like &quot;gold&quot; does not refer to a class, really; it refers to individual substance, for some sense of &quot;individual&quot;. Similarly, &quot;whiteness&quot; does not refer to a class. While this is acknowledged in a reparatory statement, it results in an expository style in which first inaccurate statements are made and then they are corrected, which, while having its charm, is perhaps suboptimal. And if this style is used, the reader should be warned of it.

--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:52, 26 September 2025 (UTC)

== EncycloPetey ==
User EncycloPetey has a decent write-up on proper names in the English Wiktionary:
* [[Wiktionary: User:EncycloPetey/English proper nouns]]
I am pretty certain his write-up was part of an inspiration for my own. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:18, 4 October 2025 (UTC)</text>
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      <text bytes="4939" sha1="etz0wsu5i3k82qfjzj7x2w934uuouue" xml:space="preserve">{{Original research}}
Author: Dan Polansky

This article looks at the value of Wiktionary, a free-as-in-freedom/libre quasi-omni-lingual) dictionary containing definitions, invented examples of use, quotations of actual use in literature, synonyms, antonyms, semantically related terms under &quot;See also&quot; head, further reading with external links, etymologies, pronunciation, inflection tables, images, a separate space with WordNet-like thesaurus, etc., using the same wiki technology as Wikipedia (MediaWiki), the free-as-in-freedom/libre encyclopedia. Just like in Wikipedia, one can use wikilinks, exteranl links and inline references in a plaintext markup rendered as HTML for a web browser.

The analysis of value/worth is going to depend on the language of the mutation. The value of the English mutation is quite different since it can be seen as the primary mutation, given the significance of English as the lingua franca of the 21st century (and earlier as well). But non-English mutations also present considerable value: they present all information in the language of the native speakers of that language.

Let me then have a look at the value of the English Wiktionary specifically. The value can be differentiated based on the information class considered, that is e.g. definitions vs. inflection tables vs. further reading.

The English Wiktionary faces formidable competition in the form of non-free/non-libre dictionaries online that are freely available but proprietary. A problem that the English Wiktionary cannot solve is that anyone can edit (including people who are inapt, stupid, slipshod, deceptive and nasty) and that it leads to the kind of errors and suboptimalities that the proprietray dictionaries do not have.

One feature that is great is the English Wiktionary as OneLook, i.e. a database of pages and page sections for lemmas in many languages that collect links to external further reading online. As a result, the reader can try to verify the information in the wiki in sources that are very conveniently one click away, and moreover, learn information that the wiki does not have. It seems this service would be valuable even if the English Wiktionary contained nothing else.

But there is also a value in information that is in some way tentative: it leads to hypothesis discovery.

The presence of talk pages to discuss the information on the page is a great additional benefit, one that e.g. Merriam-Webster online does not have. One can also place various analyses and hypotheses there that then do not make it to the main namespace.

The extent to which quotations of actual use can be presented seems unmatched by most online English dictionaries (OED is perhaps a match, but it is not freely available oline). And the same extent is available for all languages in the English Wiktionary and in principle for all language mutations.

The value or usefulness is witnessed by page views. As for page views, Wiktionaries tend to be second to Wikipedia. As a caveat, the page views in Wiktionaries are not fully comparable since the use of small pages in comparison to other projects inflates them. But the page view gap between Wiktionaries and the smaller project types (Wikisource, Wikibooks, Wikiversity, etc.) is so big that it is perhaps relatively safe to say that Wiktionaries are really second behind Wikipedia in terms of page views.

The English Wiktionary has a feedback page. An analysis of the page would reveal more about to what extent people appreciate the English Wiktionary. Sometimes, Wiktionary contributors (user accounts) get thanks/expressions of appreciation on their talk pages, which is also suggestive of value.

OneLook is a web service that provides, for each sought word or term, a collection of links to serious English dictionaries and other items, including automatically built collection of quotations of use. On the same page, it shows definitions extracted from the English Wiktionary. It can only do so since the definitions are freely licensed (free-as-in-freedom/libre).

Interwiki links (for a given page, links between pages of different language mutations) provide additional benefits. When one finds, say, a German word in the English Wiktionary and feels there is not enough information or is just curious, the German Wiktionary page for the word is one click away. In this way, the language mutations complement each other rather than solely competing.

Further questions:
* How did the page views of Wiktionaries historically develop?
* What articles praise Wiktionaries for their value?
* What do users of Wiktionaries appreciate the most? Definitions, etymologies, inflection tables, translations, coverage of small languages? Anything else?
* To what extent were Wiktionary data used in natural language processing? Are there any articles reporting? What can one find by searching for the word Wiktionary in Google Scholar?

[[Category:Wiktionary]]</text>
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== '''Introduction and Sources of Communication Law''' ==

=== Irish History and the Role of Catholicism ===
English settlers began coming to Ireland around 1169 and brought the common law system with them.&lt;ref&gt;Janet Sinder, ''Irish Legal History: An Overview and Guide to the Sources'', 93 Law Library Journal 231, 243 (2001).&lt;/ref&gt;  At the time, the Irish were governed by the brehon law system, which consisted of laws that were “the written version of oral rules that had been passed down for generations,” rather than “statutes enacted by a legislative body.”&lt;ref&gt;''Id''. at 238.&lt;/ref&gt;  The common law system brought by the English and the brehon system existed together in the State for almost 500 years, until brehon law was suppressed with the Tudor conquest and later outlawed.&lt;ref&gt;''Id''. at 243, 248.&lt;/ref&gt;  The English took control of Ireland and developed the legal system, enacting statutes to address social problems that existed because of unrest in Ireland following the English conquest.&lt;ref&gt;''Id''. at 249.&lt;/ref&gt;  Specifically, “penal laws” were passed with the intent to “convert the Irish to Protestantism and to penalize them if they remained Catholic.”&lt;ref&gt;''Id''. at 249.&lt;/ref&gt;  

In 1800, the Irish Parliament agreed to the Act of the Union, making Ireland a part of the United Kingdom, adopting practically the same legal system as that of Great Britain.&lt;ref&gt;''Id''. at 250.&lt;/ref&gt;  In 1919, the Anglo-Irish War began and Ireland established its own local government known as “The Dáil” and in 1920, the Government of Ireland Act divided Ireland into two regions – Southern and Northern Ireland.&lt;ref&gt;''Id''. at 251-52.&lt;/ref&gt;  Following a truce, the war ended and the Constitution of the Irish Free State was drafted, a departure from the British legal system which has no written constitution.&lt;ref&gt;''Id''. at 252-53.&lt;/ref&gt;  The South remained largely Catholic, while Northern Ireland was primarily Protestant.&lt;ref&gt;Gerard Whyte, ''Religion and the Irish Constitution'', 30 J. Marshall L. Rev. 725, 727 (1997).&lt;/ref&gt;  Following the British conquest of the State, a new Constitution was adopted in 1937 which reflected the current ideologies in Ireland.&lt;ref&gt;''Id''. at 728.&lt;/ref&gt;  Ireland’s history is important in understanding the underlying themes of Ireland’s current communication law, as two notable influences of the Constitution come from “the inherited liberal democratic tradition of the Free State” and “the social teaching of the Catholic Church.”&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Structure of the Irish Legal System ===
Ireland is a parliamentary republic with power divided among three branches of government, as laid out by the Constitution.&lt;ref&gt;Northwestern Pritzker School of Law, “Ireland: International Team Project, Government Structure,” [https://library.law.northwestern.edu/c.php?g=1369634&amp;p=10120307#:~:text=News%20and%20Statistics-,Government%20Structure,interprets%20and%20applies%20the%20laws. https://library.law.northwestern.edu/c.php?g=1369634&amp;p=10120307#:~:text=News%20and%20Statistics-,Government%20Structure,interprets%20and%20applies%20the%20laws.]&lt;/ref&gt;  The legislative power is vested in the Oireachtas, which consists of the President and the two houses of the Oireachtas, the Dáil and the Seanad.&lt;ref&gt;Houses of the Oireachtas, “Factsheet,” https://www.oireachtas.ie/en/press-centre/factsheet/.&lt;/ref&gt;  The executive power is given to the Government, which is headed by the Prime Minister.&lt;ref&gt;''Id''.&lt;/ref&gt;  The judicial power is vested in the court system, which is made up of five main courts.&lt;ref&gt;Northwestern Pritzker School of Law, ''supra'' n. 12; Citizens Information, “Courts,” https://www.citizensinformation.ie/en/justice/courts-system/courts/.&lt;/ref&gt;

=== '''Sources of Communication Law in Ireland''' ===
Ireland’s legal system operates through three main sources of law: The Constitution, the Common Law, and Statutes.&lt;ref&gt;Stephen Walsh &amp; Co. Solicitors, “The Irish Legal System Explained,” https://stephenwalshsolicitors.ie/irish-legal-system-explained/#:~:text=Ireland's%20legal%20system%20has%20three,law%20of%20the%20European%20Union.&lt;/ref&gt;  Ireland joined the European Communities, now the European Union (“EU”) in 1973, and is also subscribed to EU law.&lt;ref&gt;''Id''.; European Union, Representation in Ireland, “Ireland in the EU,” https://ireland.representation.ec.europa.eu/about-us/irelands-eu-membership_en.&lt;/ref&gt;. Communication law in Ireland is shaped by a combination of domestic, regional, and international sources of law.  The primary foundations lie in the Constitution, which protects fundamental freedoms.  Legislation enacted by the Oireachtas includes statutes regulating broadcasting, media, and digital communications.  In addition, European Union law and the ECHR play a significant role in ensuring Irish legislation complies with relevant regulations and guidelines.

==== The Constitution ====
The [https://www.irishstatutebook.ie/pdf/ga.cons.pdf Irish Constitution] was ratified in 1937 and “is the fundamental law of the state.”&lt;ref&gt;Stephen Walsh &amp; Co. Solicitors, ''supra'' n. 16.&lt;/ref&gt;  The Constitution lays out the separation of powers and functions of the State, and provides the fundamental rights guaranteed to Irish citizens.&lt;ref&gt;''Id''.&lt;/ref&gt;  Specifically, the Constitution guarantees citizens the right to “express freely their convictions and opinions.”&lt;ref&gt;Constitution of Ireland, Article 40.6.1(i).&lt;/ref&gt;  This grant of free expression, however, contains a limit on expression that “undermines public order or morality or the authority of the State” and specifically states that “[t]he publication or utterance of seditious or indecent matter is an offence . . . punishable [by] law.”&lt;ref&gt;''Id''.&lt;/ref&gt;

Prior to the adoption of the 1937 Irish Constitution, common law principles from England were embedded in Irish law.&lt;ref&gt;David Kenny, ''God in the Irish Constitution,'' BYU Law (Oct. 31, 2020), https://talkabout.iclrs.org/2020/10/31/god-in-the-irish-constitution/.&lt;/ref&gt;  When the 1937 Constitution was adopted, it was influenced heavily by both common law principles that previously existed, as well as and Catholic principles and traditions.&lt;ref&gt;''Id''.&lt;/ref&gt; Specifically, the Constitution was, in part, an attempt “to unite republican principle with a confessional infusion of Roman Catholic thinking and teaching on the nature of the state, the common good, and the place of the rights of the individual.”&lt;ref&gt;Kevin Boyle, “The Irish Constitution and the Rights of the Individual,” Article 19 Research and Information Centre on Censorship, London, [https://www.persee.fr/doc/irlan_0183-973x_1988_num_13_2_2821. https://www.persee.fr/doc/irlan_0183-973x_1988_num_13_2_2821.]&lt;/ref&gt;  The extent to which Catholicism shaped the Constitution can be seen through the inclusion of religious elements in much of the document.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Domestic Legislation ====
The [https://www.cnam.ie/app/uploads/2024/11/Coimisiun-na-Mean-Online-Safety-Code.pdf Online Safety Code] was developed by the Coimisiún na Meán and is a mandatory set of rules that must be followed by video-sharing platforms.&lt;ref&gt;Coimisiún na Meán, “Legislation Explained,” [https://www.cnam.ie/general-public/online-safety/online-safety-framework/legislation-explained/. https://www.cnam.ie/general-public/online-safety/online-safety-framework/legislation-explained/.]&lt;/ref&gt;  The rules prohibit illegal context, including “child sexual abuse materials, child trafficking, terrorist content, offences concerning racism/xenophobia or incitement of violence or hatred against a group of persons.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Code also prohibits harmful context, such as “cyberbullying, pornography, gross violence, promoting eating disorders, and promoting suicide or self-harm content.”&lt;ref&gt;''Id''.&lt;/ref&gt;

The [https://revisedacts.lawreform.ie/eli/2009/act/18/revised/en/pdf?annotations=true Broadcasting Act 2009], as amended by the Online Safety and Media Regulation Act 2022,  “determines the regulatory framework for the broadcasting, audiovisual on-demand, and online safety in Ireland,” and governs “issues relating to public service broadcasters, media development, and public funding.”&lt;ref&gt;Coimisiún na Meán, “Broadcasting Act 2009,” [https://www.cnam.ie/industry-and-professionals/codes-legislation/legislation/broadcasting-act/. https://www.cnam.ie/industry-and-professionals/codes-legislation/legislation/broadcasting-act/.]&lt;/ref&gt;

The Irish government has also announced approval of the General Scheme of the Media Regulation Bill, which will “give effect to the main elements” of the [https://www.irishstatutebook.ie/eli/2025/si/22/made/en/pdf European Media Freedom Act] (“EMFA”) in Ireland.&lt;ref&gt;Government of Ireland, Department of Culture, Communications and Sport, “Minister O’Donovan Secures Government Approval of the General Scheme of the Media Regulation Bill,” (Jul. 2 2025), https://www.gov.ie/en/department-of-culture-communications-and-sport/press-releases/minister-odonovan-secures-government-approval-of-the-general-scheme-of-the-media-regulation-bill/.&lt;/ref&gt;  The EMFA protects media independence via safeguards for journalist sources, protection against “unjustified online content removal,” and transparency for the media audience.&lt;ref&gt;Coimisiún na Meán, “European Media Freedom Act,” https://www.cnam.ie/industry-and-professionals/codes-legislation/legislation/european-media-freedom-act/.&lt;/ref&gt;

==== Relevant Regulatory Bodies ====
The Communications Regulation Act 2002 created the Commission for Communications Regulation (“COMREG”).&lt;ref&gt;Paul McMahon, “ComReg,” McMahon Legal Solicitors and Legal Consultants, https://mcmahonsolicitors.ie/comreg-2/#:~:text=The%20ODTR%20later%20became%20the,its%20powers%20under%20European%20regulations.&lt;/ref&gt;  The statutory body oversees “the regulation of the electronic communications sector (telecommunications, radio-communications and broadcasting transmission) and the postal sector.&lt;ref&gt;Commission for Communications Regulation, “Who We Are and What We Do,” https://www.comreg.ie/about/foi-aie-info/who-we-are-and-what-we-do/.&lt;/ref&gt;  COMREG has responsibilities in the telecommunications sector related to electronic communications services and networks, and posts and spectrum management.&lt;ref&gt;Commission for Communications Regulation, “What We Do,” https://www.comreg.ie/about/what-we-do/.&lt;/ref&gt;  The body is &quot;responsible for facilitating competition, for protecting consumers and for encouraging innovation.&quot;&lt;ref&gt;''Id''.&lt;/ref&gt;  COMREG operates under both Irish and EU legislation.&lt;ref&gt;''Id''.&lt;/ref&gt;  COMREG also &quot;has surveillance and enforcement responsibilities in relation to radio equipment regulation, and regulation of devices relating to electromagnetic compatibility.&quot;&lt;ref&gt;Commission for Communications Regulation, &quot;Who We Are and What We Do,&quot; https://www.comreg.ie/about/foi-aie-info/who-we-are-and-what-we-do/&lt;/ref&gt;. 

The Coimisiún na Meán is the “regulator of traditional and online media in Ireland,” as established by the Online Safety Media Regulation Act (“OSMR”).&lt;ref&gt;Coimisiún na Meán, “Legislation Explained,” https://www.cnam.ie/general-public/online-safety/online-safety-framework/legislation-explained/.&lt;/ref&gt;  The Coimisiún na Meán published an Online Safety Code and Online Safety Guidance Materials under the OSMR.&lt;ref&gt;Government of Ireland, Department of Culture, Communications and Sport, “Online Safety and Media Regulation Act 2022,” (last updated Apr. 15, 2025), https://www.gov.ie/en/department-of-culture-communications-and-sport/publications/online-safety-and-media-regulation-act-2022/.&lt;/ref&gt;. Prior to the establishment of the Coimisiún na Meán (&quot;Media Commission&quot;), the Broadcasting Authority of Ireland (&quot;BAI&quot;) was a primary media regulator in Ireland.&lt;ref&gt;John Cian McGrath and Kirsty Park, Dublin City University, “EDMO Policy Monitoring: The Regulation of Online Disinformation,” (Nov., 2022), [https://edmohub.ie/wp-content/uploads/2023/02/EDMO-Task-V-Dec-2022-2.pdf#:~:text=The%20Electoral%20Reform%20Act%20has%20been%20passed,not%20compatible%20with%20the%20e%2D%20Commerce%20Directive4. https://edmohub.ie/wp-content/uploads/2023/02/EDMO-Task-V-Dec-2022-2.pdf#:~:text=The%20Electoral%20Reform%20Act%20has%20been%20passed,not%20compatible%20with%20the%20e%2D%20Commerce%20Directive4.]&lt;/ref&gt;  The BAI was established by the Broadcasting Act of 2009.&lt;ref&gt;Communications Officer, &quot;Broadcasting Authority of Ireland (BAI),&quot; The Irish Film and Television Network, https://www.iftn.ie/rep_bodies/Agenices/?act1=record&amp;aid=16&amp;rid=64&amp;only=1.&lt;/ref&gt;.  The role of the BAI was &quot;to ensure that the number and categories of broadcasting services made available in the State best serve the needs of the people of the island of Ireland; to uphold the democratic values enshrined in the Constitution especially those relating to rightful liberty of expression and; to provide for open and pluralistic broadcasting services.&quot;&lt;ref&gt;''Id''.&lt;/ref&gt;  Those objectives were absorbed through the three-year transition integrating the BAI into the new Media Commission.&lt;ref&gt;McGrath and Park, ''supra'' note 32.&lt;/ref&gt;  BAI was fully dissolved in in March 2023 and the Media Commission became fully operational.&lt;ref&gt;Kate McKenna and Simon Shinkwin, “In brief: Telecoms Regulation in Ireland,” Matheson, (June 11, 2025), https://www.lexology.com/library/detail.aspx?g=62433d50-c5b1-4cb0-b3f9-5823363d35b5.&lt;/ref&gt;  The Media Commission is also deemed the Digital Services Coordinator for Ireland.&lt;ref&gt;''Id''.&lt;/ref&gt;

The Competition and Consumer Protection Commission (“CCPC”) is a regulatory authority which works with the Media Commission to enforce the Digital Services Act.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Regional Law ====
Ireland signed the European Convention on Human Rights (&quot;ECHR&quot;) in 1950 and then ratified it in 1953.&lt;ref&gt;Government of Ireland, Department of Foreign Affairs and Trade, “European Court of Human Rights,” (last updated Aug. 6, 2025), https://www.gov.ie/en/department-of-foreign-affairs/publications/european-court-of-human-rights/#:~:text=Ireland%20signed%20the%20Convention%20on,compulsory%20jurisdiction%20of%20the%20Court.&lt;/ref&gt; &lt;sup&gt; &lt;/sup&gt;Ireland later incorporated the Convention into Irish law through the European Convention on Human Rights Act 2003.&lt;ref&gt;''Id''.&lt;/ref&gt; &lt;sup&gt; &lt;/sup&gt; Specifically, Article 10 of the ECHR “gives you the right to freely express your opinions and views,” but “the right can be restricted or limited as long as this is allowed by law for a legitimate purpose and is done in a proportionate way.”&lt;ref&gt;Irish Human Rights and Equality Commission, “Human Rights and Constitutional Rights,” https://www.ihrec.ie/factsheets/human-rights-and-constitutional-rights.&lt;/ref&gt;  Although the European Court of Human Rights (“ECtHR”) can hear complaints of alleged violations of the ECHR, the case must first be brought within the Irish legal system and appealed as high as possible before it can be brought to the European Court of Human Rights.&lt;ref&gt;''Id''. The ECtHR is an international court which “consists of a judge from each EU member state” and “considers allegations that states have breached or failed to meet the requirements of the ECHR.” ''Id''.&lt;/ref&gt;

As an EU member, Ireland also enforces the [https://www.eu-digital-services-act.com/Digital_Services_Act_Articles.html Digital Services Act] (“DSA”), which is a set of rules that “applies to all online intermediary service providers (“ISPs”) that provide services in the EU.”&lt;ref&gt;Coimisiún na Meán, “Legislation Explained,” ''supra'' n. 22.&lt;/ref&gt;

== '''Principles of Communication Law and the Media''' ==
The principles of communication law in Ireland are primarily grounded in the balancing of freedom of expression and the need to protect the interest of the public.  These principles can be seen in the governing regulatory framework, which seeks to regulate the telecommunications in Ireland across all platforms.  The Coimisiún na Meán is the primarily body responsible for regulating with broadcasting, online media, and audio visual services. ComReg is the body responsible for the communications sphere in Ireland.  Together with EU law, these bodies work to oversee the telecoms sector and ensure that providers follow governing telecommunication regulations.

=== Telecommunication Law: Regulatory Framework ===
The relevant governmental department which oversees the telecoms sector in Ireland is the Department of the Environment, Climate and Communications (DECC).&lt;ref&gt;Kate McKenna and Simon Shinkwin, “In brief: Telecoms Regulation in Ireland,” Matheson, (June 11, 2025), https://www.lexology.com/library/detail.aspx?g=62433d50-c5b1-4cb0-b3f9-5823363d35b5.&lt;/ref&gt;  The governmental department which oversees the media sector is the Department of Tourism, Culture, Arts, Gaeltacht, Sport and Media.&lt;ref&gt;''Id''.&lt;/ref&gt;  The regulator of telecommunications in the nation is ComReg. &lt;ref&gt;''Id''.&lt;/ref&gt; As a member of the EU, Ireland adopted the European Electronic Communications Code (“ECC”), which includes a set of rules “regulating electronic communications (telecoms) networks, telecoms services, and associated facilities and services.”&lt;ref&gt;EUR-Lex, “Electronic Communications Code,” Publications Office of the European Union, https://eur-lex.europa.eu/EN/legal-content/glossary/electronic-communications-code.html.&lt;/ref&gt;

ComReg manages the communications sphere in Ireland by requiring authorization and enforcing the relevant regulations.&lt;ref&gt;Citizens Information, “Regulation of Postal Services and Electronic Communications,” https://www.citizensinformation.ie/en/consumer/phone-internet-tv-and-postal-services/regulation-of-postal-services-phone-internet-radion-and-tv/.&lt;/ref&gt;  ComReg regulates the sectors by ensuring the communication providers have the necessary authorization, licensing, and registration necessary to provide their services to the country.&lt;ref&gt;''Id''.&lt;/ref&gt;  As regulator of the communications sector, ComReg must “make sure providers follow the rules through enforcement[;] investigate complaints received from the wider industry and consumers[;] prevent fraud and misuse of Irish numbers to protect both end-users and operators[; and] make sure network incidents (breach of security or loss of integrity that has a significant impact on the operation of networks and services) are properly managed by network operators.”&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Telecommunication Law: Licensing Regime ===
The supply of communications services in Ireland is governed by the regime established in the European Union Electronic Communications Code (“ECC”).&lt;ref&gt;''See'' McKenna and Shinkwin, ''supra'' note 37.&lt;/ref&gt;  The ECC supplies “the general right to provide an electronic communications network (“ECN”) or an electronic communications service (“ECS”) (or both) provided certain conditions are complied with.”&lt;ref&gt;''Id''.&lt;/ref&gt;  ComReg is responsible for implementing the procedure for operators to obtain general authorizations to use an ENC or ECS.&lt;ref&gt;''Id''.&lt;/ref&gt;  The ECC regulations also dictate the conferring of rights to use numbers and radio spectrum.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Spectrum Licenses ====
The ECC also lays out the legal framework that governs ComReg’s administration of the radio frequency spectrum in Ireland. &lt;ref&gt;''Id''.&lt;/ref&gt; ComReg issues licenses on a neutral basis, but may restrict the “types of radio network of wireless access technology used for ECS where it is necessary” for non-discriminatory reasons, such as avoiding harmful interference or safeguarding the effective use of the spectrum.&lt;ref&gt;''Id''.&lt;/ref&gt;  ComReg published The Wireless Telegraphy Regulations 2014, which contains “guidelines for spectrum trading in the Radio Spectrum Policy Programme (“RSPP”) bands.&quot;&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Censorship and Violent Content''' ==
Censorship law in Ireland reflects this balanced approach between the modern constitutional freedoms and the Irish-Catholic values.  Censorship law was previously more restrictive in Ireland, but has become more relaxed as the country has moved away from such traditional rules. Hate speech is regulated in conformity with EU law, but there is tension regarding the balance between free speech and hate speech.

“Censorship laws set out rules about standards” for forms of communication which may be restricted or banned if they are “unacceptable, offensive, obscene, [or] likely to incited hatred or violence.”&lt;ref&gt;Citizens Information, “Censorship,” https://www.citizensinformation.ie/en/government-in-ireland/irish-constitution-1/censorship/.&lt;/ref&gt;  The strong influence of Catholicism in shaping the Irish nation during its fight for independence from the British resulted in ideas of public morality that were characterized by “conservative Irish-Catholic values.”&lt;ref&gt;Gracia Larsen-Schmidt, “The Moral Ideas of the Community: Censorship and Irish-Catholic Nation Building,” Nursing Clio, (Feb. 5 2025), https://nursingclio.org/2025/02/05/the-moral-ideas-of-the-community-censorship-and-irish-catholic-nation-building/.&lt;/ref&gt;  As a result, administrative agencies were established to enact censorship laws which “prevented Irish people from accessing materials that depicted, humanized, and communicated specific elements of human life relating to sexuality, desire and bodies . . . in the name of defending Catholic morals and national identity.”&lt;ref&gt;''Id''.&lt;/ref&gt;. 

=== Censorship of Publications ===
Ireland created the Censorship of Publications Board (“the Board”) through the [https://www.irishstatutebook.ie/eli/1929/act/21/enacted/en/print.html Censorship of Publications Act of 1929].&lt;ref&gt;''Id''. The Board consists of five voluntary members “who are appointed by the Minister for Justice.” ''Id''.&lt;/ref&gt;  Books and periodicals are brought to the Board by the members of the public or customs or excise officers for examination.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Board can choose whether or not to ban the publication, prohibiting the sale, purchase, or distribution of the publication in Ireland.&lt;ref&gt;''Id''. Bans can be appealed to the Censorship of Publications Appeal Board, which can choose to uphold, cancel, or modify the prohibition. ''Id''.&lt;/ref&gt;  

The Censorship of Publications Act was viewed as being influenced by the Catholic Church and existing sentiments to protect Ireland from foreign influences.&lt;ref&gt;EBSCO, “History of Censorship in Ireland,” https://www.ebsco.com/research-starters/politics-and-government/history-censorship-ireland.&lt;/ref&gt; The Board was “aided by Catholic societies and customs officials” and “banned literature based on the recommendations of Catholic activists,” until the only literature available to the Irish reading public primarily focused on religion and Irish culture.&lt;ref&gt;''Id''.&lt;/ref&gt;  Although efforts have been made to abolish the Censorship Board, it actively banned books in Ireland as recently as 2015 and the Censorship of Publications Act remains law.&lt;ref&gt;''Id''. “The Fianna Fáil attempted to abolish the Censorship Board in 2013 but was not successful.” ''Id''.&lt;/ref&gt;

=== Censorship of Film ===
The Irish Film Classification Office (“IFCO”) is a statutory body established by the [https://www.irishstatutebook.ie/eli/1923/act/23/enacted/en/print.html Censorship of Films Act 1923].&lt;ref&gt;''Id''.&lt;/ref&gt;  The IFCO examines and certifies all films, videos, and DVDs intended for distribution in Ireland with the purpose of “provid[ing] the public and parents . . . with a modern and dependable system of classification that: protects children and young persons[;] has regard for freedom of expression[; and] has respect for the values of Irish society.”&lt;ref&gt;Irish Film Classification Office, “What We Do,” https://www.ifco.ie/en/ifco/pages/what_we_do.&lt;/ref&gt;  IFCO certifies films and DVDs for viewing based on various criteria and “provides guidelines on an appropriate age group for film,” but can choose to ban a film or DVD that it deems unfit for viewing.&lt;ref&gt;Citizens Information, “Censorship” at Censorship of Films, DVDs and Video Games.&lt;/ref&gt;

=== Censorship of the Internet ===
Ireland currently does not have any law which specifically covers internet censorship, but there is legislation which affects certain online content.&lt;ref&gt;''Id''. at Censorship of the Internet. The Child Trafficking and Pornography Act 1988 mandates that ISPs remove any content that is illegal under the Act. ''Id''. The European Union Copyright and Related Rights Regulations are used to prevent the illegal downloading of copyrighted material. ''Id''.&lt;/ref&gt;  In December 2022, the [https://www.irishstatutebook.ie/eli/2022/act/41/enacted/en/print.html Online Safety and Media Regulation Act], which created a media regulator for online safety and an Online Safety Commissioner that regulates online services, went into effect.&lt;ref&gt;''Id''.&lt;/ref&gt;  Additionally, the European Union has regulations in place that target harmful or illegal online content in which Ireland participates.&lt;ref&gt;''Id''. Ireland is a member of the EU Internet forum set up to prevent international terrorists from misusing the internet and removing illegal content. ''Id''.&lt;/ref&gt;

=== '''Hate Speech''' ===
The [https://www.irishstatutebook.ie/eli/1989/act/19/enacted/en/print.html Prohibition of Incitement to Hatred Act 1989] (“1989 Act”) prohibits “incitement to hatred on account of race, religion, nationality or sexual orientation.”&lt;ref&gt;Prohibition of Incitement to Hatred Act, 1989, https://www.irishstatutebook.ie/eli/1989/act/19/enacted/en/print.html.&lt;/ref&gt;  The Act outlaws multiple forms of communication, precluding “the use of words, behavior or the publication or distribution of material which is threatening, abusive or insulting and intended, or likely, to stir up hatred.”&lt;ref&gt;OSCE Office for Democratic Institutions and Human Rights, “Hate Crime Legislation in Ireland,” https://hatecrime.osce.org/hate-crime-legislation-ireland.&lt;/ref&gt;  The 1989 Act has been criticized as outdated and ineffective, especially in combatting hate speech that occurs online.&lt;ref&gt;Roisín McFadden, “Online Hate Speech in Ireland and the United Kingdom,” UCD SLS Journal 2022, https://issuu.com/ucdstudentlegalservicesjournal/docs/sls_full_version_with_covers/s/15371427.&lt;/ref&gt;  The prosecution of Patrick Kissane is the only significant case where a party was tried under the 1989 Act.&lt;ref&gt;John O’Mahony, “Man Cleared of Online Hatred Against Travellers,” Irish Examiner (Oct. 1 2011), https://www.irishexaminer.com/news/arid-20169325.html.&lt;/ref&gt;  Following an interaction with a traveller, Kissane set up a Facebook Group named “Promote the Use of Knacker Babies as Shark Bait,” with phrases implying that Traveller babies should be used as bait and for testing new drugs for viruses.&lt;ref&gt;''Id''. “Irish Travellers are a small indigenous ethnic minority” living between Ireland, the United Kingdom, and the United States that are commonly “subjected to discrimination and exclusion.” Martin Collins, “Anti-Traveller Racism Pervasive and Deep-Rooted,” INAR, https://inar.ie/anti-traveller-racism-pervasive-and-deep-rooted/.&lt;/ref&gt;  Although the judge found the comments to be “obnoxious and revolting,” he considered them one-off comments and dismissed the case.&lt;ref&gt;John O’Mahony, “Man Cleared of Online Hatred Against Travellers,” ''supra'' n. 55.&lt;/ref&gt;  This case is a reflection of how difficult prosecution under this law was given its strict standards.&lt;ref&gt;Roisín McFadden, “Online Hate Speech in Ireland and the United Kingdom,” ''supra'' n. 54.&lt;/ref&gt;  This is in contrast to relevant law in the UK, which prosecutes hate speech more severely.&lt;ref&gt;Roger Berkeley, Law &amp; Liberty, “The Speech Battle on the Emerald Isle,” (Jul. 3 2025), https://lawliberty.org/the-speech-battle-on-the-emerald-isle/.&lt;/ref&gt;

As an EU member, the Digital Services Act required the Irish Government to enact a Hate Speech Bill.&lt;ref&gt;''Id''.&lt;/ref&gt;  In 2022, the Hate Speech Bill was introduced and passed in the Dáil with, but was held up in the Seanad for two years, with many free speech activists and groups campaigning against the Bill over its strict provisions prohibiting “possessing the wrong sort of meme” and giving “police the right to confiscate devices and compel passwords on the mere suspicion of such possession.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Compromises were made and on December 31, 2024, new hate crime legislation went into effect that only focused on increasing sentences.&lt;ref&gt;''Id''.&lt;/ref&gt;  The [https://www.irishstatutebook.ie/eli/2024/act/41/enacted/en/print.html Criminal Justice (“Hate Offences”) Act 2024] “provides for increased prison sentences for certain crimes, where proven to be motivated by hatred, or where hatred is demonstrated.&lt;ref&gt;''Id''.&lt;/ref&gt;  In addition to physical offences, such as assault of property damage, the Hate Offences Act also covers speech-related offences, including “threats to kill or cause serious harm aggravated by hatred” and “distribution or display in public place of material which is threatening, abusive, insulting or obscene aggravated by hatred.”&lt;ref&gt;''Id''.&lt;/ref&gt;  However, the EU has mandated that Ireland revive its hate speech bill in compliance with the Digital Services Act, but Ireland has responded that the Hate Offences Act is sufficient.&lt;ref&gt;''Id''.&lt;/ref&gt;  This reflects the tension between the very rigid censorship laws that were prevalent in Ireland and free speech.&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Truth, Honor, and Tolerance''' ==
Defamation law in Ireland reflects the balance between the constitutional guarantee of free expression with the protection of one's reputation.  Defamation law is primarily governed by statute and case law and provides remedies for damage to one's good name, as well as defenses such as truth and honest opinion.  Disinformation law, by contrast, is not governed by one sole regulatory structure and involves the use of multiple regulations which address different areas of communication.  Together, the law's show Ireland's commitment to balancing constitutional freedoms of free speech and expression with public and individual interests.

=== Defamation ===
Article 40.3.2 states that “[t]he States shall . . . protect as best it may from unjust attack and, in the case of injustice done, vindicate the life, person, [and] good name . . . of every citizen.&lt;ref&gt;Irish Constitution, Article 40.3.2.&lt;/ref&gt;  Accordingly, the right to freedom of expression does not extend to unjust attacks on a citizen’s good name.  In an attempt to reconcile these two Constitutional provisions, the Irish parliament enacted the Defamation Act 1961, which was repealed and replaced by the Defamation Act 2009.&lt;ref&gt;Krizia Testa, Defending Speech: A Call for Irish Defamation Reform, Trinity College Law Review, https://trinitycollegelawreview.org/defending-speech-a-call-for-irish-defamation-reform/#:~:text=1.,expression%20is%20crucial%2C%20yet%20arduous.&lt;/ref&gt;  In addition to the relevant constitutional and statutory provisions, defamation law is also governed by common law and European human rights law.&lt;ref&gt;Paul Tweed, “Republic of Ireland Media Law Guide,” Carter-Ruck, https://www.carter-ruck.com/law-guides/defamation-and-privacy-law-in-republic-of-ireland/. “Article 10(2) of the European Convention on Human Rights . . . guarantees the ‘protection of the reputation . . . of others.’” ''Id''.&lt;/ref&gt;

The [https://www.irishstatutebook.ie/eli/2009/act/31/enacted/en/pdf Defamation Act of 2009] abolished the prior division between libel and slander and created one cause of action – the tort of defamation.&lt;ref&gt;''Id''.&lt;/ref&gt;  A cause of action for defamation exists where there is a “publication, by any means, to one or more than one person, of a defamatory statement, which ‘tends to injure a person’s reputation in the eyes of reasonable members of society.’”&lt;ref&gt;''Id''. (citing Defamation Act 2009).&lt;/ref&gt;  Defamation is governed only by civil law in Ireland, meaning that no criminal action can be taken for a violation of the law.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Defenses to Defamation ====
The law presumes that any defamatory statement is false, meaning that truth plays a vital role in defamatory law.&lt;ref&gt;''Id''.&lt;/ref&gt;  When a party alleges that they have been defamed, the burden is on the defendant to prove that the statement is true or demonstrate the existence of another defense.&lt;ref&gt;''Id''.&lt;/ref&gt;  If the statement is proven to be true or substantially true, the statement is not defamatory.&lt;ref&gt;Citizens Information, “The Law on Defamation in Ireland,” https://www.citizensinformation.ie/en/justice/civil-law/law-on-defamation/.&lt;/ref&gt;  This “reflects the principle that a person should not be compensated for damage done by a statement which is, in fact, true and accurate,” and the statement is essentially protected by the Constitution as an exercise of free expression and speech.&lt;ref&gt;Irish Legal Guide, “Defamation Defences,” https://legalguide.ie/defences/.&lt;/ref&gt;  A defendant may also have a defense of honest opinion, where the opinion is “honestly held . . . [meaning] the person making the statement believes the truth of the allegation at the time of making the statement” and related to a matter of public interest.&lt;ref&gt;Citizens Information, “The Law of Defamation in Ireland.”&lt;/ref&gt; ''' '''A defense of absolute privilege applies to certain defamatory statements “made in an official capacity or as part of a testimony.”&lt;ref&gt;''Id''.&lt;/ref&gt;  There is also a defense of qualified privilege, which applies to statements which the relevant persons had a duty or interest in making and receiving the statements.&lt;ref&gt;''Id''.&lt;/ref&gt;  Finally, as to publications, a court considers a number of factors in determining whether the publication was “fair and reasonable” or “innocent,” which have protected social media companies and newspapers from being liable for defamation.&lt;ref&gt;''Id''. These factors include the seriousness of the allegation, the content of the statement, and the relation of the statement to the public interest. ''Id''.&lt;/ref&gt;

==== Caselaw ====
In [https://ww2.courts.ie/ga/view/Judgments/959ff643-11b5-4e3d-89cc-5ae2a75f1232/043833d2-d57b-4967-a76f-4ded8cf42b82/2025_IEHC_90.pdf/pdf Stillorgan Gas Heating and Plumbing v. Manning], defamation law was applied to online comments, and the High court awarded Stillorgan €40,000 for comments that the defendants left on the company’s review pages.&lt;ref&gt;Lisa Carty &amp; Jane Bourke, “Recent Irish Defamation Cases Clarify Application of Law,” Pinsent Masons, (June 4 2024), https://www.pinsentmasons.com/out-law/analysis/recent-irish-defamation-cases-clarify-application-of-law.&lt;/ref&gt;

=== '''Terrorism''' ===
The European Union enacted Regulation 2021/784 to address “the dissemination of terrorist content online.”&lt;ref&gt;Official Journal of the European Union, Regulation (EU) 2021/74 of the European Parliament and of the Council, “On Addressing the Dissemination of Terrorist Content Online,” https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX%3A32021R0784.&lt;/ref&gt;  In August 2025, the Irish Minister for Justice, Jim O’Callaghan, published the European Union (Online Dissemination of Terrorist Content), exercising the powers given to him by Section 3 of the European Communities Act 1972 in order to give further effect to Regulation (EU) 2021/784. &lt;ref&gt;Government of Ireland, “S.I. No. 375/2025 - European Union (Online Dissemination of Terrorist Content) (Designation of the Commissioner of An Garda Síochána as a Competent Authority) Regulations 2025,” (Aug. 1, 2025), https://www.irishstatutebook.ie/eli/2025/si/375/made/en/print.&lt;/ref&gt; The regulation requires “internet companies in the EU [to] take swift measures to prevent the misuse of their services for dissemination of terrorist content.”&lt;ref&gt;Thomas Wahl, “Rules on Removing Terrorist Content Online Now Applicable,” Eucrim, (June 7, 2022), https://eucrim.eu/news/rules-on-removing-terrorist-content-online-now-applicable/.&lt;/ref&gt;  

The framework set out in the regulation is directed toward precluding terrorists from using the internet to “recruit, encourage attacks, provide training and glorify their crimes.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The primary components of the regulation include an “[o]bligation for Hosting Service Providers (HSPs) to remove terrorist content online within one hour after receiving a removal order from a competent national authority of an EU Member States; [l]imited scrutiny of cross-border removal orders by the competent authority of the Member State where the HSP has its main establishment or where its legal representative resides; [o]bligation for platforms to take proactive measures when they are exposed to terrorist content; [i]nclusion of several safeguards to ensure respect with fundamental rights, in particular freedom of expression and the right to information; [and an] [o]bligation for Member States to sanction platforms for non-compliance with the obligations under the Regulation.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Irish Minister for Justice, Home Affairs and Migration also published the 2025 Amendment to the Criminal Justice (Terrorist Offenses) Bill, giving full effect to EU Regulation 2017/541.&lt;ref&gt;Oireachtas, “Criminal Justice (Terrorist Offences) (Amendment) Bill 2025,” https://data.oireachtas.ie/ie/oireachtas/bill/2025/34/eng/initiated/b3425d.pdf.&lt;/ref&gt;  Regulation 2021 adopted the language defining terrorism from Regulation 2017/541 and applied it primarily to action relating to electronic communications and dissemination of information, as well as cyber-terrorism to address “the misuse of hosting services for terrorist purposes.”&lt;ref&gt;Joan Barata, “Regulation (EU) 2021/784 of the European Parliament and of the Council of 29 April 2021 on Addressing the Dissemination of Terrorist Content Online, Regulation on Terrorist Content Online,” (May 17, 2021), https://wilmap.stanford.edu/node/31158#:~:text=The%20Regulation%20establishes%20a%20definition,raising%20purposes%20against%20terrorist%20activity.&lt;/ref&gt;

=== '''Disinformation''' ===
There is not one existing regulatory framework in Ireland that specifically governs disinformation, but together, the regulations and existing media literacy policies do address disinformation.&lt;ref&gt;John Cian McGrath and Kirsty Park, Dublin City University, “EDMO Policy Monitoring: The Regulation of Online Disinformation,” (Nov., 2022), https://edmohub.ie/wp-content/uploads/2023/02/EDMO-Task-V-Dec-2022-2.pdf#:~:text=The%20Electoral%20Reform%20Act%20has%20been%20passed,not%20compatible%20with%20the%20e%2D%20Commerce%20Directive4.&lt;/ref&gt;  Specifically, four Irish regulations and policies relate to disinformation in the State: the Online Safety and Media Regulation Act, the Electoral Reform Act, the Broadcasting Authority of Ireland’s Media Literacy Policy, and The Future of Media Commission Report.&lt;ref&gt;''Id''.&lt;/ref&gt;

The Online Safety and Media Regulation Act has no particular aspect which regulates disinformation, but “tackles specific instances of online harms” and has the potential to include misinformation and disinformation through later amendments.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Electoral Reform Act 2022 contains sections “which deal with regulating online advertising and online electoral information” and is aimed at protecting “the integrity of [Ireland’s] electoral and democratic process against the spread of disinformation and misinformation in the online sphere during electoral periods.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The BAI Media Literary Policy facilitates Media Literacy Ireland (“MLI”), “an informal and voluntary alliance of organisations and individuals that aims to promote media literacy across the country.”&lt;ref&gt;''Id''.&lt;/ref&gt;  MLI provides training sessions and webinars aimed at tackling disinformation and helping consumers “tell the difference between reliable and accurate information and deliberately false or misleading information.”&lt;ref&gt;''Id''.&lt;/ref&gt;  MLI presents its work to the Irish Parliament.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Future of Media Commission Report “addresses disinformation and recommends the development of a National Counter Disinformation Strategy” that would coordinate efforts against manipulation of Irish internet users via disinformation spread online.&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Cultural and Religious Expression''' ==
The legal framework governing cultural and religious expression in Ireland reflects a balance between constitutional freedoms and the limits on those freedoms for reasons of public order and morality.  The Irish Constitution guarantees freedom of expression and the right to assemble peacefully, rights which are commonly guaranteed by other nations to their citizens as well.  Cultural events and public festivals in Ireland must comply with a range of licensing and safety regulations, such as local authority permits and crowd control management.  The religious underpinnings in Ireland law can be seen in the nation’s previous blasphemy laws, which have since been abolished.

=== Public Festivals and Traditions ===
Article 40.6.1.ii of the Irish Constitution guarantees “the right of citizens to assemble peaceably and without arms.”&lt;ref&gt;Irish Constitution, Article 40.6.1.ii&lt;/ref&gt;  However, the right is “subject to public order and morality,” and may be limited in order to “prevent or control meetings which are determined in accordance with law to be calculated to cause a breach of the peace or to be a danger or nuisance to the general public or prevent or control meetings in the vicinity of either House of the Oireachtas.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Irish Constitution contains an explicit provision along with this guarantee which prohibits any law that regulates the right of free assembly from doing so on a political, religious, or class discrimination basis.&lt;ref&gt;Irish Constitution, Article 40.6.2.&lt;/ref&gt;

St. Patrick’s Day, which is observed on March 17th every year, originally began as a religious holiday, but has become a celebration of Irish culture over time.&lt;ref&gt;Rose Davidson, “St. Patrick’s Day,” National Geographic Kids, https://kids.nationalgeographic.com/celebrations/article/st-patricks-day.&lt;/ref&gt;  St. Patrick came to Ireland from Britain and is said to have “converted many of the country’s residents to Christians.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Originally a very religious holiday to honor St. Patrick, churchgoers later began “celebrating their Irish heritage with cheeky pints of Guinness and live music . . . and it’s [now] more widely known as a global celebration of Irish culture.&lt;ref&gt;Kevin McGraw, “Surviving &amp; THriving: Tips for Celebrating St. Patrick’s Day in Ireland,” EF, (Feb. 2, 2024), https://www.efultimatebreak.com/blog/europe/ireland/tips-celebrating-st-patricks-day.&lt;/ref&gt;  The main event of the day in Ireland is the St. Patrick’s Day parade with many floats representing Irish folklore.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Regulation of Outdoor Events ====
The Planning and Development Act, 2000 established a system of licensing for outdoor events that apply to “new venues and events, which did not have specific planning permission prior to the 2000 Act.”&lt;ref&gt;S.I. No. 154/2001 - Planning and Development (Licensing of Outdoor Events) Regulations, 2001; Irish Legal Guide, “Outdoor Events,” Irish Law Explained, &lt;nowiki&gt;https://legalguide.ie/outdoor-events/&lt;/nowiki&gt;.&lt;/ref&gt;  Any event with an audience of 5,000 members or more is considered “prescribed” and requires a license.&lt;ref&gt;Irish Law Explained, &lt;nowiki&gt;https://legalguide.ie/outdoor-events/&lt;/nowiki&gt;.&lt;/ref&gt;  The Local Authority is responsible for reviewing the application, plans, and observations available for public inspection, and making a decision on the application.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Local Authority may grant a license with or without conditions or outright refuse the license, and “may require compliance with guidance and codes of practice issued by the Minister.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Local Authority must consult with specific authorities, including the Garda police force, the Health Service Executive, and and any other local authorities particular to the area where the event is being held.&lt;ref&gt;''Id''.&lt;/ref&gt;  If a local authority believes that an event is occurring or likely to occur without a license, an enforcement notice may be served requiring the event or preparations of the event to immediately cease.&lt;ref&gt;''Id''.&lt;/ref&gt;  

In 2014, the licensing of events under the Planning and Development Act was amended after the issues regarding the proposed Garth Brooks concerts.&lt;ref&gt;''Id''.&lt;/ref&gt;  Brooks had five concerts scheduled in Dublin, but the Dublin city council denied permission for three of his concerts because of the noise, traffic, and potential behavior that a series of five concerts may create.  In response, Brooks canceled all five of the concerts he had planned.&lt;ref&gt;Sean Michaels, “Garth Brooks Calls Off Entire Run of Dublin Comeback Dates, (Jul. 9, 2014), &lt;nowiki&gt;https://www.theguardian.com/music/2014/jul/09/garth-brooks-cancels-dublin-comeback-dates&lt;/nowiki&gt;.&lt;/ref&gt;  The amendments made is mandatory for event organizers which planned to make an application to consult with the local “in order to discuss the submission of an application, including the draft plan for the management of the event.”&lt;ref&gt;S.I. No. 154/2001 - Planning and Development (Licensing of Outdoor Events) Regulations, 2001.&lt;/ref&gt;

==== Crowd Control ====
Crowd control regulations are used at public events in Ireland “to maintain public peace and order and ensure the safety of all who are gathered.”&lt;ref&gt;Citizens Information, “Crowd Control at Public Events, https://www.citizensinformation.ie/en/justice/law-enforcement/crowd-control-at-public-events-in-ireland/.&lt;/ref&gt;  The Garda Síochána, the Irish police force, is given legal authority to manage crowd control by the Criminal Justice (Public Order) Act 1994.&lt;ref&gt;''Id''.&lt;/ref&gt;  The police force is empowered to place barriers on roads up to one mile from where a large public event is taking place and may seize alcohol or other drink containers where it deems necessary.&lt;ref&gt;''Id''.&lt;/ref&gt;  The police force also may prevent public events from taking place within a half mile of the House of the Oireachtas.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Religious Discrimination ===
Article 44.2.1 guarantees Irish citizens the &quot;free profession and practice of religion . . . subject to public order and morality.&lt;ref&gt;Irish Constitution, Article 44.2.1.&lt;/ref&gt;  The Article also provides that the State will not &quot;endow any religion,&quot; nor &quot;impose any disabilities or make any discrimination on the ground of religious profession, belief of status.&quot;&lt;ref&gt;Irish Constitution, Article 44.2.2-3.&lt;/ref&gt;  Article 44, therefore, provides for freedom of religion and implicitly protects individuals from religious discrimination.&lt;ref&gt;&quot;2023 Report on International Religious Freedom: Ireland,&quot; U.S. Department of State, https://www.state.gov/reports/2023-report-on-international-religious-freedom/ireland/.&lt;/ref&gt;  In 1972, an amendment was made to the Constitution which removed the recognition of the Catholic Church and other specific denominations.&lt;ref&gt;''Anti-Discrimination Legislation'', Civic Nation (last visited Dec. 1, 2025), https://civic-nation.org/ireland/government/legislation/anti-discrimination_legislation/.&lt;/ref&gt;  

The clauses have since been compared to those protections which are often enjoyed by citizens of countries with a secular constitution, such as those guaranteed by the First Amendment of the U.S. Constitution.&lt;ref&gt;David Kenny, ''God in the Irish Constitution'', BYU Law (Oct. 31, 2020), https://talkabout.iclrs.org/2020/10/31/god-in-the-irish-constitution/.&lt;/ref&gt; Still, the influence of God can be seen in the way that Irish courts have interpreted and applied the constitutional provisions.&lt;ref&gt;''Id''.&lt;/ref&gt;  In the 1972 case of ''Quinn Supermarkets v. Attorney General'', the Irish Supreme Court found that “where discrimination in favour of religion is necessary to enable freedom of religious practice,” the Constitution would allow and possible require such discrimination.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Court therefore held that the main goal of the Constitution’s non-discrimination clause was to protect the free practice of religion.&lt;ref&gt;''Id''.&lt;/ref&gt;  Similarly, the 1979 case of ''McGrath and Ó Ruairc v. Trustees of Maynooth College'', two priests had been discharged from the religious educational institution where they taught.&lt;ref&gt;''Id''.&lt;/ref&gt;  The priests brought a discrimination claim, but lost at the Supreme Court, which found that &quot;the rights of the religious college not only allowed but required this discrimination.&quot;&lt;ref&gt;''Id''.&lt;/ref&gt;  

Article 44 of the Irish Constitution further provides that “[l]egislation providing State aid for  schools shall not discriminate between schools under the management of different religious denominations, nor be such as to affect prejudicially the right of any child to attend a school receiving public money without attending religious instruction at that school.”&lt;ref&gt;Irish Constitution, Article 44.2.4.&lt;/ref&gt;  In Ireland, &quot;national schools&quot; are privately owned and managed, but are funded by the State.&lt;ref&gt;&quot;2023 Report on International Religious Freedom: Ireland,&quot; U.S. Department of State, https://www.state.gov/reports/2023-report-on-international-religious-freedom/ireland/.&lt;/ref&gt;  The majority of the national schools are affiliated with a religious group, 88% of which are affiliated with the Roman Catholic Church.&lt;ref&gt;''Id''.&lt;/ref&gt;. Irish courts have been lenient in enforcing the endowment provisions and allow state funding for religious chaplains in school.&lt;ref&gt;David Kenny, ''God in the Irish Constitution'', BYU Law (Oct. 31, 2020), https://talkabout.iclrs.org/2020/10/31/god-in-the-irish-constitution/.&lt;/ref&gt;  Previously, state-funded schools that were affiliated with a religion were allowed to favor admitting children that were members of the relevant religious group, resulting in discrimination to non-religious children or those that were members of a different religion.&lt;ref&gt;''Id''.&lt;/ref&gt;   

=== Blasphemy Laws ===
Given that much of Ireland’s legal system was influenced by England’s common law system, Irish blasphemy law was similarly shaped by English blasphemy jurisprudence.&lt;ref&gt;Seosamh Gráinséir, ''Irish Legal Heritage: Blasphemy Law in Ireland'', Irish Legal News (Oct. 19, 2018), https://www.irishlegal.com/articles/irish-legal-heritage-blasphemy-law-in-ireland.&lt;/ref&gt;  Therefore, when adopted in 1937, the Irish Constitution explicitly included a prohibition on blasphemy as a limit to the right to freedom of speech, making the “publication or utterance of blasphemous, seditious, or indecent matter [ ] an offense which shall be punishable in accordance with law.”&lt;ref&gt;Irish Constitution, Article 40.6.1.i.&lt;/ref&gt;

In 2009, the Irish parliament passed the Defamation Act, which provided that “[a] person who publishes or utters blasphemous matter shall be guilty of an offence and shall be liable upon conviction on indictment to a fine not exceeding €25,000.”&lt;ref&gt;Defamation Act 2009, Part 5.36.&lt;/ref&gt;  The Act added clarity to what constituted blasphemous materials, describing such material as “matter that is grossly abusive or insulting in relation to matters held sacred by any religion, thereby causing outrage among a substantial number of the adherents of that religion,” but that a person must intend to cause such outrage to be found guilty of the offense.&lt;ref&gt;''Id''.&lt;/ref&gt;

Campaigns to abolish the &quot;medieval&quot; ban on blasphemy spurred since the law’s enactment in 2009.&lt;ref&gt;Emma Graham-Harrison, ''Ireland Votes to Oust ‘Midieval’ Blasphemy Law'', The Guardian (Oct. 27, 2018), https://www.theguardian.com/world/2018/oct/27/ireland-votes-to-oust-blasphemy-ban-from-constitution.&lt;/ref&gt;  In 2018, a referendum allowed citizens to vote on whether to remove the offense from the Constitution.&lt;ref&gt;''Id''.&lt;/ref&gt;  Approximately 65% of the voters wanted to remove the prohibition on blasphemy, although polls show that only 45% of eligible voters actually cast a ballot.&lt;ref&gt;''Id''.&lt;/ref&gt;  Following the vote, amendments were made to the Constitution and Defamation Act to remove the relevant clauses.&lt;ref&gt;''Irish Vote to Scrap Offence of Blasphemy'', British Broadcasting Corporation (Oct. 28, 2028), https://www.bbc.com/news/world-europe-46010077#.&lt;/ref&gt;  The Justice Minister at the time agreed with the result, stating that there was “no room for a provision such as this in [the] Constitution.”&lt;ref&gt;''Id''.&lt;/ref&gt;

===== Caselaw =====
The earliest case of blasphemy reported in Ireland was the trial of Thomas Emlyn, a unitarian minister.&lt;ref&gt;Seosamh Gráinséir, ''Irish Legal Heritage: Blasphemy Law in Ireland'', Irish Legal News (Oct. 19, 2018), https://www.irishlegal.com/articles/irish-legal-heritage-blasphemy-law-in-ireland.&lt;/ref&gt;  He was punished for publishing ''An Humble Inquiry into the Scripture-Account of Jesus Christ'', which “argued that Jesus Christ was not the equal of God.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Emlyn was found guilty of blasphemy and sentenced to one year in prison and ordered to pay a £1000 fine.&lt;ref&gt;''Id''.&lt;/ref&gt; Around 1995, as new divorce legislation was being voted on in Ireland, various publications were marked as containing blasphemous material through “their depiction of the progressive separation of church influence from the governance of Ireland,&quot; but there were no resulting prosecutions.&lt;ref&gt;Seosamh Gráinséir, ''Irish Legal Heritage: Blasphemy Law in Ireland'', Irish Legal News (Oct. 19, 2018), &lt;nowiki&gt;https://www.irishlegal.com/articles/irish-legal-heritage-blasphemy-law-in-ireland&lt;/nowiki&gt;&lt;/ref&gt;  

In 1999, the Supreme Court of Ireland held in ''Corway v. Independent Newspaper'' that a cartoon which included the phrase “Hello progress – bye bye Father?” was “in very bad taste,” but refused to prosecute because there was no clear legislative definition of criminal blasphemy.&lt;ref&gt;Seosamh Gráinséir, ''Irish Legal Heritage: Blasphemy Law in Ireland'', Irish Legal News (Oct. 19, 2018), https://www.irishlegal.com/articles/irish-legal-heritage-blasphemy-law-in-ireland.&lt;/ref&gt;  Although the Defamation Act 2009 did remedy this issue, creating a specific offense for blasphemy, there were no successful prosecutions brought under the Act.&lt;ref&gt;''Id''.&lt;/ref&gt;  However, prior to the calls for its abolishment, the laws made headlines in 2017 when an investigation into Stephen Fry, a British comedian and actor, was announced for his 2015 interview on Ireland’s public service broadcaster.&lt;ref&gt;''Ireland'', End Blasphemy Laws (last updated Jul. 14, 2020), https://end-blasphemy-laws.org/countries/europe/ireland/.&lt;/ref&gt;  During the interview, Fry referred to God as “a capricious, mean-minded, stupid[,] . . . maniac.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Irish police’s investigation did not result in any criminal liability for Fry because there was not enough &quot;public outrage&quot; over the incident, as campaigns for the abolishment of blasphemy laws were already underway.&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Privacy and Data Protection''' ==
Privacy and data protection law in Ireland is centered around the protection of an individuals' personal autonomy and control over their personal information, while ensuring the needs of relevant authorities are met where necessary.  The Irish Constitution guarantees the right of privacy, which has been developers through judicial interpretation and expanded through data protection laws.  Largely shaped by EU law, the GDPR is enforced at the national level and provides guidelines and regulations which Ireland must implement with respect to data protection.  Together, the regulatory framework seeks to uphold the right of privacy while balancing freedom of expression and individual interests.

=== Individual Right to Privacy ===
Under the common law in Ireland, there was no specific tort action which protected an individual’s privacy.&lt;ref&gt;Irish Legal Guide, “Privacy Rights,” [https://legalguide.ie/privacy-rights-2/. https://legalguide.ie/privacy-rights-2/.]&lt;/ref&gt;  The Irish Constitution grants citizens an implied right to privacy, but very few cases have addressed the right to privacy.&lt;ref&gt;''Id''.&lt;/ref&gt;  “The European Convention on Human Rights provides that everyone has the right to respect for his private and family life, his home and his correspondence.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Under the ECHR, “[t]here shall be no interference with the right to privacy family life and the home from unwarranted interference by the state.”&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Irish Constitution ====
Irish courts have acknowledged that the Constitution affords a right to privacy and anonymity, but that right is not unqualified and applies only in limited circumstances.&lt;ref&gt;''Id''.&lt;/ref&gt;  The right is recognized as an implied right granted under Article 40.3.1 of the Irish Constitution.&lt;ref&gt;''Id''.&lt;/ref&gt;  In the ''McGee'' case, the Irish Supreme Court the right to marital privacy was recognized as “protected by the Constitution” that “inheres in an individual, by reason of their human personality.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The right cannot be intruded on by the State “without good objective justification, in relation to decisions taken within the scope of the zone of privacy.”&lt;ref&gt;''Id''.&lt;/ref&gt;  In the case of ''Kennedy and others v. Ireland'', the illegal phone tapping by Irish officials was determined to have breached the right to privacy for a journalist.&lt;ref&gt;''Id''.&lt;/ref&gt;

In Ireland, the right to privacy can be limited in instances where it would be outweighed by the common good, public interest, or other Constitutional freedoms.&lt;ref&gt;''Id''.&lt;/ref&gt;  In cases that relate to media communication, the courts have afforded the right to freedom of expression more protection than the right to privacy.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Regional Law ====
Irish law has adopted the European Convention on Human Rights Act 2003, which provides that “everyone has the right to respect for his private and family life, his home and correspondence [and] that there should be no interference by a public authority with the exercise of this right, except in accordance with the law where it is necessary in a democratic society in the interests of national security, public safety or the economic wellbeing of the country, for the prevention of disorder or crime or for the protection of health or morals, rights and freedom of others.”&lt;ref&gt;''Id''.&lt;/ref&gt;

Case law interpreting the scope of the right to privacy under the Convention have found that “privacy may encompass a person’s personal information, genetic information, photograph, identity, reputation and honour.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Data Protection ===
The primary data protection laws in Ireland are the General Data Protection Regulation (“GDPR”) and the Data Protection Act 2018 (“Irish DPA”).&lt;ref&gt;“Frequently Asked Questions about Data Protection and Privacy Rights (under GDPR),” Adoption Authority of Ireland, https://aai.gov.ie/en/who-we-are/data-protection-gdpr/faqs-data-protection-gdpr.html#:~:text=1.,with%20our%20data%20protection%20obligations.&lt;/ref&gt;  Both of these laws address the protections afforded to individuals in Ireland regarding the processing of personal data.&lt;ref&gt;''Id''.&lt;/ref&gt;  The laws impose various requirements on controllers and processes of personal data and guarantee individuals with specific rights related to their data.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Legislation ====
The European Union General Data Protection Regulation (Regulation (EU) 2016/679) (“GDR”), directly applicable to all EU Member States.&lt;ref&gt;Irish Legal Guide, “Privacy Rights,” [https://legalguide.ie/privacy-rights-2/. https://legalguide.ie/privacy-rights-2/.]&lt;/ref&gt;

In Ireland, the Data Protection Act provides a higher degree of protection to sensitive personal data.  Sensitive and personal data includes information “relating to an individual’s racial or ethnic origin, political opinions, religious or philosophical beliefs, physical or mental health, sexual life, the allegations or the commission of an offence.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Exceptions under the Data Protection Act exist for certain purposes, such as journalism, art, and literary needs.&lt;ref&gt;''Id''.&lt;/ref&gt;

The GDPR is an EU data protection law which Ireland has adopted.&lt;ref&gt;“Your Rights Under the GDPR,” Data Protection Commission, [https://www.dataprotection.ie/en/individuals/rights-individuals-under-general-data-protection-regulation#:~:text=The%20GDPR%20also%20states%20that:%20*%20Data,feel%20their%20rights%20are%20not%20being%20respected. https://www.dataprotection.ie/en/individuals/rights-individuals-under-general-data-protection-regulation#:~:text=The%20GDPR%20also%20states%20that:%20*%20Data,feel%20their%20rights%20are%20not%20being%20respected.]&lt;/ref&gt;  The rights, as set out in Article 8 of the EU Charter of Fundamental Rights states that: “[E]veryone has the right to the protection of personal data concerning him or her[; s]uch data must be processed fairly for specified purposes and on the basis of the consent of the person concerned, or some other legitimate basis laid down by law[; e]veryone has the right of access to data which has been collected concerning him or her, and the right to have it rectified[; c]ompliance with these rules shall be subject to control by an independent authority.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Therefore, “in order to process personal data, organizations must have a lawful reason.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The GDPR recognizes six lawful reasons: consent; to carry out a contract; to meet a legal obligation; where the personal data is required to protect the vital interests of a person; where the personal data is required for a task to be carried out in the public interest; and in the legitimate interests of a company or organization unless those interests would harm an individual’s rights or freedoms. &lt;ref&gt;''Id''.&lt;/ref&gt;

The Irish DPA integrated the GDPR and transposes the EU Directive in Ireland, incorporating most of the GDPR provisions with certain additions and deletions in accordance with Irish law.&lt;ref&gt;Maria Khan, “What is Irish Data Protection Act of 2018, Securiti, (last updated Aug. 22, 2024), [https://securiti.ai/what-is-irish-data-protection-act-of-2018/#:~:text=The%20Irish%20DPA%20also%20outlines%20the%20responsibilities,data%20protection%20and%20enforcing%20GDPR%20in%20Ireland. https://securiti.ai/what-is-irish-data-protection-act-of-2018/#:~:text=The%20Irish%20DPA%20also%20outlines%20the%20responsibilities,data%20protection%20and%20enforcing%20GDPR%20in%20Ireland.]&lt;/ref&gt;  The Irish DPA affords the same rights to individuals regarding their personal data as that of the GDPR.&lt;ref&gt;''Id''.&lt;/ref&gt;  These rights include the right to be informed when and how an individual’s personal data is being used and collected, the right to access personal data, the right to restriction of processing data, the right to data portability across IT environments, the right to object to personal data being used for certain purposes, the right to not be discriminated against, and the right to erasure.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Children's Personal Data ====
Children are given the same data protection rights as adults, but have special protection of their personal data.&lt;ref&gt;Overview of the General Data Protection Regulation (GDPR), Citizens Information, (last updated Feb. 17, 2023), https://www.citizensinformation.ie/en/government-in-ireland/data-protection/overview-of-general-data-protection-regulation/.&lt;/ref&gt;  This is because children “may be less aware of the risks and consequences of sharing their personal data” and “less aware of the safeguards available and their rights in relation to how personal information is processed.”&lt;ref&gt;''Id''.&lt;/ref&gt;  Parents and guardians have the ability to make access requests or exercise other data protection rights on behalf of their children, but it is ultimately left to the data controller to determine what is in the child’s best interest in such circumstances. &lt;ref&gt;''Id''.&lt;/ref&gt;

Online service providers, such as social media companies, are able to rely on a child’s own consent for processing their personal data at age 16, as established by the Data Protection Act 2018.  Otherwise, a child’s parent or legal guardian must give consent.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Regulatory Body ====
The Data Protection Commission (“DPC”) is the organization “responsible for upholding the fundamental rights of individuals in the European Union to have their personal data protected.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Commission observes the relevant organizations to ensure that they are complying with the GDPR and other data protection laws and addresses complaints related to the breach of data protection rights.&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Right to Bodily, Spiritual and Digital Identity''' ==
Irish law recognized bodily integrity, spiritual identity, and digital identity as fundamental rights.  These are primarily protected under the Irish Constitution and expanded by judicial interpretation. The areas have been further developed under legislation and caselaw with specific respect to gender recognition, birth information, and digital privacy. Influenced by EU law and the ECHR, Irish law works to balance individual interest and self-determination with the interests of the State.

=== Right to Bodily Integrity ===
Article 40.3.1 of the Irish Constitution guarantees individuals “laws to respect, and, as far as practicable, . . . laws to defend and vindicate the personal rights of the citizen.”&lt;ref&gt;&quot;Article 40.3.1, The Right to Bodily Integrity,&quot; Irish Council for Human Rights, [https://ichr.ie/our-work/#:~:text=The%20ICHR%20shall%20work%20tirelessly,beings%20over%20their%20own%20bodies. https://ichr.ie/our-work/#:~:text=The%20ICHR%20shall%20work%20tirelessly,beings%20over%20their%20own%20bodies.]&lt;/ref&gt;  The right to bodily integrity has been recognized as an unenumerated right under this Article.&lt;ref&gt;''Id''.&lt;/ref&gt;  In the case of ''Gladys Ryan v. The Attorney General'', the right to bodily integrity was interpreted “to mean that no mutilation of the body or any of its members may be carried out on any citizen under any authority of the law except for the good of the whole body and that no process which is or may, as a matter of probability, be dangerous or harmful to the life or health of the citizens or any of them may be imposed . . . by an Act of the Oirechtas.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The right relates to the protection of “personal autonomy, self-ownership, and self-determination of human beings over their own bodies.”&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Personal Identity Law ===
Article 12 of the Universal Declaration of Human Rights and Article 8 of the European Convention on Human Rights provide the right to one’s identity.&lt;ref&gt;''A Case Study of the Right to One’s Identity in Relation to Ireland’s History of the Institutionalisation of Citizens in the Current Context of the Birth Information and Tracing Act 2022'', Irish Centre for Human Rights (Feb. 16, 2023), [https://ichrgalway.org/2023/02/16/a-case-study-of-the-right-to-ones-identity-in-relation-to-irelands-history-of-the-institutionalisation-of-citizens-in-the-current-context-of-the-birth-information-and-tracing-act-2022/#:~:text=The%20Birth%20Information%20and%20Tracing%20Act%202022%20firmly%20and%20finally,the%20Convention%27%20as%20per%20Art. https://ichrgalway.org/2023/02/16/a-case-study-of-the-right-to-ones-identity-in-relation-to-irelands-history-of-the-institutionalisation-of-citizens-in-the-current-context-of-the-birth-information-and-tracing-act-2022/#:~:text=The%20Birth%20Information%20and%20Tracing%20Act%202022%20firmly%20and%20finally,the%20Convention%27%20as%20per%20Art.]&lt;/ref&gt;  The ECHR states that “everyone has the right to respect for his private and family life, his home and his correspondence.”&lt;ref&gt;''Id''.&lt;/ref&gt;  This article has been interpreted to provide the right to one’s identity.&lt;ref&gt;''Id''.&lt;/ref&gt; As an EU member bound by te ECHR, Ireland is “required to ‘secuer to everyone within their jurisdiction the rights and freedoms defined” in the ECHR, which includes the right to one’s identity.&lt;ref&gt;''Id''.&lt;/ref&gt;

The first instance when the right to identity was recognized in Ireland in relation to adoption was in the case of ''O’T v. B'' in 1998.&lt;ref&gt;Jamie Aspell, ''Ireland’s Birth Information and Tracing Act: Reconciling the Right to Identity'', Blog of the European Journal of International Law (Sep. 23, 2022), https://www.ejiltalk.org/irelands-birth-information-and-tracing-act-reconciling-the-right-to-identity/.&lt;/ref&gt;  The Irish court held that “the right to identity was not absolute and had to be balanced against the mother’s right to privacy.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The case was commonly cited for the proposition that adoptees did not have unequivocal access to their birth information.&lt;ref&gt;''Id''.&lt;/ref&gt;  A decade later, in the 2008 case of ''South Western Area Health Board v. Information Commissioner'', the Irish High Court found that “the disclosure of records containing an adopted person’s birth information was impermissible, as the birth mother had not been accorded an opportunity to ‘make representations in support of the rights she sought to protect.’”&lt;ref&gt;''Id''.&lt;/ref&gt;  The cases led to confusion over how the constitutional right to privacy and the constitutional right to one’s identity can operate with one another in the adoption context.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Birth Information and Tracing Act 2022 ====
In June 2022, Ireland enacted the [https://www.irishstatutebook.ie/eli/2022/act/14/enacted/en/html Birth Information and Tracing Act].&lt;ref&gt;Birth Information and Tracing Act, 2022.&lt;/ref&gt;  This law established a “right to full birth, early life, care and medical information for all those with questions on their origins.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The law allows people who were adopted to access information about their birth parents’ identity once they reach the age of 16.&lt;ref&gt;''Id''.&lt;/ref&gt;  The intent behind the legislation was to right previous wrongs that had been committed to adopted people in Ireland. &lt;ref&gt;Jamie Aspell, ''Ireland’s Birth Information and Tracing Act: Reconciling the Right to Identity'', Blog of the European Journal of International Law (Sep. 23, 2022), https://www.ejiltalk.org/irelands-birth-information-and-tracing-act-reconciling-the-right-to-identity/.&lt;/ref&gt; Specifically, this was seen as a response to the Irish Government’s commission of the Mother and Baby Homes Report, which “investigated the abuses perpetrated against women and children in institutions which were used throughout 20th century Ireland to house women who became pregnant outside of marriage.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The report recommended that adopted persons from such institutions should have an established right to their birth information.&lt;ref&gt;''Id''.&lt;/ref&gt;  This report and recommendation is viewed as a “catalyst for the Birth Information Tracing Act.”&lt;ref&gt;''Id''.&lt;/ref&gt;
The Act seems to lend support to the idea that Ireland is prioritizing the right to identity over the privacy of parents in the context of adoption.&lt;ref&gt;''Id''.&lt;/ref&gt;  Other EU member countries have taken different approaches, such as France, which allows mothers of adoptees to waive their anonymity.&lt;ref&gt;''Id''.&lt;/ref&gt;  While the ECtHR has not expressly taken a position as to which of these rights should be prioritized, case law seems to suggest that the ECtHR has &quot;tended to prioritise the right to identity over the privacy rights of parents,” similar to the legislation in Ireland.&lt;ref&gt;''Id''.&lt;/ref&gt;  This can be seen in ''Odièvre v. France'', in which the ECtHR decided a case regarding the practice of anonymous birthing, in which a mother can give up her newborn child for adoption and request that her identity remain anonymous, as protected by the French Civil Code.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Court’s holding suggested that there should be a balance in legislation that ensures protection of the privacy rights of a mother and competing rights to identity of an adopted child.&lt;ref&gt;''Id''.&lt;/ref&gt;

==== Gender Recognition Act of 2015 ====
The Gender Recognition Act (“GRA”) of 2015 established the rights of transgender individuals in Ireland.&lt;ref&gt;''The Role of Self-Determination in Ireland’s Gender Recognition Act'', Washington Center for Human Rights (Oct, 22, 2025), [https://washingtoncentre.org/the-role-of-self-determination-in-irelands-gender-recognition-act/#:~:text=The%20Gender%20Recognition%20Act%20(GRA,gender%20identity%20of%20medical%20necessity. https://washingtoncentre.org/the-role-of-self-determination-in-irelands-gender-recognition-act/#:~:text=The%20Gender%20Recognition%20Act%20(GRA,gender%20identity%20of%20medical%20necessity.]&lt;/ref&gt;  Prior law in Ireland was “based on medical gatekeeping to legitimize the identity of transgender.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The 2015 legislation “provides a process enabling trans people to achieve full legal recognition of their preferred gender and allows for the acquisition of a new birth certificate that reflects this change.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The law applies to individuals over 18, who can declare their own gender identity, and allows for people aged 16-17 to be recognized as their declared gender under another process.&lt;ref&gt;''Id''.&lt;/ref&gt;

When the GRA was enacted, Ireland was the last EU country that did not allow for the legal recognition of transfer people.&lt;ref&gt;''Id''.&lt;/ref&gt;  The process leading to the GRA took over five years, with various published frameworks and debate until the GRA was accepted and enacted.&lt;ref&gt;''Id''.&lt;/ref&gt;  The law came after Thomas Hammarberg, the European Commission for Human Rights, announced the need for EU members to adopt their own system for recognizing the preferred gender of their citizens.&lt;ref&gt;''Id''.&lt;/ref&gt;  Additional international pressure came from the UN Human Rights Committee’s report regarding Ireland’s conformity with the ICCPR.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Committee specifically raised concerns with the need for a gender recognition bill.&lt;ref&gt;''Id''.&lt;/ref&gt;  

Since its enactment, “more than 70 percent of respondents show their support to transgender rights, which is a sharp contrast to the attitude of the period before 2015.”&lt;ref&gt;''Id''.&lt;/ref&gt;  A large cultural shift has emerged supporting inclusivity in school programs and national campaigns.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Irish Department of Education has introduced new gender-neutral policies for school uniform and paperwork.&lt;ref&gt;''Id''.&lt;/ref&gt;  The current point of contention with regard to gender recognition relates to legislation allowing the formal recognition of non-binary and intersex people, which was not included in the GRA when enacted.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Digital Identity ===
As the digital services offered by the private and public spheres have grown, the need for secure digital authentication of individuals’ identities has also grown.&lt;ref&gt;“European Digital Identity,” Digital Economy and Society, Directorate-General for Communication of the European Commission, [https://commission.europa.eu/topics/digital-economy-and-society/european-digital-identity_en#:~:text=Digital%20Identity%20for%20all%20Europeans,by%20the%20end%20of%202026. https://commission.europa.eu/topics/digital-economy-and-society/european-digital-identity_en#:~:text=Digital%20Identity%20for%20all%20Europeans,by%20the%20end%20of%202026.]&lt;/ref&gt;  Threats to digital privacy have also emerged and individuals are concerned about profiling and surveillance. &lt;ref&gt;''Id''.&lt;/ref&gt; The EU has created the EU Digital Identity Framework in response.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Framework is “based on the principle that everyone should always control their digital identity.”&lt;ref&gt;''Id''.&lt;/ref&gt;  The Framework involved EU Digital Identity Wallets (“eID wallets”) which would allow individuals to carry a digital wallet with them across all of the EU without any issues across borders or worries about losing control of personal data, while prioritizing privacy and security.&lt;ref&gt;''Id''.&lt;/ref&gt;  The eID wallets would “enable users to access online and offline public and private services, store and share digital documents, and create binding signatures.”&lt;ref&gt;''Id''.&lt;/ref&gt;  As a member state, Ireland would have to make eID wallets available to its citizens, residents, and businesses by the end of 2026.&lt;ref&gt;''Id''.&lt;/ref&gt;

== '''Right to Reject Information, Clothing and Human Exhibitions''' ==
In Ireland, the right to erasure laws are governed by the GDPR, which seeks to balance the right of one's access to their personal data and freedom of expression with the public interest. By contrast, laws relating to nudity and child pornography are rooted in criminal and public order laws, regulating public behavior to protect morality.  Clothing is not heavily regulated in Ireland and allows for the wearing of religious and cultural clothing as a form of freedom of expression and religion.

=== Right to Object/Erasure ===
The right to erasure, also known as the “right to be forgotten” is given by Articles 17 and 19 of the GDPR.&lt;ref&gt;''The Right to Erasure (Articles 17 and 19 of the GDPR)'', Data Protection Commission (last visited Dec. 3, 2025), [https://www.dataprotection.ie/en/individuals/know-your-rights/right-erasure-articles-17-19-gdpr. https://www.dataprotection.ie/en/individuals/know-your-rights/right-erasure-articles-17-19-gdpr.]&lt;/ref&gt;  The articles give Irish citizens “the right to have [their] data erased, without undue delay, by the data controller” in the following circumstances: (1) where personal data is “no longer necessary in relation to the purpose for which it was collected or processed;” (2) where consent is withdrawn and there is no other lawful basis for retaining the data; (3) where a person objects to the processing of their data and there is no legitimate grounds for continuing; (4) where a person objects and their personal data is being used for marketing purposes; (5) where personal data has been processed unlawfully; (6) where personal data has been erased for legal reasons; and (7) where personal data has been collected in relation to offering information to a child.&lt;ref&gt;''Id''.&lt;/ref&gt;  The right does not apply where the processing of personal data is “necessary for exercising the right of freedom of expression and information,” to comply with legal obligations, if necessary to preserve public interest, or if being used to establish a legal defense.&lt;ref&gt;''Id''.&lt;/ref&gt;  The right is also limited under Sections 43 and 60 of the Data Protection Act, which provide for the right of freedom of expression and information and restrictions necessary for the public interest.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Cookie Consent ===
In 2019, the DPC sent out a questionnaire to relevant organizations to examine the use of cookies across popular Irish websites.&lt;ref&gt;''Irish DPC Publishes New Cookie Guidance'', Hunton (Apr. 8, 2020), &lt;nowiki&gt;https://www.hunton.com/privacy-and-information-security-law/irish-dpc-publishes-new-cookie-guidance#:~:text=If%20a%20cookie%20is%20used,actual%20facts%20of%20the%20processing&lt;/nowiki&gt;.&lt;/ref&gt;  The goal of DPC’s sweep was “to examine how cookies and similar technologies are deployed, and to establish how and whether organizations are (1) complying with the current Irish cookie law rules, implementing the EU ePrivacy Directive into Irish law (the “Irish ePrivacy Regulations”) in particular; and (2) whether users’ consent for non-necessary cookies or tracking technologies is being obtained in line with the requirements of the [GDPR].”&lt;ref&gt;''Id''.&lt;/ref&gt;  The DPC offered new cookie guidance in which cookie consent has a lifespan of six months, like the CNIL in France, and must then be renewed.&lt;ref&gt;''Id''.&lt;/ref&gt;

In 2024, the DPC announced its decision after an investigation into LinkIn for its alleged use of personal data for behavioral analysis and targeted advertising.&lt;ref&gt;''Irish Data Protection Commission Fines LinkedIn Ireland €310 million'', Data Protection Commission (Oct. 24, 2024), &lt;nowiki&gt;https://www.dataprotection.ie/en/news-media/press-releases/irish-data-protection-commission-fines-linkedin-ireland-eu310-million&lt;/nowiki&gt;.&lt;/ref&gt;  The DPC determined that LinedIn had used personal data in violation of multiple Articles of the GDPR and fined the company €310 million, along with a reprimand and order to bring its processing in compliance with the GDPR.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Right to Clothing ===
&lt;u&gt;Textile Labeling:&lt;/u&gt; As an EU member, the EU Textile Fibre Names and Related Labelling and Marking of the Fibre Composition of Textile Products Regulations 2012 (S.I. No. 142 of 2012) governs Irish textiles.&lt;ref&gt;''Textile Labelling Regulations'', Competition and Consumer Protection Commission (last updated Dec. 5, 2025), &lt;nowiki&gt;https://www.ccpc.ie/business/help-for-business/guidelines-for-business/textile-labelling-regulations/&lt;/nowiki&gt;.&lt;/ref&gt;  The Regulations “protect consumers by laying down rules governing the labelling or marking of products in relation to their textile fibre content and provides uniform methods for quantitative analysis of binary textile fibre mixtures.”&lt;ref&gt;''Id''.&lt;/ref&gt;  All textiles must have a label which indicates the fibre content, in&lt;ref&gt;''Id''.&lt;/ref&gt;cluding fibre names, descriptions, and labels.&lt;ref&gt;''Id''.&lt;/ref&gt;  Any textiles sold in Ireland must comply with the Regulations.&lt;ref&gt;''Id''.&lt;/ref&gt;  The Competition and Consumer Protection Commission (“CCPC”) is the regulatory body responsible for enforcing the Regulations in Ireland.&lt;ref&gt;''Id''.&lt;/ref&gt;

&lt;u&gt;Cultural Clothing:&lt;/u&gt; There are currently no modern regulations regarding wearing Irish cultural clothing, there were historical laws which did ban certain Irish clothing.&lt;ref&gt;Marcus Harris, ''Discover the Charm of Traditional Irish Clothing | Embrace Heritage and Style'', Tartan Vibes Clothing (Jan. 5, 2024), &lt;nowiki&gt;https://www.tartanvibesclothing.com/blogs/fashion/traditional-irish-clothing?srsltid=AfmBOoouoHaNJ-0p_YXKybKf5vEOToOPhVMcioRVc5vbYK_Bx9-XZPL5&lt;/nowiki&gt;&lt;/ref&gt;  The traditional clothing in Ireland consists of a léine, typically a loose fitting linen shift that reached the knee, bróga (wool trousers), a caoat (wool jacket), and a caubeen (flat wool cap).&lt;ref&gt;''Id''.&lt;/ref&gt;  Women traditionally wore a síodóir (dress made of wool) and a brat (apron).&lt;ref&gt;''Id''.&lt;/ref&gt;  This traditional clothing can be traced back to the Irish Celts in 500BC.&lt;ref&gt;''Id''.&lt;/ref&gt;  When Christianity spread in Ireland, new traditions flooded in and in the 16th and 17th centuries, as English colonization continued, Penal Laws prohibited the Irish from wearing their traditional clothing and forced them to adopt English styles.&lt;ref&gt;''Id''.&lt;/ref&gt;  However, in the late 19th century, the Irish Cultural Movement led to an increase in interest in traditional Irish clothing and it remains an important party of the nation’s culture today, being worn on special occasions and festivals.&lt;ref&gt;''Id''.&lt;/ref&gt;

&lt;u&gt;Religious Expression and Clothing:&lt;/u&gt; Ireland does not have any laws which prohibit wearing religious clothing or symbols in public employment.&lt;ref&gt;''Religious Clothing and Symbols in Employment'', European Commission (Nov. 2017), &lt;nowiki&gt;https://www.google.com/url?sa=t&amp;source=web&amp;rct=j&amp;opi=89978449&amp;url=https://ec.europa.eu/newsroom/just/redirection/document/48810&amp;ved=2ahUKEwjc-IS-sr6RAxVPF1kFHUPeAGEQFnoECBkQAQ&amp;usg=AOvVaw3vEluFl9Q3FVWGlyg0B0QS&lt;/nowiki&gt;.&lt;/ref&gt; In 2007, there was a debate regarding the Irish police force’s uniform policy in which a Sikh man wanted to challenge a ban on wearing turbans for Reserve Police members after he was told he would not be permitted to wear his turban.&lt;ref name=&quot;:0&quot;&gt;''Id''.&lt;/ref&gt;&lt;ref name=&quot;:0&quot; /&gt;  However, the complaint was unsuccessful because the action fell outside of the conduct of the Employment Equality Acts and the issue was not addressed further.&lt;ref&gt;''Id''.&lt;/ref&gt;  In 2008, controversy arose about the use of religious symbols and clothing when a school principal asked the Minister for Education about a request by a Muslim student to wear a hijab.&lt;ref&gt;''Id''.&lt;/ref&gt;  This Irish Government chose not to issue a directive and left the decision to the schools under the Education Act 1998, but did issue a recommend that no school policy should discrimination against students of a particular religion.&lt;ref&gt;''Id''.&lt;/ref&gt;

=== Regulation of Bodily Displays and Obscenity Laws ===
&lt;u&gt;Intimate Images:&lt;/u&gt; Intimate images are defined by the Harassment, Harmful Communications and Related Offences Act 2020.&lt;ref&gt;''What is Coco’s Law? ISPCC is Offering a Free Webinar All About the Law Around the Sharing of Intimate Images'', Irish Society for the Prevention of Cruelty to Children (last visited Dec. 4, 2025), &lt;nowiki&gt;https://www.ispcc.ie/what-is-cocos-law-ispcc-is-offering-a-free-webinar-all-about-the-law-around-the-sharing-of-intimate-images/&lt;/nowiki&gt;''.''&lt;/ref&gt;  The law, also known as “Coco’s Law,” was enacted after the tragic death of Nicole “Coco” Fox, following the sharing of her intimate images online.&lt;ref&gt;''Id''.&lt;/ref&gt;  The law criminalized the making or sharing of intimate images that cause harm.&lt;ref&gt;''Sharing of Intimate Images Without Consent'', Citizens Information (last visited Dec. 4, 2025), &lt;nowiki&gt;https://www.citizensinformation.ie/en/justice/criminal-law/criminal-offences/sharing-of-intimate-images-without-consent/&lt;/nowiki&gt;.&lt;/ref&gt;  Specifically, the law makes it a crime to record, distribute, share, publish or threaten to publish intimate images without the permission of the person featured in the images and can result in a sentence up to 7 years.&lt;ref&gt;''Id''.&lt;/ref&gt;

&lt;u&gt;Nudity:&lt;/u&gt; Public indecent exposure is regulated under multiple Irish laws.&lt;ref&gt;''Law on Public Indecent Exposure'', Irish Independent (Nov. 4, 2010), &lt;nowiki&gt;https://www.independent.ie/irish-news/law-on-public-indecent-exposure/26696631.html&lt;/nowiki&gt;&lt;/ref&gt;  The Public Order Act (1994) makes it an offence in to be nude in public and can result in a fine of up to €500.&lt;ref&gt;''Id''.&lt;/ref&gt;  Section 18 of the Criminal Law (Amendment) Act (1990) also covers indecent exposure, finding an offence by “any person who commits, in public, any act in such a way as to offend modesty or cause scandal or injure the morals of the community shall be guilty . . . the person may receive a fine up to €634.87 or, if the court decides, they may be sent to prison for up to six months.”&lt;ref&gt;''Id''.&lt;/ref&gt;

With the previously heavy undertones of catholicism in Irish laws, religious attitudes led to censorship laws which also governed art.&lt;ref&gt;''The Nude'', Ask About Ireland (last visited Dec. 4, 2025), &lt;nowiki&gt;https://www.askaboutireland.ie/learning-zone/secondary-students/art/art-in-ireland/themes-in-irish-art/people-in-art/the-nude/#&lt;/nowiki&gt;.&lt;/ref&gt;  Many artists working with nude figures would work outside of Ireland when doing so to avoid the relevant laws.&lt;ref&gt;''Id''.&lt;/ref&gt;  In the 1951, Louis le Brocquy’s ''A Family'', which contained nude figures, was criticized in Ireland, but was nationally acclaimed.&lt;ref&gt;''Id''.&lt;/ref&gt;  Now, the nude appears in Irish art in many fashions and is not heavily regulated in favor of artistic expression.&lt;ref&gt;''Id''.&lt;/ref&gt; 

&lt;u&gt;Child Pornography:&lt;/u&gt; The Child Ponography Offence (2017 Act) outlaws the knowing production, distribution, transmission, dissemination, importing, exporting, selling, and supplying of child pornography.&lt;ref&gt;Criminal Law (Sexual Offences) Act 2017.&lt;/ref&gt; The Act also includes language allowing for the punishment of a person who by means of communication technology communicates with another person, including a child, for the purpose of facilitating sexual exploitation.&lt;ref&gt;''Child Pornography'', Irish Legal Blog (last visited Dec. 4, 2025), &lt;nowiki&gt;https://legalblog.ie/child-pornography/&lt;/nowiki&gt;.&lt;/ref&gt;  It also prohibits sending sexually explicit material, which is defined as “any indecent or obscene images or words.”&lt;ref&gt;''Id''.&lt;/ref&gt;

== References ==</text>
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    <title>Supply Chain Management</title>
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= Supply Chain Management =
ABSTRACT

Supply Chain Management (SCM) is a multidisciplinary field that focuses on the strategic coordination of business functions and  operations within and across organizations. Its objective is to improve the long-term performance of individual organizations, supply networks, and entire economies. In an era characterized by globalization, digital transformation, and heightened sustainability concerns, supply chain management has become a central pillar of organizational effectiveness, public service delivery, and national development. 

1. INTRODUCTION

Supply Chain Management refers to the planning, implementation, control, and optimization of the flow of goods, services, information, and finances from raw material extraction to final consumption. It encompasses procurement, production, logistics, inventory management, distribution, and customer service.

Modern organizations operate in complex and interconnected supply networks rather than isolated entities. As a result, effective supply chain management requires collaboration, information sharing, and strategic alignment among suppliers, manufacturers, service providers, distributors, governments, and end users. SCM is applicable in both private and public sectors, supporting manufacturing, healthcare, infrastructure development, disaster response, public services delivery and humanitarian operations.

2. HISTORICAL DEVELOPMENT OF SUPPLY CHAIN MANAGEMENT

2.1 Traditional Procurement and Logistics

Historically, procurement, production, transportation, and warehousing were treated as independent functions. Organizations focused on minimizing costs within individual departments rather than optimizing the entire system. This fragmented approach often resulted in inefficiencies, duplication of efforts, and poor service delivery.

2.2 Integrated Logistics Management

Between the 1960s and 1980s, organizations began integrating logistics activities to improve coordination and reduce costs. Concepts such as materials management and physical distribution gained prominence. Advances in transportation, containerization, and information systems supported this integration.

2.3 Emergence of Supply Chain Management

In the 1990s, the term “supply chain management” gained widespread acceptance. Organizations recognized that competitiveness depended not only on internal efficiency but also on the performance of suppliers and distributors. Strategic partnerships, outsourcing, and global sourcing became common practices.

2.4 Digital and Sustainable Supply Chains

In the 21st century, supply chains have been transformed by digital technologies, sustainability imperatives, and risk management considerations. Organizations now emphasize transparency, resilience, environmental responsibility, and ethical sourcing.

3. CORE CONCEPTS IN SUPPLY CHAIN MANAGEMENT

Supply Chain: A network of organizations, people, activities, information, and resources involved in delivering a product or service.

Value Chain: Activities that add value to a product or service at each stage.

Upstream Activities: Supplier-related processes such as sourcing and procurement.

Downstream Activities: Distribution, marketing, and customer service.

Supply Chain Integration: Coordination of processes within and across organizations.

Bullwhip Effect: Demand variability amplification as information moves upstream.

4. COMPONENTS OF SUPPLY CHAIN MANAGEMENT

4.1 Procurement and Strategic Sourcing

Procurement involves identifying needs, selecting suppliers, negotiating contracts, and managing supplier relationships. Strategic sourcing emphasizes long-term value, supplier development, cost efficiency, quality assurance, and risk mitigation.

4.2 Production and Operations Management

Operations management focuses on transforming inputs into outputs efficiently. This includes capacity planning, scheduling, quality control, and continuous improvement. In service organizations, operations management ensures timely and reliable service delivery.

4.3 Inventory Management

Inventory management seeks to balance availability and cost. Excess inventory ties up capital, while shortages disrupt operations. Common techniques include Economic Order Quantity (EOQ), safety stock analysis, demand forecasting, and Just-In-Time (JIT) systems.

4.4 Logistics and Distribution Management

Logistics ensures the efficient movement and storage of goods. It covers transportation, warehousing, order fulfillment, and last-mile delivery. Effective logistics management improves customer satisfaction and reduces operational costs.

4.5 Information Management and Technology

Information is the backbone of supply chain management. Accurate and timely data enables coordination, forecasting, performance measurement, and decision-making.

5. SUPPLY CHAIN STRATEGIES AND MODELS

5.1 Push-Based Supply Chains

Push systems rely on demand forecasts to plan production and distribution. While efficient in stable environments, they are vulnerable to demand uncertainty.

5.2 Pull-Based Supply Chains

Pull systems respond to actual customer demand. They reduce inventory levels but require responsive operations and reliable information systems.

5.3 Lean Supply Chains

Lean supply chains focus on waste elimination, standardization, and continuous improvement.

5.4 Agile Supply Chains

Agile supply chains prioritize flexibility and responsiveness in volatile markets.

5.5 Hybrid (Leagile) Supply Chains

Leagile supply chains combine lean efficiency with agile responsiveness.

6. TECHNOLOGY IN SUPPLY CHAIN MANAGEMENT

Technological advancements have revolutionized supply chain operations. Enterprise Resource Planning (ERP) systems integrate organizational processes. Blockchain enhances transparency and traceability. Artificial Intelligence supports demand forecasting and optimization. The Internet of Things enables real-time monitoring of assets and shipments.

7. SUPPLY CHAIN RISK MANAGEMENT AND RESILIENCE

Supply chains face risks including supplier disruptions, geopolitical instability, pandemics, cyber threats, and climate change. Risk management strategies include supplier diversification, strategic stockholding, contractual safeguards, and contingency planning.

8. SUSTAINABLE AND ETHICAL SUPPLY CHAIN MANAGEMENT

Sustainable supply chain management integrates economic, environmental, and social objectives. Green supply chains reduce emissions and waste. Ethical sourcing promotes fair labor practices. Circular supply chains emphasize reuse, recycling, and resource efficiency.

9. PUBLIC SECTOR SUPPLY CHAIN MANAGEMENT

Public sector supply chains support essential services such as healthcare, security, immigration, education, and infrastructure. They operate under strict regulatory frameworks and emphasize transparency, accountability, and value for money.

10. SUPPLY CHAIN MANAGEMENT IN DEVELOPING ECONOMIES

Developing economies face challenges such as limited infrastructure, skills gaps, and technology constraints. Strengthening supply chain management can significantly improve service delivery, food security, and economic growth.

11. FUTURE TRENDS IN SUPPLY CHAIN MANAGEMENT

Future supply chains will be increasingly digital, data-driven, and resilient. Key trends include automation, predictive analytics, regionalization, climate-resilient supply chains, and increased collaboration across supply networks.

12. CONCLUSION

Supply Chain Management is a strategic discipline essential for organizational success, public service delivery, and sustainable development. Continuous learning, innovation, and collaboration are critical to advancing supply chain performance in an increasingly complex global environment.

13. LEARNING ACTIVITIES

Case studies, simulations, research projects, and comparative analyses are recommended to enhance understanding of supply chain management concepts.

14. REFERENCES AND FURTHER READING

Chopra, S., and Meindl, P. Supply Chain Management: Strategy, Planning, and Operation.

Christopher, M. Logistics and Supply Chain Management.

Handfield, R. Introduction to Supply Chain Management.

[[Category:Management]]</text>
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    <title>User:Dc.samizdat/Golden chords of the 120-cell</title>
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      <text bytes="49849" sha1="oxuuygvuy8ms9xqd7alpbr8kspvy1hq" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The cuboctahedron and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the skew regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is a construct of eight Petrie dodecahedrons with disjoint sets of 12 edges each.

...

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are &lt;small&gt;&lt;math&gt;\sqrt{3}=120^\circ&lt;/math&gt;&lt;/small&gt; apart. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

...

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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    <revision>
      <id>2810150</id>
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      <text bytes="49916" sha1="dtotlpcn5lgf4rhjwlsusgnyqdqfl7r" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The cuboctahedron and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;


The 24-cell is a construct of eight skew dodecahedrons with disjoint sets of 12 edges each.

...

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are &lt;small&gt;&lt;math&gt;\sqrt{3}=120^\circ&lt;/math&gt;&lt;/small&gt; apart. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

...

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>dtotlpcn5lgf4rhjwlsusgnyqdqfl7r</sha1>
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    <revision>
      <id>2810170</id>
      <parentid>2810150</parentid>
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        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="50042" sha1="6zdm4dvzigr9za2fnzvdbwlbz035wk3" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The cuboctahedron and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

...

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are &lt;small&gt;&lt;math&gt;\sqrt{3}=120^\circ&lt;/math&gt;&lt;/small&gt; apart. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

...

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>6zdm4dvzigr9za2fnzvdbwlbz035wk3</sha1>
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    <revision>
      <id>2810176</id>
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      <contributor>
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      <text bytes="50044" sha1="d8cq3a3apaa3z3vpt684omgoxdjj6b7" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The cuboctahedron and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

...

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2810204</id>
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      <text bytes="50473" sha1="pg00wvm1gsybwlxzhubcpxhcydph7wl" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The cuboctahedron and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=1,r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° into each other's plane while rotating 60° internally. All 24 vertices move at once on four disjoint circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="50500" sha1="3hm72fyclkwjd3wd6u6321gxnq0ai3v" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each. Two Petrie octagons cross at each vertex.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° into each other's plane while rotating 60° internally. All 24 vertices move at once on four disjoint circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>3hm72fyclkwjd3wd6u6321gxnq0ai3v</sha1>
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    <revision>
      <id>2810223</id>
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      <text bytes="50458" sha1="gxxi9h17wouohqj7h851tbr9psg0hls" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. Only the edges of the two disjoint squares lie parallel to the projection plane, in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° into each other's plane while rotating 60° internally. All 24 vertices move at once on four disjoint circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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    <revision>
      <id>2810240</id>
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      <text bytes="50400" sha1="14yx4ekds3g3398bb2w0iyjmpoyyoqw" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since this unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>14yx4ekds3g3398bb2w0iyjmpoyyoqw</sha1>
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    <revision>
      <id>2810245</id>
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      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="50399" sha1="gj88ojt7nhxelr7rb5gzsnkhfm2rnj9" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>gj88ojt7nhxelr7rb5gzsnkhfm2rnj9</sha1>
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    <revision>
      <id>2810246</id>
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      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="52428" sha1="e769sa18xzt8pc6y2thr0mayufr24a4" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew {8/3} hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>e769sa18xzt8pc6y2thr0mayufr24a4</sha1>
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    <revision>
      <id>2810247</id>
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      <text bytes="52422" sha1="3epbmvf719jfe7ioa461yd1qt32zckt" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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    <revision>
      <id>2810271</id>
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      <text bytes="52771" sha1="hspd9pvdhewmndz491lna09dfrzg6g6" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black edges have unit length, blue chords have length &lt;math&gt;\sqrt{2}&lt;/math&gt;, and green chords have length &lt;math&gt;\sqrt{3}&lt;/math&gt;.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="52869" sha1="7bmfff8fm2epc4akcgr8gjrq5oajgg3" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black chords are edges of unit length, blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges and isocline chords of a great square rotation, and green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; isocline chords of a great hexagon rotation.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="52949" sha1="igphkbphvekzsxz17akb77rfv5llt51" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of a square rotation. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of a hexagonal rotation.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>igphkbphvekzsxz17akb77rfv5llt51</sha1>
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    <revision>
      <id>2810300</id>
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      <text bytes="52947" sha1="8ez137xcydfsg69plye58rksejzy7p6" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. The 24-cell's Clifford polygon is a skew hexagram of its &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

{{Efn|In this orthogonal projection of the 24-point 24-cell to a [[W:Dodecagon#Related figures|{12/4}=4{3} dodecagram]], each point represents two vertices, and each line represents multiple {{radic|3}} chords. Each disjoint triangle can be seen as a skew {6/2} [[W:Hexagram|hexagram]] with {{radic|3}} edges: two open skew triangles with their opposite ends connected in a [[W:Möbius strip|Möbius loop]] with a circumference of 4𝝅. The hexagram projects to a single triangle in two dimensions because it skews through all four dimensions. Those 4 disjoint skew [[#Helical hexagrams and their isoclines|hexagram isoclines]] are the Clifford parallel circular vertex paths of the fibration's characteristic left (and right) [[#Isoclinic rotations|isoclinic rotation]].{{Efn|name=isoclinic geodesic}} The 4 Clifford parallel great hexagons of the fibration are invariant planes of this rotation. The great hexagons rotate in incremental displacements of 60° like wheels ''and'' 60° orthogonally like coins flipping, displacing each vertex by 120°, as their vertices move along parallel helical isocline paths through successive Clifford parallel hexagon planes.{{Efn|Each hexagon rides on only three skew hexagram isoclines, not six, because opposite vertices of each hexagon ride on opposing rails of the same Clifford hexagram, in the same (not opposite) rotational direction.{{Efn|name=Clifford polygon}}}} Alternatively, the 4 triangles can be seen as 8 disjoint triangles: 4 pairs of Clifford parallel [[#Great triangles|great triangles]], where two opposing great triangles lie in the same [[#Great hexagons|great hexagon central plane]], so a fibration of 4 Clifford parallel great hexagon planes is represented.{{Efn|name=four hexagonal fibrations}} This illustrates that the 4 hexagram isoclines also correspond to a distinct fibration, in fact the ''same'' fibration as 4 great hexagons.|name=hexagram}}

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>8ez137xcydfsg69plye58rksejzy7p6</sha1>
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    <revision>
      <id>2810303</id>
      <parentid>2810300</parentid>
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      <contributor>
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      <text bytes="51113" sha1="79q2i3x1offyyjz6lbs554jzb9r4sw9" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
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|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits of the 24 vertices form a circular triple helix of &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four disjoint skew hexagon geodesic orbits of the 24 vertices form a circular quadruple helix of &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>79q2i3x1offyyjz6lbs554jzb9r4sw9</sha1>
    </revision>
    <revision>
      <id>2810306</id>
      <parentid>2810303</parentid>
      <timestamp>2026-05-18T23:11:30Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="51079" sha1="4jkssygtn6x2y47x67318liev2qoj7x" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] objects that form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four disjoint skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>4jkssygtn6x2y47x67318liev2qoj7x</sha1>
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    <revision>
      <id>2810312</id>
      <parentid>2810306</parentid>
      <timestamp>2026-05-18T23:14:16Z</timestamp>
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        <username>Dc.samizdat</username>
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      <text bytes="51070" sha1="71753ujnez6ats7bvf7ja4qazx6cq5z" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] and form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three disjoint skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four disjoint skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>71753ujnez6ats7bvf7ja4qazx6cq5z</sha1>
    </revision>
    <revision>
      <id>2810315</id>
      <parentid>2810312</parentid>
      <timestamp>2026-05-18T23:15:26Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* The 24-cell */</comment>
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      <text bytes="51088" sha1="98xjhgfb7yigvvb44tac1nuqeo4tcep" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] and form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle once over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>98xjhgfb7yigvvb44tac1nuqeo4tcep</sha1>
    </revision>
    <revision>
      <id>2810325</id>
      <parentid>2810315</parentid>
      <timestamp>2026-05-18T23:30:10Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
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      <text bytes="51089" sha1="bp6b96vbcknxk7vti8y2cg1sm42r6hi" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality, which are [[w:Clifford_parallel|Clifford parallel]] and form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. The three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <text bytes="51153" sha1="2jjmioahtdna8xiobjqvggg5j0s828j" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords of square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices in two 16-cells, also isocline chords of hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <parentid>2810332</parentid>
      <timestamp>2026-05-18T23:53:22Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 24-cell */</comment>
      <origin>2810336</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="51194" sha1="6o287t7otitzf5z64v61yl335m89rxq" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in two completely orthogonal invariant hexagonal central planes, which takes every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation planes in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Its Clifford polygon is a skew hexagram. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>6o287t7otitzf5z64v61yl335m89rxq</sha1>
    </revision>
    <revision>
      <id>2810339</id>
      <parentid>2810336</parentid>
      <timestamp>2026-05-19T00:20:37Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 24-cell */</comment>
      <origin>2810339</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="51217" sha1="euvcwfdo6ihqs7xz6l24d6pemb1aomv" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane, taking every hexagonal central plane to a Clifford parallel hexagonal central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Its Clifford polygon is a skew hexagram. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>euvcwfdo6ihqs7xz6l24d6pemb1aomv</sha1>
    </revision>
    <revision>
      <id>2810341</id>
      <parentid>2810339</parentid>
      <timestamp>2026-05-19T00:28:06Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 24-cell */</comment>
      <origin>2810341</origin>
      <model>wikitext</model>
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      <text bytes="51148" sha1="nj8cym5i85athxii5hi5c6644dsra4r" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal steps of 120° each rather than 8 chordal steps of 90° each. Its Clifford polygon is a skew hexagon helix in 4-space. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>nj8cym5i85athxii5hi5c6644dsra4r</sha1>
    </revision>
    <revision>
      <id>2810344</id>
      <parentid>2810341</parentid>
      <timestamp>2026-05-19T00:33:28Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 600-cell */</comment>
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      <text bytes="51164" sha1="783xn1r49m9emyth65zjqwwbia04txu" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations.]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal displacements of 120° each rather than 8 chordal displacements of 90° each. Its Clifford polygon is a skew hexagon helix in 4-space. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>783xn1r49m9emyth65zjqwwbia04txu</sha1>
    </revision>
    <revision>
      <id>2810346</id>
      <parentid>2810344</parentid>
      <timestamp>2026-05-19T00:44:30Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 24-cell */</comment>
      <origin>2810346</origin>
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      <text bytes="51232" sha1="kgx2j1mv2bfvtpcu8s0ll9w932kl6c5" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. The two disjoint hexagons lie in Clifford parallel central planes. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal displacements of 120° each rather than 8 chordal displacements of 90° each. Its Clifford polygon is a skew hexagon helix in 4-space. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>kgx2j1mv2bfvtpcu8s0ll9w932kl6c5</sha1>
    </revision>
    <revision>
      <id>2810347</id>
      <parentid>2810346</parentid>
      <timestamp>2026-05-19T00:46:45Z</timestamp>
      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
      </contributor>
      <comment>/* The 24-cell */</comment>
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      <text bytes="51232" sha1="rmdww6lxgo2qbu6t9rrqpju5tyg2vah" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a skew {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal displacements of 120° each rather than 8 chordal displacements of 90° each. Its Clifford polygon is a skew hexagon helix in 4-space. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>rmdww6lxgo2qbu6t9rrqpju5tyg2vah</sha1>
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    <revision>
      <id>2810375</id>
      <parentid>2810347</parentid>
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      <contributor>
        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <comment>/* The 8-point regular polytopes */</comment>
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      <text bytes="51232" sha1="7qf2ifeam8aksu72i8q4gd5i4jew9nc" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. 

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 6 chordal displacements of 120° each rather than 8 chordal displacements of 90° each. Its Clifford polygon is a skew hexagon helix in 4-space. Four Clifford parallel skew hexagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular quadruple helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>7qf2ifeam8aksu72i8q4gd5i4jew9nc</sha1>
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    <revision>
      <id>2810376</id>
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        <username>Dc.samizdat</username>
        <id>2856930</id>
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      <text bytes="51493" sha1="f0uo2hebxjn2dkz82o3qe3dhsoarewv" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. When the 24-cell is constructed by skewing two completely orthogonal planar dodecagons, the lengths of the dodecagon chords change to: 

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. Its Clifford polygon is a skew {12/5} dodecagram, visible in the orthogonal projection. Two Clifford parallel skew dodecagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-sixth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over six &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 6 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2810377</id>
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      <text bytes="51500" sha1="6r25rfrgs2yyqaytn2map43tqhs1651" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. When the 24-cell is constructed by skewing two completely orthogonal planar dodecagons, the lengths of the dodecagon chords change to: 

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. Its Clifford polygon is a skew {12/5} dodecagram, visible in the orthogonal projection. Two Clifford parallel skew dodecagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on four Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelveth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2810378</id>
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      <text bytes="51498" sha1="lip6ex49p2xrvq0d22thu4uesp28yjs" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecahedron {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecahedron do not occur in the 24-cell, which is a construct of eight skew dodecahedrons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. When the 24-cell is constructed by skewing two completely orthogonal planar dodecagons, the lengths of the dodecagon chords change to: 

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. Its Clifford polygon is a skew {12/5} dodecagram, visible in the orthogonal projection. Two Clifford parallel skew dodecagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on two Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
      <sha1>lip6ex49p2xrvq0d22thu4uesp28yjs</sha1>
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    <revision>
      <id>2810379</id>
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      <text bytes="51489" sha1="beg54lu8m1lum96tum2mt2gvwwyimvu" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. When the 24-cell is constructed by skewing two completely orthogonal planar dodecagons, the lengths of the dodecagon chords change to: 

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. Its Clifford polygon is a skew {12/5} dodecagram, visible in the orthogonal projection. Two Clifford parallel skew dodecagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on two Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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      <id>2810380</id>
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      <text bytes="51516" sha1="hr8bkrzybjhyvnu9zbkktsinrbw2ymo" xml:space="preserve">{{align|center|David Brooks Christie}}
{{align|center|dc@samizdat.org}}
{{align|center|Draft in progress}}
{{align|center|January 2026 - April 2026}}

&lt;blockquote&gt;Steinbach discovered the formula for the ratios of diagonal to side in the regular polygons. Fontaine and Hurley extended this result, discovering a formula for the reciprocal of a regular polygon chord derived geometrically from the chord's star polygon. We observe that these findings in plane geometry apply more generally, to polytopes of any dimensionality. Fontaine and Hurley's geometric procedure for finding the reciprocals of the chords of a regular polygon from their star polygons also finds the rotational geodesics of any polytope of any dimensionality.&lt;/blockquote&gt;
== Introduction ==
Steinbach discovered the Diagonal Product Formula and the Golden Fields family of ratios of diagonal to side in the regular polygons. He showed how this family extends beyond the pentagon {5} with its well-known golden bisection proportional to 𝜙, finding that the heptagon {7} has an analogous trisection, the nonagon {9} has an analogous quadrasection, and the hendecagon {11} has an analogous pentasection, an extended family of golden proportions with quasiperiodic properties. 

Kappraff and Adamson extended these findings in plane geometry to a theory of Generalized Fibonacci Sequences, showing that the Golden Fields not only do not end with the hendecagon, they form an infinite number of periodic trajectories when operated on by the Mandelbrot operator. They found a relation between the edges of star polygons and dynamical systems in the state of chaos, revealing a connection between chaos theory, number, and rotations in Coxeter Euclidean geometry. 

Fontaine and Hurley examined Steinbach's finding that the length of each chord of a regular polygon is both the product of two chords and the sum of a set of smaller chords, so that in rotations to add is to multiply. They illustrated Steinbach's sets of additive chords lying parallel to each other in the plane (pointing in the same direction), and by applying Steinbach's formula more generally they found another summation relation of signed parallel chords (pointing in opposite directions) which relates each chord length to its reciprocal, and relates the summation to a distinct star polygon rotation. 

We examine these remarkable findings (which stem from study of the chords of humble regular polygons) in higher-dimensional spaces, specifically in the chords, polygons and rotations of the [[120-cell]], the largest four-dimensional regular convex polytope.

== Visualizing the 120-cell ==
{| class=&quot;wikitable floatright&quot; width=&quot;400&quot;
|style=&quot;vertical-align:top&quot;|[[File:120-cell.gif|200px]]&lt;br&gt;Orthographic projection of the 600-point 120-cell &lt;small&gt;&lt;math&gt;\{5,3,3\}&lt;/math&gt;&lt;/small&gt; performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].{{Sfn|Hise|2011|loc=File:120-cell.gif|ps=; &quot;Created by Jason Hise with Maya and Macromedia Fireworks. A 3D projection of a 120-cell performing a [[W:SO(4)#Geometry of 4D rotations|simple rotation]].&quot;}} In this simplified rendering only the 120-cell's own edges are shown; its 29 interior chords are not rendered. Therefore even though it is translucent, only its outer surface is visible. The complex interior parts of the 120-cell, all its inscribed 5-cells, 16-cells, 8-cells, 24-cells, 600-cells and its much larger inventory of polyhedra, are completely invisible in this view, as none of their edges are rendered at all.
|style=&quot;vertical-align:top&quot;|[[File:Ortho solid 016-uniform polychoron p33-t0.png|200px]]&lt;br&gt;Orthographic projection of the 600-point [[W:Great grand stellated 120-cell|great grand stellated 120-cell]] &lt;small&gt;&lt;math&gt;\{\tfrac{5}{2},3,3\}&lt;/math&gt;&lt;/small&gt;.{{Sfn|Ruen: Great grand stellated 120-cell|2007}} The 120-cell is its convex hull. The projection to the left renders only the 120-cell's shortest chord, its 1200 edges. The projection above also renders only one of the 120-cell's 30 chords, the edges of its 120 inscribed regular 5-cells. The 120-cell itself (the convex hull) is invisible in this view, as its edges are not rendered.
|}

[[120-cell#Geometry|The 120-cell is the maximally complex regular 4-polytope]], containing inscribed instances of every regular 1-, 2-, 3-, and 4-polytope, except the regular polygons of more than {15} sides. 

The 120-cell is the convex hull of a regular [[120-cell#Relationships among interior polytopes|compound of each of the 6 regular convex 4-polytopes]]. They are the [[5-cell|5-point (5-cell) 4-simplex]], the [[16-cell|8-point (16-cell) 4-orthoplex]], the [[W:Tesseract|16-point (8-cell) tesseract]], the [[24-cell|24-point (24-cell)]], the [[600-cell|120-point (600-cell)]], and the [[120-cell|600-point (120-cell)]]. The 120-cell is the convex hull of a compound of 120 disjoint regular 5-cells, of 75 disjoint 16-cells, of 25 disjoint 24-cells, and of 5 disjoint 600-cells.

The 120-cell contains an even larger inventory of irregular polytopes, created by the intersection of multiple instances of these component regular 4-polytopes. Many are quite unexpected, because they do not occur as components of any regular polytope smaller than the 120-cell. As just one example among the [[120-cell#Concentric hulls|sections of the 120-cell]], there is an irregular 24-point polyhedron with 16 triangle faces and 4 nonagon {9} faces.{{Sfn|Moxness|}}

Most renderings of the 120-cell, like the rotating projection here, only illustrate its outer surface, which is a honeycomb of face-bonded dodecahedral cells. Only the objects in its 3-dimensional surface are rendered, namely the 120 dodecahedra, their pentagon faces, and their edges. Although the 120-cell has chords of 30 distinct lengths, in this kind of simplified rendering only the 120-cell's own edges (its shortest chord) are shown. Its 29 interior chords, the edges of objects in the interior of the 120-cell, are not rendered, so interior objects are not visible at all.

Visualizing the complete interior of the 600-vertex 120-cell in a single image is impractical because of its complexity. Only four 120-cell edges are incident at each vertex, but [[120-cell#Chords|600 chords (of all 30 lengths)]] are incident at ''each'' vertex.

== Compounds in the 120-cell ==
The 8-point (16-cell), not the 5-point (5-cell), is the smallest building block; it compounds to every larger regular 4-polytope. The 5-point (5-cell) does compound to the 600-point (120-cell), but it does not fit into any smaller regular 4-polytope. 

The 8-point (16-cell) compounds by 2 in the 16-point (8-cell), and by 3 in the 24-point (24-cell). The 16-point (8-cell) compounds in the 24-point (24-cell) by 3 non-disjoint instances of itself, with each of the 24 vertices shared by two 16-point (8-cells). The 24-point (24-cell) compounds by 5 disjoint instances of itself in the 120-point (600-cell), and the 120-point (600-cell) compounds by 5 disjoint instances of itself in the 600-point (120-cell).

The 24-point (24-cell) also compounds by &lt;math&gt;5^2&lt;/math&gt; non-disjoint instances of itself in the 120-point (600-cell); it compounds in 5 disjoint instances of itself, 10 (not 5) different ways. Whichever set of 5 disjoint 24-point (24-cells) are assembled, the resulting 120-point (600-cell) contains 25 distinct 24-point (24-cells), not just 5 (or 10). This implies that 15 disjoint 8-point (16-cells) will construct a 120-point (600-cell), which will contain 75 distinct 8-point (16-cells). 

The 600-point (120-cell) is 5 disjoint 120-point (600-cells), just 2 different ways (not 5 or 10 ways), so it is 10 distinct 120-point (600-cells). This implies that the 8-point (16-cell) compounds by 3 times &lt;math&gt;5^2&lt;/math&gt; (75) disjoint instances of itself in the 600-point (120-cell), which contains &lt;math&gt;3^2&lt;/math&gt; times  &lt;math&gt;5^2&lt;/math&gt; (225) distinct instances of the 24-point (24-cell), and  &lt;math&gt;3^3&lt;/math&gt; times &lt;math&gt;5^2&lt;/math&gt; (675) distinct instances of the 8-point (16-cell). 

These facts were discovered painstakingly by various researchers, and no one has found a general rule governing subsumption relations among regular polytopes. The reasons for some of their numeric incidence relations are far from obvious. [[W:Pieter Hendrik Schoute|Schoute]] was the first to see that the 120-point (600-cell) is a compound of 5 24-point (24-cells) ''10 different ways'', and after he saw it a hundred years lapsed until Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne proved his result, and showed why.{{Sfn|Denney, Hooker, Johnson, Robinson, Butler &amp; Claiborne|2020|loc=''The geometry of H4 polytopes''}}

So much for the compounds of 16-cells. The 120-cell is also the convex hull of the compound of 120 disjoint regular 5-cells. That stellated compound (without its convex hull of 120-cell edges) is the [[w:Great_grand_stellated_120-cell|great grand stellated 120-cell]] illustrated above, the final regular [[W:Stellation|stellation]] of the 120-cell, and the only [[W:Schläfli-Hess polychoron|regular star 4-polytope]] to have the 120-cell for its convex hull. The edges of the great grand stellated 120-cell are &lt;math&gt;\phi^6&lt;/math&gt; as long as those of its 120-cell [[W:List of polyhedral stellations#Stellation process|stellation core]] deep inside.

The compound of 120 disjoint 5-point (5-cells) can be seen to be equivalent to the compound of 5 disjoint 120-point (600-cells), as follows. Beginning with a single 120-point (600-cell), expand each vertex into a regular 5-cell, by adding 4 new equidistant vertices, such that the 5 vertices form a regular 5-cell inscribed in the 3-sphere. The 120 5-cells are disjoint, and the 600 vertices form 5 disjoint 120-point (600-cells): a 120-cell.

== Thirty distinguished distances ==
The 30 numbers listed in the table are all-important in Euclidean geometry. A case can be made on symmetry grounds that their squares are the 30 most important numbers between 0 and 4. The 30 rows of the table are the 30 distinct [[120-cell#Geodesic rectangles|chord lengths of the unit-radius 120-cell]], the largest regular convex 4-polytope. Since the 120-cell subsumes all smaller regular polytopes, its 30 chords are the complete chord set of all the regular polytopes that can be constructed in the first four dimensions of Euclidean space, except for regular polygons of more than 15 sides.

{| class=&quot;wikitable&quot; style=&quot;white-space:nowrap;text-align:center&quot;
!rowspan=2|&lt;math&gt;c_t&lt;/math&gt;
!rowspan=2|arc
!rowspan=2|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{n}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|&lt;math&gt;\left\{p\right\}&lt;/math&gt;
!rowspan=2|&lt;small&gt;&lt;math&gt;m\left\{\frac{k}{d}\right\}&lt;/math&gt;&lt;/small&gt;
!rowspan=2|Steinbach roots
!colspan=7|Chord lengths of the unit 120-cell
|-
!colspan=5|unit-radius length &lt;math&gt;c_t&lt;/math&gt;
!colspan=2|unit-edge length &lt;math&gt;c_t/c_1&lt;/math&gt;&lt;br&gt;in 120-cell of radius &lt;math&gt;c_8=\sqrt{2}\phi^2&lt;/math&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{1,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;15.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{30\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{4,1}-c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.270091&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^4}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.072949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;25.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{15\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(c_{18,1}-c_{4,1}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{3-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.437016&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2} \phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.190983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{3,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;36{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{10\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3 \left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right) c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(\sqrt{5}-1\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.618034&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.381966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.28825&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;41.4{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.707107&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.61803&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{5,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;44.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \left\{\frac{15}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{2,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.756934&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{3}{2}}}{\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2 \phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.572949}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.80252&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{6,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;49.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{17}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{5-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{5-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.831254&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\frac{1}{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5}}{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.690983}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.07768&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{7,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;56.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;0.93913&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\psi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{0.881966}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.47709&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;60{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{6\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.70246&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{9,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;66.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{2 \phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}-\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.09132&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{\frac{\chi }{\phi }}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\chi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.04057&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{10,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;69.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1+\sqrt{5}}{2 \sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.14412&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi }{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{11,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;72{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{6}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{5\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{1}{\phi }} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.17557&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3-\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.38197}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \sqrt{3-\phi } \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.3525&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;75.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{24}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.22474&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.53457&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{13,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;81.1{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{9-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.30038&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{9-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(9-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(9-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.8146&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{14,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;84.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{40}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi } c_{8,1}}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt[4]{5} \sqrt{1+\sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.345&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt[4]{5} \sqrt{\phi }}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\sqrt{5} \phi }{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt[4]{5} \sqrt{\phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;4.9798&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{15,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;90.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{4\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{4,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.41421&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.23607&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{16,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;95.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{29}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.4802&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.19098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(11-\sqrt{5}\right)} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.48037&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{17,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;98.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{31}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.51954&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{7+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(7+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\psi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.62605&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{18,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;104.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{8}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{4}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.58114&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{5} \sqrt{\phi ^4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{19,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;108.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{9}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{10}{3}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;c_{3,1}+c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.61803&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{1+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;5.9907&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{20,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;110.2{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13-\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.64042&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13-\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13-\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.69098}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\phi ^2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.07359&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{21,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;113.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{60}{19}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.67601&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{1}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\chi }{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.20537&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{22,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;120{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{10}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{3\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.73205&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{6} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.41285&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{23,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;124.0{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{120}{41}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{\phi }+\frac{5}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{5}{2}+\frac{2}{1+\sqrt{5}}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.7658&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4-\frac{\psi }{2 \phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.11803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\chi  \phi ^5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.53779&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{24,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;130.9{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{20}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{11+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.81907&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{11+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(11+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.30902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{\sqrt{5}}{\phi }}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.73503&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{25,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;135.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{11}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{7+3 \sqrt{5}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.85123&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\phi ^2}{\sqrt{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{\phi ^4}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.42705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^4&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.8541&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{26,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;138.6{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{12}{5}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.87083&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{7}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.5}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{7} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;6.92667&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{27,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;144{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{12}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{5}{2}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{2} \left(5+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.90211&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\phi +2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{2+\phi }&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.61803}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{2 \phi +4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.0425&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{28,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;154.8{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{13}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{13+\sqrt{5}} c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.95167&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{\sqrt{13+\sqrt{5}}}{2}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{1}{4} \left(13+\sqrt{5}\right)}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.80902}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi ^2 \sqrt{8-\frac{1}{\phi ^2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.22598&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{29,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;164.5{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{14}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{15}{7}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\phi  c_{12,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\frac{1}{2} \sqrt{\frac{3}{2}} \left(1+\sqrt{5}\right)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.98168&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3}{2}} \phi &lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{\frac{3 \phi ^2}{2}}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3.92705}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{3} \phi ^3&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.33708&lt;/math&gt;&lt;/small&gt;
|-
|&lt;small&gt;&lt;math&gt;c_{30,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;180{}^{\circ}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{\frac{30}{15}\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\left\{2\right\}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 c_{8,1}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;\sqrt{4.}&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2 \sqrt{2} \phi ^2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;7.40492&lt;/math&gt;&lt;/small&gt;
|-
|rowspan=4 colspan=6|
|rowspan=4 colspan=4|
&lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; is the golden ratio:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi ^2-\phi -1=0&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }+1=\phi&lt;/math&gt;&lt;/small&gt;, and: &lt;small&gt;&lt;math&gt;\phi+1=\phi^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;\frac{1}{\phi }::1::\phi ::\phi ^2&lt;/math&gt;&lt;/small&gt;&lt;br&gt;
&lt;small&gt;&lt;math&gt;1/\phi&lt;/math&gt;&lt;/small&gt; and &lt;small&gt;&lt;math&gt;\phi&lt;/math&gt;&lt;/small&gt; are the golden sections of &lt;small&gt;&lt;math&gt;\sqrt{5}&lt;/math&gt;&lt;/small&gt;:&lt;br&gt;
&lt;small&gt;&lt;math&gt;\phi +\frac{1}{\phi }=\sqrt{5}&lt;/math&gt;&lt;/small&gt;
|colspan=2|&lt;small&gt;&lt;math&gt;\phi = (\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;1.618034&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\chi = (3\sqrt{5} + 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;3.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = (3\sqrt{5} - 1)/2&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|-
|colspan=2|&lt;small&gt;&lt;math&gt;\psi = 11/\chi = 22/(3\sqrt{5} + 1)&lt;/math&gt;&lt;/small&gt;
|&lt;small&gt;&lt;math&gt;2.854102&lt;/math&gt;&lt;/small&gt;
|}

...

== The 8-point regular polytopes ==
In 2-space we have the regular 8-point octagon, in 3-space the regular 8-point cube, and in 4-space the regular 8-point [[16-cell]].

A planar octagon with rigid edges of unit length has chords of length:

:&lt;math&gt;r_1=1,r_2=\sqrt{2+\sqrt{2}} \approx 1.84776,r_3=1+\sqrt{2} \approx 2.41421,r_4=\sqrt{4 + \sqrt{8}} \approx 2.61313&lt;/math&gt;

The chord ratio &lt;math&gt;r_3=1+\sqrt{2}&lt;/math&gt; is a geometrical proportion, the [[W:Silver ratio|silver ratio]]. Fontaine and Hurley's procedure for obtaining the reciprocal of a chord tells us that:

:&lt;math&gt;r_3-r_1-r_1=1/r_3 \approx 0.41421&lt;/math&gt;

Note that &lt;math&gt;1/r_3=\sqrt{2}-1=r_3-2&lt;/math&gt;.

If we embed this planar octagon in 3-space, we can make it skew, repositioning its vertices so that each is one unit-edge length distant from three others instead of two others, at the vertices of a unit-edge cube with chords of length:

:&lt;math&gt;r_1=1, r_2=\sqrt{2}, r_3=\sqrt{3}, r_4=\sqrt{2}&lt;/math&gt;

If we embed this cube in 4-space, we can skew it some more, repositioning its vertices so that each is one unit-edge length distant from six others instead of three others, at the vertices of a unit-edge 4-polytope with chords of length:

:&lt;math&gt;r_1=1,r_2=1,r_3=1,r_4=\sqrt{2}&lt;/math&gt;

All of its chords except its long diameters are the same unit length as its edge. In fact they are its 24 edges, and it is a 16-cell of radius &lt;small&gt;&lt;math&gt;1/\sqrt{2}&lt;/math&gt;&lt;/small&gt;.

[[File:octagon16cell.png|thumb|Orthogonal projection of a regular 16-cell to the [[16-cell#Projections|B&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only its edges are shown; its long diameter chords are not drawn. All 24 edges are the same length. The two disjoint squares lie in completely orthogonal central planes.]]

The [[16-cell]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {3,3,4}. It has 8 vertices, 24 edges, 32 equilateral triangle faces, and 16 regular tetrahedron cells. It is the [[16-cell#Octahedral dipyramid|four-dimensional analogue of the octahedron]], and each of its four orthogonal central hyperplanes is an octahedron.

The only planar regular polygons found in the 16-cell are face triangles and central plane squares, but the 16-cell also contains a skew regular octagon, its [[W:Petrie polygon|Petrie polygon]]. The chords of this regular octagon, which lies skew in 4-space, are those given above for the 16-cell, as opposed to those for the cube or the regular octagon in the plane. The 16-cell is a construct of 3 Petrie octagons which share the same 8 vertices but have disjoint sets of 8 edges each.

The regular octad has higher symmetry in 4-space than it does in 2-space. The 16-cell is the 4-orthoplex, the simplest regular 4-polytope after the [[5-cell|4-simplex]]. All the larger regular convex 4-polytopes are compounds of the 16-cell. The regular octagon exhibits this high symmetry only when embedded in 4-space at the vertices of the 16-cell.

The 16-cell constitutes an [[W:Orthonormal basis|orthonormal basis]] for the choice of a 4-dimensional Cartesian reference frame, because its vertices define four orthogonal axes. The eight vertices of a unit-radius 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges except opposite pairs. 

The vertex coordinates of the 16-cell form 6 central squares lying in 6 pairwise [[W:Orthogonal|orthogonal]] coordinate planes. Great squares in ''opposite'' planes that do not share an axis (e.g. in the ''xy'' and ''wz'' planes) are completely disjoint (they do not intersect at any vertices). These planes are [[W:Completely orthogonal|completely orthogonal]].{{Efn|name=Six orthogonal planes of the Cartesian basis}}

Since the unit-radius coordinate system is convenient, let us derive the unit-radius 16-cell by skewing a unit-radius planar octagon, which has chords of length:

:&lt;math&gt;r_1=\sqrt{2-\sqrt{2}} \approx 0.76537,r_2=\sqrt{2},r_3=\sqrt{2+\sqrt{2}} \approx 1.84776,r_4=2&lt;/math&gt;

We will need a planar octagon with rigid &lt;math&gt;r_2&lt;/math&gt; chords, rather than one with rigid &lt;math&gt;r_1&lt;/math&gt; edges. The octagon's &lt;math&gt;r_2&lt;/math&gt; chords form two disjoint great squares, visible in the orthogonal projection, which we can reposition in 3-space to form a cube by making them parallel, and in 4-space to form a 16-cell by making them completely orthogonal.

In the 16-cell the two completely orthogonal great squares formed by the &lt;math&gt;r_2&lt;/math&gt; chords are both parallel and perpendicular to each other. A ''simple'' rotation of the 16-cell in ''one'' of those two central planes rotates that square like a wheel, while the other square does not move. The four vertices of the rotating square orbit on a great circle in the plane.

The &lt;math&gt;r_1&lt;/math&gt; chords of the 16-cell form a Petrie polygon which zig-zags back and forth between the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; squares.

The &lt;math&gt;r_3&lt;/math&gt; chords of the 16-cell form a circular helix, visible as a blue {8/3} octagram in the orthogonal projection. A ''double'' rotation of the 16-cell, in ''both'' of the two completely orthogonal &lt;math&gt;r_2&lt;/math&gt; square planes at once by the same angle, moves the eight vertices along the circular helix over the &lt;math&gt;r_3&lt;/math&gt; chords. The circular helix is a [[w:Geodesic|geodesic]] great circle on the 3-sphere of a special kind: it does not lie in a central plane, its circumference is &lt;math&gt;4 \pi&lt;/math&gt;, and it occurs in either a left or right chiral form. We shall refer to the circular helix geodesic as an ''isocline'', and to the skew {8/3} octagram of its chords as a ''Clifford polygon''.

[[W:Rotations in 4-dimensional Euclidean space|Rotations in 4-dimensional Euclidean space]] can be seen as the composition of two 2-dimensional rotations in completely orthogonal planes. The general rotation in 4-space is a double rotation in pairs of completely orthogonal planes. Two completely orthogonal planes are called invariant planes of the rotation when all points in the plane rotate on circles that remain in the plane, even as the whole plane tilts sideways (like a coin flipping) into another plane. The two completely orthogonal rotations of each plane (like a wheel, and like a coin flipping) are simultaneous but independent, in that they are not geometrically constrained to turn at the same rate. However, the most circular kind of rotation (as opposed to an elliptical double rotation of a rigid spherical object) occurs when the invariant planes do rotate through the same angle in the same time interval. Such equi-angled double rotations are called [[w:SO(4)#Isoclinic_rotations|isoclinic]], also [[w:William_Kingdon_Clifford|Clifford]] displacements.

The 16-cell is the simplest possible frame in which to [[16-cell#Rotations|observe 4-dimensional rotations]] because its characteristic rotations feature a single pair of invariant rotation planes. In the 16-cell an isoclinic rotation by 90° in any pair of invariant completely orthogonal square central planes takes every square central plane to its completely orthogonal square central plane in a twisting displacement, as they tilt sideways 90° into each other's plane while rotating 90° internally. All the vertices move at once on the same circular helix geodesic isocline, displaced 90° in 8 orthogonal directions, and the rigid 16-cell assumes a new orientation in 4-space. When the 90° isoclinic rotation is continued in the same rotational direction through an additional 90°, each vertex is again displaced 90°, but from the new orientation in a direction orthogonal to its first 90° displacement. After 360° of rotation each vertex reaches its antipodal position.

The trajectory of each vertex over each 90° isoclinic rotational displacement is a one-eighth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over eight &lt;math&gt;r_3&lt;/math&gt; chords, and also traces an ordinary great circle twice over the four &lt;math&gt;r_2&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from all 8 vertex positions just once and returns to its original position, and the 16-cell returns to its original orientation.

== Hypercubes ==
The long diameter of the unit-edge [[W:Hypercube|hypercube]] of dimension &lt;small&gt;&lt;math&gt;n&lt;/math&gt;&lt;/small&gt; is &lt;small&gt;&lt;math&gt;\sqrt{n}&lt;/math&gt;&lt;/small&gt;, so the unit-edge [[w:Tesseract|4-hypercube, the 16-point (8-cell) tesseract,]] has chords:
:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;
Uniquely in its 4-dimensional case, the hypercube's edge length equals its radius, like the hexagon. We call such polytopes ''radially equilateral'', because they can be constructed from equilateral triangles which meet at their center, each contributing two radii and an edge. The [[w:Cuboctahedron|cuboctahedron]] and the 24-cell are also radially equilateral.

The [[W:Tesseract|tesseract]] is the [[W:Regular convex 4-polytope|regular convex 4-polytope]] with [[W:Schläfli symbol|Schläfli symbol]] {4,3,3}. It has 16 vertices, 32 edges, 24 square faces, and 8 cube cells. It is the four-dimensional analogue of the cube.

The 16-point tesseract is the convex hull of a compound of two 8-point 16-cells, in exact dimensional analogy to the way the 8-point cube is the convex hull of a [[W:Stellated octahedron|compound of two 4-point regular tetrahedra]]. The [[W:Demihypercube|demihypercubes]] occupy alternate vertices of the hypercubes. The diagonals of the square faces of the unit-edge, unit-radius tesseract are the &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; edges of two unit-radius 16-cells, also the edges of the square central planes.

We can rotate the tesseract isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on both alternate-position 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cell. The skew octagon geodesic orbits of the 16 vertices lie on two disjoint octagram circular helix isoclines of the same chirality. Two [[w:Clifford_parallel|Clifford parallel]] skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

The tesseract is the [[W:Dual polytope|dual polytope]] of the 16-cell. They have the same Petrie polygon, the regular skew octagon, but the tesseract is a construct of 4 Petrie octagons with disjoint sets of 8 tesseract edges each.

We can construct the tesseract by skewing two planar octagons. Because the tesseract is radially equilateral (unlike the 16-cell), we use two octagons of unit-edge length to build the unit-radius tesseract. To start we embed the planar octagons in 4-space at the same point and make them completely orthogonal. Then we skew each planar octagon into a cube, so we have a compound of two completely orthogonal cubes. Provided we skewed them both in the same direction, the 16 vertices will be the vertices of a tesseract with half its 32 edges missing.

Because the tesseract contains two 16-cells in alternate positions it has two sets of 6 orthogonal square central planes. Two angles are required to specify the relationship between two planes in 4-space. Pairs of square central planes within each 16-cell are 90° apart in one angle, and either 0° or 90° apart in the other angle. They are 90° apart in both angles if and only if they are completely orthogonal planes, 90° apart by isoclinic rotation, with no vertices in common. Otherwise they are 0° apart in one of the angles, 90° apart by simple rotation, and they intersect in one axis and lie in a common 3-dimensional hyperplane.{{Efn|A double rotation in which one of the two angles of rotation is 0°, so that one of the completely orthogonal invariant planes does not rotate, is called a simple rotation. Ordinary rotations observed in a 3-dimensional space are simple rotations.}}

A pair of square central planes from alternate-position 16-cells are 60° apart by isoclinic rotation, with their corresponding vertices 120° apart. The planes are not orthogonal or parallel, so they intersect in a line somewhere, but they have no vertices in common, they have no 3-dimensional hyperplane in common, and they cannot reach each other by simple rotation. Such pairs of objects are called [[W:Clifford parallel|Clifford parallel]] because all their corresponding pairs of vertices are the same distance apart, although they are not parallel in the usual sense, because they have a common center. Not only the alternate-position 16-cells' corresponding square central planes, but also the 16-cells themselves, are Clifford parallel objects. More generally, multiple disjoint instances of a 4-polytope which compound to make a larger 4-polytope are Clifford parallel objects.

== The 24-cell ==
In 2-space we have the radially equilateral 6-point hexagon. In 3-space we have the radially equilateral 12-point cuboctahedron, with 4 hexagonal central planes. In 4-space we have the radially equilateral 24-point 24-cell, with 4 cuboctahedron central hyperplanes and 16 hexagonal central planes.

[[File:dodecagon24cell.png|thumb|Orthogonal projection of half a 24-cell to the [[24-cell#Geodesics|F&lt;sub&gt;4&lt;/sub&gt; Coxeter plane]]. Only one Petrie dodecagon {12} of the 24-cell is shown. In a unit-radius 24-cell, all black lines are 24-cell edges of unit length, also tesseract edges. The two disjoint hexagons lie in Clifford parallel central planes. Blue chords are &lt;math&gt;\sqrt{2}&lt;/math&gt; 16-cell edges, also isocline chords in square rotations. Green chords are &lt;math&gt;\sqrt{3}&lt;/math&gt; distances between corresponding vertices of two 16-cells, also isocline chords in hexagonal rotations. ]]

The [[24-cell]] is the regular convex 4-polytope with Schläfli symbol {3,4,3}. It has 24 vertices, 96 edges, 96 equilateral triangle faces, and 24 octahedron cells. It is the four-dimensional analogue of the cuboctahedron.

The 24-cell has the same chord set as the 4-hypercube tesseract:

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{2},r_3=\sqrt{3},r_4=\sqrt{4}&lt;/math&gt;

The 24-cell is its own [[W:Dual polytope|dual polytope]]. Its Petrie polygon is the regular dodecagon {12}, which has chords:

:&lt;math&gt;r_1=\tfrac{\sqrt{3}-1}{\sqrt{2}},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\tfrac{\sqrt{3}+1}{\sqrt{2}},r_6=\sqrt{4}&lt;/math&gt;

The &lt;math&gt;r_1&lt;/math&gt; and &lt;math&gt;r_5&lt;/math&gt; chords of the planar dodecagon do not occur in the 24-cell, which is a construct of eight skew dodecagons with disjoint sets of twelve &lt;math&gt;\sqrt{1}&lt;/math&gt; edges each. When the 24-cell is constructed by skewing two completely orthogonal planar dodecagons, the lengths of the dodecagon chords change to: 

:&lt;math&gt;r_1=\sqrt{1},r_2=\sqrt{1},r_3=\sqrt{2},r_4=\sqrt{3},r_5=\sqrt{3},r_6=\sqrt{4}&lt;/math&gt;

The 24-point 24-cell is the convex hull of a compound of three disjoint 8-point 16-cells, rotated 60° isoclinically with respect to each other. Each of the three pairs of 16-cells is a tesseract. Each 24-cell edge is also a tesseract edge. The corresponding vertices of two 16-cells or two tesseracts are 120° apart by a &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chord. Each tesseract has 8 cube cells, and each cube has four &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; long diameters. The &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords joining the corresponding vertices of two tesseracts belong to the third tesseract as cube long diameters.

We can rotate the 24-cell isoclinically the way we rotated the 16-cell, by 90° in two completely orthogonal invariant square central planes, with the same effect on all three 16-cells. In the course of a 720° isoclinic rotation in invariant square central planes each vertex departs from all 8 vertex positions of its 16-cell just once and returns to its original position, but it does not visit the vertex positions of the other 16-cells. Three Clifford parallel skew octagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{2}&lt;/math&gt;&lt;/small&gt; chords form a circular triple helix.

We can also rotate the 24-cell isoclinically by 60° in a hexagonal invariant central plane and its completely orthogonal invariant central plane. Great hexagons are a rounder choice than great squares for the invariant rotation plane in which to rotate a 4-polytope. A complete hexagonal isoclinic revolution requires 720° like a complete square isoclinic revolution, but it is completed in 12 isoclinic displacements of 60° each rather than 8 isoclinic displacements of 90° each. Its Clifford polygon is a skew {12/5} dodecagram of &lt;math&gt;r_5&lt;/math&gt; chords, visible in the orthogonal projection. Two Clifford parallel skew dodecagon geodesic orbits over &lt;small&gt;&lt;math&gt;\sqrt{3}&lt;/math&gt;&lt;/small&gt; chords form a circular double helix.

In the 24-cell an isoclinic rotation by 60° in any pair of invariant completely orthogonal hexagonal central planes takes every hexagonal central plane to a Clifford parallel hexagonal central plane in a twisting displacement, as they tilt sideways 60° while rotating 60° internally. All 24 vertices move at once on two Clifford parallel circular helix geodesic isoclines, displaced 120° in different directions.

The trajectory of each vertex over each 60° isoclinic rotational displacement is a one-twelfth segment of its geodesic orbit. Its entire orbit traces a circular helix isocline in 4-space over twelve &lt;math&gt;\sqrt{3}&lt;/math&gt; chords, and also traces an ordinary great circle twice over the six &lt;math&gt;\sqrt{1}&lt;/math&gt; chords within one of the two moving invariant rotation planes. In the course of a 720° isoclinic rotation each vertex departs from 12 vertex positions just once and returns to its original position, and the 24-cell returns to its original orientation.

== The 600-cell ==

...

== Finally the 120-cell ==

...

== Conclusions ==

Fontaine and Hurley's discovery is more than a formula for the reciprocal of a regular ''n''-polygon diagonal. It also yields the discrete sequence of isocline chords of the distinct isoclinic rotation characteristic of a ''d''-dimensional regular polytope. The characteristic rotational chord sequence of the ''d''-polytope can be represented geometrically in two dimensions on a distinct star polygon, but it lies on a geodesic circle through ''d''-dimensional space. Fontaine and Hurley discovered the geodesic topology of polytopes generally. Their procedure will reveal the geodesics of arbitrary non-uniform polytopes, since it can be applied to a polytope of any dimensionality and irregularity, by first fitting the polytope to the smallest regular polygon whose chords include its chords.

Fontaine and Hurley's discovery of a chordal formula for isoclinic rotations closes the circuit on Kappraff and Adamson's discovery of a rotational connection between dynamical systems, Steinbach's golden fields, and Coxeter's Euclidean geometry of ''n'' dimensions. Application of the Fontaine and Hurley procedure in higher-dimensional spaces demonstrates why the connection exists: because polytope sequences generally, from Steinbach's golden polygon chord sequences, to chord sequences in isoclinic rotation helixes, to subsumption relations in the sequence of regular 4-polytopes, arise as expressions of the reflections and rotations of distinct Coxeter symmetry groups, when those various groups interact.

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

== Notes ==
{{Notelist}}

== Citations ==
{{Reflist}}

== References ==
{{Refbegin}}
* {{Cite journal | last=Steinbach | first=Peter | year=1997 | title=Golden fields: A case for the Heptagon | journal=Mathematics Magazine | volume=70 | issue=Feb 1997 | pages=22–31 | doi=10.1080/0025570X.1997.11996494 | jstor=2691048 | ref={{SfnRef|Steinbach|1997}} }}
* {{Cite journal | last=Steinbach | first=Peter | year=2000 | title=Sections Beyond Golden| journal=Bridges: Mathematical Connections in Art, Music and Science | issue=2000 | pages=35-44 | url=https://archive.bridgesmathart.org/2000/bridges2000-35.pdf | ref={{SfnRef|Steinbach|2000}}}}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Jablan | first2=Slavik | last3=Adamson | first3=Gary | last4=Sazdanovich | first4=Radmila | year=2004 | title=Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices | journal=Forma | volume=19 | pages=367-387 | url=https://archive.bridgesmathart.org/2005/bridges2005-369.pdf | ref={{SfnRef|Kappraff, Jablan, Adamson &amp; Sazdanovich|2004}} }}
* {{Cite journal | last1=Kappraff | first1=Jay | last2=Adamson | first2=Gary | year=2004 | title=Polygons and Chaos | journal=Dynamical Systems and Geometric Theories | url=https://archive.bridgesmathart.org/2001/bridges2001-67.pdf | ref={{SfnRef|Kappraff &amp; Adamson|2004}} }}
* {{Cite journal | last1=Fontaine | first1=Anne | last2=Hurley | first2=Susan | year=2006 | title=Proof by Picture: Products and Reciprocals of Diagonal Length Ratios in the Regular Polygon | journal=Forum Geometricorum | volume=6 | pages=97-101 | url=https://scispace.com/pdf/proof-by-picture-products-and-reciprocals-of-diagonal-length-1aian8mgp9.pdf }}
{{Refend}}</text>
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== New titles for user right nominations ==
&lt;div class=&quot;cd-moveMark&quot;&gt;''Moved from [[Wikiversity talk:Candidates for Custodianship#New titles for user right nominations]].  [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:20, 17 April 2026 (UTC)''&lt;/div&gt;

I would like to propose the following retitles should a user be nominated for any of the following user rights:
* Curator: Candidates for Curatorship
* Bureaucrat: Candidates for Bureaucratship
The reason is that many curator (and probably bureaucrat) requests have run solely under {{tq|Candidates for Custodianship}}, but that title might sound misleading (especially in regards to the permission a user is requesting). CheckUser and Oversight (suppressor) are not included above since no user was nominated for these sensitive permissions, probably. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 01:30, 19 March 2026 (UTC)

:And it's not that when someone at the beginning misplaced the request, no one thought to move it and the others copied it. Even today, it would be possible to simply take it all and move it. Otherwise, for me, the more fundamental problem is that there is [[Wikiversity:Curators|no approved policy for curators]] than where the requests are based. Curators then operate in a certain vacuum and if one of them &quot;breaks out of the chain&quot;, the average user doesn't have many transparent tools to deal with it, because there is no policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:02, 19 March 2026 (UTC)
::I am not talking about the curator page (policy proposal). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:08, 21 March 2026 (UTC)
: @[[User:Juandev|Juandev]] I'll see if I can do an overhaul of [[Wikiversity:Candidates for Custodianship]], just like I recently did with the Requests for adminship page on English Wikiquote. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:17, 18 April 2026 (UTC)
:Yes, great idea - ideally there will be separate &quot;Candidates for ...&quot; pages for each user right group. The most important for now is to separate curator and custodian pages as CN suggests. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:39, 1 May 2026 (UTC)
:So maybe I previously misunderstood. Are you proposing separated pages for nominations (i.e. [[Wikiversity:Candidates for Curatorship]], [[Wikiversity:Candidates for Bureaucratship]], [[Wikiversity:Candidates for Custodianship]])? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 12:30, 5 May 2026 (UTC)
:: Yes. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:33, 5 May 2026 (UTC)
:::I see, then I am fine with that @[[User:Codename Noreste|Codename Noreste]]. Sorry for misunderstanding. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 18:35, 9 May 2026 (UTC)

I've split the user rights nomination pages into:
* [[Wikiversity:Candidates for CheckUser]]
* [[Wikiversity:Candidates for Curatorship]]
* [[Wikiversity:Candidates for Custodianship]]
* [[Wikiversity:Candidates for Bureaucratship]]

Please review. There are likely several links to update, text to adjust, categories to manage, short-cuts to fix etc. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 04:22, 10 May 2026 (UTC)

:Thanks, great job @[[User:Jtneill|Jtneill]]. I am wondering if we need to move archived nominations too, or if we are OK with the actual state. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:08, 10 May 2026 (UTC)
::Yes, I think that would be helpful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:46, 10 May 2026 (UTC)
:::I can do it @[[User:Jtneill|Jtneill]], I am just looking what system is there. I can see [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] which is a good complementary overview to the subpages with full history. The name of the pages is probably stably, but I would consider to create more specific redirect like [[Wikiversity:Candidates for Custodianship/Overview of staff nominations]], which would link to the above one. Then there is a [[Wikiversity:Candidates for Custodianship/Archived]], which are probably incomplete nominations, right? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:37, 11 May 2026 (UTC)
::::Tx @[[User:Juandev|Juandev]]. Yes, this makes sense. And maybe we move:
::::* archived '''curator''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship]] to e.g., [[Wikiversity:Candidates for Curatorship/Archive of nominations]]
::::* archived '''bureaucrat''' nominations from [[Wikiversity:Candidates for Custodianship/Archive of nominations for full custodianship ]] to e.g., [[Wikiversity:Candidates for Bureaucratship/Archive of nominations]]
::::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:12, 11 May 2026 (UTC)
:::::OK. That sounds good. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 07:25, 12 May 2026 (UTC)
:An svg icon for [[Wikiversity:Curatorship|curators]] would also be helpful. We have them for other user rights: [[c:Category:Wikiversity user rights icons]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:54, 10 May 2026 (UTC)
::Done: [[Wikiversity:Curators]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:44, 11 May 2026 (UTC)

== Global ban for Faster than Thunder ==

Hello, this message is to notify that [[User:Faster than Thunder|Faster than Thunder]] has been nominated for a global ban at [[m:Requests for comment/Global ban for Faster than Thunder]]. You are receiving this notification as required per the [[m:global ban|global ban]] policy as they have made at least 1 edit on this wiki. Thanks, --[[User:SHB2000|SHB2000]] ([[User talk:SHB2000|discuss]] • [[Special:Contributions/SHB2000|contribs]]) 02:01, 22 March 2026 (UTC)

== Upcoming Wikimedia Café meetup regarding the [[:meta:Wikimedia Foundation Annual Plan/2026-2027|the 2026-2027 Wikimedia Foundation Annual Plan]] ==

{{tmbox
| image = [[File:Wikimedia Café logo in plain SVG format.svg|45px]]
| type=notice
| text  = Hello! There will be a '''[[:meta:Wikimedia Café|Wikimedia Café]]''' meetup on '''Saturday, 11 April 2026 at 14:00 UTC''' ([https://zonestamp.toolforge.org/1775916000 timestamp conversion tool]), focusing on the [[:meta:Wikimedia Foundation Annual Plan/2026-2027|the 2026-2027 Wikimedia Foundation Annual Plan]]. The featured guests will be &lt;span class=&quot;plainlinks&quot;&gt;[//meta.wikimedia.org/wiki/User:KStineRowe_(WMF) Kelsi Stine-Rowe]&lt;/span&gt; (senior manager, [[:meta:Movement Communications|Movement Communications]], Wikimedia Foundation), and &lt;span class=&quot;plainlinks&quot;&gt;[//meta.wikimedia.org/wiki/User:Samwalton9_(WMF) Sam Walton] (senior product manager, [[:mw:Moderator Tools|Moderator Tools]], Wikimedia Foundation). {{pbr}}In addition to this Café session, [[:meta:Wikimedia Foundation Annual Plan/2026-2027/Collaboration|several additional meetings regarding the Annual Plan are listed on the Collaboration page]], and you may participate on the [[:meta:Talk:Wikimedia Foundation Annual Plan/2026-2027|talk page]].{{pbr}}This Café meetup will be approximately two hours long. Attendees may choose to attend only for a part. Please see the Café page for more information, including [[:meta:Wikimedia Café#Signups for the April 2026 session|how to register]]. &lt;br /&gt;[[File:Buntstifte Eberhard Faber crop 64h.jpg|860px|alt=cropped image of colored pencils]]&lt;/span&gt;
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&lt;span style=&quot;white-space:nowrap;&quot;&gt;[[User:Pine|&lt;span style=&quot;color:#01796f; text-shadow:#00BFFF 0 0 1.0em&quot;&gt;↠Pine&lt;/span&gt;]] [[User talk:Pine|&lt;span style=&quot;color:DeepSkyBlue&quot;&gt;(&lt;b style=&quot;color:#FFDF00;text-shadow:#FFDF00 0 0 1.0em&quot;&gt;✉&lt;/b&gt;)&lt;/span&gt;]]&lt;/span&gt; 05:34, 29 March 2026 (UTC)

== [[Wikiversity:Artificial intelligence]] to become an official policy ==
{{Archive top|After running for a week, there is consensus, alongside comments, for [[Wikiversity:Artificial intelligence]] to be implemented as an official policy. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 23:27, 17 April 2026 (UTC)}}
With the introduction of AI-material, and some material just plain disruptive, its imperative that Wikiversity catches up with its sister projects and implements an official AI policy that we can work with. The recent issue of [[User:Lbeaumont|Lbeaumont]]'s 50+ articles that contain significantly large AI-generated material has made me came to the Colloquium. This user has also been removing the [[Template:AI-generated]] template from their pages, calling it &quot;misleading&quot;, &quot;alarmist&quot;, and &quot;pejorative&quot; - which is all just simply nonsensical rationales. Not to even mention this user's contributions to the English Wikipedia have been [https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Inner_Development_Goals contested] and [https://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Multipolar_trap removed] a couple of times (for being low-quality and clearly LLM-generated), highlighting the need for an actual policy to be implemented here on Wikiversity. I would like to ping {{ping|Juandev}} and {{ping|Jtneill}} for their thoughts as well, since I'd like this to be implemented as soon as possible. 

Wikiversity has a significant issue with implementing anti-disruptive measures, hence why we have received numerous complaints as a community about our quality. I originally was reverting the removal of the templates, but realized that this is still a proposed policy, which it shouldn't be anymore. It should be a recognized Wikiversity policy. 14:54, 10 March 2026 (UTC) —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 14:54, 10 March 2026 (UTC)

:@[[User:Atcovi|Atcovi]] '''I agree''' that the draft, should become official policy. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 17:00, 10 March 2026 (UTC)
:I provided a detailed response at: [[Wikiversity talk:Artificial intelligence#Evolving a Wikiversity policy on AI]]
:I will appreaciate it if you consder that carefully. [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 22:49, 10 March 2026 (UTC)
:Agree it should become official Wikiversity policy on the condition &lt;u&gt;that point point 5 is about [significant/substantial] LLM-generated text specifically&lt;/u&gt;. Not a good idea to overuse it, it should be added when there is substantial AI-generated text on the page, not for other cases. [[User:Prototyperspective|Prototyperspective]] ([[User talk:Prototyperspective|discuss]] • [[Special:Contributions/Prototyperspective|contribs]]) 12:37, 11 March 2026 (UTC)
:What policy is being debated? Is it the text on this page, which is pointed to by the general banner, or the text at:   [[Wikiversity:Artificial intelligence|Wikiversity:Artificial intelligence,]]   which is pointed to by the specific banner? Let's begin with coherence on the text being debated. Thanks!  [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 11:49, 17 March 2026 (UTC)
::@[[User:Lbeaumont|Lbeaumont]] This is a call for approval of the new Wikiversity policy. You expressed your opinion [[Wikiversity talk:Artificial intelligence#Evolving a Wikiversity policy on AI|on the talk page of the proposal]], I replied to you and await your response.When creating policies, it is necessary to propose specific solutions. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 14:12, 17 March 2026 (UTC)
:::Toward a Justified and Parsimonious AI Policy 
:::As we collaborate to develop a consensus policy on the use of Large Language Models, it is wise to begin by considering the needs of the various stakeholders to the policy.
:::The stakeholders are:
:::1)     The users, 
:::2)     The source providers, and
:::3)     The editors
:::There may also be others with a minor stake in this policy, including the population at large.
:::The many needs of the users are currently addressed by long-standing [[Wikiversity:Policies|Wikiversity policies]], so we can focus on what, if any, additional needs arise as LLMs are deployed. 
:::As always, users need assurance that propositional statements are accurate. This is covered by the existing policy on [[Wikiversity:Verifiability|verifiably]]. In addition, it is expected by both the users and those that provide materials used as sources for the text are [[Wikiversity:Cite sources|accurately attributed]]. This is also covered by [[Wikiversity:Cite sources|existing policies]].
:::To respect the time and effort of editors, a parsimonious policy will unburden editors from costly requirements that exceed benefits to the users.
:::Finally, it is important to recognize that because attention is our most valuable seizing attention unnecessarily is a form of theft. 
:::The following proposed policy statement results from these considerations:
:::Recommended Policy statement:
:::·       Editors [[Wikiversity:Verifiability|verify the accuracy]] of propositional statements, regardless of the source.
:::·       Editors [[Wikiversity:Cite sources|attribute the source]] of propositional statements. In the case of LLM, cite the LLM model and the prompt used.
:::·       Use of various available templates to mark the use of LLM are optional. Templates that are flexible in noting the type and extend of LLM usage are preferred. Templates that avoid unduly distracting or alarming the user are preferred. [[User:Lbeaumont|Lbeaumont]] ([[User talk:Lbeaumont|discuss]] • [[Special:Contributions/Lbeaumont|contribs]]) 19:56, 19 March 2026 (UTC)
::::Do we discuss here or there? I have replied you there as your proposal is about that policy so it is tradition to discuss it at the affected talk page. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:59, 19 March 2026 (UTC)
: {{support}} Thanks for the proposed policy development and discussion; also note proposed policy talk page discussion: [[Wikiversity talk:Artificial intelligence]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 12:05, 24 March 2026 (UTC)
::I think the Wikiversity AI policy shall be official. – [[User:RestoreAccess111|RestoreAccess111]] &lt;sup style=&quot;font-family:Arimo, Arial;&quot;&gt;[[User talk:RestoreAccess111|Talk!]]&lt;/sup&gt; &lt;sup style=&quot;font-family:Times New Roman, Tinos;&quot;&gt;[[Special:Contributions/RestoreAccess111|Watch!]]&lt;/sup&gt; 06:11, 13 April 2026 (UTC)
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== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)</text>
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== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)</text>
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== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)</text>
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== Action Required: Update templates/modules for electoral maps (Migrating from P1846 to P14226) ==

Hello everyone,

This is a notice regarding an ongoing data migration on Wikidata that may affect your election-related templates and Lua modules (such as &lt;code&gt;Module:Itemgroup/list&lt;/code&gt;).

'''The Change:'''&lt;br /&gt;
Currently, many templates pull electoral maps from Wikidata using the property [[:d:Property:P1846|P1846]], combined with the qualifier [[:d:Property:P180|P180]]: [[:d:Q19571328|Q19571328]]. 

We are migrating this data (across roughly 4,000 items) to a newly created, dedicated property: '''[[:d:Property:P14226|P14226]]'''.

'''What You Need To Do:'''&lt;br /&gt;
To ensure your templates and infoboxes do not break or lose their maps, please update your local code to fetch data from [[:d:Property:P14226|P14226]] instead of the old [[:d:Property:P1846|P1846]] + [[:d:Property:P180|P180]] structure. A [[m:Wikidata/Property Migration: P1846 to P14226/List|list of pages]] was generated using Wikimedia Global Search.

'''Deadline:'''&lt;br /&gt;
We are temporarily retaining the old data on [[:d:Property:P1846|P1846]] to allow for a smooth transition. However, to complete the data cleanup on Wikidata, the old [[:d:Property:P1846|P1846]] statements will be removed after '''May 1, 2026'''. Please update your modules and templates before this date to prevent any disruption to your wiki's election articles.

Let us know if you have any questions or need assistance with the query logic. Thank you for your help! [[User:ZI Jony|ZI Jony]] using [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 17:11, 3 April 2026 (UTC)
&lt;!-- Message sent by User:ZI Jony@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&amp;oldid=29941252 --&gt;
:I didnt find such properties, so we are probably fine. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 21:00, 12 April 2026 (UTC)
:: +1 (agreed). [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 22:19, 12 April 2026 (UTC)

== Advice needed: A Neurodiversity-inspired Idea/observation ==

If I want the greatest participation of others to &quot;provide constructive criticism to my idea&quot; or to &quot;shoot down my idea&quot; or &quot;idea&quot;.

What I've called it so far is &quot;The Neurodiversity-inspired Idea&quot;. At other times I used more sensationalist wording but here on Wikiversity I don't dare do that. I actually woke up with thinking about putting this into my userspace draft: &quot;Personal Observations Made By Meeting Autistic and Non-Autistic Adults&quot;.

My ultimate goal is to stop blathering about my &quot;idea&quot; to friend and family without feeling my &quot;methodology&quot; is going into any progressive direction whatsoever. My latest encounter was somewhat constructive though. A friend of a friend who worked with people presenting ideas in attempting to getting grants. I don't want a grant. I just want to figure out how I can express my &quot;idea&quot; in a way so that I can more clearly figure out what flaws it got.

At the same time I tend to overthink. If anyone thinks etherpad might be a good place and considering Wikimedia already got an etherpad at https://etherpad.wikimedia.org/ if anyone feels like they know me better in the future feel free to suggest a &quot;session&quot; on etherpad.

'''If I don't receive a reply to this in 1 week's time I will begin to explore this &quot;idea&quot; into my userspace''' unless you replied and refrained me from doing so, of course. Then maybe after &quot;developing it there&quot; I might reference it to you another future time here in the Colloquium, with my &quot;idea&quot; still in my userspace draft. This &quot;idea&quot; is sort of a burden, I'm happy I've made the choice to get rid of it and hopefully move on with my life, unless there is something to this &quot;idea&quot;. 

My failure is probably evident: I feel I haven't told you anything. Same happened to when I talked to friends and family. In danger of overthinking it further I'll publish this right now. I need to &quot;keep it together&quot; [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 10:36, 16 April 2026 (UTC)

:Good on you putting it out there ... and hitting publish :). I'd say go for it (no need to wait), give birth to your idea and share about it here and elsewhere. Let it take shape and see where it might go. In many ways, this is exactly what an open collaborative learning community should be doing. Others might not know well how to respond, so perhaps consider creating some questions to accompany the idea. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 11:21, 16 April 2026 (UTC)
::Thank you for encouraging me in developing the idea.
::I have created a &quot;questions&quot; section in the draft which is visible in the table of contents now. My brain was &quot;frozen&quot; today metaphorically speaking in that I felt I had like a &quot;writer's block&quot; so the draft has more &quot;AI/LLM&quot; content than before. I used the LLM for generating questions. The answers are so far human-only.
::I've also created a subsection where I could add the prompts that made the LLM generate the questions. That could help people make better prompts perhaps. I've described what it is about inside of it and there are some chaotically written notes.
::[[Draft:The_Neurodiversity-inspired_Idea#Questions_that_might_encourage_the_development_of_this_idea_and_its_methodology]]
::My draft is missing stuff. Any questions that you contribute to my draft will probably help me and if I don't understand the questions I'll probably notify you and also at the same time &quot;feed them&quot; to an LLM and ask in my input like &quot;explain in simple words what this question means, what is it searching for?&quot; etc. while I wait for an answer. If you have any more feedback please give it to me here or on the Draft page, its talk page or my user talk page. Thank you for helping me! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 21:20, 18 April 2026 (UTC)
::Today I woke up with not only thinking about supplying questions along with the &quot;idea&quot; but also answers. ie. Is it possible to &quot;test&quot; this idea? Is it possible to create one or multiple hypotheses based on this &quot;idea&quot;?(etc.) I've thought about this before in this &quot;idea&quot; but since I'm beginning to add to Wikiversity what was previously 'locked in my mind' it's also easier for me to see what I've done so far. Thank you for this comment! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 09:11, 23 April 2026 (UTC)
:May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish. Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet. Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible. Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents. --  [[User:Eric.LEWIN|Eric.LEWIN]] ([[User talk:Eric.LEWIN|discussion]] • [[Special:Contributions/Eric.LEWIN|contributions]]) 10:06, 17 April 2026 (UTC)
::Sorry about the false positive on the profanity filter - I've fixed it. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:26, 17 April 2026 (UTC)
:::&quot;May I think that you should not add deadlines ; being read, and rising interest for collaboration, or even simply for exchange of thoughts, such an effective meeting event loads a huge bunch of unprobability, which time can help to… somehow diminish.&quot;
::Thank you Eric for this comment. Trust in time is how I interpret it. I should not feel like I need to be in a hurry. I'll try to give this time. Thank you!
:::&quot;Maybe, I would advice you having a central place for developping your ideas, your needs, your advances, maybe a page in your own user zone, and from time to time, depending your feeling, it could be every trimester or so, or more frequently, you could write a short account of progress (or even of no progress), or a call for participation, in such a place as this present one ; I think that will increase much exposure of your projet.&quot;
::A central place for developing or making &quot;project notes&quot; regarding the Neurodiversity idea on my userspace, I might need that, like a diary or &quot;project notes&quot; of the Neurodiversity idea similar to my course notes regarding my experience with Coursera.
::Any actions I take are going to be related to my Userspace from now on but I'll also update the draft when necessary. Now in the beginning I might be working daily to once every 3 days on both the draft and the daily notes I plan to make.
:::&quot;Maybe also, if you can find a project name, not necessarily very meaningfull by itseilf (at least it will gain signification with time, as your project develops), that will serve as a kind-of hook, and make your announcement titles more visible.&quot;
::Thank you for the advice. I was brainstorming yesterday about it. I concluded that since I've not yet developed a methodology that adheres to &quot;Do no harm&quot; and this is my first time working my &quot;idea&quot; into a way that is compatible with how projects develop on English Wikiversity this is new to me. My methodology isn't developed and therefore trying to get attention to my project through a name can wait. Yesterday I figured out a silly title that has nothing to do with the project: &quot;Planetary Awareness Potato Cabbage Rolls&quot; or something like that. Google output read that no such thing exists so I wanted it mainly to be unique. I don't want to raise attention that I'm unsure whether I'll actually be capable of developing a methodology for but project notes is my best bet so far in tracking my progress. Every day I think about this &quot;idea&quot; but I need to improve the important parts.
:::&quot;Best regards (and my excuses for my poor command of English, which seems to be unplease an anti-abuse filter, &quot;Questionable Language (profanity)&quot;, which I don't understand…). My few cents.&quot;
::You added great points and I felt that I was helped by you! I encourage you to post again and I can understand that interacting with any kind of automated filter can be discouraging and can be for me too! Thank you for giving me feedback! [[User:ThinkingScience|ThinkingScience]] ([[User talk:ThinkingScience|discuss]] • [[Special:Contributions/ThinkingScience|contribs]]) 16:01, 18 April 2026 (UTC)

== Enable the abuse filter block action? ==

In light of [[Special:AbuseLog/80178]] (coupon spam), I would like to propose enabling the block action for the abuse filter. Only custodians will be able to enable and disable that action on an abuse filter, and it is useful to block ongoing vandalism. Thoughts? [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 19:12, 13 April 2026 (UTC)

:Seems like a good idea, almost all of the users which create such pages are spambots so this shouldn’t be a problem. [[User:PieWriter|PieWriter]] ([[User talk:PieWriter|discuss]] • [[Special:Contributions/PieWriter|contribs]]) 23:41, 13 April 2026 (UTC)
:Can you explain some more (I am new to abuse filters)? It looks like the attempted edit was prevented? Which abuse filter?
:Note on your suggestion, have also reactivated Antispam Filter 12 - see [[WV:RCA]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:45, 15 April 2026 (UTC)
:: I am proposing that we activate the abuse filter block action, which if a user triggers an abuse filter, it would actually block the user in question - the same mechanism that a custodian would use to block users. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 13:11, 15 April 2026 (UTC)
:::OK, thankyou, that makes sense. And, reviewing the abuse filter 12 log, it would be helpful because it would prevent the need for manual blocking. But I don't see a setting for autoblocking? -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:14, 15 April 2026 (UTC)
:::: I think it probably adds an autoblock. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 00:43, 16 April 2026 (UTC)
: [[User:Jtneill|Jtneill]] and [[User:PieWriter|PieWriter]], given that a little bit more than a week has passed and there is minimal consensus to activate the abuse filter block action, I filed [[phab:T424053]]. [[User:Codename Noreste|Codename Noreste]] ([[User talk:Codename Noreste|discuss]] • [[Special:Contributions/Codename Noreste|contribs]]) 15:05, 21 April 2026 (UTC)
::Thank-you for doing this. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 08:03, 24 April 2026 (UTC)</text>
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    <title>AIPA Method</title>
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{{notice|This page presents exploratory original research and should not be interpreted as established science}}
The AIPA Method (Awakening Into Pure Awareness) is a cognitive‑phenomenological framework that proposes a mechanism linking content‑reduced awareness states to identity‑level transformation and long‑term behavioral stabilization. It is presented as a hypothesis‑generating model that integrates phenomenology, longitudinal autoethnographic self‑research, independent practitioner cases, and comparative analysis with established methods such as CBT, MBSR, MBCT, and general meditation.

== Introduction ==
The AIPA Method addresses a gap in contemporary personal development and consciousness science: most evidence‑based approaches (CBT, MBSR, MBCT, standard meditation) operate at the level of mental content—reframing thoughts, observing them, or reducing their impact—rather than at the level of identity structure. In contrast, AIPA targets the structural relationship between the self and the mind, aiming at durable identity reconstruction rooted in Pure Awareness rather than symptom management.

The central research question of the primary AIPA preprint is whether a structured, sequentially staged method can produce permanent identity reconstruction rooted in Pure Awareness, and how such a method compares to established approaches in scope, mechanism, and outcome.

== Theoretical foundations ==
The AIPA framework is grounded in the cognitive‑phenomenological tradition (e.g., McAdams, Varela, Metzinger, Erikson), contemporary consciousness science on minimal phenomenal experience, and qualitative methods advocacy in psychology. It builds directly on:

* Empirical work on pure awareness and Minimal Phenomenal Experience (MPE), especially Gamma &amp; Metzinger’s large‑scale study of content‑reduced awareness states.
* Metzinger’s proposal of minimal phenomenal experience as an entry point for a minimal unifying model of consciousness.
* Narrative identity and partial‑self models within personality and identity theory.

Within this backdrop, AIPA proposes Pure Awareness as a distinct, operationally specified state that can become a structural ground of identity rather than a transient meditative experience.

== Experiential empiricism ==
The empirical foundation of the AIPA Method is explicitly first‑person and experiential, combining:

* A 22‑year longitudinal autoethnographic self‑study (2003–2025) documenting partial personality episodes, protocol use, and outcomes.
* A 13‑year prospective verification period with zero self‑reported recurrence of targeted harmful behaviors after a dated stabilization point (1 January 2006).
* A high‑ecological‑validity “stress test” during acute bereavement, used to examine whether non‑reactive awareness remains stable under maximal provocation.
* Two independent practitioner cases (an Amazon‑verified report and a structured questionnaire case) providing preliminary convergent signals across cognitive, emotional, behavioral, and identity dimensions.

All central constructs (Pure Awareness, partial personalities, the Switch, identity stabilization) are operationalized with explicit phenomenological and behavioral criteria intended to enable replication and future third‑person measurement.

== Identity reconstruction ==
AIPA conceptualizes ordinary identity as a fragmented “partial personality system”: recurring behavioral‑cognitive‑somatic substructures such as the “Important One” and “Poor One,” each with characteristic triggers, narratives, emotions, behaviors, and bodily encodings. Through sustained awareness‑based observation and withdrawal of reinforcement, these partial personalities are gradually destabilized and dissolved, allowing identity to reorganize around Pure Awareness.

Key elements of the identity model include:

* A three‑level architecture: physical body, energy/attention body, and Pure Awareness as a non‑directional, non‑object‑bound ground of experience.
* Pure Awareness defined by four phenomenological properties: Peace, Unity/Integrity, Clarity, and Goodwill.
* A staged developmental sequence from fragmented, mind‑identified identity to stabilized meta‑observational functioning.

The 10‑step AIPA Awakening Protocol (observe, stop harm, breathe, relax body, attend to energy body, contact awareness, review, document, decide, return to observation) operationalizes this reconstruction process as a repeatable practice cycle.

== Faith deconstruction application ==
One of the applied domains explicitly developed for AIPA is faith deconstruction and religious trauma resolution. In this context, AIPA is framed as a method for:

* Dissolving belief‑based partial personalities (e.g., internalized religious identities and fear structures) through awareness‑based de‑identification rather than argument or intellectual debate.
* Establishing a stable, non‑reactive identity in Pure Awareness that can relate to former beliefs, communities, and scripts without re‑immersion or retraumatization.

The model suggests that a practitioner stabilized in Pure Awareness can, for the first time, experience a self that is larger than their trauma or inherited religious identity, making genuine processing possible from a stable ground rather than from within the traumatized self‑structure.

For an accessible, non‑technical presentation of this application, see:

* “AIPA Method for Faith Deconstruction: Awakening Into Pure Awareness for Religious Believers and Ex‑Believers Seeking Rationality and Inner Freedom”. [https://www.letterstopalkies.com/2026/03/08/aipa-method-for-faith-deconstruction-awakening-into-pure-awareness-for-religious-believers-and-ex-believers-seeking-rationality-and-inner-freedom/]
* “How the AIPA Method Works – Official Diagram of the Cognitive‑Phenomenological Model”. [https://god-doesntexist.com/how-the-aipa-method-works-official-diagram-of-the-cognitive-phenomenological-model/]

== Visual models ==
The core identity process is summarized visually in the Sliding Tile Model of Identity Reconstruction, which uses the metaphor of a 3×3 sliding puzzle filled with “tiles” representing partial personalities. Transformation is depicted as the progressive dissolution of tiles until an “empty space” appears and expands, representing Pure Awareness becoming the structural ground. The model highlights seven phases:

* Initial non‑fragmented childhood presence
* Gradual cracking into partial personalities under pressure
* Full fragmentation into a dense partial‑personality ensemble
* Recognition of an underlying Pure Awareness layer
* Sequential dissolution of partial personalities
* Emergence of a stable Pure Awareness‑based identity
* Integrated functioning in daily life with minimal reactivity

The official diagram is published as:

* “AIPA Method: The Sliding Tile Model of Identity Reconstruction Diagram” (Zenodo record 19174500).

== Research notes ==
The AIPA Method is explicitly presented as a theory‑building and hypothesis‑generating framework, not as an efficacy claim. The primary preprint and companion manuals outline proposed validation pathways, including:

* Randomized controlled trials comparing AIPA with CBT and MBSR/MBCT across domains such as stress management, addiction recovery, faith deconstruction, depression, anxiety disorders, and complex PTSD.
* Multi‑participant phenomenological studies using standardized outcome measures (e.g., PHQ‑9, GAD‑7) and identity‑stability metrics.
* Physiological studies (e.g., HRV, cortisol, EEG) to explore candidate correlates of Pure Awareness and long‑term non‑reactivity.

The primary author positions the work within ongoing efforts toward a minimal unifying model of consciousness and invites independent empirical testing, replication, and critical engagement.

== Bibliography and external resources ==

== Primary preprint ==

* Dizdarevič, S. (2026). ''AIPA Method: A Cognitive‑Phenomenological Model for Identity Reconstruction and Stabilization in Pure Awareness (Version 2.0)''. Zenodo. DOI: 10.5281/zenodo.19155200.
** Zenodo record: https://zenodo.org/records/19155200
** DOI link: https://doi.org/10.5281/zenodo.19155200

== Companion materials ==

* ''AIPA Method Core Protocols and Exercise Manual (V2).'' Zenodo. DOI: 10.5281/zenodo.19155458.
** DOI: https://doi.org/10.5281/zenodo.19155458
** Record: https://zenodo.org/records/19155458
* ''AIPA Method Additional Application Domains (V1).'' Zenodo. DOI: 10.5281/zenodo.19155103.
** DOI: https://doi.org/10.5281/zenodo.19155103
** Record: https://zenodo.org/records/19155103
* ''AIPA Method: The Sliding Tile Model of Identity Reconstruction Diagram.'' Zenodo.
** Record: https://zenodo.org/records/19174500

== About the author ==
This learning resource was developed by [[User:Senad Dizdarević|Senad Dizdarević]], an independent researcher working on the AIPA Method and related applications in consciousness science, faith deconstruction, addiction recovery, people with disabilities assistance, digital overload, screen addiction, and other applications.

== Web resources ==

* AIPA Method for Faith Deconstruction – article on Letters to Palkies (applied explanation for religious believers and ex‑believers), [https://www.letterstopalkies.com/2026/03/08/aipa-method-for-faith-deconstruction-awakening-into-pure-awareness-for-religious-believers-and-ex-believers-seeking-rationality-and-inner-freedom/].
* How the AIPA Method Works – Official Diagram of the Cognitive‑Phenomenological Model (overview and visual explanation), [https://god-doesntexist.com/how-the-aipa-method-works-official-diagram-of-the-cognitive-phenomenological-model/].</text>
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  <page>
    <title>User:ThinkingScience/ND Inspired Idea Notebook</title>
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* {{tl|Draft}}
* {{tl|underconstruction}}

'''On this page I plan to add daily notes regarding [[Draft:The Neurodiversity-inspired Idea]].'''

== &quot;Diary&quot; ==

== April 18, 2026 ==

A suggestion I got was that it may help the project if I provide some questions along with the idea. Also to make a main space where I gather info about my progress but that will probably be the draft itself if I move forward. Now if I write a &quot;diary&quot; that will be only regarding the project.

Turned &quot;me language&quot; into expressing that everyone is welcome, that I don't &quot;own&quot; [[Draft:The Neurodiversity-inspired Idea]]. Now everything that says &quot;I did this&quot; &quot;I did that&quot; should be gone. I think this was an improvement of some sort.

Plan for next edits on the draft page: Add an &lt;nowiki&gt;&quot; == Old Methodology needing updating == &quot;&lt;/nowiki&gt; where I will add old methodologies where I had not planned ahead too good and the &quot;Do no harm&quot; I did not know about or could not focus on. That was before I created my own Draft that feels like it only happened some days ago.

Interaction I thought was an efficient method but how would methodology be modified today with what I know now and will know in the future?

== April 20, 2026 ==

Why does it seem like I'm the only one using the word &quot;methodology&quot;? Did the [[Wikiversity:Research ethics]] mention it?
* I cannot find it! I checked all infoboxes! It must have been generated and I probably never questioned it...until now.

== April 21, 2026 ==

I think I put a new subsection on the Draft space something that was related to developing my method/methodology into the &quot;Do no harm&quot;. Considering I have almost not developed anything but I still gotta work on this...to do...

== April 22, 2026 ==

I am yearning / looking forward to working on video notes in a &quot;Do no harm&quot; way. I don't feel like it has happened yet. I did make modifications but it may have increased complexity. A complexity that will make it harder for me to work or just different.

== April 27, 2026 ==

I met with my father and he is a friend of the sciences. One word: hypothesis. He asked what my main hypothesis is. Of course hypothesis is a way to test if the idea is sound or if it's for the trashcan. I'm glad he gave me this feedback or interest in trying to learn more.

Today I woke up being inspired by that:

* Is there a hypothesis or a number of hypotheses related to the idea?
** Can this idea be proven false?

Why it's important to prove a hypothesis false: so that we don't waste time on trash ideas. If they are not provable we give time to the creator of the suggestion/idea to prove make a hypothesis. Only when the creator fails to provide any sort of hypothesis and maybe suggests their own idea be removed because as hard as they tried they couldn't make a functioning hypothesis...then I guess that's one of the more 'natural' ways for a project to more naturally leave Wikiversity.

Deadlines etc. can help me keep moving...

What a hypothesis is: &quot;I predict this will happen&quot; and then checking results what happens and whether it fulfilled the prediction or not and sometimes we stumble upon new things we did not expect.

[[Operationalization]] is then also needed to make &quot;ambiguous ideas&quot; measurable. My father remembers that I &quot;wanted to save the world&quot; but it was nothing other than an observation I wanted to share with other people that I had made that began years earlier. June 16 should be 2 months roughly after the creation of the Draft:Idea...

== April 29, 2026 ==

Just made my father aware of this &quot;idea&quot; that so far doesn't have a published hypothesis of any kind, not even in a &quot;basic stage&quot;. Only the deadline for June 16 exists right now.

I'm happy he did not reject me working on it. He encourages me to work harder. I got a &quot;Great job so far!&quot; compliment.

=== Google's &quot;AI Mode&quot; ===

This part was 100% AI-generated:

{{quote|What you are describing is a core concept in the philosophy of science called Falsification. It was popularized by Karl Popper, who argued that science doesn't progress by &quot;proving things right,&quot; but by rigorously trying to prove things wrong and failing to do so.}}

== April 30, 2026 ==

Was gonna start writing on the Colloquium again and composed a large message to reply/'talk to' Jtneill but I got input from &quot;AI Mode&quot; and then I realized after a while, maybe what I'm trying to ask I can find out with the help of &quot;AI Mode&quot; leading me to the right resources? ie. formatting on talk pages...how important is that? Prioritizing...

Also replying to everything? Is it really needed? Would I like to be known as &quot;Needy ThinkingScience&quot;? I can't do anything on my own? So yeah, I started thinking maybe I can focus on doing more.
Starting by talking less and the tools we have available can fix a lot anyway, LLMs are great but designed in interesting and challenging ways!

Do I even need a mentor or do I '''just think I need one'''? I am very much a needy guy in terms of hand-holding and being related to a social context &quot;historically&quot; in my life, or at least that's what I thought. What I think I need for myself may be completely wrong.

People in talk pages I interpreted as saying that I shouldn't put obstacles in my path by being mean to myself and putting pressure on myself to do certain things in a certain amount of time but I guess I couldn't stop myself! I also need a social context but would I just drag others into my &quot;bad routines&quot;? It all depends on who one interacts with...which now makes me think about &quot;the idea&quot; again. I guess I should see this as a warning sign :)

My father suggested peer-review related activities and here I am looking inward and isolating myself. I don't know...

:I figured today I begin with {{quote|April 20th experiment, &quot;AI Decisions, sure. AI-generation NEVER&quot;}}

== May 5, 2026 ==

Today I became very emotional when thinking about the importance of taking the decision to finally &quot;unload&quot; my idea on and trying to develop it on Wikiversity while talking to a friend. It's important to know when I last felt this deep of an &quot;emotion unload&quot;.

The original question from my friend in the original language: {{quote|&quot;Σκεφτόμουν εάν αυτή η συναισθηματική αντίδραση σου συμβαίνει συχνά ή εάν έτυχε απλώς τώρα στην συνάντησή μας?&quot;}} which I'll translate for you. I was also pondering the &quot;suitability&quot; of adding foreign languages to Wikiversity. It would make sense as long as that is the training material for the course which is in English about learning a foreign language.

The question as I interpret it as of this moment and which may be incorrect is this:

{{quote|I was thinking if this emotional reaction happens to you often or if it just happened now at the meeting?}}

And I think I remember my answer being that it only happened now.

It was very important for me because no longer will only I think about this draft in my own mind but other people can think too about what I describe about it. Any data I can find will also then be able to be studied by contributors or interested parties. So far, no data at all.

My point: Not having to carry this weight anymore. It was too heavy. It was basically too hard for me to formulate &quot;coherent&quot; sentences and only thought about them at brief periods while waking up or during &quot;Aha!&quot; moments.

== May 18, 2026, Monday ==

As I wrote in the diary of my main user account, screen arrived. I can now work.

I will continue work on the translation for my unfinished draft &quot;idea&quot; on the Greek Wikiversity. I'm following the &quot;Be bold&quot;. Translating also means processing, that means that a different &quot;take&quot; on the idea may happen. That may lead to a better formulated text.

== May 19, 2026, Tuesday ==

[[v:el:Χρήστης:ThinkingScience|User ThinkingScience on Greek Wikiversity]]

Today I can work on the translation and other work on Greek Wikiversity regarding my idea. This is good so I can continue the work on explaining to friends and family regarding my &quot;idea&quot;/&quot;observation&quot;. I might work right now...maybe make more notes later today?</text>
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    <title>User talk:BigKrow</title>
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      <text bytes="2979" sha1="dw3vlodua714i0qj9ha0hxa4beop4iw" xml:space="preserve">==Welcome==
{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  BigKrow!'''|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Koavf|me personally]] if you would like some [[Help:Contents|help]].

Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. Using the signature icon [[File:OOjs UI icon signature-ltr.svg]] makes it simple.

We invite you to [[Wikiversity:Be bold|be bold]] and [[Wikiversity|assume good faith]]. Please abide by our [[Wikiversity:Civility|civility]], [[Wikiversity:Privacy policy|privacy]], and [[Foundation:Terms of Use|terms of use]] policies.

To find your way around, check out:
&lt;!-- The Left column --&gt;
&lt;div style=&quot;width:50.0%; float:left&quot;&gt;
* [[Wikiversity:Introduction|Introduction to Wikiversity]]
* [[Help:Guides|Take a guided tour]] and learn [[Help:Editing|how to edit]]
* [[Wikiversity:Browse|Browse]] or visit an educational level portal:&lt;br&gt;[[Portal:Pre-school Education|pre-school]] | [[Portal:Primary Education|primary]] | [[Portal:Secondary Education|secondary]] | [[Portal:Tertiary Education|tertiary]] | [[Portal:Non-formal Education|non-formal]]
* [[Wikiversity:Introduction explore|Explore]] links in left-hand navigation menu
&lt;/div&gt;
&lt;!-- The Right column --&gt;
&lt;div style=&quot;width:50.0%; float:left&quot;&gt;

* Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]]
* Learn [[Help:How to write an educational resource|how to write an educational resource]]
* Find out about [[Wikiversity:Research|research]] activities
* Give [[Wikiversity:Feedback|feedback]] about your observations
* Discuss issues or ask questions at the [[Wikiversity:Colloquium|colloquium]]
&lt;/div&gt;
&lt;br clear=&quot;both&quot;/&gt;

To get started, experiment in the [[wikiversity:sandbox|sandbox]] or on [[special:mypage|your userpage]].

See you around Wikiversity! --—[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:39, 1 May 2026 (UTC)&lt;/div&gt;
&lt;!-- Template:Welcome --&gt;
{{Robelbox/close}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:39, 1 May 2026 (UTC)

:Thanks! [[User:BigKrow|BigKrow]] ([[User talk:BigKrow|discuss]] • [[Special:Contributions/BigKrow|contribs]]) 01:08, 2 May 2026 (UTC)

== Camel Spider ==

FYI, this page has been moved to [[Spiders/Camel Spider]] -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 01:46, 19 May 2026 (UTC)</text>
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    <title>Wikiversity:Candidates for Bureaucratship</title>
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== Nominations for [[Wikiversity:Bureaucratship|Bureaucratship]] == 
&lt;!-- {{Wikiversity:Candidates for Bureaucratship/Username}} --&gt;
{{Wikiversity:Candidates for Bureaucratship/Koavf}}
{{Wikiversity:Candidates for Bureaucratship/Atcovi}}
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== See also ==
*[[Wikiversity:Curatorship|Curatorship]]
*[[Wikiversity:Custodianship|Custodianship]]
*[[Wikiversity:Bureaucratship|Bureaucratship]]
**[[Wikiversity:Candidates for Bureaucratship/Archive of pending nominations|Candidates for Bureaucratship/Archive of pending nominations]]
*[[Wikiversity:Support staff]]

[[Category:Wikiversity bureaucratship]]</text>
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  <page>
    <title>Athena problem</title>
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      <comment>project box(es)</comment>
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      <text bytes="45622" sha1="dqai3snthcqiu5q4kk1j2cny0djliuq" xml:space="preserve">{{mathematics}}
'''Athena problem''' is an [[:w:List of unsolved problems in mathematics|unsolved problem]] in [[:w:Number theory|number theory]] and [[:w:Formal language theory|formal language theory]] and [[:w:Order theory|order theory]], this problem is named after the ancient Greek goddess [[:w:Athena|Athena]] (which is associated with [[:w:Wisdom|wisdom]]). Athena problem is: Give a [[:w:Natural number|natural number]] ''b'' &gt; 1, find the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the set of the &quot;[[:w:Prime number|prime number]] [[:w:Greater than|&gt;]] ''b''&quot; [[:w:Numerical digit|digit]] [[:w:String (computer science)|string]]s in the [[:w:Positional numeral system|positional numeral system]] with [[:w:Radix|base]] ''b'' for the [[:w:Subsequence|subsequence]] [[:w:Partially ordered set|ordering]]. (A string ''x'' is a subsequence of another string ''y'', if ''x'' can be obtained from ''y'' by deleting zero or more of the [[:w:Character (computing)|character]]s in ''y''. For example, 514 is a subsequence of 352148, &quot;string&quot; is a subsequence of &quot;meistersinger&quot;. In contrast, 758 is not a subsequence of 378259, &quot;abc&quot; is not a subsequence of &quot;cbacacba&quot;, since the characters must be in the same order) (Unlike [[:w:Substring|substring]], subsequence is not required to occupy consecutive positions within the original sequences, e.g. the [[:w:Longest common subsequence|longest common subsequence problem]] is different from the [[:w:Longest common substring|longest common substring problem]])

Using [[:w:Formal language theory|formal language theory]] terminology, Athena problem is finding the [[:w:Set (mathematics)|set]] of the [[:w:Minimal element|minimal element]]s of the [[:w:Formal language|language]] of base-''b'' [[:w:Representation (mathematics)|representation]]s of the [[:w:Prime number|prime number]]s [[:w:Greater than|&gt;]] ''b'' (which is a set of [[:w:String (computer science)|string]]s of [[:w:Symbol|symbol]]s over the [[:w:Alphabet (formal languages)|alphabet]] ''Σ''&lt;sub&gt;''b''&lt;/sub&gt; := {0, 1, ..., ''b''−1}), under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), for a given natural number ''b'' &gt; 1. (You can draw this partial ordering as [[:w:Hasse diagram|Hasse diagram]] to find all [[:w:Minimal element|minimal element]]s)

By [[:w:Higman's lemma|Higman's lemma]], there are no [[:w:Infinite set|infinite]] [[:w:Antichain|antichain]]s for the subsequence ordering (i.e. the subsequence ordering is always a [[:w:Well-quasi-ordering|well quasi order]]) (i.e. under the subsequence ordering (i.e. the [[:w:Binary relation|binary relation]] &quot;is a subsequence of&quot;, which is a [[:w:Partially ordered set|partial ordering]]), every set of pairwise incomparable (i.e. not [[:w:Comparability|comparable]]) strings is finite), thus there must be only finitely many such minimal elements. In other words, the set of such minimal elements must be a [[:w:Finite set|finite set]], e.g. in [[:w:Decimal|decimal]] (base ''b'' = 10), this set has exactly 77 [[:w:Element of a set|element]]s: {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}.

For bases 2 ≤ ''b'' ≤ 36, Athena problem is fully solved in bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 24, and also solved in bases ''b'' = 11, 13, 16, 22, 30 if [[:w:Probable prime|probable prime]]s are allowed. For the unsolved bases ''b'' = 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, Athena problem is solved (if probable primes are allowed) except 771 [[:w:Indexed family|families]] of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be [[:w:Empty string|empty]]) of digits in base ''b'', ''y'' is a digit in base ''b'') = sequence {''xz'', ''xyz'', ''xyyz'', ''xyyyz'', ''xyyyyz'', ''xyyyyyz'', ...} (i.e. &quot;''xy''&lt;sup&gt;+&lt;/sup&gt;''z''&quot; in [[:w:Regular expression|regular expression]]), all of these 771 families contain no primes &gt; ''b'' or probable primes &gt; ''b'' with length ≤ 100000.

== Results ==

To solve the Athena problem for a given base ''b'', we must [[:w:Computing|compute]] the elements up to families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') (we call such families ''linear families''), and find the smallest prime &gt; ''b'' in all such families.

Shrinking the family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'')

* If ''y'' ∈ ''Y'' and the string ''xyyz'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''}''z'' ∪ ''x''{''Y'' \ ''y''}''y''{''Y'' \ ''y''}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and the string ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' represents a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or has a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.
* If ''y''&lt;sub&gt;1&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;2&lt;/sub&gt; ∈ ''Y'' and ''y''&lt;sub&gt;1&lt;/sub&gt; ≠ ''y''&lt;sub&gt;2&lt;/sub&gt; and both the strings ''xy''&lt;sub&gt;1&lt;/sub&gt;''y''&lt;sub&gt;2&lt;/sub&gt;''z'' and ''xy''&lt;sub&gt;2&lt;/sub&gt;''y''&lt;sub&gt;1&lt;/sub&gt;''z'' represent a prime &gt; ''b'' in base ''b'' (in this case, add this prime to the list) or have a subsequence which represents a prime &gt; ''b'' in base ''b'', then ''x''{''Y''}''z'' can be replaced with ''x''{''Y'' \ ''y''&lt;sub&gt;1&lt;/sub&gt;}''z'' ∪ ''x''{''Y'' \ ''y''&lt;sub&gt;2&lt;/sub&gt;}''z''.

e.g. in decimal (base ''b'' = 10):

* 2221 is a prime &gt; 10, thus the family 2{0,2}1 splits into the two families 2{0}1 and 2{0}2{0}1.
* 227 is a prime &gt; 10, and it is a subsequence of 5227, thus the family 5{0,2}7 splits into the two families 5{0}7 and 5{0}2{0}7.
* 449 is a prime &gt; 10, and it is a subsequence of 6449, thus the family 6{0,3,4,6,9}9 splits into the two families 6{0,3,6,9}9 and 6{0,3,6,9}4{0,3,6,9}9.
* Both 5051 and 5501 are primes &gt; 10, thus the family 5{0,5}1 splits into the two families 5{0}1 and 5{5}1 = {5}1.
* 8501 is a prime &gt; 10, thus the family 8{0,5}1 splits into the family 8{0}{5}1.
* 887 is a prime &gt; 10, and it is a subsequence of 2887, also 2087 is a prime &gt; 10, thus the family 2{0,8}7 splits into the two families 2{0}7 and 28{0}7.
* 349 and 449 are primes &gt; 10, and they are subsequences of 9349 and 9449, respectively, also 9049, 9649, 9949 are primes &gt; 10, thus the family 9{0,3,4,6,9}9 splits into the two families 9{0,3,6,9}9 and 94{0,3,6,9}9.
* 251, 281, 521, 821, 881 are primes &gt; 10, and they are subsequences of 9251, 9281, 9521, 9821, 9881, respectively, also 9001, 9221, 9551, 9851 are primes &gt; 10, thus the family 9{0,2,5,8}1 splits into the numbers {91, 901, 921, 951, 981, 9021, 9051, 9081, 9201, 9501, 9581, 9801, 90581, 95081, 95801}.

If the methods we have discussed cannot be used to rule out or shrink ''x''{''Y''}''z'' where ''Y'' = {''y''&lt;sub&gt;1&lt;/sub&gt;, ''y''&lt;sub&gt;2&lt;/sub&gt;, ..., ''y''&lt;sub&gt;''n''&lt;/sub&gt;}, then we can replace ''x''{''Y''}''z'' by ''xy''&lt;sub&gt;1&lt;/sub&gt;{''Y''}''z'' ∪ ''xy''&lt;sub&gt;2&lt;/sub&gt;{''Y''}''z'' ∪ ... ∪ ''xy''&lt;sub&gt;''n''&lt;/sub&gt;{''Y''}''z'' and re-run the methods on this new [[:w:Formal language|language]].

If all remain families are linear families (i.e. of the form ''x''{''y''}''z'', where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b''), then we search the smallest (probable) primes in these families and add these primes to the list.

e.g. in decimal (base ''b'' = 10):

* The smallest prime in the family 5{0}27 is 5000000000000000000000000000027.
* The smallest prime in the family {5}1 is 555555555551.
* The smallest prime in the family 8{5}1 is 8555555555555555555551, but 8555555555555555555551 is not a minimal element since 555555555551 is a subsequence of 8555555555555555555551.

There is no guarantee that the techniques discussed will ever terminate, but in practice they often do. They are able to determine the set of the minimal elements in base ''b'' for 2 ≤ ''b'' ≤ 16 and ''b'' = 18, 20, 22, 24, 30. The bases ''b'' = 17, 19, 21, 23, 25 ≤ ''b'' ≤ 29, 31 ≤ ''b'' ≤ 36 are solved with the exception of 771 families of the form ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'').

The following is a &quot;[[:w:Semi-algorithm|semi-algorithm]]&quot; that is guaranteed to solve the Athena problem for a given base ''b'', but it is not so easy to implement:

# ''M'' = ''[[:w:Empty string|∅]]''
# while (''L'' ≠ ''∅'') do
# choose ''x'', a shortest string in ''L''
# ''M'' := ''M'' ∪ {''x''}
# ''L'' := ''L'' − ''sup''({''x''})

In practice, for arbitrary ''L'', we cannot feasibly carry out step 5. Instead, we work with ''L''&amp;#39;, some regular overapproximation to ''L'', until we can show ''L''&amp;#39; = ''∅'' (which implies ''L'' = ''∅''). In practice, ''L''&amp;#39; is usually chosen to be a finite [[:w:Union (set theory)|union]] of sets of the form ''L''&lt;sub&gt;1&lt;/sub&gt;{''L''&lt;sub&gt;2&lt;/sub&gt;}''L''&lt;sub&gt;3&lt;/sub&gt;, where each of ''L''&lt;sub&gt;1&lt;/sub&gt;, ''L''&lt;sub&gt;2&lt;/sub&gt;, ''L''&lt;sub&gt;3&lt;/sub&gt; is finite. In the case we consider in this project, we then have to determine whether such a family contains a prime or not.

Thus, Athena problem in bases ''b'' around 500 may be [[:w:NP-complete|NP-complete]] or [[:w:NP-hard|NP-hard]], or an [[:w:Undecidable problem|undecidable problem]], or an example of [[:w:Gödel's incompleteness theorems|Gödel's incompleteness theorems]] (like the [[:w:Continuum hypothesis|continuum hypothesis]] and the [[:w:Halting problem|halting problem]]).

To solve the Athena problem, we need to determine whether a given family contains a prime. In practice, if family ''x''{''Y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''Y'' is a set of digits in base ''b'') could not be ruled out as only containing composites and ''Y'' contains two or more digits, then a relatively small prime &gt; ''b'' could always be found in this family. Intuitively, this is because there are a large number of small strings in such a family, and at least one is likely to be prime (e.g. there are 2&lt;sup&gt;''n''−2&lt;/sup&gt; strings of length ''n'' in the family 1{3,7}9, and there are over a thousand strings of length 12 in the family 1{3,7}9, thus it is very impossible that these numbers are all composite). In the case ''Y'' contains only one digit, this family is of the form ''x''{''y''}''z'', and there is only a single string of each length &gt; (the length of ''x'' + the length of ''z''), and it is not known if the following [[:w:Decision problem|decision problem]] is recursively solvable (just like [[:w:Sierpiński number|Sierpiński problem]] and [[:w:Riesel number|Riesel problem]], Sierpiński problem and Riesel problem can be generalized to other bases ''b'', in fact, Athena problem in base ''b'' covers the Sierpiński problem in base ''b'' and the Riesel problem in base ''b'' with ''k'' &lt; ''b'', i.e. finding the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (or prove such prime does not exist) with ''k'' &lt; ''b'', since the smallest prime of the form ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;+1 and ''k''×''b''&lt;sup&gt;''n''&lt;/sup&gt;−1 (if exists) must be a minimal element in base ''b''):

Problem: Given strings ''x'', ''z'' (may be empty), a digit ''y'', and a base ''b'' (''x'' does not [[:w:Leading zero|start with the digit 0]], ''z'' ends with a digit which [[:w:Coprime integers|coprime]] to ''b'', ''y'' is not 0 if ''x'' is empty, ''y'' is coprime to ''b'' if ''z'' is empty), does there exist a prime number whose base-''b'' expansion is of the form ''xy''&lt;sub&gt;''n''&lt;/sub&gt;''z'' for some ''n'' ≥ 0?

Some families can be ruled out to contain no prime &gt; ''b'' by [[:w:Covering set|covering congruence]], [[:w:Factorization of polynomials|algebraic factorization]] (e.g. [[:w:Difference of two squares|difference of two squares]], [[:w:Sum of two cubes|sum of two cubes]], [[:w:Sophie Germain's identity|Sophie Germain's identity of ''x''&lt;sup&gt;4&lt;/sup&gt;+4×''y''&lt;sup&gt;4&lt;/sup&gt;]]), or combine of them, e.g.

* The base 9 family 2{7}: Always divisible by 2 or 5
* The base 16 family {8}F: Always divisible by 3, 7, or 13
* The base 21 family {7}D: Always divisible by 2, 13, or 17
* The base 23 family {D}GA: Always divisible by 2, 5, 7, 37, or 79
* The base 9 family 3{8}: Can be written as 4×9&lt;sup&gt;''n''&lt;/sup&gt;−1 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−1) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 8 family 1{0}1: Can be written as 8&lt;sup&gt;''n''&lt;/sup&gt;+1 and can be factored as (2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (4&lt;sup&gt;''n''&lt;/sup&gt;−2&lt;sup&gt;''n''&lt;/sup&gt;+1)
* The base 16 family {4}1: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;−49)/15 and can be factored as (2×3&lt;sup&gt;''n''&lt;/sup&gt;−7) × (2×3&lt;sup&gt;''n''&lt;/sup&gt;+7) / 15
* The base 16 family {C}D: Can be written as (4×16&lt;sup&gt;''n''&lt;/sup&gt;+1)/5 and can be factored as (2×4&lt;sup&gt;''n''&lt;/sup&gt;−2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) × (2×4&lt;sup&gt;''n''&lt;/sup&gt;+2×2&lt;sup&gt;''n''&lt;/sup&gt;+1) / 5
* The base 14 family 8{D}: Can be written as 9×14&lt;sup&gt;''n''&lt;/sup&gt;−1, it is divisible by 5 if ''n'' is odd and can be factored as (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (3×14&lt;sup&gt;''n''/2&lt;/sup&gt;+1) if ''n'' is even
* The base 12 family {B}9B: Can be written as 12&lt;sup&gt;''n''&lt;/sup&gt;−25, it is divisible by 13 if ''n'' is odd and can be factored as (12&lt;sup&gt;''n''/2&lt;/sup&gt;−5) × (12&lt;sup&gt;''n''/2&lt;/sup&gt;+5) if ''n'' is even
* The base 17 family 1{9}: Can be written as (25×17&lt;sup&gt;''n''&lt;/sup&gt;−9)/16, it is divisible by 2 if ''n'' is odd and can be factored as (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;−3) × (5×17&lt;sup&gt;''n''/2&lt;/sup&gt;+3) / 16 if ''n'' is even
* The base 19 family 1{6}: Can be written as (4×19&lt;sup&gt;''n''&lt;/sup&gt;−1)/3, it is divisible by 5 if ''n'' is odd and can be factored as (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;−1) × (2×19&lt;sup&gt;''n''/2&lt;/sup&gt;+1) / 3 if ''n'' is even

By the [[:w:Prime number theorem|prime number theorem]], the [[:w:Probability|chance]] that a [[:w:Random number|random]] ''n''-digit base ''b'' number is prime is [[:w:Asymptotic analysis|approximately]] 1/''n'' (more accurately, the chance is approximately 1/(''n''×''ln''(''b'')), where ''ln'' is the [[:w:Natural logarithm|natural logarithm]]). If one conjectures the numbers ''x''{''y''}''z'' behave similarly (i.e. the numbers ''x''{''y''}''z'' is a [[:w:Pseudorandomness|pseudorandom sequence]]) you would expect [[:w:Harmonic_series (mathematics)|1/1 + 1/2 + 1/3 + 1/4 + ... = ∞]] primes of the form ''x''{''y''}''z'' (of course, this does not always happen, since some ''x''{''y''}''z'' families can be ruled out to contain no prime &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them), but it is at least a reasonable conjecture in the absence of evidence to the contrary. Hence, the [[:w:Heuristic argument|heuristic argument]] suggests there are always infinitely many primes in family ''x''{''y''}''z'' (where ''x'' and ''z'' are strings (may be empty) of digits in base ''b'', ''y'' is a digit in base ''b'') if it cannot be ruled out to contain no prime or only contain finitely many primes, by covering congruence, algebraic factorization, or combine of them. However, some families ''x''{''y''}''z'' could not be proven to contain no primes &gt; ''b'' (by covering congruence, algebraic factorization, or combine of them) but no primes &gt; ''b'' could be found in the family, even after searching through numbers with over 100000 digits. In such a case, the only way to proceed is to [[:w:Primality test|test the primality]] of larger and larger numbers of such form and hope a prime is eventually discovered. e.g. the smallest (probable) prime in the family A{3}A in base ''b'' = 13 is A3&lt;sub&gt;592197&lt;/sub&gt;A, which written in decimal contains 659677 digits (it is only probable prime, i.e. not definitely prime).

== Data ==

These are the results of the Athena problem in bases 2 ≤ ''b'' ≤ 36 (we stop at base 36 since this base is the maximum base for which it is possible to write the numbers with the [[:w:Symbol|symbol]]s 0, 1, 2, ..., 9 and A, B, C, ..., Z (i.e. the 10 [[:w:Arabic numerals|Arabic numerals]] and the 26 [[:w:Latin script|Latin letters]]): (some large primes are only probable primes, i.e. not definitely primes, since they are too large to be [[:w:Elliptic curve primality|ECPP proved]] and [[:w:Pocklington primality test#Extensions and variants|neither ''N''−1 nor ''N''+1 can be ≥ 1/3 factored]], all of them pass the [[:w:Baillie–PSW primality test|Baillie–PSW primality test]] and the [[:w:Strong pseudoprime|strong primality test]] (i.e. the [[:w:Miller–Rabin primality test|Miller–Rabin primality test]]) with all prime bases ''p'' ≤ 61, however, all primes &lt; 10&lt;sup&gt;25000&lt;/sup&gt; for bases ''b'' = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 36 are definitely primes, most of them &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Elliptic curve primality|ECPP proving]], others &gt; 10&lt;sup&gt;299&lt;/sup&gt; are proven primes with [[:w:Pocklington primality test#Extensions and variants|''N''−1 or ''N''+1 proving]])

All numbers are written in base ''b'', [[:w:Senary#Base 36 as senary compression|using A to Z to represent digit values 10 to 35]], &quot;{}&quot; means repeating, e.g. family 12{3}45 means the sequence {1245, 12345, 123345, 1233345, 12333345, 123333345, ...} (where the members are expressed as base ''b'' strings), subscripts are used to indicate repetitions of digits, e.g. 123&lt;sub&gt;4&lt;/sub&gt;567 means 123333567 (all subscripts are written in decimal).

Base 2: 1 prime (the largest of which has 2 digits): {11}

Base 3: 3 primes (the largest of which has 3 digits): {12, 21, 111}

Base 4: 5 primes (the largest of which has 3 digits): {11, 13, 23, 31, 221}

Base 5: 22 primes (the largest of which has 96 digits): {12, 21, 23, 32, 34, 43, 104, 111, 131, 133, 313, 401, 414, 3101, 10103, 14444, 30301, 33001, 33331, 44441, 300031, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000013}

Base 6: 11 primes (the largest of which has 5 digits): {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041}

Base 7: 71 primes (the largest of which has 17 digits): {14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1022, 1051, 1112, 1202, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 11201, 30011, 30101, 31001, 31111, 33001, 33311, 35555, 40054, 100121, 150001, 300053, 351101, 531101, 1100021, 33333301, 5100000001, 33333333333333331}

Base 8: 75 primes (the largest of which has 221 digits): {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441, 77774444441, 7777777777771, 555555555555525, 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444447}

Base 9: 151 primes (the largest of which has 1161 digits): {12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 117, 131, 135, 151, 155, 175, 177, 238, 272, 308, 315, 331, 337, 355, 371, 375, 377, 438, 504, 515, 517, 531, 537, 557, 564, 601, 638, 661, 702, 711, 722, 735, 737, 751, 755, 757, 771, 805, 838, 1011, 1015, 1101, 1701, 2027, 2207, 3017, 3057, 3101, 3501, 3561, 3611, 3688, 3868, 5035, 5051, 5071, 5101, 5501, 5554, 5705, 5707, 7017, 7075, 7105, 7301, 8535, 8544, 8555, 8854, 20777, 22227, 22777, 30161, 33388, 50161, 50611, 53335, 55111, 55535, 55551, 57061, 57775, 70631, 71007, 77207, 100037, 100071, 100761, 105007, 270707, 301111, 305111, 333035, 333385, 333835, 338885, 350007, 500075, 530005, 555611, 631111, 720707, 2770007, 3030335, 7776662, 30300005, 30333335, 38333335, 51116111, 70000361, 300030005, 300033305, 351111111, 1300000007, 5161111111, 8333333335, 300000000035, 311111111161, 544444444444, 2000000000007, 5700000000001, 7270000000007, 88888888833335, 100000000000507, 5111111111111161, 7277777777777777707, 8888888888888888888335, 30000000000000000000051, 1000000000000000000000000057, 56111111111111111111111111111111111111, 7666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666662, 27777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777707, 300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011}

Base 10: 77 primes (the largest of which has 31 digits): {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 227, 251, 257, 277, 281, 349, 409, 449, 499, 521, 557, 577, 587, 727, 757, 787, 821, 827, 857, 877, 881, 887, 991, 2087, 2221, 5051, 5081, 5501, 5581, 5801, 5851, 6469, 6949, 8501, 9001, 9049, 9221, 9551, 9649, 9851, 9949, 20021, 20201, 50207, 60649, 80051, 666649, 946669, 5200007, 22000001, 60000049, 66000049, 66600049, 80555551, 555555555551, 5000000000000000000000000000027}

Base 11: 1068 primes (including 1 unproven probable prime: 57&lt;sub&gt;62668&lt;/sub&gt;), the largest of which has 62669 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel11 Data of Athena problem base 11]

Base 12: 106 primes (the largest of which has 42 digits): {11, 15, 17, 1B, 25, 27, 31, 35, 37, 3B, 45, 4B, 51, 57, 5B, 61, 67, 6B, 75, 81, 85, 87, 8B, 91, 95, A7, AB, B5, B7, 221, 241, 2A1, 2B1, 2BB, 401, 421, 447, 471, 497, 565, 655, 665, 701, 70B, 721, 747, 771, 77B, 797, 7A1, 7BB, 907, 90B, 9BB, A41, B21, B2B, 2001, 200B, 202B, 222B, 229B, 292B, 299B, 4441, 4707, 4777, 6A05, 6AA5, 729B, 7441, 7B41, 929B, 9777, 992B, 9947, 997B, 9997, A0A1, A201, A605, A6A5, AA65, B001, B0B1, BB01, BB41, 600A5, 7999B, 9999B, AAAA1, B04A1, B0B9B, BAA01, BAAA1, BB09B, BBBB1, 44AAA1, A00065, BBBAA1, AAA0001, B00099B, AA000001, BBBBBB99B, B0000000000000000000000000009B, 400000000000000000000000000000000000000077}

Base 13: 3197 primes (including 4 unproven probable primes: C5&lt;sub&gt;23755&lt;/sub&gt;C, 80&lt;sub&gt;32017&lt;/sub&gt;111, 95&lt;sub&gt;197420&lt;/sub&gt;, A3&lt;sub&gt;592197&lt;/sub&gt;A), the largest of which has 592199 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel13 Data of Athena problem base 13]

Base 14: 650 primes, the largest of which has 19699 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel14 Data of Athena problem base 14]

Base 15: 1284 primes, the largest of which has 157 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel15 Data of Athena problem base 15]

Base 16: 2347 primes (including 3 unproven probable primes: DB&lt;sub&gt;32234&lt;/sub&gt;, 4&lt;sub&gt;72785&lt;/sub&gt;DD, 3&lt;sub&gt;116137&lt;/sub&gt;AF), the largest of which has 116139 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel16 Data of Athena problem base 16]

Base 17: 10415 known primes (including many unproven probable primes) and 12 unsolved families (1{7}, 1F{0}7, 4{7}A, 70F{0}D, 8{B}9, 9{5}9, A{D}F, B{0}B3, {B}E9, {B}EE, F1{9}, FD0{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel17 Data of Athena problem base 17] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left17 Data of unsolved families for base 17]

Base 18: 549 primes, the largest of which has 6271 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel18 Data of Athena problem base 18]

Base 19: 31417 known primes (including many unproven probable primes) and 17 unsolved families (4B5{0}H, {5}3, 5{H}05, 5{H}0H, 5{H}5, 66{B}, 71{0}177, 7AF{0}H, 97{0}3, C{H}C, EE1{6}, F{7}5, F{B}G, F{D}F, H0F{0}7A, HB{0}5B5, II{D}, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel19 Data of Athena problem base 19] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left19 Data of unsolved families for base 19]

Base 20: 3314 primes, the largest of which has 6271 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel20 Data of Athena problem base 20]

Base 21: 13386 known primes (including many unproven probable primes) and 8 unsolved families (5{0}DJ, {9}D, B3{0}EB, B{H}6H, C{F}0K, {F}35, G{0}FK, H{0}7771, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel21 Data of Athena problem base 21] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left21 Data of unsolved families for base 21]

Base 22: 8003 primes (including 1 unproven probable prime: BK&lt;sub&gt;22001&lt;/sub&gt;5), the largest of which has 22003 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel22 Data of Athena problem base 22]

Base 23: 65178 known primes (including many unproven probable primes) and 87 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel23 Data of Athena problem base 23] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left23 Data of unsolved families for base 23]

Base 24: 3409 primes, the largest of which has 8134 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel24 Data of Athena problem base 24]

Base 25: 133639 known primes (including many unproven probable primes) and 85 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel25 Data of Athena problem base 25] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left25 Data of unsolved families for base 25]

Base 26: 25256 known primes (including 7 unproven probable primes: 5&lt;sub&gt;19391&lt;/sub&gt;6F, 7&lt;sub&gt;20279&lt;/sub&gt;OL, LD0&lt;sub&gt;20975&lt;/sub&gt;7, 6K&lt;sub&gt;23300&lt;/sub&gt;5, J0&lt;sub&gt;44303&lt;/sub&gt;KCB, M0&lt;sub&gt;61186&lt;/sub&gt;2BB, 85M&lt;sub&gt;197060&lt;/sub&gt;B) and 3 unsolved families ({A}6F, {H}MH, {I}GL, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel26 Data of Athena problem base 26]

Base 27: 102852 known primes (including many unproven probable primes) and 44 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel27 Data of Athena problem base 27] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left27 Data of unsolved families for base 27]

Base 28: 25528 known primes (including 3 unproven probable primes: N6&lt;sub&gt;24051&lt;/sub&gt;LR, 5OA&lt;sub&gt;31238&lt;/sub&gt;F, O4O&lt;sub&gt;94535&lt;/sub&gt;9) and 1 unsolved family (O{A}F, no primes or probable primes with length ≤ 709070, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel28 Data of Athena problem base 28]

Base 29: 355242 known primes (including many unproven probable primes) and 125 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel29 Data of Athena problem base 29] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left29 Data of unsolved families for base 29]

Base 30: 2619 primes (including 1 unproven probable prime: I0&lt;sub&gt;24608&lt;/sub&gt;D), the largest of which has 34206 digits, see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel30 Data of Athena problem base 30]

Base 31: 569323 known primes (including many unproven probable primes) and 77 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel31 Data of Athena problem base 31] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left31 Data of unsolved families for base 31]

Base 32: 168882 known primes (including many unproven probable primes) and 120 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel32 Data of Athena problem base 32] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left32 Data of unsolved families for base 32]

Base 33: 280012 known primes (including many unproven probable primes) and 81 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel33 Data of Athena problem base 33] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left33 Data of unsolved families for base 33]

Base 34: 184785 known primes (including many unproven probable primes) and 47 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel34 Data of Athena problem base 34] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left34 Data of unsolved families for base 34]

Base 35: 720002 known primes (including many unproven probable primes) and 60 unsolved families (no primes or probable primes with length ≤ 100000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel35 Data of Athena problem base 35] and [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/left35 Data of unsolved families for base 35]

Base 36: 35286 known primes (including 3 unproven probable primes: 7K&lt;sub&gt;26567&lt;/sub&gt;Z, S0&lt;sub&gt;75007&lt;/sub&gt;8H, P&lt;sub&gt;81993&lt;/sub&gt;SZ) and 4 unsolved families (B{0}EUV, HM{0}N, N{0}YYN, O{L}Z, no primes or probable primes with length ≤ 200000, nor can be proven to only contain composites), see [https://raw.githubusercontent.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/main/kernel36 Data of Athena problem base 36]

== The fully proof of Athena problem in decimal (base ''b'' = 10) ==

'''Bold''' for the minimal elements, ''x'' ◁ ''y'' means ''x'' is a subsequence of ''y''.

Assume ''p'' is a prime &gt; 10, and the last digit of ''p'' must lie in {1,3,7,9}.

Case 1: ''p'' ends with 1.

In this case we can write ''p'' = ''x''1. If ''x'' contains 1, 3, 4, 6, or 7, then (respectively) '''11''' ◁ ''p'', '''31''' ◁ ''p'', '''41''' ◁ ''p'', '''61''' ◁ ''p'', or '''71''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 8, or 9.

Case 1.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''1. If 5 ◁ ''y'', then '''251''' ◁ ''p''. If 8 ◁ ''y'', then '''281''' ◁ ''p''. If 9 ◁ ''y'', then 29 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then '''2221''' ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 2{0}1. But then, since the sum of the digits of ''p'' is 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 2''z''2''w''1, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''20201''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 22{0}1, and the smallest prime ''p'' ∈ 22{0}1 is '''22000001'''.

If ''w'' is empty, then ''p'' ∈ 2{0}21, and the smallest prime ''p'' ∈ 2{0}21 is '''20021'''.

Case 1.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''1. If 2 ◁ ''y'', then '''521''' ◁ ''p''. If 9 ◁ ''y'', then 59 ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 5, or 8.

If 05 ◁ ''y'', then '''5051''' ◁ ''p''. If 08 ◁ ''y'', then '''5081''' ◁ ''p''. If 50 ◁ ''y'', then '''5501''' ◁ ''p''. If 58 ◁ ''y'', then '''5581''' ◁ ''p''. If 80 ◁ ''y'', then '''5801''' ◁ ''p''. If 85 ◁ ''y'', then '''5851''' ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ {5} ∪ {8}.

If ''y'' ∈ {0}, then ''p'' ∈ 5{0}1. But then, since the sum of the digits of ''p'' is 6, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' ∈ {5}, then ''p'' ∈ 5{5}1, and the smallest prime ''p'' ∈ 5{5}1 is '''555555555551'''.

If ''y'' ∈ {8}, since if 88 ◁ ''y'', then 881 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'',8}, and thus ''p'' ∈ {51,581}, but 51 and 581 are both composite.

Case 1.3: ''p'' begins with 8.

In this case we can write p = 8''y''1. If 2 ◁ ''y'', then '''821''' ◁ ''p''. If 8 ◁ ''y'', then '''881''' ◁ ''p''. If 9 ◁ ''y'', then 89 ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 5.

If 50 ◁ ''y'', then '''8501''' ◁ ''p''. Hence we may assume y ∈ {0}{5}.

If 005 ◁ ''y'', then '''80051''' ◁ p. Hence we may assume y ∈ {0} ∪ {5} ∪ 0{5}.

If y ∈ {0}, then ''p'' ∈ 8{0}1. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ {5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {''𝜆'', 5, 55, 555, 5555, 55555, 555555, 5555555, 55555555, 555555555, 5555555555}, and thus ''p'' ∈ {81, 851, 8551, 85551, 855551, 8555551, 85555551, 855555551, 8555555551, 85555555551, 855555555551}, but all of these numbers are composite.

If y ∈ 0{5}, since if 55555555555 ◁ ''y'', then 555555555551 ◁ ''p'', hence we may assume ''y'' ∈ {0, 05, 055, 0555, 05555, 055555, 0555555, 05555555, 055555555, 0555555555, 05555555555}, and thus ''p'' ∈ {801, 8051, 80551, 805551, 8055551, 80555551, 805555551, 8055555551, 80555555551, 805555555551, 8055555555551}, and of these numbers only 80555551 and 8055555551 are primes, but 80555551 ◁ 8055555551, thus only '''80555551''' is a minimal element.

Case 1.4: ''p'' begins with 9.

In this case we can write p = 9''y''1. If 9 ◁ ''y'', then '''991''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0, 2, 5, or 8.

If 00 ◁ ''y'', then '''9001''' ◁ ''p''. If 22 ◁ ''y'', then '''9221''' ◁ ''p''. If 55 ◁ ''y'', then '''9551''' ◁ ''p''. If 88 ◁ ''y'', then 881 ◁ ''p''. Hence we may assume ''y'' contains at most one 0, at most one 2, at most one 5, and at most one 8.

If ''y'' only contains at most one 0 and does not contain any of {2,5,8}, then ''y'' ∈ {''𝜆'',0}, and thus ''p'' ∈ {91,901}, but 91 and 901 are both composite. If ''y'' only contains at most one 0 and only one of {2,5,8}, then the sum of the digits of ''p'' is divisible by 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume ''y'' contains at least two of {2,5,8}.

If 25 ◁ ''y'', then 251 ◁ ''p''. If 28 ◁ ''y'', then 281 ◁ ''p''. If 52 ◁ ''y'', then 521 ◁ ''p''. If 82 ◁ ''y'', then 821 ◁ ''p''. Hence we may assume ''y'' contains no 2's (since if ''y'' contains 2, then ''y'' cannot contain either 5's or 8's, which is a contradiction).

If 85 ◁ ''y'', then '''9851''' ◁ ''p''. Hence we may assume ''y'' ∈ {58,580,508,058}, and thus ''p'' ∈ {9581,95801,95081,90581}, and of these numbers only 95801 is prime, but 95801 is not a minimal element since 5801 ◁ 95801.

Case 2: ''p'' ends with 3.

In this case we can write p = ''x''3. If ''x'' contains 1, 2, 4, 5, 7, or 8, then (respectively) '''13''' ◁ ''p'', '''23''' ◁ ''p'', '''43''' ◁ ''p'', '''53''' ◁ ''p'', '''73''' ◁ ''p'', or '''83''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 3: ''p'' ends with 7.

In this case we can write ''p'' = ''x''7. If ''x'' contains 1, 3, 4, 6, or 9, then (respectively) '''17''' ◁ ''p'', '''37''' ◁ ''p'', '''47''' ◁ ''p'', '''67''' ◁ ''p'', or '''97''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 2, 5, 7, or 8.

Case 3.1: ''p'' begins with 2.

In this case we can write ''p'' = 2''y''7. If 2 ◁ ''y'', then '''227''' ◁ ''p''. If 5 ◁ ''y'', then '''257''' ◁ ''p''. If 7 ◁ ''y'', then '''277''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 8.

If 08 ◁ ''y'', then '''2087''' ◁ ''p''. If 88 ◁ ''y'', then 887 ◁ ''p''. Hence we may assume ''y'' ∈ {0} ∪ 8{0}.

If ''y'' ∈ {0}, then ''p'' ∈ 2{0}7. But then, since the sum of the digits of ''p'' is 9, ''p'' is divisible by 3, so ''p'' cannot be prime.

If y ∈ 8{0}, then ''p'' ∈ 28{0}7. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 40&lt;sub&gt;''n''&lt;/sub&gt;1 = 280&lt;sub&gt;''n''&lt;/sub&gt;7.

Case 3.2: ''p'' begins with 5.

In this case we can write ''p'' = 5''y''7. If 5 ◁ ''y'', then '''557''' ◁ ''p''. If 7 ◁ ''y'', then '''577''' ◁ ''p''. If 8 ◁ ''y'', then '''587''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 2.

If 22 ◁ ''y'', then 227 ◁ ''p''. Hence we may assume ''y'' contains zero or one 2's.

If ''y'' contains no 2's, then ''p'' ∈ 5{0}7. But then, since the sum of the digits of ''p'' is 12, ''p'' is divisible by 3, so ''p'' cannot be prime.

If ''y'' contains exactly one 2, then we can write ''p'' = 5''z''2''w''7, where ''z'',''w'' ∈ {0}. If 0 ◁ ''z'' and 0 ◁ ''w'', then '''50207''' ◁ ''p''. Hence we may assume either ''z'' or ''w'' is empty.

If ''z'' is empty, then ''p'' ∈ 52{0}7, and the smallest prime ''p'' ∈ 52{0}7 is '''5200007'''.

If ''w'' is empty, then ''p'' ∈ 5{0}27, and the smallest prime ''p'' ∈ 5{0}27 is '''5000000000000000000000000000027'''.

Case 3.3: ''p'' begins with 7.

In this case we can write ''p'' = 7''y''7. If 2 ◁ ''y'', then '''727''' ◁ ''p''. If 5 ◁ ''y'', then '''757''' ◁ ''p''. If 8 ◁ ''y'', then '''787''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 7, and thus all digits of ''p'' are 0 or 7. But then, since the digits of ''p'' all have a common factor 7, ''p'' is divisible by 7, so ''p'' cannot be prime.

Case 3.4: ''p'' begins with 8.

In this case we can write ''p'' = 8''y''7. If 2 ◁ ''y'', then '''827''' ◁ ''p''. If 5 ◁ ''y'', then '''857''' ◁ ''p''. If 7 ◁ ''y'', then '''877''' ◁ ''p''. If 8 ◁ ''y'', then '''887''' ◁ ''p''. Hence we may assume ''y'' ∈ {0}, and thus ''p'' ∈ 8{0}7. But then, since the sum of the digits of ''p'' is 15, ''p'' is divisible by 3, so ''p'' cannot be prime.

Case 4: ''p'' ends with 9.

In this case we can write ''p'' = ''x''9. If ''x'' contains 1, 2, 5, 7, or 8, then (respectively) '''19''' ◁ ''p'', '''29''' ◁ ''p'', '''59''' ◁ ''p'', '''79''' ◁ ''p'', or '''89''' ◁ ''p''. Hence we may assume all digits of ''x'' are 0, 3, 4, 6, or 9.

If 44 ◁ ''x'', then '''449''' ◁ ''p''. Hence we may assume ''x'' contains zero or one 4's.

If x contains no 4's, then all digits of ''x'' are 0, 3, 6, or 9, and thus all digits of ''p'' are 0, 3, 6, or 9. But then, since the digits of ''p'' all have a common factor 3, ''p'' is divisible by 3, so ''p'' cannot be prime. Hence we may assume that ''x'' contains exactly one 4.

Case 4.1: ''p'' begins with 3.

In this case we can write ''p'' = 3''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. We must have '''349''' ◁ ''p''.

Case 4.2: ''p'' begins with 4.

In this case we can write ''p'' = 4''y''9, where all digits of ''y'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''409''' ◁ ''p''. If 3 ◁ ''y'', then 43 ◁ ''p''. If 9 ◁ ''y'', then '''499''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}, and thus ''p'' ∈ 4{6}9. But then ''p'' is divisible by 7, since for ''n'' ≥ 0 we have 7 × 6&lt;sub&gt;''n''&lt;/sub&gt;7 = 46&lt;sub&gt;''n''&lt;/sub&gt;9.

Case 4.3: ''p'' begins with 6.

In this case we can write p = 6''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 6 ◁ ''z'', then '''6469''' ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' is empty.

If 3 ◁ ''y'', then 349 ◁ ''p''. If 9 ◁ ''y'', then '''6949''' ◁ ''p''. Hence we may assume all digits of ''y'' are 0 or 6.

If 06 ◁ ''y'', then '''60649''' ◁ ''p''. Hence we may assume ''y'' ∈ {6}{0}.

If 666 ◁ ''y'', then '''666649''' ◁ ''p''. If 00000 ◁ ''y'', then '''60000049''' ◁ ''p''. Hence we may assume ''y'' ∈ {''𝜆'', 0, 00, 000, 0000, 6, 60, 600, 6000, 60000, 66, 660, 6600, 66000, 660000}, and thus ''p'' ∈ {649, 6049, 60049, 600049, 6000049, 6649, 66049, 660049, 6600049, 66000049, 66649, 666049, 6660049, 66600049, 666000049}, and of these numbers only '''66000049''' and '''66600049''' are primes.

Case 4.4: ''p'' begins with 9.

In this case we can write p = 9''y''4''z''9, where all digits of ''y'', ''z'' are 0, 3, 6, or 9. If 0 ◁ ''y'', then '''9049''' ◁ ''p''. If 3 ◁ ''y'', then 349 ◁ ''p''. If 6 ◁ ''y'', then '''9649''' ◁ ''p''. If 9 ◁ ''y'', then '''9949''' ◁ ''p''. Hence we may assume ''y'' is empty.

If 0 ◁ ''z'', then 409 ◁ ''p''. If 3 ◁ ''z'', then 43 ◁ ''p''. If 9 ◁ ''z'', then 499 ◁ ''p''. Hence we may assume ''z'' ∈ {6}, and thus ''p'' ∈ 94{6}9, and the smallest prime ''p'' ∈ 94{6}9 is 946669.

[[Category:Number theory]]</text>
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* {{tl|Walsh permutation/sequences/styles.css}}
* {{tl|Walsh permutation/sequences/A002884}}
* {{tl|Walsh permutation/sequences/A053601}}
* {{tl|Walsh permutation/sequences/A127944}}
* {{tl|Walsh permutation/sequences/A023758}}
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[[Category:Integer sequences related to Walsh permutations]]
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[[Category:Integer sequences related to Walsh permutations]]
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[[Category:Integer sequences related to Walsh permutations]]</text>
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[[Category:Integer sequences]]
[[Category:Walsh permutation]]</text>
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* {{tl|Walsh permutation/sequences/A023758}} triangle
* {{tl|Walsh permutation/sequences/A002884}} main = bases · factorial
* {{tl|Walsh permutation/sequences/A053601}} bases
* {{tl|Walsh permutation/sequences/A000142}} factorial
* {{tl|Walsh permutation/sequences/A127944}} exponents of powers of two in bases


[[Category:Integer sequences]]
[[Category:Walsh permutation]]</text>
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* {{tl|Walsh permutation/sequences/A002884}} main = bases · factorial
* {{tl|Walsh permutation/sequences/A053601}} bases
* {{tl|Walsh permutation/sequences/A000142}} factorial
* {{tl|Walsh permutation/sequences/A127944}} exponents of powers of two in bases
* {{tl|Walsh permutation/sequences/styles.css}}


[[Category:Integer sequences]]
[[Category:Walsh permutation]]</text>
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{{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]],  OasisPatzer!'''|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Atcovi|me personally]] if you would like some [[Help:Contents|help]].

Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. Using the signature icon [[File:OOjs UI icon signature-ltr.svg]] makes it simple.

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	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: var(--background-color-neutral-subtle, #f8f9fa);
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle
}

.wikipediauserbox .userbox-id {
	border: 0;
	width: 45px;
	height: 45px;
	background: var(--background-color-neutral, #eaecf0);
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle
}</text>
      <sha1>jq2viwvd5y8ikc9sn4i0wlmmepmjrlt</sha1>
    </revision>
    <revision>
      <id>2810254</id>
      <parentid>2810253</parentid>
      <timestamp>2025-09-12T18:30:47Z</timestamp>
      <contributor>
        <username>w&gt;Matrix</username>
        <id>0</id>
      </contributor>
      <origin>2810254</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="811" sha1="1lp8f551aaycs5psr7jom0zs5qc6w38" xml:space="preserve">.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: var(--background-color-neutral-subtle, #f8f9fa);
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle
}

.wikipediauserbox .userbox-id {
	border: 0;
	width: 45px;
	height: 45px;
	background: var(--background-color-neutral, #eaecf0);
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle
}</text>
      <sha1>1lp8f551aaycs5psr7jom0zs5qc6w38</sha1>
    </revision>
    <revision>
      <id>2810255</id>
      <parentid>2810254</parentid>
      <timestamp>2025-09-12T21:34:31Z</timestamp>
      <contributor>
        <username>w&gt;Ymblanter</username>
        <id>0</id>
      </contributor>
      <minor />
      <comment>Protected &quot;[[Template:Userbox/styles.css]]&quot;: [[WP:High-risk templates|High-risk template or module]]: request at [[WP:RFPP]] ([Edit=Require template editor access] (indefinite) [Move=Require template editor access] (indefinite))</comment>
      <origin>2810254</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="811" sha1="1lp8f551aaycs5psr7jom0zs5qc6w38" xml:space="preserve">.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: var(--background-color-neutral-subtle, #f8f9fa);
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle
}

.wikipediauserbox .userbox-id {
	border: 0;
	width: 45px;
	height: 45px;
	background: var(--background-color-neutral, #eaecf0);
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle
}</text>
      <sha1>1lp8f551aaycs5psr7jom0zs5qc6w38</sha1>
    </revision>
    <revision>
      <id>2810256</id>
      <parentid>2810255</parentid>
      <timestamp>2025-09-12T22:24:25Z</timestamp>
      <contributor>
        <username>w&gt;WOSlinker</username>
        <id>0</id>
      </contributor>
      <comment>add missing userbox-id2</comment>
      <origin>2810256</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="845" sha1="bzre6qwcxh07wh3fu0xclytfdnqwc2t" xml:space="preserve">.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: var(--background-color-neutral-subtle, #f8f9fa);
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: var(--background-color-neutral, #eaecf0);
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}</text>
      <sha1>bzre6qwcxh07wh3fu0xclytfdnqwc2t</sha1>
    </revision>
    <revision>
      <id>2810257</id>
      <parentid>2810256</parentid>
      <timestamp>2025-09-13T11:11:27Z</timestamp>
      <contributor>
        <username>w&gt;Matrix</username>
        <id>0</id>
      </contributor>
      <origin>2810257</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="859" sha1="joudq01owy8ramd1w5iep5eiteiod9p" xml:space="preserve">.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: var(--background-color-neutral-subtle, #f8f9fa);
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: var(--background-color-neutral, #eaecf0);
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}</text>
      <sha1>joudq01owy8ramd1w5iep5eiteiod9p</sha1>
    </revision>
    <revision>
      <id>2810258</id>
      <parentid>2810257</parentid>
      <timestamp>2025-09-16T16:44:33Z</timestamp>
      <contributor>
        <username>w&gt;Matrix</username>
        <id>0</id>
      </contributor>
      <comment>change colours so they are the same per request on talk page</comment>
      <origin>2810258</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1358" sha1="8y23rlhynwr3hn5qnw16ryz6zfeejsf" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: black;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
}</text>
      <sha1>8y23rlhynwr3hn5qnw16ryz6zfeejsf</sha1>
    </revision>
    <revision>
      <id>2810259</id>
      <parentid>2810258</parentid>
      <timestamp>2025-09-16T17:04:31Z</timestamp>
      <contributor>
        <username>w&gt;Matrix</username>
        <id>0</id>
      </contributor>
      <comment>improve performance of userbox in dark mode</comment>
      <origin>2810259</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1742" sha1="h4x8wjwci1oht67ef6cecew5qltt89o" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: inherit;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

/* Dark mode fixes */

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-night .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-os .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}</text>
      <sha1>h4x8wjwci1oht67ef6cecew5qltt89o</sha1>
    </revision>
    <revision>
      <id>2810260</id>
      <parentid>2810259</parentid>
      <timestamp>2025-10-04T02:03:58Z</timestamp>
      <contributor>
        <username>w&gt;Jonesey95</username>
        <id>0</id>
      </contributor>
      <comment>fix text color in dark mode; this generally works but may cause problems, in which case revert or try specifying a different CSS value</comment>
      <origin>2810260</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1847" sha1="3sx0tsg194sph82mxluzbxc9jy1uqcl" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: inherit;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

/* Dark mode fixes */

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	    color: inherit;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	    color: inherit;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-night .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	    color: inherit;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	    color: inherit;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-os .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	    color: inherit;
	}
}</text>
      <sha1>3sx0tsg194sph82mxluzbxc9jy1uqcl</sha1>
    </revision>
    <revision>
      <id>2810261</id>
      <parentid>2810260</parentid>
      <timestamp>2026-05-15T20:36:49Z</timestamp>
      <contributor>
        <username>w&gt;Redrose64</username>
        <id>0</id>
      </contributor>
      <comment>Undid revision [[Special:Diff/1314946445|1314946445]] by [[Special:Contributions/Jonesey95|Jonesey95]] ([[User talk:Jonesey95|talk]]) per [[Template talk:Userbox#Template-protected edit request on 15 May 2026]] and [[Wikipedia:Village pump (technical)#Userboxes have white text on a white background in automatic dark mode]]</comment>
      <origin>2810261</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1742" sha1="h4x8wjwci1oht67ef6cecew5qltt89o" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: inherit;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

/* Dark mode fixes */

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-night .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-os .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}</text>
      <sha1>h4x8wjwci1oht67ef6cecew5qltt89o</sha1>
    </revision>
    <revision>
      <id>2810262</id>
      <parentid>2810261</parentid>
      <timestamp>2026-05-18T22:01:43Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <minor />
      <comment>14 revisions imported from [[:w:Template:Userbox/styles.css]]</comment>
      <origin>2810261</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1742" sha1="h4x8wjwci1oht67ef6cecew5qltt89o" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: inherit;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

/* Dark mode fixes */

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-night .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-os .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}</text>
      <sha1>h4x8wjwci1oht67ef6cecew5qltt89o</sha1>
    </revision>
    <revision>
      <id>2810265</id>
      <parentid>2810262</parentid>
      <timestamp>2026-05-18T22:04:19Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <minor />
      <comment>Protected &quot;[[Template:Userbox/styles.css]]&quot;: To match the same protections as its parent page. ([Edit=Allow only curators and custodians] (indefinite) [Move=Allow only curators and custodians] (indefinite))</comment>
      <origin>2810261</origin>
      <model>sanitized-css</model>
      <format>text/css</format>
      <text bytes="1742" sha1="h4x8wjwci1oht67ef6cecew5qltt89o" xml:space="preserve">/* {{pp-template}} */
.wikipediauserbox {
	margin: 1px;
	border: 1px solid var(--border-color-base, #a2a9b1);
	width: 238px;
	float: left;
}

.wikipediauserbox table {
	border-collapse: collapse;
	width: 238px;
	margin-bottom: 0;
	margin-top: 0;
	background: #eee;
	color: inherit;
}

.wikipediauserbox td {
	border: 0;
	vertical-align: middle;
}

.wikipediauserbox .userbox-info {
	border: 0;
	text-align: left;
	font-size: 8pt;
	padding: 0 4px 0 4px;
	height: 45px;
	line-height: 1.25em;
	color: inherit;
	vertical-align: middle;
}

.wikipediauserbox .userbox-id,
.wikipediauserbox .userbox-id2 {
	border: 0;
	width: 45px;
	height: 45px;
	background: #ddd;
	text-align: center;
	font-size: 14pt;
	font-weight: bold;
	color: inherit;
	padding: 0 1px 0 0;
	line-height: 1.25em;
	vertical-align: middle;
}

/* Dark mode fixes */

@media screen {
	html.skin-theme-clientpref-night .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-night .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-night .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}

@media screen and ( prefers-color-scheme: dark ) {
	html.skin-theme-clientpref-os .wikipediauserbox table {
		background: #202122;
	}
	
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id,
	html.skin-theme-clientpref-os .wikipediauserbox .userbox-id2 {
		background: #27292d;
	}
	
	/* Defined background, no foreground color (temporary fix) */
	html.skin-theme-clientpref-os .wikipediauserbox table[style*=&quot;background&quot;] .userbox-info {
		color: #202122;
	}
}</text>
      <sha1>h4x8wjwci1oht67ef6cecew5qltt89o</sha1>
    </revision>
  </page>
  <page>
    <title>Template:Pharmacy</title>
    <ns>10</ns>
    <id>329724</id>
    <revision>
      <id>2810269</id>
      <timestamp>2026-05-18T22:29:21Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>Create.</comment>
      <origin>2810269</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="198" sha1="gtoch51ajh1nsslztbsb4b6uha6lolz" xml:space="preserve">{{subject_box
|name=Pharmacy
|link=School:Pharmacy
|icon={{{icon|Tablets Flat Icon Vector.svg}}}
|add={{{add|}}}
|style={{{style|userbox}}}
|visible={{{visible|yes}}}
|{{#if:{{{theme}}}|theme=6}}
}}</text>
      <sha1>gtoch51ajh1nsslztbsb4b6uha6lolz</sha1>
    </revision>
  </page>
  <page>
    <title>Category:Easy Readers</title>
    <ns>14</ns>
    <id>329725</id>
    <revision>
      <id>2810287</id>
      <timestamp>2026-05-18T22:39:33Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <comment>Create.</comment>
      <origin>2810287</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="54" sha1="5tojbj66pkfencblc99ekboabn854yq" xml:space="preserve">[[Category:Elementary Education]]
[[Category:Reading]]</text>
      <sha1>5tojbj66pkfencblc99ekboabn854yq</sha1>
    </revision>
  </page>
  <page>
    <title>Spiders/Camel Spider</title>
    <ns>0</ns>
    <id>329726</id>
    <revision>
      <id>2810327</id>
      <timestamp>2026-05-18T23:30:36Z</timestamp>
      <contributor>
        <username>BigKrow</username>
        <id>3069766</id>
      </contributor>
      <comment>Created page with &quot;The '''Camel Spider''' is a type of Spider. {{stub}}&quot;</comment>
      <origin>2810327</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="52" sha1="no26hxwbyjncs1hys43n0dzb2q6wgzf" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
{{stub}}</text>
      <sha1>no26hxwbyjncs1hys43n0dzb2q6wgzf</sha1>
    </revision>
    <revision>
      <id>2810328</id>
      <parentid>2810327</parentid>
      <timestamp>2026-05-18T23:31:19Z</timestamp>
      <contributor>
        <username>BigKrow</username>
        <id>3069766</id>
      </contributor>
      <minor />
      <origin>2810328</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="72" sha1="qd1njponpthy8n3bhcwkzwwyyq9pknw" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
== What they eat ==
{{stub}}</text>
      <sha1>qd1njponpthy8n3bhcwkzwwyyq9pknw</sha1>
    </revision>
    <revision>
      <id>2810329</id>
      <parentid>2810328</parentid>
      <timestamp>2026-05-18T23:31:59Z</timestamp>
      <contributor>
        <username>BigKrow</username>
        <id>3069766</id>
      </contributor>
      <minor />
      <origin>2810329</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="98" sha1="6kd1lhh09ucvmm2bzy44nk6ydxt2dhq" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
== What they eat ==
== What they look like ==
{{stub}}</text>
      <sha1>6kd1lhh09ucvmm2bzy44nk6ydxt2dhq</sha1>
    </revision>
    <revision>
      <id>2810359</id>
      <parentid>2810329</parentid>
      <timestamp>2026-05-19T01:36:23Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>+ [[Category:Zoology]]</comment>
      <origin>2810359</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="120" sha1="5lmb044jhjrjcc7i4kovwmoohvgwdhm" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
== What they eat ==
== What they look like ==
{{stub}}

[[Category:Zoology]]</text>
      <sha1>5lmb044jhjrjcc7i4kovwmoohvgwdhm</sha1>
    </revision>
    <revision>
      <id>2810360</id>
      <parentid>2810359</parentid>
      <timestamp>2026-05-19T01:39:11Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Change to more specific category</comment>
      <origin>2810360</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="120" sha1="0f9fcwhob34pc00yya79fp58r4j96s2" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
== What they eat ==
== What they look like ==
{{stub}}

[[Category:Spiders]]</text>
      <sha1>0f9fcwhob34pc00yya79fp58r4j96s2</sha1>
    </revision>
    <revision>
      <id>2810364</id>
      <parentid>2810360</parentid>
      <timestamp>2026-05-19T01:43:13Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <minor />
      <comment>Jtneill moved page [[Camel Spider]] to [[Spiders/Camel Spider]] without leaving a redirect: Move to sub-page</comment>
      <origin>2810360</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="120" sha1="0f9fcwhob34pc00yya79fp58r4j96s2" xml:space="preserve">The '''Camel Spider''' is a type of Spider.
== What they eat ==
== What they look like ==
{{stub}}

[[Category:Spiders]]</text>
      <sha1>0f9fcwhob34pc00yya79fp58r4j96s2</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Bot</title>
    <ns>4</ns>
    <id>329727</id>
    <redirect title="Wikiversity:Bots" />
    <revision>
      <id>2810333</id>
      <timestamp>2026-05-18T23:35:35Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Redirected page to [[Wikiversity:Bots]]</comment>
      <origin>2810333</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="30" sha1="7cv8spg2wzsw48pdkaw9qoxcddtije3" xml:space="preserve">#REDIRECT [[Wikiversity:Bots]]</text>
      <sha1>7cv8spg2wzsw48pdkaw9qoxcddtije3</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Pseudo-bots</title>
    <ns>4</ns>
    <id>329728</id>
    <revision>
      <id>2810335</id>
      <timestamp>2026-05-18T23:46:12Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Created page with &quot;{{draft}}  The pseudo-bot (flood) user group allows users to perform repetitive actions without flushing the recent changes feed (with only the bot user right).  This right can be granted and revoked by custodians.  Users can remove themselves from it.  However, can curators add and remove pseudo-bot from their own accounts (and not others)?  ==See also== * [[Wikiversity:Bots]] * [[b:Wikibooks:Pseudo-bots]] * [[meta:Flooder]] * [[q:Special:ListGroupRights]]&quot;</comment>
      <origin>2810335</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="461" sha1="cp4vkrof2nxmt6wl7yjwyb2mmk68izb" xml:space="preserve">{{draft}}

The pseudo-bot (flood) user group allows users to perform repetitive actions without flushing the recent changes feed (with only the bot user right).

This right can be granted and revoked by custodians.

Users can remove themselves from it.

However, can curators add and remove pseudo-bot from their own accounts (and not others)?

==See also==
* [[Wikiversity:Bots]]
* [[b:Wikibooks:Pseudo-bots]]
* [[meta:Flooder]]
* [[q:Special:ListGroupRights]]</text>
      <sha1>cp4vkrof2nxmt6wl7yjwyb2mmk68izb</sha1>
    </revision>
    <revision>
      <id>2810340</id>
      <parentid>2810335</parentid>
      <timestamp>2026-05-19T00:27:56Z</timestamp>
      <contributor>
        <username>Codename Noreste</username>
        <id>2969951</id>
      </contributor>
      <comment>Starting with the introduction, and acceptable and unacceptable uses; per [[b:en:Wikibooks:Pseudo-bots]].</comment>
      <origin>2810340</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="917" sha1="5qyo62pxrcg5lcfjmm68i9cqazdzi7k" xml:space="preserve">{{draft}}

The '''pseudo-bot''' user group, also known as the '''flood flag''' or '''flooder''', allows users to perform repetitive actions without flushing the [[Special:RecentChanges|recent changes feed]]. This permission can be granted and revoked by [[Wikiversity:Custodianship|custodians]], and users in the pseudo-bot group can remove themselves from it.

== When to use the pseudo-bot flag ==
Acceptable uses may include, but not limited to:
* Deleting many spambot pages
* Deleting a large number of pages, after consensus has been reached at [[Wikiversity:Requests for Deletion]]
* Blocking many open proxies

== When not to use the pseudo-bot flag ==
The pseudo-bot user group must not be used to perform controversial actions, as this decreases the amount of oversight they may receive.

== See also ==
* [[Wikiversity:Bots]]
* [[b:Wikibooks:Pseudo-bots]]
* [[meta:Flooder]]
* [[q:Special:ListGroupRights]]</text>
      <sha1>5qyo62pxrcg5lcfjmm68i9cqazdzi7k</sha1>
    </revision>
  </page>
  <page>
    <title>User talk:~2026-30001-76</title>
    <ns>3</ns>
    <id>329730</id>
    <revision>
      <id>2810348</id>
      <timestamp>2026-05-19T00:55:56Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Welcome ip</comment>
      <origin>2810348</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="20" sha1="awszlv4i0onyqwwegcz1c5ltkkjlwq2" xml:space="preserve">{{subst:Welcome ip))</text>
      <sha1>awszlv4i0onyqwwegcz1c5ltkkjlwq2</sha1>
    </revision>
    <revision>
      <id>2810349</id>
      <parentid>2810348</parentid>
      <timestamp>2026-05-19T00:56:13Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <minor />
      <origin>2810349</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2057" sha1="8alzjhfl4jl89ixw95p5zgp810chnj2" xml:space="preserve">{{#ifeq:{{NAMESPACE}}|User talk||{{error|Error: substitution required. Use &lt;nowiki&gt;{{subst:Welcomeip}}&lt;/nowiki&gt; instead.}}[[Category:Template substitution errors]]&lt;div style=&quot;display:none;&quot;&gt;}}{{Robelbox|theme=9|title=Welcome!|width=100%}}
&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
Hello, and [[Wikiversity:Welcome, newcomers|welcome]] to [[Wikiversity]]. Thank you for your contributions.

Currently, you are [[Help:Editing|editing]] without a permanent account. You can continue to do so, as you are not required to log in to Wikiversity to read and edit articles; however, logging in will result in a username being shown instead of a temporary account (which will expire 90 days after first edit). Logging in does not require any personal details, and there are many other '''[[Wikiversity:Why create an account|benefits for logging in]]'''.

When you edit pages:

* Please [[Wikiversity:Copyrights|respect others' copyrights]]; do not copy and paste the contents from webpages directly.
* Please use a [[Wikiversity:Disclosures|neutral point of view]] when editing articles.
* If you are testing, please use the [[Wikiversity:Sandbox|Sandbox]] to &lt;span class=&quot;plainlinks&quot;&gt;[http://en.wikiversity.org/w/index.php?title=Wikiversity:Sandbox&amp;action=edit do so].&lt;/span&gt; 
* Do not add unreasonable contents into any [[Wikiversity:Browse|articles]], such as copyrighted text, advertisement messages, and text that is not related to an areas's subject. Adding such content or editing articles maliciously is considered [[Wikiversity:Blocking policy|vandalism]].

The [[Wikiversity:Introduction|Introduction]] is a good place to start learning about Wikiversity. For now, if you are stuck, you can ask a question on {{#if:|[[user talk:{{{1}}}|my Talk page]]|my Talk page}}. I will answer your questions as far as I can! Thank you again for contributing to Wikiversity. -- -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 19 May 2026 (UTC)
&lt;/div&gt;
{{Robelbox/close}}
{{#ifeq:{{NAMESPACE}}|User talk||&lt;/div&gt;}}</text>
      <sha1>8alzjhfl4jl89ixw95p5zgp810chnj2</sha1>
    </revision>
  </page>
  <page>
    <title>Category:Spiders</title>
    <ns>14</ns>
    <id>329731</id>
    <revision>
      <id>2810362</id>
      <timestamp>2026-05-19T01:41:36Z</timestamp>
      <contributor>
        <username>Jtneill</username>
        <id>10242</id>
      </contributor>
      <comment>Created page with &quot;[[Category:Entomology]]&quot;</comment>
      <origin>2810362</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="23" sha1="mj7uy4cnc9avhghjyczr9n3usqxj054" xml:space="preserve">[[Category:Entomology]]</text>
      <sha1>mj7uy4cnc9avhghjyczr9n3usqxj054</sha1>
    </revision>
  </page>
  <page>
    <title>Template:Walsh permutation/sequences</title>
    <ns>10</ns>
    <id>329736</id>
    <redirect title="Walsh permutation/sequences" />
    <revision>
      <id>2810396</id>
      <timestamp>2026-05-19T09:57:27Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>Watchduck moved page [[Template:Walsh permutation/sequences]] to [[Walsh permutation/sequences]]</comment>
      <origin>2810396</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="41" sha1="mvsx94y8zlmx264s273l894symibq7p" xml:space="preserve">#REDIRECT [[Walsh permutation/sequences]]</text>
      <sha1>mvsx94y8zlmx264s273l894symibq7p</sha1>
    </revision>
  </page>
</mediawiki>